7.7 Chemical Equilibrium and Biological Systems 345
inquire about the mechanism of the coupling of such reactions. According to the
principle of Le Châtelier the phosphoric acid produced in the reaction of Eq. (7.7-4a)
would shift the equilibrium of the regeneration reaction in Eq. (7.7-4b), producing more
ATP. In the next example we show that the effect of this shift is insignificant. Another
mechanism must exist for the coupling to be effective.EXAMPLE7.23
Calculate the concentration of ATP produced at 298.15 K by the equilibrium shift because
of the principle of Le Châtelier if the initial concentrations of PEP and ADP are equal to
0.0100 mol L−^1.
Solution
The equilibrium constant for reaction A is equal toKAexp⎡
⎣^5.^36 ×^10(^4) J mol− 1
(
8 .3145 J K−^1 mol−^1
)
( 298 .15 K)
⎤
⎦
2. 46 × 109
Since its equilibrium constant is much larger than unity, this reaction proceeds essentially
to completion, giving an equilibrium concentration of phosphate that is nearly equal to
0.0100 mol L−^1.
The equilibrium constant for reaction B is the reciprocal of that for the reaction of
Eq. (7.7-1), or 7. 35 × 10 −^6. We letxceq(ATP)/c◦. The equilibrium expression gives
x(8. 35 × 10 −^6 )(0. 0100 −x)^2 ≈(8. 35 × 10 −^6 )(0.0100)^2
7. 35 × 10 −^10
ceq(ATP)≈ 7. 35 × 10 −^10 mol L−^1
The principle of Le Châtelier is not sufficient to explain the coupling of reactions.
There must be a molecular mechanism that makes a single reaction out of two reactions.
A proposed mechanism for the coupling of these two reactions involves an enzyme,
pyruvate kinase, abbreviated by E.^6 The action of this enzyme is represented by a
two-step mechanism:
(1) E+PEPEP+Py (7.7-5a)
(2) EP+ADPE+AT P (7.7-5b)
ADP+PEPAT P+Py (7.7-5c)
An enzyme molecule generally possesses anactive siteinto which a reactant molecule
can fit. Once in the active site, the reactant molecule is rendered more reactive, possibly
(^6) K. J. Laidler,Physical Chemistry with Biological Applications, Benjamin/Cummings, Menlo Park, CA,
1978, p. 246ff.