water

WATER
2.1 Weak Interactions in Aqueous Systems 47
2.2 Ionization of Water, Weak Acids, and
Weak Bases 60
2.3 Buffering against pH Changes in Biological
Systems 65
2.4 Water as a Reactant 69
2.5 The Fitness of the Aqueous Environment
for Living Organisms 70
I believe that as the methods of structural chemistry are
further applied to physiological problems, it will be found
that the significance of the hydrogen bond for physiology
is greater than that of any other single structural feature.
—Linus Pauling, The Nature of the Chemical Bond, 1939
What in water did Bloom, water lover, drawer of water, water
carrier returning to the range, admire? Its universality, its
democratic quality.
—James Joyce, Ulysses, 1922
O O
C
C H H
– 2
47
Water is the most abundant substance in living systems,
making up 70% or more of the weight of most
organisms. The first living organisms doubtless arose in
an aqueous environment, and the course of evolution
has been shaped by the properties of the aqueous
medium in which life began.
This chapter begins with descriptions of the physical
and chemical properties of water, to which all aspects
of cell structure and function are adapted. The attractive
forces between water molecules and the slight tendency
of water to ionize are of crucial importance to the
structure and function of biomolecules. We review the
topic of ionization in terms of equilibrium constants, pH,
and titration curves, and consider how aqueous solutions
of weak acids or bases and their salts act as buffers
against pH changes in biological systems. The water
molecule and its ionization products, H and OH , profoundly
influence the structure, self-assembly, and properties
of all cellular components, including proteins,
nucleic acids, and lipids. The noncovalent interactions
responsible for the strength and specificity of “recognition”
among biomolecules are decisively influenced by
the solvent properties of water, including its ability to
form hydrogen bonds with itself and with solutes.
2.1 Weak Interactions in Aqueous Systems
Hydrogen bonds between water molecules provide the
cohesive forces that make water a liquid at room temperature
and that favor the extreme ordering of molecules
that is typical of crystalline water (ice). Polar biomolecules
dissolve readily in water because they can
replace water-water interactions with more energetically
favorable water-solute interactions. In contrast, nonpolar
biomolecules interfere with water-water interactions
but are unable to form water-solute interactions—
consequently, nonpolar molecules are poorly soluble in
water. In aqueous solutions, nonpolar molecules tend to
cluster together.
Hydrogen bonds and ionic, hydrophobic (Greek,
“water-fearing”), and van der Waals interactions are individually
weak, but collectively they have a very significant
influence on the three-dimensional structures
of proteins, nucleic acids, polysaccharides, and membrane
lipids.
Hydrogen Bonding Gives Water Its Unusual Properties
Water has a higher melting point, boiling point, and heat
of vaporization than most other common solvents (Table
2–1). These unusual properties are a consequence of
attractions between adjacent water molecules that give
liquid water great internal cohesion. A look at the electron
structure of the H2O molecule reveals the cause of
these intermolecular attractions.
Each hydrogen atom of a water molecule shares an
electron pair with the central oxygen atom. The geometry
of the molecule is dictated by the shapes of the
outer electron orbitals of the oxygen atom, which are
similar to the sp3 bonding orbitals of carbon (see Fig.
1–14). These orbitals describe a rough tetrahedron, with
a hydrogen atom at each of two corners and unshared
electron pairs at the other two corners (Fig. 2–1a). The
HOOOH bond angle is 104.5 , slightly less than the
109.5 of a perfect tetrahedron because of crowding by
the nonbonding orbitals of the oxygen atom.
The oxygen nucleus attracts electrons more
strongly than does the hydrogen nucleus (a proton);
that is, oxygen is more electronegative. The sharing of
electrons between H and O is therefore unequal; the
electrons are more often in the vicinity of the oxygen
atom than of the hydrogen. The result of this unequal
electron sharing is two electric dipoles in the water molecule,
one along each of the HOO bonds; each hydrogen
bears a partial positive charge ( ) and the oxygen
atom bears a partial negative charge equal to the sum
of the two partial positives (2 ). As a result, there is
an electrostatic attraction between the oxygen atom of
one water molecule and the hydrogen of another (Fig.
2–1c), called a hydrogen bond. Throughout this book,
we represent hydrogen bonds with three parallel blue
lines, as in Figure 2–1c.
Hydrogen bonds are relatively weak. Those in liquid
water have a bond dissociation energy (the energy
required to break a bond) of about 23 kJ/mol, compared
with 470 kJ/mol for the covalent OOH bond in
48 Part I Structure and Catalysis
TABLE 2–1 Melting Point, Boiling Point, and Heat of Vaporization of Some Common Solvents
Melting point (°C) Boiling point (°C) Heat of vaporization (J/g)*
Water 0 100 2,260
Methanol (CH3OH) 98 65 1,100
Ethanol (CH3CH2OH) 117 78 854
Propanol (CH3CH2CH2OH) 127 97 687
Butanol (CH3(CH2)2CH2OH) 90 117 590
Acetone (CH3COCH3) 95 56 523
Hexane (CH3(CH2)4CH3) 98 69 423
Benzene (C6H6) 6 80 394
Butane (CH3(CH2)2CH3) 135 0.5 381
Chloroform (CHCl3) 63 61 247
*The heat energy required to convert 1.0 g of a liquid at its boiling point, at atmospheric pressure, into its gaseous state at the same
temperature. It is a direct measure of the energy required to overcome attractive forces between molecules in the liquid phase.
104.5
Hydrogen bond
0.177 nm
Covalent bond
0.0965 nm
H






(a) (b)
(c)
2
H
O
FIGURE 2–1 Structure of the water molecule. The dipolar nature of
the H2O molecule is shown by (a) ball-and-stick and (b) space-filling
models. The dashed lines in (a) represent the nonbonding orbitals.
There is a nearly tetrahedral arrangement of the outer-shell electron
pairs around the oxygen atom; the two hydrogen atoms have localized
partial positive charges ( ) and the oxygen atom has a partial
negative charge (2 ). (c) Two H2O molecules joined by a hydrogen
bond (designated here, and throughout this book, by three blue lines)
between the oxygen atom of the upper molecule and a hydrogen atom
of the lower one. Hydrogen bonds are longer and weaker than covalent
OOH bonds.
water or 348 kJ/mol for a covalent COC bond. The hydrogen
bond is about 10% covalent, due to overlaps in
the bonding orbitals, and about 90% electrostatic. At
room temperature, the thermal energy of an aqueous
solution (the kinetic energy of motion of the individual
atoms and molecules) is of the same order of magnitude
as that required to break hydrogen bonds. When water
is heated, the increase in temperature reflects the faster
motion of individual water molecules. At any given time,
most of the molecules in liquid water are engaged in hydrogen
bonding, but the lifetime of each hydrogen bond
is just 1 to 20 picoseconds (1 ps 10 12 s); upon breakage
of one hydrogen bond, another hydrogen bond
forms, with the same partner or a new one, within 0.1 ps.
The apt phrase “flickering clusters” has been applied to
the short-lived groups of water molecules interlinked by
hydrogen bonds in liquid water. The sum of all the hydrogen
bonds between H2O molecules confers great internal
cohesion on liquid water. Extended networks of
hydrogen-bonded water molecules also form bridges between
solutes (proteins and nucleic acids, for example)
that allow the larger molecules to interact with each
other over distances of several nanometers without
physically touching.
The nearly tetrahedral arrangement of the orbitals
about the oxygen atom (Fig. 2–1a) allows each water
molecule to form hydrogen bonds with as many as four
neighboring water molecules. In liquid water at room
temperature and atmospheric pressure, however, water
molecules are disorganized and in continuous motion,
so that each molecule forms hydrogen bonds with an average
of only 3.4 other molecules. In ice, on the other
hand, each water molecule is fixed in space and forms
hydrogen bonds with a full complement of four other
water molecules to yield a regular lattice structure (Fig.
2–2). Breaking a sufficient proportion of hydrogen
bonds to destabilize the crystal lattice of ice requires
much thermal energy, which accounts for the relatively
high melting point of water (Table 2–1). When ice melts
or water evaporates, heat is taken up by the system:
H2O(solid) 88n H2O(liquid) H 5.9 kJ/mol
H2O(liquid) 88n H2O(gas) H 44.0 kJ/mol
During melting or evaporation, the entropy of the
aqueous system increases as more highly ordered arrays
of water molecules relax into the less orderly hydrogenbonded
arrays in liquid water or the wholly disordered
gaseous state. At room temperature, both the melting of
ice and the evaporation of water occur spontaneously;
the tendency of the water molecules to associate through
hydrogen bonds is outweighed by the energetic push
toward randomness. Recall that the free-energy change
( G) must have a negative value for a process to occur
spontaneously: G H T S, where G represents
the driving force, H the enthalpy change from making
and breaking bonds, and S the change in randomness.
Because H is positive for melting and evaporation, it
is clearly the increase in entropy ( S) that makes G
negative and drives these transformations.
Water Forms Hydrogen Bonds with Polar Solutes
Hydrogen bonds are not unique to water. They readily
form between an electronegative atom (the hydrogen
acceptor, usually oxygen or nitrogen with a lone pair of
electrons) and a hydrogen atom covalently bonded to
another electronegative atom (the hydrogen donor) in
the same or another molecule (Fig. 2–3). Hydrogen
atoms covalently bonded to carbon atoms do not participate
in hydrogen bonding, because carbon is only
Chapter 2 Water 49
FIGURE 2–2 Hydrogen bonding in ice. In ice, each water molecule
forms the maximum of four hydrogen bonds, creating a regular crystal
lattice. By contrast, in liquid water at room temperature and atmospheric
pressure, each water molecule hydrogen-bonds with an average
of 3.4 other water molecules. This crystal lattice of ice makes it
less dense than liquid water, and thus ice floats on liquid water.
Hydrogen
Hydrogen
donor
acceptor
H
O
O
P C
D
G D
O O
J
H
N
O
O O
D J
H
N
N
O O
D D
H
O
O
O O
H
O
N
P C
G D
O O
D D
H
N
O
O O
FIGURE 2–3 Common hydrogen bonds in biological systems. The
hydrogen acceptor is usually oxygen or nitrogen; the hydrogen donor
is another electronegative atom.
slightly more electronegative than hydrogen and thus
the COH bond is only very weakly polar. The distinction
explains why butanol (CH3(CH2)2CH2OH) has a relatively
high boiling point of 117 C, whereas butane
(CH3(CH2)2CH3) has a boiling point of only 0.5 C. Butanol
has a polar hydroxyl group and thus can form intermolecular
hydrogen bonds. Uncharged but polar biomolecules
such as sugars dissolve readily in water
because of the stabilizing effect of hydrogen bonds between
the hydroxyl groups or carbonyl oxygen of the
sugar and the polar water molecules. Alcohols, aldehydes,
ketones, and compounds containing NOH bonds
all form hydrogen bonds with water molecules (Fig. 2–4)
and tend to be soluble in water.
Hydrogen bonds are strongest when the bonded
molecules are oriented to maximize electrostatic interaction,
which occurs when the hydrogen atom and the
two atoms that share it are in a straight line—that is,
when the acceptor atom is in line with the covalent bond
between the donor atom and H (Fig. 2–5). Hydrogen
bonds are thus highly directional and capable of holding
two hydrogen-bonded molecules or groups in a specific
geometric arrangement. As we shall see later, this
property of hydrogen bonds confers very precise threedimensional
structures on protein and nucleic acid
molecules, which have many intramolecular hydrogen
bonds.
Water Interacts Electrostatically
with Charged Solutes
Water is a polar solvent. It readily dissolves most biomolecules,
which are generally charged or polar compounds
(Table 2–2); compounds that dissolve easily in
water are hydrophilic (Greek, “water-loving”). In contrast,
nonpolar solvents such as chloroform and benzene
are poor solvents for polar biomolecules but easily dissolve
those that are hydrophobic—nonpolar molecules
such as lipids and waxes.
Water dissolves salts such as NaCl by hydrating and
stabilizing the Na and Cl ions, weakening the electrostatic
interactions between them and thus counteracting
their tendency to associate in a crystalline lattice
(Fig. 2–6). The same factors apply to charged biomolecules,
compounds with functional groups such as ionized
carboxylic acids (OCOO ), protonated amines
(ONH3 ), and phosphate esters or anhydrides. Water
readily dissolves such compounds by replacing solutesolute
hydrogen bonds with solute-water hydrogen
bonds, thus screening the electrostatic interactions between
solute molecules.
Water is especially effective in screening the electrostatic
interactions between dissolved ions because it
has a high dielectric constant, a physical property reflecting
the number of dipoles in a solvent. The strength,
or force (F), of ionic interactions in a solution depends
upon the magnitude of the charges (Q), the distance
between the charged groups (r), and the dielectric constant
( ) of the solvent in which the interactions occur:
F
Q

1
r
Q
2
2
50 Part I Structure and Catalysis
Between the
hydroxyl group
of an alcohol
and water
Between the
carbonyl group
of a ketone
and water
Between peptide
groups in
polypeptides
Between
complementary
bases of DNA
O
H A O
G
R
H H
H
O
G
R1
R O
E
A H
O
B
H N
A
H
H
B
O
H
N
C
C EC A
R
HC
H
NAH
EC A
NO
HA
A N
H R EC
H
N
C
ECH3
H
C
K H
N
H
ENN ENH
EN
R
OCH
D
R2
A
OKC
N B C
C
A C
l
A
Thymine
Adenine
B C
i
A
H
H
H
E
H
FIGURE 2–4 Some biologically important hydrogen bonds.
Strong
hydrogen bond
Weaker
hydrogen bond
P
KO
H A O A R
P
KO
H A O A R
G
D O
G
D O
FIGURE 2–5 Directionality of the hydrogen bond. The attraction between
the partial electric charges (see Fig. 2–1) is greatest when the
three atoms involved (in this case O, H, and O) lie in a straight line.
When the hydrogen-bonded moieties are structurally constrained (as
when they are parts of a single protein molecule, for example), this
ideal geometry may not be possible and the resulting hydrogen bond
is weaker.
For water at 25 C, (which is dimensionless) is 78.5,
and for the very nonpolar solvent benzene, is 4.6. Thus,
ionic interactions are much stronger in less polar environments.
The dependence on r2 is such that ionic attractions
or repulsions operate only over short distances—
in the range of 10 to 40 nm (depending on the
electrolyte concentration) when the solvent is water.
Entropy Increases as Crystalline Substances Dissolve
As a salt such as NaCl dissolves, the Na and Cl ions
leaving the crystal lattice acquire far greater freedom of
motion (Fig. 2–6). The resulting increase in entropy
(randomness) of the system is largely responsible for
the ease of dissolving salts such as NaCl in water. In
Chapter 2 Water 51
TABLE 2–2 Some Examples of Polar, Nonpolar, and Amphipathic Biomolecules (Shown as Ionic Forms at pH 7)
+ Hydrated
Na+ ion
Note the orientation
of the water molecules
Hydrated
Cl– ion
H2O
Na+
Cl–
+
–
+
–
+
–
–
–
–
+
+ +
+
–
–
–
–
–
–
–
–
–
+
–
–
FIGURE 2–6 Water as solvent. Water dissolves many crystalline salts
by hydrating their component ions. The NaCl crystal lattice is disrupted
as water molecules cluster about the Cl and Na ions. The ionic
charges are partially neutralized, and the electrostatic attractions necessary
for lattice formation are weakened.
H
HO
CH2OH
O
OH
OH
OH
CH2
NH3 COO
CH2
OOC COO
H
H
H
H
NH3
CH
CH
OH
OH
CH3 CH COO
HOCH2 CH2OH
CH3(CH2)7 CH CH (CH2)6 CH2 C
CH3(CH2)7 CH CH (CH2)7 CH2
CH2 CH
GNH3
GN(CH3)3
O
O
COOJ
CH3(CH2)15CH2
CH2 O CH2 CH2
O
OJ
C
CH3(CH2)15CH2 O CH
O
O CH2
P
C
O
O
Polar groups Nonpolar groups
Polar
Glucose
Glycine
Aspartate
Lactate
Glycerol
Nonpolar
Typical wax
Amphipathic
Phenylalanine
Phosphatidylcholine
thermodynamic terms, formation of the solution occurs
with a favorable free-energy change: G H T S,
where H has a small positive value and T S a large
positive value; thus G is negative.
Nonpolar Gases Are Poorly Soluble in Water
The molecules of the biologically important gases CO2,
O2, and N2 are nonpolar. In O2 and N2, electrons are
shared equally by both atoms. In CO2, each CUO bond
is polar, but the two dipoles are oppositely directed and
cancel each other (Table 2–3). The movement of molecules
from the disordered gas phase into aqueous solution
constrains their motion and the motion of water
molecules and therefore represents a decrease in entropy.
The nonpolar nature of these gases and the decrease
in entropy when they enter solution combine to
make them very poorly soluble in water (Table 2–3).
Some organisms have water-soluble carrier proteins
(hemoglobin and myoglobin, for example) that facilitate
the transport of O2. Carbon dioxide forms carbonic acid
(H2CO3) in aqueous solution and is transported as the
HCO3 (bicarbonate) ion, either free—bicarbonate is
very soluble in water (~100 g/L at 25 C)—or bound to
hemoglobin. Two other gases, NH3 and H2S, also have
biological roles in some organisms; these gases are polar
and dissolve readily in water.
Nonpolar Compounds Force Energetically Unfavorable
Changes in the Structure of Water
When water is mixed with benzene or hexane, two
phases form; neither liquid is soluble in the other. Nonpolar
compounds such as benzene and hexane are
hydrophobic—they are unable to undergo energetically
favorable interactions with water molecules, and they
interfere with the hydrogen bonding among water molecules.
All molecules or ions in aqueous solution interfere
with the hydrogen bonding of some water molecules
in their immediate vicinity, but polar or charged
solutes (such as NaCl) compensate for lost water-water
hydrogen bonds by forming new solute-water interactions.
The net change in enthalpy ( H) for dissolving
these solutes is generally small. Hydrophobic solutes,
however, offer no such compensation, and their addition
to water may therefore result in a small gain of enthalpy;
the breaking of hydrogen bonds between water
molecules takes up energy from the system. Furthermore,
dissolving hydrophobic compounds in water produces
a measurable decrease in entropy. Water molecules
in the immediate vicinity of a nonpolar solute are
constrained in their possible orientations as they form
a highly ordered cagelike shell around each solute molecule.
These water molecules are not as highly oriented
as those in clathrates, crystalline compounds of nonpolar
solutes and water, but the effect is the same in
both cases: the ordering of water molecules reduces entropy.
The number of ordered water molecules, and
therefore the magnitude of the entropy decrease, is proportional
to the surface area of the hydrophobic solute
enclosed within the cage of water molecules. The freeenergy
change for dissolving a nonpolar solute in water
is thus unfavorable: G H T S, where H has
a positive value, S has a negative value, and G is
positive.
Amphipathic compounds contain regions that are
polar (or charged) and regions that are nonpolar (Table
2–2). When an amphipathic compound is mixed with
52 Part I Structure and Catalysis
TABLE 2–3 Solubilities of Some Gases in Water
Solubility
Gas Structure* Polarity in water (g/L)†
Nitrogen NmN Nonpolar 0.018 (40 °C)
Oxygen OPO Nonpolar 0.035 (50 °C)
Carbon dioxide Nonpolar 0.97 (45 °C)
Ammonia Polar 900 (10 °C)
Hydrogen sulfide H Polar 1,860 (40 °C)
G
S
D
H

H
G
N A H
D
H

OPCPO

*The arrows represent electric dipoles; there is a partial negative charge ( ) at the head of the arrow, a partial positive charge
( ; not shown here) at the tail.
†Note that polar molecules dissolve far better even at low temperatures than do nonpolar molecules at relatively high temperatures.
Dispersion of
lipids in H2O
Clusters of lipid
molecules
Micelles
(b)
(a)
“Flickering clusters” of H2O
molecules in bulk phase
Highly ordered H2O molecules form
“cages” around the hydrophobic alkyl chains
Hydrophilic
O O “head group”
C
C H H
H
H O
Each lipid
molecule forces
surrounding H2O
molecules to become
highly ordered.
Only lipid portions
at the edge of
the cluster force the
ordering of water.
Fewer H2O molecules
are ordered, and
entropy is increased.
All hydrophobic
groups are
sequestered from
water; ordered
shell of H2O
molecules is
minimized, and
entropy is further
increased.
–
Hydrophobic
alkyl group
water, the polar, hydrophilic region interacts favorably
with the solvent and tends to dissolve, but the nonpolar,
hydrophobic region tends to avoid contact with the
water (Fig. 2–7a). The nonpolar regions of the molecules
cluster together to present the smallest hydrophobic
area to the aqueous solvent, and the polar regions
are arranged to maximize their interaction with
the solvent (Fig. 2–7b). These stable structures of amphipathic
compounds in water, called micelles, may
contain hundreds or thousands of molecules. The forces
that hold the nonpolar regions of the molecules together
are called hydrophobic interactions. The strength of
hydrophobic interactions is not due to any intrinsic attraction
between nonpolar moieties. Rather, it results
from the system’s achieving greatest thermodynamic
stability by minimizing the number of ordered water
molecules required to surround hydrophobic portions of
the solute molecules.
Many biomolecules are amphipathic; proteins, pigments,
certain vitamins, and the sterols and phospholipids
of membranes all have polar and nonpolar surface
regions. Structures composed of these molecules are
stabilized by hydrophobic interactions among the nonpolar
regions. Hydrophobic interactions among lipids,
and between lipids and proteins, are the most important
determinants of structure in biological membranes.
Hydrophobic interactions between nonpolar amino
acids also stabilize the three-dimensional structures of
proteins.
Hydrogen bonding between water and polar solutes
also causes some ordering of water molecules, but the
effect is less significant than with nonpolar solutes. Part
Chapter 2 Water 53
FIGURE 2–7 Amphipathic compounds in aqueous solution. (a) Longchain
fatty acids have very hydrophobic alkyl chains, each of which
is surrounded by a layer of highly ordered water molecules. (b) By
clustering together in micelles, the fatty acid molecules expose the
smallest possible hydrophobic surface area to the water, and fewer
water molecules are required in the shell of ordered water. The energy
gained by freeing immobilized water molecules stabilizes the micelle.
of the driving force for binding of a polar substrate (reactant)
to the complementary polar surface of an enzyme
is the entropy increase as the enzyme displaces
ordered water from the substrate (Fig. 2–8).
van der Waals Interactions Are Weak
Interatomic Attractions
When two uncharged atoms are brought very close together,
their surrounding electron clouds influence each
other. Random variations in the positions of the electrons
around one nucleus may create a transient electric dipole,
which induces a transient, opposite electric dipole
in the nearby atom. The two dipoles weakly attract each
other, bringing the two nuclei closer. These weak attractions
are called van der Waals interactions. As
the two nuclei draw closer together, their electron
clouds begin to repel each other. At the point where the
van der Waals attraction exactly balances this repulsive
force, the nuclei are said to be in van der Waals contact.
Each atom has a characteristic van der Waals radius,
a measure of how close that atom will allow another to
approach (Table 2–4). In the “space-filling” molecular
models shown throughout this book, the atoms are depicted
in sizes proportional to their van der Waals radii.
Weak Interactions Are Crucial to Macromolecular
Structure and Function
The noncovalent interactions we have described (hydrogen
bonds and ionic, hydrophobic, and van der Waals
interactions) (Table 2–5) are much weaker than covalent
bonds. An input of about 350 kJ of energy is required
to break a mole of (6 1023) COC single bonds,
and about 410 kJ to break a mole of COH bonds, but
as little as 4 kJ is sufficient to disrupt a mole of typical
van der Waals interactions. Hydrophobic interactions
are also much weaker than covalent bonds, although
they are substantially strengthened by a highly polar solvent
(a concentrated salt solution, for example). Ionic
interactions and hydrogen bonds are variable in
strength, depending on the polarity of the solvent and
54 Part I Structure and Catalysis
Substrate
Enzyme
Disordered water
displaced by
enzyme-substrate
interaction
Enzyme-substrate interaction
stabilized by hydrogen-bonding,
ionic, and hydrophobic interactions
Ordered water
interacting with
substrate and enzyme
FIGURE 2–8 Release of ordered water favors formation of an
enzyme-substrate complex. While separate, both enzyme and substrate
force neighboring water molecules into an ordered shell. Binding
of substrate to enzyme releases some of the ordered water, and
the resulting increase in entropy provides a thermodynamic push toward
formation of the enzyme-substrate complex.
Sources: For van der Waals radii, Chauvin, R. (1992) Explicit periodic trend of van der
Waals radii. J. Phys. Chem. 96, 9194–9197. For covalent radii, Pauling, L. (1960) Nature of
the Chemical Bond, 3rd edn, Cornell University Press, Ithaca, NY.
Note: van der Waals radii describe the space-filling dimensions of atoms. When two atoms
are joined covalently, the atomic radii at the point of bonding are less than the van der
Waals radii, because the joined atoms are pulled together by the shared electron pair. The
distance between nuclei in a van der Waals interaction or a covalent bond is about equal
to the sum of the van der Waals or covalent radii, respectively, for the two atoms. Thus the
length of a carbon-carbon single bond is about 0.077 nm 0.077 nm 0.154 nm.
van der Waals Covalent radius for
Element radius (nm) single bond (nm)
H 0.11 0.030
O 0.15 0.066
N 0.15 0.070
C 0.17 0.077
S 0.18 0.104
P 0.19 0.110
I 0.21 0.133
van der Waals Radii and Covalent
(Single-Bond) Radii of Some Elements
TABLE 2–4
the alignment of the hydrogen-bonded atoms, but they
are always significantly weaker than covalent bonds. In
aqueous solvent at 25 C, the available thermal energy
can be of the same order of magnitude as the strength
of these weak interactions, and the interaction between
solute and solvent (water) molecules is nearly as favorable
as solute-solute interactions. Consequently, hydrogen
bonds and ionic, hydrophobic, and van der Waals
interactions are continually formed and broken.
Although these four types of interactions are individually
weak relative to covalent bonds, the cumulative
effect of many such interactions can be very significant.
For example, the noncovalent binding of an enzyme to
its substrate may involve several hydrogen bonds and
one or more ionic interactions, as well as hydrophobic
and van der Waals interactions. The formation of each
of these weak bonds contributes to a net decrease in
the free energy of the system. We can calculate the stability
of a noncovalent interaction, such as that of a small
molecule hydrogen-bonded to its macromolecular partner,
from the binding energy. Stability, as measured by
the equilibrium constant (see below) of the binding reaction,
varies exponentially with binding energy. The
dissociation of two biomolecules (such as an enzyme
and its bound substrate) associated noncovalently
through multiple weak interactions requires all these interactions
to be disrupted at the same time. Because
the interactions fluctuate randomly, such simultaneous
disruptions are very unlikely. The molecular stability bestowed
by 5 or 20 weak interactions is therefore much
greater than would be expected intuitively from a simple
summation of small binding energies.
Macromolecules such as proteins, DNA, and RNA
contain so many sites of potential hydrogen bonding or
ionic, van der Waals, or hydrophobic interactions that
the cumulative effect of the many small binding forces
can be enormous. For macromolecules, the most stable
(that is, the native) structure is usually that in which
weak-bonding possibilities are maximized. The folding
of a single polypeptide or polynucleotide chain into its
three-dimensional shape is determined by this principle.
The binding of an antigen to a specific antibody depends
on the cumulative effects of many weak interactions.
As noted earlier, the energy released when an
enzyme binds noncovalently to its substrate is the main
source of the enzyme’s catalytic power. The binding of
a hormone or a neurotransmitter to its cellular receptor
protein is the result of weak interactions. One consequence
of the large size of enzymes and receptors is
that their extensive surfaces provide many opportunities
for weak interactions. At the molecular level, the
complementarity between interacting biomolecules reflects
the complementarity and weak interactions between
polar, charged, and hydrophobic groups on the
surfaces of the molecules.
When the structure of a protein such as hemoglobin
(Fig. 2–9) is determined by x-ray crystallography (see
Chapter 2 Water 55
Hydrogen bonds
Between neutral groups
Between peptide bonds
Ionic interactions
Attraction
Repulsion
Hydrophobic interactions
van der Waals interactions Any two atoms in
close proximity
Four Types of Noncovalent (“Weak”)
Interactions among Biomolecules in Aqueous Solvent
TABLE 2–5
G
C
D
PO HOOO
G
C
D
G
D
PO HON
B
NH3
O
O OOC
NH3 H3N O
O
A
O
CH3 CH3
CH2
CH2
A
A
G
CH
D
water
(a) (b)
FIGURE 2–9 Water binding in hemoglobin. The crystal structure of
hemoglobin, shown (a) with bound water molecules (red spheres) and
(b) without the water molecules. These water molecules are so firmly
bound to the protein that they affect the x-ray diffraction pattern as
though they were fixed parts of the crystal. The gray structures with
red and orange atoms are the four hemes of hemoglobin, discussed
in detail in Chapter 5.
Box 4–4, p. XX), water molecules are often found to be
bound so tightly as to be part of the crystal structure;
the same is true for water in crystals of RNA or DNA.
These bound water molecules, which can also be detected
in aqueous solutions by nuclear magnetic resonance,
have distinctly different properties from those of
the “bulk” water of the solvent. They are, for example,
not osmotically active (see below). For many proteins,
tightly bound water molecules are essential to their function.
In a reaction central to the process of photosynthesis,
for example, light drives protons across a biological
membrane as electrons flow through a series of
electron-carrying proteins (see Fig. 19–XX). One of these
proteins, cytochrome f, has a chain of five bound water
molecules (Fig. 2–10) that may provide a path for protons
to move through the membrane by a process known
as “proton hopping” (described below). Another such
light-driven proton pump, bacteriorhodopsin, almost certainly
uses a chain of precisely oriented bound water
molecules in the transmembrane movement of protons
(see Fig. 19–XX).
Solutes Affect the Colligative Properties
of Aqueous Solutions
Solutes of all kinds alter certain physical properties of
the solvent, water: its vapor pressure, boiling point,
melting point (freezing point), and osmotic pressure.
These are called colligative (“tied together”) properties,
because the effect of solutes on all four properties
has the same basis: the concentration of water is lower
in solutions than in pure water. The effect of solute concentration
on the colligative properties of water is independent
of the chemical properties of the solute; it
depends only on the number of solute particles (molecules,
ions) in a given amount of water. A compound
such as NaCl, which dissociates in solution, has twice
the effect on osmotic pressure, for example, as does an
equal number of moles of a nondissociating solute such
as glucose.
Solutes alter the colligative properties of aqueous
solutions by lowering the effective concentration of water.
For example, when a significant fraction of the molecules
at the surface of an aqueous solution are not water
but solute, the tendency of water molecules to
escape into the vapor phase—that is, the vapor pressure—
is lowered (Fig. 2–11). Similarly, the tendency of
water molecules to move from the aqueous phase to the
surface of a forming ice crystal is reduced when some
of the molecules that collide with the crystal are solute,
not water. In that case, the solution will freeze more
slowly than pure water and at a lower temperature. For
a 1.00 molal aqueous solution (1.00 mol of solute per
1,000 g of water) of an ideal, nonvolatile, and nondissociating
solute at 101 kPa (1 atm) of pressure, the
freezing point is 1.86 C lower and the boiling point is
0.543 C higher than for pure water. For a 0.100 molal
solution of the same solute, the changes are one-tenth
as large.
Water molecules tend to move from a region of
higher water concentration to one of lower water concentration.
When two different aqueous solutions are
separated by a semipermeable membrane (one that allows
the passage of water but not solute molecules), water
molecules diffusing from the region of higher water
concentration to that of lower water concentration produce
osmotic pressure (Fig. 2–12). This pressure,
,
measured as the force necessary to resist water movement
(Fig. 2–12c), is approximated by the van’t Hoff
equation:

icRT
in which R is the gas constant and T is the absolute temperature.
The term ic is the osmolarity of the solution,
the product of the solute’s molar concentration c and
the van’t Hoff factor i, which is a measure of the extent
to which the solute dissociates into two or more ionic
species. In dilute NaCl solutions, the solute completely
56 Part I Structure and Catalysis
Asn232
Arg156
Asn168
Asn153
Heme
propionate
NH2
Gln158
Val60 Gln59
water
H
H
H
H
H
H
H
H
N
H
O
O
–O
O
O
O
O
O
O
O
N
N
N
N
HN
HN
Fe
H H
HO C CH
H
N
Ala27
Pro231
FIGURE 2–10 Water chain in cytochrome f.Water is bound in a proton
channel of the membrane protein cytochrome f, which is part of
the energy-trapping machinery of photosynthesis in chloroplasts (see
Fig. 19–XX). Five water molecules are hydrogen-bonded to each other
and to functional groups of the protein, which include the side chains
of valine, proline, arginine, alanine, two asparagine, and two glutamine
residues. The protein has a bound heme (see Fig. 5–1), its iron
ion facilitating electron flow during photosynthesis. Electron flow is
coupled to the movement of protons across the membrane, which
probably involves “electron hopping” (see Fig. 2–14) through this
chain of bound water molecules.
dissociates into Na and Cl , doubling the number of
solute particles, and thus i 2. For nonionizing solutes,
i is always 1. For solutions of several (n) solutes,
 is
the sum of the contributions of each species:

  RT(i1c1 i2c2 … incn)
Osmosis, water movement across a semipermeable
membrane driven by differences in osmotic pressure, is
an important factor in the life of most cells. Plasma
membranes are more permeable to water than to most
other small molecules, ions, and macromolecules. This
permeability is due partly to simple diffusion of water
through the lipid bilayer and partly to protein channels
(aquaporins; see Fig. 11–XX) in the membrane that selectively
permit the passage of water. Solutions of equal
osmolarity are said to be isotonic. Surrounded by an
isotonic solution, a cell neither gains nor loses water
(Fig. 2–13). In a hypertonic solution, one with higher
osmolarity than the cytosol, the cell shrinks as water
flows out. In a hypotonic solution, with lower osmolarity
than the cytosol, the cell swells as water enters.
In their natural environments, cells generally contain
higher concentrations of biomolecules and ions than
their surroundings, so osmotic pressure tends to drive
water into cells. If not somehow counterbalanced, this
inward movement of water would distend the plasma
membrane and eventually cause bursting of the cell
(osmotic lysis).
Several mechanisms have evolved to prevent this
catastrophe. In bacteria and plants, the plasma membrane
is surrounded by a nonexpandable cell wall of sufficient
rigidity and strength to resist osmotic pressure
and prevent osmotic lysis. Certain freshwater protists
that live in a highly hypotonic medium have an organelle
(contractile vacuole) that pumps water out of the cell.
In multicellular animals, blood plasma and interstitial
fluid (the extracellular fluid of tissues) are maintained
at an osmolarity close to that of the cytosol. The high
concentration of albumin and other proteins in blood
plasma contributes to its osmolarity. Cells also actively
pump out ions such as Na into the interstitial fluid to
stay in osmotic balance with their surroundings.
Chapter 2 Water 57
Forming
ice crystal
(a) (b)
In pure water, every
molecule at the surface is
H2O, and all contribute
to the vapor pressure.
Every molecule in the bulk
solution is H2O, and can
contribute to formation of
ice crystals.
In this solution, the
effective concentration of
H2O is reduced; only 3 of
every 4 molecules at the
surface and in the bulk
phase are H2O. The vapor
pressure of water and the
tendency of liquid water to
enter a crystal are reduced
proportionately.
=
=
H2O
Solute
FIGURE 2–11 Solutes alter the colligative properties of aqueous solutions.
(a) At 101 kPa (1 atm) pressure, pure water boils at 100 C
and freezes at 0 C. (b) The presence of solute molecules reduces the
probability of a water molecule leaving the solution and entering the
gas phase, thereby reducing the vapor pressure of the solution and increasing
the boiling point. Similarly, the probability of a water molecule
colliding with and joining a forming ice crystal is reduced when
some of the molecules colliding with the crystal are solute, not water,
molecules. The effect is depression of the freezing point.
h
Nonpermeant
solute dissolved
in water
Pure
water Piston
Semipermeable
membrane
(a) (b) (c)
FIGURE 2–12 Osmosis and the measurement of osmotic pressure.
(a) The initial state. The tube contains an aqueous solution, the beaker
contains pure water, and the semipermeable membrane allows the
passage of water but not solute. Water flows from the beaker into the
tube to equalize its concentration across the membrane. (b) The final
state. Water has moved into the solution of the nonpermeant compound,
diluting it and raising the column of water within the tube. At
equilibrium, the force of gravity operating on the solution in the tube
exactly balances the tendency of water to move into the tube, where
its concentration is lower. (c) Osmotic pressure (
) is measured as the
force that must be applied to return the solution in the tube to the
level of that in the beaker. This force is proportional to the height, h,
of the column in (b).
Because the effect of solutes on osmolarity depends
on the number of dissolved particles, not their mass,
macromolecules (proteins, nucleic acids, polysaccharides)
have far less effect on the osmolarity of a solution
than would an equal mass of their monomeric components.
For example, a gram of a polysaccharide
composed of 1,000 glucose units has the same effect on
osmolarity as a milligram of glucose. One effect of storing
fuel as polysaccharides (starch or glycogen) rather
than as glucose or other simple sugars is prevention of
an enormous increase in osmotic pressure within the
storage cell.
Plants use osmotic pressure to achieve mechanical
rigidity. The very high solute concentration in the plant
cell vacuole draws water into the cell (Fig. 2–13). The
resulting osmotic pressure against the cell wall (turgor
pressure) stiffens the cell, the tissue, and the plant body.
When the lettuce in your salad wilts, it is because loss
of water has reduced turgor pressure. Sudden alterations
in turgor pressure produce the movement of plant
parts seen in touch-sensitive plants such as the Venus
flytrap and mimosa (Box 2–1).
Osmosis also has consequences for laboratory protocols.
Mitochondria, chloroplasts, and lysosomes, for example,
are bounded by semipermeable membranes. In
isolating these organelles from broken cells, biochemists
must perform the fractionations in isotonic solutions
(see Fig. 1–8). Buffers used in cellular fractionations
commonly contain sufficient concentrations (about 0.2 M)
of sucrose or some other inert solute to protect the
organelles from osmotic lysis.
SUMMARY 2.1 Weak Interactions in Aqueous
Systems
■ The very different electronegativities of H and
O make water a highly polar molecule, capable
of forming hydrogen bonds with itself and with
solutes. Hydrogen bonds are fleeting, primarily
electrostatic, and weaker than covalent bonds.
Water is a good solvent for polar (hydrophilic)
solutes, with which it forms hydrogen bonds,
and for charged solutes, with which it interacts
electrostatically.
■ Nonpolar (hydrophobic) compounds dissolve
poorly in water; they cannot hydrogen-bond
with the solvent, and their presence forces an
energetically unfavorable ordering of water
molecules at their hydrophobic surfaces. To
minimize the surface exposed to water, nonpolar
compounds such as lipids form aggregates
(micelles) in which the hydrophobic moieties
are sequestered in the interior, associating
through hydrophobic interactions, and only the
more polar moieties interact with water.
■ Numerous weak, noncovalent interactions decisively
influence the folding of macromolecules
such as proteins and nucleic acids. The most
stable macromolecular conformations are those
in which hydrogen bonding is maximized within
the molecule and between the molecule and
the solvent, and in which hydrophobic moieties
cluster in the interior of the molecule away
from the aqueous solvent.
■ The physical properties of aqueous solutions
are strongly influenced by the concentrations
of solutes. When two aqueous compartments
are separated by a semipermeable membrane
(such as the plasma membrane separating a
cell from its surroundings), water moves across
that membrane to equalize the osmolarity in
the two compartments. This tendency for water
to move across a semipermeable membrane is
the osmotic pressure.
58 Part I Structure and Catalysis
(b) Cell in hypertonic
solution; water moves out
and cell shrinks.
(c) Cell in hypotonic
solution; water moves in,
creating outward pressure;
cell swells, may eventually
burst.
(a) Cell in isotonic
solution; no net water
movement.
Extracellular
solutes
Intracellular
solutes
FIGURE 2–13 Effect of extracellular osmolarity on water movement
across a plasma membrane. When a cell in osmotic balance with its
surrounding medium (that is, in an isotonic medium) (a) is transferred
into a hypertonic solution (b) or hypotonic solution (c), water moves
across the plasma membrane in the direction that tends to equalize
osmolarity outside and inside the cell.
Chapter 2 Water 59
BOX 2–1 THE WORLD OF BIOCHEMISTRY
(a) (b)
(a) (b)
FIGURE 1 Touch response in the
Venus flytrap. A fly approaching an
open leaf (a) is trapped for digestion
by the plant (b).
FIGURE 2 The feathery leaflets of
the sensitive plant (a) close and
drop (b) to protect the plant from
structural damage by wind.
Touch Response in Plants: An Osmotic Event
The highly specialized leaves of the Venus flytrap
(Dionaea muscipula) rapidly fold together in response
to a light touch by an unsuspecting insect, entrapping
the insect for later digestion. Attracted by
nectar on the leaf surface, the insect touches three
mechanically sensitive hairs, triggering the traplike
closing of the leaf (Fig. 1). This leaf movement is produced
by sudden (within 0.5 s) changes of turgor pressure
in mesophyll cells (the inner cells of the leaf),
probably achieved by the release of K ions from the
cells and the resulting efflux, by osmosis, of water. Digestive
glands in the leaf’s surface release enzymes
that extract nutrients from the insect.
The sensitive plant (Mimosa pudica) also undergoes
a remarkable change in leaf shape triggered
by mechanical touch (Fig. 2). A light touch or vibration
produces a sudden drooping of the leaves, the result
of a dramatic reduction in turgor pressure in cells
at the base of each leaflet and leaf. As in the Venus
flytrap, the drop in turgor pressure results from K
release followed by the efflux of water.
2.2 Ionization of Water, Weak Acids,
and Weak Bases
Although many of the solvent properties of water can
be explained in terms of the uncharged H2O molecule,
the small degree of ionization of water to hydrogen ions
(H ) and hydroxide ions (OH ) must also be taken into
account. Like all reversible reactions, the ionization of
water can be described by an equilibrium constant.
When weak acids are dissolved in water, they contribute
H by ionizing; weak bases consume H by becoming
protonated. These processes are also governed by equilibrium
constants. The total hydrogen ion concentration
from all sources is experimentally measurable and is expressed
as the pH of the solution. To predict the state
of ionization of solutes in water, we must take into account
the relevant equilibrium constants for each ionization
reaction. We therefore turn now to a brief discussion
of the ionization of water and of weak acids and
bases dissolved in water.
Pure Water Is Slightly Ionized
Water molecules have a slight tendency to undergo reversible
ionization to yield a hydrogen ion (a proton)
and a hydroxide ion, giving the equilibrium
H2O H OH (2–1)
Although we commonly show the dissociation product
of water as H , free protons do not exist in solution; hydrogen
ions formed in water are immediately hydrated
to hydronium ions (H3O ). Hydrogen bonding between
water molecules makes the hydration of dissociating
protons virtually instantaneous:
The ionization of water can be measured by its electrical
conductivity; pure water carries electrical current
as H migrates toward the cathode and OH toward the
anode. The movement of hydronium and hydroxide ions
in the electric field is anomalously fast compared with
that of other ions such as Na , K , and Cl . This high
ionic mobility results from the kind of “proton hopping”
shown in Figure 2–14. No individual proton moves very
far through the bulk solution, but a series of proton hops
between hydrogen-bonded water molecules causes the
net movement of a proton over a long distance in a remarkably
short time. As a result of the high ionic mobility
of H (and of OH , which also moves rapidly by
proton hopping, but in the opposite direction), acid-base
reactions in aqueous solutions are generally exceptionally
fast. As noted above, proton hopping very likely also
plays a role in biological proton-transfer reactions (Fig.
2–10; see also Fig. 19–XX).
Because reversible ionization is crucial to the role
of water in cellular function, we must have a means of
O
H
H O OH
H
H HO H
H
zy
expressing the extent of ionization of water in quantitative
terms. A brief review of some properties of reversible
chemical reactions shows how this can be done.
The position of equilibrium of any chemical reaction
is given by its equilibrium constant, Keq (sometimes
expressed simply as K). For the generalized
reaction
A B C D (2–2)
an equilibrium constant can be defined in terms of the
concentrations of reactants (A and B) and products (C
and D) at equilibrium:
Keq
[
[
C
A
]
]
[
[
D
B]
]
Strictly speaking, the concentration terms should be
the activities, or effective concentrations in nonideal
solutions, of each species. Except in very accurate work,
however, the equilibrium constant may be approxizy
60 Part I Structure and Catalysis
O+
O
O
O
O
O
O
H H
Proton hop
Hydronium ion gives up a proton
Water accepts proton and
becomes a hydronium ion
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
O
O
O
H
H
H
H
FIGURE 2–14 Proton hopping. Short “hops” of protons between a series
of hydrogen-bonded water molecules effect an extremely rapid
net movement of a proton over a long distance. As a hydronium ion
(upper left) gives up a proton, a water molecule some distance away
(lower right) acquires one, becoming a hydronium ion. Proton hopping
is much faster than true diffusion and explains the remarkably
high ionic mobility of H ions compared with other monovalent
cations such as Na or K .
mated by measuring the concentrations at equilibrium.
For reasons beyond the scope of this discussion, equilibrium
constants are dimensionless. Nonetheless, we
have generally retained the concentration units (M) in
the equilibrium expressions used in this book to remind
you that molarity is the unit of concentration used in
calculating Keq.
The equilibrium constant is fixed and characteristic
for any given chemical reaction at a specified temperature.
It defines the composition of the final equilibrium
mixture, regardless of the starting amounts of
reactants and products. Conversely, we can calculate
the equilibrium constant for a given reaction at a given
temperature if the equilibrium concentrations of all its
reactants and products are known. As we will show in
Chapter 13, the standard free-energy change ( G ) is
directly related to Keq.
The Ionization of Water Is Expressed by an
Equilibrium Constant
The degree of ionization of water at equilibrium (Eqn
2–1) is small; at 25 °C only about two of every 109 molecules
in pure water are ionized at any instant. The equilibrium
constant for the reversible ionization of water
(Eqn 2–1) is
Keq
[H
[

H
][
2
O
O
H
]
]
(2–3)
In pure water at 25 C, the concentration of water is
55.5 M (grams of H2O in 1 L divided by its gram molecular
weight: (1,000 g/L)/(18.015 g/mol)) and is essentially
constant in relation to the very low concentrations
of H and OH , namely, 1 10 7
M. Accordingly, we
can substitute 55.5 M in the equilibrium constant expression
(Eqn 2–3) to yield
Keq
[H
5

5
][
.5
OH
M
]
,
which, on rearranging, becomes
(55.5 M)(Keq) [H ][OH ] Kw (2–4)
where Kw designates the product (55.5 M)(Keq), the ion
product of water at 25 °C.
The value for Keq, determined by electrical-conductivity
measurements of pure water, is 1.8 10 16
M
at 25 C. Substituting this value for Keq in Equation 2–4
gives the value of the ion product of water:
Kw [H ][OH ] (55.5 M)(1.8 10 16 M)
1.0 10 14 M2
Thus the product [H ][OH ] in aqueous solutions at
25 C always equals 1 10 14
M
2. When there are exactly
equal concentrations of H and OH , as in pure
water, the solution is said to be at neutral pH. At this
pH, the concentration of H and OH can be calculated
from the ion product of water as follows:
Kw [H ][OH ] [H ]2
Solving for [H ] gives
[H ] K w 1 10 14 M 2
[H ] [OH ] 10 7 M
As the ion product of water is constant, whenever [H ]
is greater than 1 10 7
M, [OH ] must become less
than 1 10 7
M, and vice versa. When [H ] is very high,
as in a solution of hydrochloric acid, [OH ] must be very
low. From the ion product of water we can calculate
[H ] if we know [OH ], and vice versa (Box 2–2).
The pH Scale Designates the H and OH
Concentrations
The ion product of water, Kw, is the basis for the pH
scale (Table 2–6). It is a convenient means of designating
the concentration of H (and thus of OH ) in
any aqueous solution in the range between 1.0 M H and
1.0 M OH . The term pH is defined by the expression
pH log
[H
1
]
log [H ]
The symbol p denotes “negative logarithm of.” For a precisely
neutral solution at 25 C, in which the concentration
of hydrogen ions is 1.0 10 7
M, the pH can be
calculated as follows:
pH log
1.0
1
10 7 log (1.0 107)
log 1.0 log 107 0 7 7
Chapter 2 Water 61
TABLE 2–6 The pH Scale
[H ] (M) pH [OH ] (M) pOH*
100 (1) 0 10 14 14
10 1 1 10 13 13
10 2 2 10 12 12
10 3 3 10 11 11
10 4 4 10 10 10
10 5 5 10 9 9
10 6 6 10 8 8
10 7 7 10 7 7
10 8 8 10 6 6
10 9 9 10 5 5
10 10 10 10 4 4
10 11 11 10 3 3
10 12 12 10 2 2
10 13 13 10 1 1
10 14 14 100 (1) 0
*The expression pOH is sometimes used to describe the basicity, or OH concentration, of
a solution; pOH is defined by the expression pOH log [OH ], which is analogous to
the expression for pH. Note that in all cases, pH pOH 14.
The value of 7 for the pH of a precisely neutral solution
is not an arbitrarily chosen figure; it is derived
from the absolute value of the ion product of water at
25 C, which by convenient coincidence is a round number.
Solutions having a pH greater than 7 are alkaline or
basic; the concentration of OH is greater than that of
H . Conversely, solutions having a pH less than 7 are
acidic.
Note that the pH scale is logarithmic, not arithmetic.
To say that two solutions differ in pH by 1 pH unit means
that one solution has ten times the H concentration of
the other, but it does not tell us the absolute magnitude
of the difference. Figure 2–15 gives the pH of some common
aqueous fluids. A cola drink (pH 3.0) or red wine
(pH 3.7) has an H concentration approximately 10,000
times that of blood (pH 7.4).
The pH of an aqueous solution can be approximately
measured using various indicator dyes, including litmus,
phenolphthalein, and phenol red, which undergo color
changes as a proton dissociates from the dye molecule.
Accurate determinations of pH in the chemical or clinical
laboratory are made with a glass electrode that is selectively
sensitive to H concentration but insensitive to
Na , K , and other cations. In a pH meter the signal from
such an electrode is amplified and compared with the signal
generated by a solution of accurately known pH.
Measurement of pH is one of the most important and
frequently used procedures in biochemistry. The pH affects
the structure and activity of biological macromolecules;
for example, the catalytic activity of enzymes is
strongly dependent on pH (see Fig. 2–21). Measurements
of the pH of blood and urine are commonly used in medical
diagnoses. The pH of the blood plasma of people
62 Part I Structure and Catalysis
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Household bleach
Household ammonia
Solution of baking
soda (NaHCO3)
Seawater, egg white
Human blood, tears
Milk, saliva
Black coffee
Beer
Tomato juice
Red wine
Cola, vinegar
Lemon juice
Gastric juice
1 M HCl
14 1 M NaOH
Neutral
Increasingly
basic
Increasingly
acidic
FIGURE 2–15 The pH of some aqueous fluids.
BOX 2–2 WORKING IN BIOCHEMISTRY
The Ion Product of Water: Two Illustrative
Problems
The ion product of water makes it possible to calculate
the concentration of H , given the concentration
of OH , and vice versa; the following problems demonstrate
this.
1. What is the concentration of H in a solution of
0.1 M NaOH?
Kw [H ][OH ]
Solving for [H ] gives
[H ]
[O
K
H
w
]

1
0
1
.
0
1

M
14 M2

1
1
0
0


14
1
M
M
2

10 13 M (answer)
2. What is the concentration of OH in a solution
with an H concentration of 1.3 10 4
M?
Kw [H ][OH ]
Solving for [OH ] gives
[OH ]
[H
Kw
]

1
1
.0
.3


1
1
0
0


14
4
M
M
2

7.7 10 11 M (answer)
When doing these or any other calculations, be
sure to round your answers to the correct number of
significant figures.
with severe, uncontrolled diabetes, for example, is often
below the normal value of 7.4; this condition is called
acidosis. In certain other disease states the pH of the
blood is higher than normal, the condition of alkalosis.
Weak Acids and Bases Have Characteristic
Dissociation Constants
Hydrochloric, sulfuric, and nitric acids, commonly called
strong acids, are completely ionized in dilute aqueous
solutions; the strong bases NaOH and KOH are also completely
ionized. Of more interest to biochemists is the
behavior of weak acids and bases—those not completely
ionized when dissolved in water. These are common in
biological systems and play important roles in metabolism
and its regulation. The behavior of aqueous solutions
of weak acids and bases is best understood if we
first define some terms.
Acids may be defined as proton donors and bases
as proton acceptors. A proton donor and its corresponding
proton acceptor make up a conjugate acid-base
pair (Fig. 2–16). Acetic acid (CH3COOH), a proton
donor, and the acetate anion (CH3COO ), the corresponding
proton acceptor, constitute a conjugate acidbase
pair, related by the reversible reaction
CH3COOH H CH3COO
Each acid has a characteristic tendency to lose its
proton in an aqueous solution. The stronger the acid,
the greater its tendency to lose its proton. The tendency
of any acid (HA) to lose a proton and form its conjugate
base (A ) is defined by the equilibrium constant
(Keq) for the reversible reaction
HA H A ,
which is
Keq
[H
[

H
][
A
A
]
]
Ka
Equilibrium constants for ionization reactions are usually
called ionization or dissociation constants, often
designated Ka. The dissociation constants of some acids
are given in Figure 2–16. Stronger acids, such as phosphoric
and carbonic acids, have larger dissociation constants;
weaker acids, such as monohydrogen phosphate
(HPO4
2 ), have smaller dissociation constants.
zy
zy
Chapter 2 Water 63
Monoprotic acids
Acetic acid
(Ka = 1.74 10 5 M)
Diprotic acids
Carbonic acid
(Ka = 1.70 10 4 M);
Bicarbonate
(Ka = 6.31 10 11 M)
Triprotic acids
Phosphoric acid
(Ka = 7.25 10 3 M);
Dihydrogen phosphate
(Ka = 1.38 10 7 M);
Monohydrogen phosphate
(Ka = 3.98 10 13 M)
Glycine, carboxyl
(Ka = 4.57 10 3 M);
Glycine, amino
(Ka = 2.51 10 10 M)
Ammonium ion
(Ka = 5.62 10 10 M)
CH3C
OH
O
CH3C
O
H
O
pKa = 4.76
H2CO3 HCO3
H
pKa = 3.77
HCO3
CO3
2 H
pKa = 10.2
NH4
NH3 H
pKa = 9.25
H3PO4 H2PO4
H
pKa = 2.14
H2PO4
HPO4
2 H
pKa = 6.86
HPO4 2 PO4 3 H
pKa = 12.4
CH2C
OH
O
CH2C
O
H
O
pKa = 2.34
NH3
NH3

CH2C
O
O
CH2C
O
H
O
pKa = 9.60
NH3
NH2
1 2 3 4 5 6 7 8 9 10 11 12 13
pH
FIGURE 2–16 Conjugate acid-base pairs consist of a proton donor
and a proton acceptor. Some compounds, such as acetic acid and
ammonium ion, are monoprotic; they can give up only one proton.
Others are diprotic (H2CO3 (carbonic acid) and glycine) or triprotic
(H3PO4 (phosphoric acid)). The dissociation reactions for each pair are
shown where they occur along a pH gradient. The equilibrium or dissociation
constant (Ka) and its negative logarithm, the pKa, are shown
for each reaction.
Also included in Figure 2–16 are values of pKa,
which is analogous to pH and is defined by the equation
pKa log
K
1
a
log Ka
The stronger the tendency to dissociate a proton, the
stronger is the acid and the lower its pKa. As we shall
now see, the pKa of any weak acid can be determined
quite easily.
Titration Curves Reveal the pKa of Weak Acids
Titration is used to determine the amount of an acid in
a given solution. A measured volume of the acid is
titrated with a solution of a strong base, usually sodium
hydroxide (NaOH), of known concentration. The NaOH
is added in small increments until the acid is consumed
(neutralized), as determined with an indicator dye or a
pH meter. The concentration of the acid in the original
solution can be calculated from the volume and concentration
of NaOH added.
A plot of pH against the amount of NaOH added (a
titration curve) reveals the pKa of the weak acid. Consider
the titration of a 0.1 M solution of acetic acid (for
simplicity denoted as HAc) with 0.1 M NaOH at 25 C
(Fig. 2–17). Two reversible equilibria are involved in the
process:
H2O H OH (2–5)
HAc H Ac (2–6)
The equilibria must simultaneously conform to their
characteristic equilibrium constants, which are, respectively,
Kw [H ][OH ] 1 10 14 M2 (2–7)
Ka
[H
[

H
][
A
A
c
c
]
]
1.74 105 M (2–8)
At the beginning of the titration, before any NaOH is
added, the acetic acid is already slightly ionized, to an
extent that can be calculated from its dissociation constant
(Eqn 2–8).
As NaOH is gradually introduced, the added OH
combines with the free H in the solution to form H2O,
to an extent that satisfies the equilibrium relationship
in Equation 2–7. As free H is removed, HAc dissociates
further to satisfy its own equilibrium constant (Eqn
2–8). The net result as the titration proceeds is that
more and more HAc ionizes, forming Ac , as the NaOH
is added. At the midpoint of the titration, at which exactly
0.5 equivalent of NaOH has been added, one-half
of the original acetic acid has undergone dissociation,
so that the concentration of the proton donor, [HAc],
now equals that of the proton acceptor, [Ac ]. At this
midpoint a very important relationship holds: the pH of
the equimolar solution of acetic acid and acetate is exzy
zy
actly equal to the pKa of acetic acid (pKa 4.76; Figs
2–16, 2–17). The basis for this relationship, which holds
for all weak acids, will soon become clear.
As the titration is continued by adding further increments
of NaOH, the remaining nondissociated acetic
acid is gradually converted into acetate. The end point
of the titration occurs at about pH 7.0: all the acetic acid
has lost its protons to OH , to form H2O and acetate.
Throughout the titration the two equilibria (Eqns 2–5,
2–6) coexist, each always conforming to its equilibrium
constant.
Figure 2–18 compares the titration curves of three
weak acids with very different dissociation constants:
acetic acid (pKa 4.76); dihydrogen phosphate, H2PO4
(pKa 6.86); and ammonium ion, NH4 (pKa 9.25).
Although the titration curves of these acids have the
same shape, they are displaced along the pH axis because
the three acids have different strengths. Acetic
acid, with the highest Ka (lowest pKa) of the three, is
the strongest (loses its proton most readily); it is al-
64 Part I Structure and Catalysis
1.0
CH3COO
CH3COOH
pH pKa 4.76
pH
Buffering
region
OH added (equivalents)
0 50 100%
Percent titrated
9
8
7
3
2
1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
[CH3COOH] [CH3COO ]
pH 5.76
pH 3.76
6
5
4
FIGURE 2–17 The titration curve of acetic acid. After addition of
each increment of NaOH to the acetic acid solution, the pH of the
mixture is measured. This value is plotted against the amount of NaOH
expressed as a fraction of the total NaOH required to convert all the
acetic acid to its deprotonated form, acetate. The points so obtained
yield the titration curve. Shown in the boxes are the predominant ionic
forms at the points designated. At the midpoint of the titration, the
concentrations of the proton donor and proton acceptor are equal,
and the pH is numerically equal to the pKa. The shaded zone is the
useful region of buffering power, generally between 10% and 90%
titration of the weak acid.
ready half dissociated at pH 4.76. Dihydrogen phosphate
loses a proton less readily, being half dissociated at pH
6.86. Ammonium ion is the weakest acid of the three
and does not become half dissociated until pH 9.25.
The most important point about the titration curve
of a weak acid is that it shows graphically that a weak
acid and its anion—a conjugate acid-base pair—can act
as a buffer.
SUMMARY 2.2 Ionization of Water, Weak Acids,
and Weak Bases
■ Pure water ionizes slightly, forming equal numbers
of hydrogen ions (hydronium ions, H3O )
and hydroxide ions. The extent of ionization is
described by an equilibrium constant, Keq

[H
[H
][
2
O
O
H
]
]
, from which the ion product of
water, Kw, is derived. At 25 C, Kw [H ][OH ]
(55.5 M)(Keq) = 10 14
M
2.
■ The pH of an aqueous solution reflects, on a
logarithmic scale, the concentration of
hydrogen ions: pH log [H
1
] log [H ].
■ The greater the acidity of a solution, the lower
its pH. Weak acids partially ionize to release a
hydrogen ion, thus lowering the pH of the
aqueous solution. Weak bases accept a hydrogen
ion, increasing the pH. The extent of these
processes is characteristic of each particular
weak acid or base and is expressed as a dissociation
constant, Ka: Keq
[H
[

H
][
A
A
]
]
Ka.
■ The pKa expresses, on a logarithmic scale, the
relative strength of a weak acid or base:
pKa log K
1
a
log Ka.
■ The stronger the acid, the lower its pKa; the
stronger the base, the higher its pKa. The pKa
can be determined experimentally; it is the pH
at the midpoint of the titration curve for the
acid or base.
2.3 Buffering against pH Changes
in Biological Systems
Almost every biological process is pH dependent; a small
change in pH produces a large change in the rate of the
process. This is true not only for the many reactions in
which the H ion is a direct participant, but also for those
in which there is no apparent role for H ions. The enzymes
that catalyze cellular reactions, and many of the
molecules on which they act, contain ionizable groups
with characteristic pKa values. The protonated amino
and carboxyl groups of amino acids and the phosphate
groups of nucleotides, for example, function as weak
acids; their ionic state depends on the pH of the surrounding
medium. As we noted above, ionic interactions
are among the forces that stabilize a protein molecule
and allow an enzyme to recognize and bind its substrate.
Cells and organisms maintain a specific and constant
cytosolic pH, keeping biomolecules in their optimal
ionic state, usually near pH 7. In multicellular organisms,
the pH of extracellular fluids is also tightly
regulated. Constancy of pH is achieved primarily by biological
buffers: mixtures of weak acids and their conjugate
bases.
We describe here the ionization equilibria that account
for buffering, and we show the quantitative relationship
between the pH of a buffered solution and the
pKa of the buffer. Biological buffering is illustrated by the
phosphate and carbonate buffering systems of humans.
Chapter 2 Water 65
1.0
NH3
Midpoint
of
titration
Buffering
regions:
pKa 9.25
NH3
[NH
4] [NH3]
CH3COO pKa 6.86
pKa 4.76
[CH3COOH] [CH3COO ]
CH3COOH
pH
10.25
5.76
3.76
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
[H2PO4
] [HPO2
4
]
Phosphate
Acetate
NH4

H2PO4

8.25
7.86
5.86
HPO4
2
OH added (equivalents)
0 50 100%
Percent titrated
FIGURE 2–18 Comparison of the titration curves of three weak acids.
Shown here are the titration curves for CH3COOH, H2PO4
, and NH4
.
The predominant ionic forms at designated points in the titration are
given in boxes. The regions of buffering capacity are indicated at the
right. Conjugate acid-base pairs are effective buffers between approximately
10% and 90% neutralization of the proton-donor species.
Buffers Are Mixtures of Weak Acids
and Their Conjugate Bases
Buffers are aqueous systems that tend to resist changes
in pH when small amounts of acid (H ) or base (OH )
are added. A buffer system consists of a weak acid (the
proton donor) and its conjugate base (the proton acceptor).
As an example, a mixture of equal concentrations
of acetic acid and acetate ion, found at the midpoint
of the titration curve in Figure 2–17, is a buffer
system. The titration curve of acetic acid has a relatively
flat zone extending about 1 pH unit on either side of its
midpoint pH of 4.76. In this zone, an amount of H or
OH added to the system has much less effect on pH
than the same amount added outside the buffer range.
This relatively flat zone is the buffering region of the
acetic acid–acetate buffer pair. At the midpoint of the
buffering region, where the concentration of the proton
donor (acetic acid) exactly equals that of the proton acceptor
(acetate), the buffering power of the system is
maximal; that is, its pH changes least on addition of H
or OH . The pH at this point in the titration curve of
acetic acid is equal to its pKa. The pH of the acetate
buffer system does change slightly when a small amount
of H or OH is added, but this change is very small
compared with the pH change that would result if the
same amount of H or OH were added to pure water
or to a solution of the salt of a strong acid and strong
base, such as NaCl, which has no buffering power.
Buffering results from two reversible reaction equilibria
occurring in a solution of nearly equal concentrations
of a proton donor and its conjugate proton acceptor.
Figure 2–19 explains how a buffer system works.
Whenever H or OH is added to a buffer, the result is
a small change in the ratio of the relative concentrations
of the weak acid and its anion and thus a small change
in pH. The decrease in concentration of one component
of the system is balanced exactly by an increase in the
other. The sum of the buffer components does not
change, only their ratio.
Each conjugate acid-base pair has a characteristic
pH zone in which it is an effective buffer (Fig. 2–18).
The H2PO4 /HPO4
2 pair has a pKa of 6.86 and thus can
serve as an effective buffer system between approximately
pH 5.9 and pH 7.9; the NH4 /NH3 pair, with a pKa
of 9.25, can act as a buffer between approximately pH
8.3 and pH 10.3.
A Simple Expression Relates pH, pKa, and Buffer
Concentration
The titration curves of acetic acid, H2PO4 , and NH4
(Fig. 2–18) have nearly identical shapes, suggesting that
these curves reflect a fundamental law or relationship.
This is indeed the case. The shape of the titration curve
of any weak acid is described by the Henderson-
Hasselbalch equation, which is important for understanding
buffer action and acid-base balance in the
blood and tissues of vertebrates. This equation is simply
a useful way of restating the expression for the
dissociation constant of an acid. For the dissociation of
a weak acid HA into H and A , the Henderson-
Hasselbalch equation can be derived as follows:
Ka
[H
[

H
][
A
A
]
]

First solve for [H ]:
[H ] Ka
[
[
H
A
A
]
]
Then take the negative logarithm of both sides:
log [H ] log Ka log
[
[
H
A
A
]
]
Substitute pH for log [H ] and pKa for log Ka:
pH pKa log
[
[
H
A
A
]
]
66 Part I Structure and Catalysis
Kw [H ][OH ]
Acetic acid
(CH3COOH)
HAc Ac
H
OH H2O
Acetate
(CH3COO )
[H ][Ac ]
[HAc]
Ka
FIGURE 2–19 The acetic acid–acetate pair as a buffer system. The
system is capable of absorbing either H or OH through the reversibility
of the dissociation of acetic acid. The proton donor, acetic
acid (HAc), contains a reserve of bound H , which can be released
to neutralize an addition of OH to the system, forming H2O. This
happens because the product [H ][OH ] transiently exceeds Kw (1
10 14 M2). The equilibrium quickly adjusts so that this product equals
1 10 14 M2 (at 25 C), thus transiently reducing the concentration
of H . But now the quotient [H ][Ac ] / [HAc] is less than Ka, so HAc
dissociates further to restore equilibrium. Similarly, the conjugate base,
Ac , can react with H ions added to the system; again, the two ionization
reactions simultaneously come to equilibrium. Thus a conjugate
acid-base pair, such as acetic acid and acetate ion, tends to resist
a change in pH when small amounts of acid or base are added.
Buffering action is simply the consequence of two reversible reactions
taking place simultaneously and reaching their points of equilibrium
as governed by their equilibrium constants, KW and Ka.
Now invert log [HA]/[A ], which involves changing its
sign, to obtain the Henderson-Hasselbalch equation:
pH pKa log
[
[
H
A
A
]
]
(2–9)
Stated more generally,
pH pKa log
This equation fits the titration curve of all weak acids
and enables us to deduce a number of important quantitative
relationships. For example, it shows why the pKa
of a weak acid is equal to the pH of the solution at the
midpoint of its titration. At that point, [HA] equals [A ],
and
pH pKa log 1 pKa 0 pKa
As shown in Box 2–3, the Henderson-Hasselbalch equation
also allows us to (1) calculate pKa, given pH and
the molar ratio of proton donor and acceptor; (2) calculate
pH, given pKa and the molar ratio of proton donor
and acceptor; and (3) calculate the molar ratio of proton
donor and acceptor, given pH and pKa.
Weak Acids or Bases Buffer Cells and Tissues
against pH Changes
The intracellular and extracellular fluids of multicellular
organisms have a characteristic and nearly constant
[proton acceptor]

[proton donor]
pH. The organism’s first line of defense against changes
in internal pH is provided by buffer systems. The cytoplasm
of most cells contains high concentrations of proteins,
which contain many amino acids with functional
groups that are weak acids or weak bases. For example,
the side chain of histidine (Fig. 2–20) has a pKa of 6.0;
proteins containing histidine residues therefore buffer
effectively near neutral pH. Nucleotides such as ATP, as
well as many low molecular weight metabolites, contain
ionizable groups that can contribute buffering power to
the cytoplasm. Some highly specialized organelles and
extracellular compartments have high concentrations of
compounds that contribute buffering capacity: organic
acids buffer the vacuoles of plant cells; ammonia buffers
urine.
Chapter 2 Water 67
BOX 2–3 WORKING IN BIOCHEMISTRY
Solving Problems Using the Henderson-
Hasselbalch Equation
1. Calculate the pKa of lactic acid, given that when
the concentration of lactic acid is 0.010 M and
the concentration of lactate is 0.087 M, the pH is
4.80.
pH pKa log
[la
[l
c
a
t
c
ic
ta
a
t
c
e
i
]
d]

pKa pH log
[la
[l
c
a
t
c
ic
ta
a
t
c
e
i
]
d]

4.80 log
0
0
.
.
0
0
8
1
7
0
4.80 log 8.7
4.80 0.94 3.9 (answer)
2. Calculate the pH of a mixture of 0.10 M acetic
acid and 0.20 M sodium acetate. The pKa of
acetic acid is 4.76.
pH pKa log
[a
[
c
a
e
c
t
e
ic
ta
a
t
c
e
i
]
d]

4.76 log
0
0
.
.
2
1
0
0
4.76 0.30
5.1 (answer)
3. Calculate the ratio of the concentrations of
acetate and acetic acid required in a buffer
system of pH 5.30.
pH pKa log
[a
[
c
a
e
c
t
e
ic
ta
a
t
c
e
i
]
d]

log
[a
[
c
a
e
c
t
e
ic
ta
a
t
c
e
i
]
d]
pH pKa
5.30 4.76 0.54

[a
[
c
a
e
c
t
e
ic
ta
a
t
c
e
i
]
d]
antilog 0.54 3.5 (answer)
To see the effect of pH on the degree of ionization of a weak
acid, see the Living Graph for Equation 2–9.
A
G
J
A
CH2
C
H
CH H
HC
A
G
J
A
CH2
C
H
CH

HC
Protein Protein
3::4
N N
N N
H
FIGURE 2–20 The amino acid histidine, a component of proteins, is a
weak acid. The pKa of the protonated nitrogen of the side chain is 6.0.
Two especially important biological buffers are the
phosphate and bicarbonate systems. The phosphate
buffer system, which acts in the cytoplasm of all cells,
consists of H2PO4 as proton donor and HPO4
2 as proton
acceptor:
H2PO4
H HPO4
2
The phosphate buffer system is maximally effective at
a pH close to its pKa of 6.86 (Figs 2–16, 2–18) and thus
tends to resist pH changes in the range between about
5.9 and 7.9. It is therefore an effective buffer in biological
fluids; in mammals, for example, extracellular fluids
and most cytoplasmic compartments have a pH in
the range of 6.9 to 7.4.
Blood plasma is buffered in part by the bicarbonate
system, consisting of carbonic acid (H2CO3) as proton
donor and bicarbonate (HCO3
) as proton acceptor:
H2CO3 H HCO3
K1
[H
[

H
][
2
H
CO
CO
3]
3
]

This buffer system is more complex than other conjugate
acid-base pairs because one of its components, carbonic
acid (H2CO3), is formed from dissolved (d) carbon
dioxide and water, in a reversible reaction:
CO2(d) H2O H2CO3
K2
[CO
[H
2(
2
d
C
)]
O
[H
3]
2O]

Carbon dioxide is a gas under normal conditions, and
the concentration of dissolved CO2 is the result of equilibration
with CO2 of the gas (g) phase:
CO2(g) CO2(d)
K3
[
[
C
C
O
O
2
2
(
(
d
g)
)
]
]
The pH of a bicarbonate buffer system depends on the
concentration of H2CO3 and HCO3
, the proton donor
and acceptor components. The concentration of H2CO3
in turn depends on the concentration of dissolved CO2,
which in turn depends on the concentration of CO2 in
the gas phase, called the partial pressure of CO2. Thus
the pH of a bicarbonate buffer exposed to a gas phase
is ultimately determined by the concentration of HCO3

in the aqueous phase and the partial pressure of CO2 in
the gas phase (Box 2–4).
Human blood plasma normally has a pH close to 7.4.
Should the pH-regulating mechanisms fail or be overwhelmed,
as may happen in severe uncontrolled diabetes
when an overproduction of metabolic acids causes
acidosis, the pH of the blood can fall to 6.8 or below,
leading to irreparable cell damage and death. In other
diseases the pH may rise to lethal levels.
zy
zy
zy
zy
Although many aspects of cell structure and function
are influenced by pH, it is the catalytic activity of
enzymes that is especially sensitive. Enzymes typically
show maximal catalytic activity at a characteristic pH,
called the pH optimum (Fig. 2–21). On either side of
the optimum pH their catalytic activity often declines
sharply. Thus, a small change in pH can make a large
difference in the rate of some crucial enzyme-catalyzed
reactions. Biological control of the pH of cells and body
fluids is therefore of central importance in all aspects of
metabolism and cellular activities.
SUMMARY 2.3 Buffering against pH Changes
in Biological Systems
■ A mixture of a weak acid (or base) and its salt
resists changes in pH caused by the addition of
H or OH . The mixture thus functions as a
buffer.
■ The pH of a solution of a weak acid (or base)
and its salt is given by the Henderson-
Hasselbalch equation: pH pKa log
[
[
H
A
A
]
]
.
■ In cells and tissues, phosphate and bicarbonate
buffer systems maintain intracellular and extracellular
fluids at their optimum (physiological)
pH, which is usually close to pH 7. Enzymes
generally work optimally at this pH.
68 Part I Structure and Catalysis
100
7
pH
Percent maximum activity
Alkaline
phosphatase
50
0
1 2 3 4 5 6 8 9 10
Pepsin
Trypsin
FIGURE 2–21 The pH optima of some enzymes. Pepsin is a digestive
enzyme secreted into gastric juice; trypsin, a digestive enzyme that
acts in the small intestine; alkaline phosphatase of bone tissue, a hydrolytic
enzyme thought to aid in bone mineralization.
2.4 Water as a Reactant
Water is not just the solvent in which the chemical reactions
of living cells occur; it is very often a direct participant
in those reactions. The formation of ATP from
ADP and inorganic phosphate is an example of a condensation
reaction in which the elements of water are
eliminated (Fig. 2–22a). The reverse of this reaction—
cleavage accompanied by the addition of the elements
of water—is a hydrolysis reaction. Hydrolysis reactions
are also responsible for the enzymatic depolymerization
of proteins, carbohydrates, and nucleic acids.
Hydrolysis reactions, catalyzed by enzymes called
Chapter 2 Water 69
BOX 2–4 BIOCHEMISTRY IN MEDICINE
Blood, Lungs, and Buffer: The Bicarbonate
Buffer System
In animals with lungs, the bicarbonate buffer system
is an effective physiological buffer near pH 7.4, because
the H2CO3 of blood plasma is in equilibrium with
a large reserve capacity of CO2(g) in the air space of
the lungs. This buffer system involves three reversible
equilibria between gaseous CO2 in the lungs and bicarbonate
(HCO3
) in the blood plasma (Fig. 1).
When H (from lactic acid produced in muscle tissue
during vigorous exercise, for example) is added
to blood as it passes through the tissues, reaction 1
proceeds toward a new equilibrium, in which the concentration
of H2CO3 is increased. This increases the
concentration of CO2(d) in the blood plasma (reaction
2) and thus increases the pressure of CO2(g) in
the air space of the lungs (reaction 3); the extra CO2
is exhaled. Conversely, when the pH of blood plasma
is raised (by NH3 production during protein catabolism,
for example), the opposite events occur: the H
concentration of blood plasma is lowered, causing
more H2CO3 to dissociate into H and HCO3
. This in
turn causes more CO2(g) from the lungs to dissolve
in the blood plasma. The rate of breathing—that is,
the rate of inhaling and exhaling CO2—can quickly
adjust these equilibria to keep the blood pH nearly
constant.
(a)
ROOOP B
O
AO

OOOP B
O
A O

OO H2O R OOP B
O
AO

O H HOOP B
O
A
O O
(ATP) (ADP)
(b)
ROOOP
B O
AO

OO H2
O
ROOH HOOP B
O
AO

OO
(c)
R1OC
J
O
G
OR2
H2 R1OC
J
O
G
OH
HOOR2
(d)
ROCOOOP B
O
AO

OO H2 ROC
J
O
G
OH
HOOP B
O
AO

OO
O
O
B O
O O
O
Acyl phosphate
Carboxylate ester
Phosphate ester
Phosphoanhydride
FIGURE 2–22 Participation of water in biological reactions. (a) ATP
is a phosphoanhydride formed by a condensation reaction (loss of the
elements of water) between ADP and phosphate. R represents adenosine
monophosphate (AMP). This condensation reaction requires energy.
The hydrolysis of (addition of the elements of water to) ATP to
form ADP and phosphate releases an equivalent amount of energy.
Also shown are some other condensation and hydrolysis reactions
common in biological systems (b), (c), (d).
H HCO
3
Aqueous phase
(blood in capillaries)
H2CO3
H H2O 2O
reaction 2
CO2(g)
reaction 3
Gas phase
(lung air space)
reaction 1
CO2(d)
FIGURE 1 The CO2 in the air space of the lungs is in equilibrium
with the bicarbonate buffer in the blood plasma passing through the
lung capillaries. Because the concentration of dissolved CO2 can
be adjusted rapidly through changes in the rate of breathing, the bicarbonate
buffer system of the blood is in near-equilibrium with a
large potential reservoir of CO2.
hydrolases, are almost invariably exergonic. The formation
of cellular polymers from their subunits by simple
reversal of hydrolysis (that is, by condensation reactions)
would be endergonic and therefore does not
occur. As we shall see, cells circumvent this thermodynamic
obstacle by coupling endergonic condensation reactions
to exergonic processes, such as breakage of the
anhydride bond in ATP.
You are (we hope!) consuming oxygen as you read.
Water and carbon dioxide are the end products of the
oxidation of fuels such as glucose. The overall reaction
can be summarized as
C6H12O6 6O2 8n 6CO2 6H2O
Glucose
The “metabolic water” formed by oxidation of foods and
stored fats is actually enough to allow some animals in
very dry habitats (gerbils, kangaroo rats, camels) to survive
for extended periods without drinking water.
The CO2 produced by glucose oxidation is converted
in erythrocytes to the more soluble HCO3
, in a
reaction catalyzed by the enzyme carbonic anhydrase:
CO2 H2O HCO3
H
In this reaction, water not only is a substrate but also
functions in proton transfer by forming a network of
hydrogen-bonded water molecules through which proton
hopping occurs (Fig. 2–14).
Green plants and algae use the energy of sunlight
to split water in the process of photosynthesis:
light 2H2O 2A 88n O2 2AH2
In this reaction, A is an electron-accepting species,
which varies with the type of photosynthetic organism,
and water serves as the electron donor in an oxidationreduction
sequence (see Fig. 19–XX) that is fundamental
to all life.
SUMMARY 2.4 Water as a Reactant
■ Water is both the solvent in which metabolic
reactions occur and a reactant in many biochemical
processes, including hydrolysis, condensation,
and oxidation-reduction reactions.
2.5 The Fitness of the Aqueous
Environment for Living Organisms
Organisms have effectively adapted to their aqueous environment
and have evolved means of exploiting the
unusual properties of water. The high specific heat of
water (the heat energy required to raise the temperature
of 1 g of water by 1 C) is useful to cells and orzy
ganisms because it allows water to act as a “heat buffer,”
keeping the temperature of an organism relatively constant
as the temperature of the surroundings fluctuates
and as heat is generated as a byproduct of metabolism.
Furthermore, some vertebrates exploit the high heat of
vaporization of water (Table 2–1) by using (thus losing)
excess body heat to evaporate sweat. The high degree
of internal cohesion of liquid water, due to hydrogen
bonding, is exploited by plants as a means of transporting
dissolved nutrients from the roots to the leaves
during the process of transpiration. Even the density of
ice, lower than that of liquid water, has important biological
consequences in the life cycles of aquatic organisms.
Ponds freeze from the top down, and the layer
of ice at the top insulates the water below from frigid
air, preventing the pond (and the organisms in it) from
freezing solid. Most fundamental to all living organisms
is the fact that many physical and biological properties
of cell macromolecules, particularly the proteins and nucleic
acids, derive from their interactions with water
molecules of the surrounding medium. The influence of
water on the course of biological evolution has been profound
and determinative. If life forms have evolved elsewhere
in the universe, they are unlikely to resemble
those of Earth unless their extraterrestrial origin is also
a place in which plentiful liquid water is available.
70 Part I Structure and Catalysis
Aqueous environments support countless species. Soft corals, sponges,
bryozoans, and algae compete for space on this reef substrate off the
Philippine Islands.
Chapter 2 Water 71
Key Terms
Further Reading
hydrogen bond 48
bond energy 48
hydrophilic 50
hydrophobic 50
amphipathic 52
micelle 53
hydrophobic interactions 53
van der Waals interactions 54
osmolarity 56
osmosis 57
isotonic 57
hypertonic 57
hypotonic 57
equilibrium constant (Keq) 60
ion product of water (Kw) 61
pH 61
conjugate acid-base pair 63
dissociation constant (Ka) 63
pKa 64
titration curve 64
buffer 66
Henderson-Hasselbalch
equation 66
condensation 69
hydrolysis 69
Terms in bold are defined in the glossary.
General
Belton, P.S. (2000) Nuclear magnetic resonance studies of the
hydration of proteins and DNA. Cell. Mol. Life Sci. 57, 993–998.
Denny, M.W. (1993) Air and Water: The Biology and Physics of
Life’s Media, Princeton University Press, Princeton, NJ.
A wonderful investigation of the biological relevance of the
properties of water.
Eisenberg, D. & Kauzmann, W. (1969) The Structure and
Properties of Water, Oxford University Press, New York.
An advanced, classic treatment of the physical chemistry of water
and hydrophobic interactions.
Franks, F. & Mathias, S.F. (eds) (1982) Biophysics of Water,
John Wiley & Sons, Inc., New York.
A large collection of papers on the structure of pure water and
of the cytoplasm.
Gerstein, M. & Levitt, M. (1998) Simulating water and the molecules
of life. Sci. Am. 279 (November), 100–105.
A well-illustrated description of the use of computer simulation
to study the biologically important association of water with
proteins and nucleic acids.
Gronenborn, A. & Clore, M. (1997) Water in and around proteins.
The Biochemist 19 (3), 18–21.
A brief discussion of protein-bound water as detected by crystallography
and NMR.
Kandori, H. (2000) Role of internal water molecules in bacteriorhodopsin.
Biochim. Biophys. Acta 1460, 177–191.
Intermediate-level review of the role of an internal chain of water
molecules in proton movement through this protein.
Kornblatt, J. & Kornblatt, J. (1997) The role of water in recognition
and catalysis by enzymes. The Biochemist 19 (3), 14–17.
A short, useful summary of the ways in which bound water influences
the structure and activity of proteins.
Kuntz, I.D. & Zipp, A. (1977) Water in biological systems.
N. Engl. J. Med. 297, 262–266.
A brief review of the physical state of cytosolic water and its interactions
with dissolved biomolecules.
Ladbury, J. (1996) Just add water! The effect of water on the
specificity of protein-ligand binding sites and its potential application
to drug design. Chem. Biol. 3, 973–980.
Luecke, H. (2000) Atomic resolution structures of bacteriorhodopsin
photocycle intermediates: the role of discrete water
molecules in the function of this light-driven ion pump. Biochim.
Biophys. Acta 1460, 133–156.
Advanced review of a proton pump that employs an internal
chain of water molecules.
Nicolls, P. (2000) Introduction: the biology of the water molecule.
Cell. Mol. Life Sci. 57, 987–992.
A short review of the properties of water, introducing several
excellent advanced reviews published in the same issue (see
especially Pocker and Rand et al., listed below).
Pocker, Y. (2000) Water in enzyme reactions: biophysical aspects
of hydration-dehydration processes. Cell. Mol. Life Sci. 57,
1008–1017.
Review of the role of water in enzyme catalysis, with carbonic
anhydrase as the featured example.
Rand, R.P., Parsegian, V.A., & Rau, D.C. (2000) Intracellular
osmotic action. Cell. Mol. Life Sci. 57, 1018–1032.
Review of the roles of water in enzyme catalysis as revealed by
studies in water-poor solutes.
Record, M.T., Jr., Courtenay, E.S., Cayley, D.S., & Guttman,
H.J. (1998) Responses of E. coli to osmotic stress: large changes
in amounts of cytoplasmic solutes and water. Trends Biochem.
Sci. 23, 143–148.
Intermediate-level review of the ways in which a bacterial cell
counters changes in the osmolarity of its surroundings.
Stillinger, F.H. (1980) Water revisited. Science 209, 451–457.
A short review of the physical structure of water, including the
importance of hydrogen bonding and the nature of hydrophobic
interactions.
Symons, M.C. (2000) Spectroscopy of aqueous solutions: protein
and DNA interactions with water. Cell. Mol. Life Sci. 57,
999–1007.
Westhof, E. (ed.) (1993) Water and Biological Macromolecules,
CRC Press, Inc., Boca Raton, FL.
Fourteen chapters, each by a different author, cover (at an advanced
level) the structure of water and its interactions with
proteins, nucleic acids, polysaccharides, and lipids.
72 Part I Structure and Catalysis
Wiggins, P.M. (1990) Role of water in some biological processes.
Microbiol. Rev. 54, 432–449.
A review of water in biology, including discussion of the physical
structure of liquid water, its interaction with biomolecules,
and the state of water in living cells.
Weak Interactions in Aqueous Systems
Fersht, A.R. (1987) The hydrogen bond in molecular recognition.
Trends Biochem. Sci. 12, 301–304.
A clear, brief, quantitative discussion of the contribution of hydrogen
bonding to molecular recognition and enzyme catalysis.
Frieden, E. (1975) Non-covalent interactions: key to biological
flexibility and specificity. J. Chem. Educ. 52, 754–761.
Review of the four kinds of weak interactions that stabilize
macromolecules and confer biological specificity, with clear
examples.
Jeffrey, G.A. (1997) An Introduction to Hydrogen Bonding,
Oxford University Press, New York.
A detailed, advanced discussion of the structure and properties
of hydrogen bonds, including those in water and biomolecules.
Martin, T.W. & Derewenda, Z.S. (1999) The name is bondOH
bond. Nat. Struct. Biol. 6, 403–406.
Brief review of the evidence that hydrogen bonds have some
covalent character.
Schwabe, J.W.R. (1997) The role of water in protein-DNA interactions.
Curr. Opin. Struct. Biol. 7, 126–134.
An examination of the important role of water in both the
specificity and the affinity of protein-DNA interactions.
Tanford, C. (1978) The hydrophobic effect and the organization
of living matter. Science 200, 1012–1018.
A review of the chemical and energetic bases for hydrophobic
interactions between biomolecules in aqueous solutions.
Weak Acids, Weak Bases, and Buffers:
Problems for Practice
Segel, I.H. (1976) Biochemical Calculations, 2nd edn, John Wiley
& Sons, Inc., New York.
1. Simulated Vinegar One way to make vinegar (not the
preferred way) is to prepare a solution of acetic acid, the sole
acid component of vinegar, at the proper pH (see Fig. 2–15)
and add appropriate flavoring agents. Acetic acid (Mr 60) is
a liquid at 25 C, with a density of 1.049 g/mL. Calculate the
volume that must be added to distilled water to make 1 L of
simulated vinegar (see Fig. 2–16).
2. Acidity of Gastric HCl In a hospital laboratory,
a 10.0 mL sample of gastric juice, obtained several
hours after a meal, was titrated with 0.1 M NaOH to neutrality;
7.2 mL of NaOH was required. The patient’s stomach contained
no ingested food or drink, thus assume that no buffers
were present. What was the pH of the gastric juice?
3. Measurement of Acetylcholine Levels by pH
Changes The concentration of acetylcholine (a neurotransmitter)
in a sample can be determined from the pH
changes that accompany its hydrolysis. When the sample is
incubated with the enzyme acetylcholinesterase, acetylcholine
is quantitatively converted into choline and acetic
acid, which dissociates to yield acetate and a hydrogen ion:
In a typical analysis, 15 mL of an aqueous solution containing
an unknown amount of acetylcholine had a pH of 7.65.
When incubated with acetylcholinesterase, the pH of the solution
decreased to 6.87. Assuming that there was no buffer
in the assay mixture, determine the number of moles of
acetylcholine in the 15 mL sample.
4. Osmotic Balance in a Marine Frog The crab-eating
frog of Southeast Asia, Rana cancrivora, develops and matures
in fresh water but searches for its food in coastal mangrove
swamps (composed of 80% to full-strength seawater).
When the frog moves from its freshwater home to seawater
it experiences a large change in the osmolarity of its environment
(from hypotonic to hypertonic).
(a) Eighty percent seawater contains 460 mM NaCl,
10 mM KCl, 10 mM CaCl2, and 50 mM MgCl2. What are the concentrations
of the various ionic species in this seawater? Assuming
that these salts account for nearly all the solutes in
seawater, calculate the osmolarity of the seawater.
(b) The chart below lists the cytoplasmic concentrations
of ions in R. cancrivora. Ignoring dissolved proteins, amino
acids, nucleic acids, and other small metabolites, calculate
the osmolarity of the frog’s cells based solely on the ionic concentrations
given below.
(c) Like all frogs, the crab-eating frog can exchange
gases through its permeable skin, allowing it to stay underwater
for long periods of time without breathing. How does
the high permeability of frog skin affect the frog’s cells when
it moves from fresh water to seawater?
Na K Cl Ca2 Mg2
(mM) (mM) (mM) (mM) (mM)
R. cancrivora 122 10 100 2 1
O
N
Acetylcholine
Choline Acetate
H2O
CH3 C O CH2
O
CH2 CH3
CH3
CH3
N C H
O
HO CH3
CH3
CH3
CH2 CH2 CH3
Problems
Chapter 2 Water 73
(d) The crab-eating frog uses two mechanisms to maintain
its cells in osmotic balance with its environment. First,
it allows the Na and Cl concentrations in its cells to increase
slowly as the ions diffuse down their concentration
gradients. Second, like many elasmobranchs (sharks), it retains
the waste product urea in its cells. The addition of both
NaCl and urea increases the osmolarity of the cytosol to a
level nearly equal to that of the surrounding environment.
Assuming the volume of water in a typical frog is 100 mL, calculate
how many grams of NaCl (formula weight (FW) 58.44)
the frog must take up to make its tissues isotonic with seawater.
(e) How many grams of urea (FW 60) must it retain to
accomplish the same thing?
5. Properties of a Buffer The amino acid glycine is often
used as the main ingredient of a buffer in biochemical experiments.
The amino group of glycine, which has a pKa of
9.6, can exist either in the protonated form (ONH3 ) or as
the free base (ONH2), because of the reversible equilibrium
(a) In what pH range can glycine be used as an effective
buffer due to its amino group?
(b) In a 0.1 M solution of glycine at pH 9.0, what fraction
of glycine has its amino group in the ONH3 form?
(c) How much 5 M KOH must be added to 1.0 L of 0.1 M
glycine at pH 9.0 to bring its pH to exactly 10.0?
(d) When 99% of the glycine is in its ONH3 form, what
is the numerical relation between the pH of the solution and
the pKa of the amino group?
6. The Effect of pH on Solubility The strongly polar,
hydrogen-bonding properties of water make it an excellent
solvent for ionic (charged) species. By contrast, nonionized,
nonpolar organic molecules, such as benzene, are relatively
insoluble in water. In principle, the aqueous solubility of any
organic acid or base can be increased by converting the molecules
to charged species. For example, the solubility of benzoic
acid in water is low. The addition of sodium bicarbonate
to a mixture of water and benzoic acid raises the pH and deprotonates
the benzoic acid to form benzoate ion, which is
quite soluble in water.
Are the following compounds more soluble in an aqueous
solution of 0.1 M NaOH or 0.1 M HCl? (The dissociable protons
are shown in red.)
7. Treatment of Poison Ivy Rash The components
of poison ivy and poison oak that produce the
characteristic itchy rash are catechols substituted with longchain
alkyl groups.
If you were exposed to poison ivy, which of the treatments
below would you apply to the affected area? Justify your
choice.
(a) Wash the area with cold water.
(b) Wash the area with dilute vinegar or lemon juice.
(c) Wash the area with soap and water.
(d) Wash the area with soap, water, and baking soda
(sodium bicarbonate).
8. pH and Drug Absorption Aspirin is a weak acid
with a pKa of 3.5.
It is absorbed into the blood through the cells lining the stomach
and the small intestine. Absorption requires passage
through the plasma membrane, the rate of which is determined
by the polarity of the molecule: charged and highly polar
molecules pass slowly, whereas neutral hydrophobic ones
pass rapidly. The pH of the stomach contents is about 1.5,
and the pH of the contents of the small intestine is about 6.
Is more aspirin absorbed into the bloodstream from the stomach
or from the small intestine? Clearly justify your choice.
C B O
G
O
C B O
G
OH
CH3
D
OH
(CH2)nOCH3
pKa ≈ 8
OH
NI
AH
Pyridine ion
pKa ≈ 5
(b)
(c)
(a)
-Naphthol
pKa ≈ 10
C B
H
G
N
D
H
OC A
H
AC
J
O
G
OOCH3
OCH2
N-Acetyltyrosine methyl ester
pKa ≈ 10
CH3
D
OH
O
O
C
B O
OOH COO
Benzoic acid Benzoate ion
pKa ≈ 5
B O
R H NH3 R NH2
Urea (CH4N2O)
H2N NH2
C
O
74 Part I Structure and Catalysis
9. Preparation of Standard Buffer for Calibration of
a pH Meter The glass electrode used in commercial pH
meters gives an electrical response proportional to the concentration
of hydrogen ion. To convert these responses into
pH, glass electrodes must be calibrated against standard solutions
of known H concentration. Determine the weight in
grams of sodium dihydrogen phosphate (NaH2PO4 H2O; FW
138.01) and disodium hydrogen phosphate (Na2HPO4; FW
141.98) needed to prepare 1 L of a standard buffer at pH 7.00
with a total phosphate concentration of 0.100 M (see
Fig. 2–16).
10. Calculating pH from Hydrogen Ion Concentration
What is the pH of a solution that has an H concentration of
(a) 1.75 10 5 mol/L; (b) 6.50 10 10 mol/L; (c) 1.0 10 4
mol/L; (d) 1.50 10 5 mol/L?
11. Calculating Hydrogen Ion Concentration from pH
What is the H concentration of a solution with pH of (a) 3.82;
(b) 6.52; (c) 11.11?
12. Calculating pH from Molar Ratios Calculate the pH
of a dilute solution that contains a molar ratio of potassium
acetate to acetic acid (pKa 4.76) of (a) 2:1; (b) 1:3; (c) 5:1;
(d) 1:1; (e) 1:10.
13. Working with Buffers A buffer contains 0.010 mol of
lactic acid (pKa 3.86) and 0.050 mol of sodium lactate per
liter. (a) Calculate the pH of the buffer. (b) Calculate the
change in pH when 5 mL of 0.5 M HCl is added to 1 L of the
buffer. (c) What pH change would you expect if you added
the same quantity of HCl to 1 L of pure water?
14. Calculating pH from Concentrations What is the
pH of a solution containing 0.12 mol/L of NH4Cl and 0.03 mol/L
of NaOH (pKa of NH4 /NH3 is 9.25)?
15. Calculating pKa An unknown compound, X, is thought
to have a carboxyl group with a pKa of 2.0 and another
ionizable group with a pKa between 5 and 8. When 75 mL of
0.1 M NaOH was added to 100 mL of a 0.1 M solution of X at
pH 2.0, the pH increased to 6.72. Calculate the pKa of the
second ionizable group of X.
16. Control of Blood pH by Respiration Rate
(a) The partial pressure of CO2 in the lungs can be varied
rapidly by the rate and depth of breathing. For example,
a common remedy to alleviate hiccups is to increase the concentration
of CO2 in the lungs. This can be achieved by holding
one’s breath, by very slow and shallow breathing (hypoventilation),
or by breathing in and out of a paper bag.
Under such conditions, the partial pressure of CO2 in the air
space of the lungs rises above normal. Qualitatively explain
the effect of these procedures on the blood pH.
(b) A common practice of competitive short-distance
runners is to breathe rapidly and deeply (hyperventilate) for
about half a minute to remove CO2 from their lungs just before
running in, say, a 100 m dash. Blood pH may rise to 7.60.
Explain why the blood pH increases.
(c) During a short-distance run the muscles produce a
large amount of lactic acid (CH3CH(OH)COOH, Ka 1.38
10 4) from their glucose stores. In view of this fact, why might
hyperventilation before a dash be useful?