Molecular Biology of the Cell by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter by by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morg

62 Chapter 2: Cell Chemistry and Bioenergetics
FOR THE ENERGETICALLY FAVORABLE REACTION Y → X,
Figure 2–30 Chemical equilibrium. When
a reaction reaches equilibrium, the forward
and backward fluxes of reacting molecules
are equal and opposite.
Y
when X and Y are at equal concentrations, [Y] = [X], the formation of X
is energetically favored. In other words, the ΔG of Y → X is negative and
the ΔG of X → Y is positive. But because of thermal bombardments,
there will always be some X converting to Y.
THUS, FOR EACH INDIVIDUAL MOLECULE,
X
Y
X
Therefore the ratio of X to Y
molecules will increase with time
X
Y
conversion of
Y to X will
occur often.
Conversion of X to Y
will occur less often
than the transition
Y → X, because it
requires a more
energetic collision.
EVENTUALLY, there will be a large enough excess of X over Y to just
compensate for the slow rate of X → Y, such that the number of Y molecules
being converted to X molecules each second is exactly equal to the number
of X molecules being converted to Y molecules each second. At this point,
the reaction will be at equilibrium.
Y
X
AT EQUILIBRIUM, there is no net change in the ratio of Y to X, and the
ΔG for both forward and backward reactions is zero.
The Equilibrium Constant and ∆G° Are Readily Derived from
Each Other
Inspection of the above equation reveals that the ∆G equals the value of ∆G°
when the concentrations of Y and X are equal. But as any favorable reaction proceeds,
the concentrations of the products will increase as the concentration of the
substrates decreases. This change in relative concentrations will cause [X]/[Y] to
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become increasingly large, making the initially favorable ∆G less and less negative
(the logarithm of a number x is positive for x > 1, negative for x < 1, and zero for x
=1). Eventually, when ∆G = 0, a chemical equilibrium will be attained; here there
is no net change in free energy to drive the reaction in either direction, inasmuch
as the concentration effect just balances the push given to the reaction by ∆G°.
As a result, the ratio of product to substrate reaches a constant value at chemical
equilibrium (Figure 2–30).
We can define the equilibrium constant, K, for the reaction Y → X as
K = [X]
[Y]
where [X] is the concentration of the product and [Y] is the concentration of the
reactant at equilibrium. Remembering that ∆G = ∆G° + RT ln [X]/[Y], and that
∆G = 0 at equilibrium, we see that
∆G° = –RT ln [X] = –RT ln K
[Y]
At 37°C, where RT = 2.58, the equilibrium equation is therefore:
∆G° = –2.58 ln K