Physical Chemistry Third Edition

7.7 Chemical Equilibrium and Biological Systems 343

7.7 Chemical Equilibrium and Biological Systems

An important feature of biochemical reactions of metabolism and respiration is the

couplingof pairs of reactions, which can result in the driving of a nonspontaneous reac-

tion by the progress of a spontaneous reaction. The hydrolysis of adenosine triphosphate

(abbreviated by ATP) to form adenosine diphosphate (abbreviated by ADP) and phos-

phoric acid (abbreviated by P) is shown in Figure 7.3. This is a spontaneous reaction

that drives a number of useful reactions in various organisms.

The hydrolysis reaction equation is abbreviated:

AT P+H 2 O
ADP+Pi (7.7-1)

where Pistands for “inorganic phosphate,” collectively phosphoric acid and its various

anions. Since ATP, ADP, and phosphoric acid are all weak polyprotic acids, they exist

as various anions in aqueous solution as well as in the forms shown in Figure 7.3. The

abbreviations in Eq. (7.7-1) stand for whatever ionized and unionized forms of ATP,

ADP, and phosphoric acid occur.

The anions of ATP and ADP form complexes with positive ions such as Mg^2 +

or Ca^2 +. It is customary to define a modified standard-state reaction in which the

substances in the reaction equation are at unit activities but the hydrogen ions and any

complexing cations are at specified activities not necessarily equal to unity. The symbol

∆G◦′is used for the Gibbs energy change of such a modified standard-state reaction.

Using the concentration description∆G◦′for the reaction of Eq. (7.7-1) is equal

to− 29 .3kJmol−^1 at 298.15 K if pH 7 .00 and pMg 4 .00. The pMg is defined in

the concentration description by analogy with pH:

pMg−log 10 a(Mg^2 +)

−log 10 γ(Mg^2 +)c(Mg^2 +)/c◦ (7.7-2)

EXAMPLE7.22

a.Find the equilibrium constant for the reaction of Eq. (7.7-1).

b.Find the equilibrium concentrations of ADP and ATP at pH 7 .00 and pMg 4 .00 if

all of the phosphoric acid present comes from the hydrolysis of ATP and if the initial

concentration of ATP is 0.0100 mol L−^1. Approximate all activity coefficients by unity.

O

P~O

O^2

O

P~O

O^2

OCH 2

C

H C

C

H

H

H

O

P

O^2

O

O

P

O^2

(^2) O
O
P~O
O^2

• O

O

P OH

O^2

(^2) O
NH 2
C
C
C C C H
N
N
o
OH
C
H
OH
N
N
ATP ADP Pi
1 H 2 O CH 2
C
H C
C
H
H
H
NH 2
C
C
C C C H
N
N
o
OH
C
H
OH
N
N
11 H^1
Figure 7.3 The Hydrolysis of Adenosine Triphosphate.