Page 364 - Physical Chemistry

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n
n
Using G° n m° [Eq. (11.5)] and n ln a (ln a ) i ln ß (a ) i [Eqs. (1.70) Section 11.10
i
i
i
i
i
i
i
i
i
i
and (1.69)], we get Coupled Reactions
0G
a b ¢G° RT ln Q, Q q 1a 2 n i (11.35)
i
0j T,P i
where Q is the reaction quotient (first used in Sec. 6.4). Since G° RT ln K°
[Eq. (11.4)], Eq. (11.35) can be written as
10G>0j2 RT ln 1Q>K°2 (11.36)
T,P
The activities of the products appear in the numerator of Q. At the start of the reaction
when no products are present, Q 0 and (11.36) gives ( G/ j) T,P q. (Note the
negatively infinite slope of the G-versus-j curve in Fig. 4.7 at j 0.) Before equilib-
rium is reached, we have Q K° and ( G/ j) T,P 0. At equilibrium, Q K° and
( G/ j) T,P 0. For a system with Q K°, (11.36) gives ( G/ j) T,P 0 and the re-
action proceeds in reverse; Q decreases until at equilibrium Q K°, ( G/ j) T,P 0,
and G is minimized. The direction of spontaneous reaction at constant T and P is de-
termined by the sign of ( G/ j) .
T,P
A given reaction at fixed T and P has a single value of G°, but ( G/ j) T,P in the
system can have any value from q to q.
Instead of G°, biochemists often use the quantity G°
, defined as
¢G°¿ a n m° n1H 2m°¿1H 2 (11.37)

i
i
i H

7

where m°
(H ) is the chemical potential of H at an H activity of 10 . Because

biological fluids have H molalities close to 10 7 mol/kg, G°
values are more
relevant to reactions in living organisms than are G°values, which have a 1-mol/kg
standard-state molality.
11.10 COUPLED REACTIONS
Suppose two chemical reactions are occurring in a system, and there is a chemical
species that takes part in both reactions. The reactions are then coupled, since one
reaction will influence the equilibrium position of the second reaction. Thus, suppose
species M is a product of reaction 1 and is a reactant in reaction 2:
Reaction 1: A B ∆ M D
Reaction 2: M R ∆ S T
If reaction 1 has G° W 0 and equilibrium constant K V 1, then at ordinary concen-
trations very little A and B will react to produce M and D in the absence of reaction
2. If reaction 2 has G° V 0 and K W 1, then if both reactions occur, reaction 2 will
use up large amounts of M, thereby allowing reaction 1 to proceed to a substantial
degree.
An example of coupled reactions is the observation that most phosphate salts are
virtually insoluble in water but quite soluble in aqueous solutions of strong acids. In
acidic solutions, the rather strong Brønsted base PO 4 3 reacts to a very great extent

with H O to yield the extremely weak acid HPO 4 2 (which reacts further with H O
3
3

to yield H PO ), thereby greatly reducing the PO 3 concentration in solution and
4
2
4
shifting the solubility-product equilibrium (11.26) of the phosphate salt to the right.
A different kind of reaction coupling is important in biology. The hydrolysis of
adenosine triphosphate (ATP) to adenosine diphosphate (ADP) plus inorganic phos-
phate (P ) has G° 0 and is thermodynamically favored. In living organisms, this
i
hydrolysis is coupled to such thermodynamically unfavored processes as the synthesis