Essential Cell Biology 5th edition

Free Energy and Catalysis
93
FOR THE ENERGETICALLY FAVORABLE REACTION Y → X,
Figure 3–18 Reactions will eventually
reach a chemical equilibrium. At that
point, the forward and the backward
fluxes of reacting molecules are equal and
opposite. The widths of the arrows indicate
the relative rates at which an individual
molecule converts.
Y
X
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. Nevertheless because of thermal bombardments,
there will always be some X converting to Y.
THUS, FOR EACH INDIVIDUAL MOLECULE,
Y
X
Therefore, if one starts with an
equal mixture, the ratio of X to Y
molecules will increase
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 X molecules
being converted to Y molecules each second is exactly equal to the number
of Y molecules being converted to X 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.
on their behavior under ideal conditions where the concentrations of all
the reactants are set to the same fixed value of 1 mole/liter in aqueous
solution.
A large body of thermodynamic data has been collected from which ΔG°
can be calculated for most ECB5 metabolic e3.18/3.18 reactions. Some common reactions
are compared in terms of their ΔG° in Panel 3–1 (pp. 94–95).
The ΔG of a reaction can be calculated from ΔG° if the concentrations of
the reactants and products are known. For the simple reaction Y → X,
their relationship follows this equation:
[X]
ΔG = ΔG° + RT ln
[Y]
where ΔG° is in kilojoules per mole, [Y] and [X] denote the concentrations
of Y and X in moles/liter (a mole is 6 × 10 23 molecules of a substance), ln
is the natural logarithm, and RT is the product of the gas constant, R, and
the absolute temperature, T. At 37°C, RT = 2.58.
From this equation, we can see that when the concentrations of reactants
and products are equal—in other words, [X]/[Y] = 1—the value of ΔG
equals the value of ΔG° (because ln 1 = 0). Thus when the reactants and
products are present in equal concentrations, the direction of the reaction
depends entirely on the intrinsic properties of the molecules.
QUESTION 3–3
Consider the analogy of the jiggling
box containing coins that was
described on page 83. The reaction,
the flipping of coins that either
face heads up (H) or tails up (T), is
described by the equation
H ↔ T, where the rate of the
forward reaction equals the rate of
the reverse reaction.
A. What are ΔG and ΔG° in this
analogy?
B. What corresponds to the
temperature at which the reaction
proceeds? What corresponds to the
activation energy of the reaction?
Assume you have an “enzyme,”
called jigglase, which catalyzes this
reaction. What would the effect of
jigglase be and what, mechanically,
might jigglase do in this analogy?