Page 191 - Physical chemistry understanding our chemical world

158 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

The amount of energy liberated per incremental increase in reaction is quite large
at the start of reaction, but decreases until, at equilibrium, a tiny increase in the extent
of reaction would not change G (total) . The graph has reached a minimum, so the
gradient at the bottom of the trough is zero.
The minimum in the graph of G against ξ is the reaction’s position of equilib-
rium – we call it ξ (eq) . The maximum amount of energy has already been expended
at equilibrium, so G is zero.
Any further reaction beyond ξ (eq) would not only fail to liberate any further energy,
but also would in fact consume energy (we would start to go ‘uphill’ on the right-
hand side of the figure). Any further increment of reaction would be character-
ized by G > 0, implying a non-spontaneous process, which is why the reaction
stops at ξ (eq) .

Why does the pH of the weak acid remain constant?

The law of mass action and equilibrium constants

The amount of ethanoic acid existing as ionized ethanoate anion and solvated proton
is always small (see p. 253). For that reason, the pH of a solution of weak acid is
always higher than a solution of the same concentration of a strong acid. A na¨ ıve
view suggests that, given time, all the undissociated acid will manage to dissociate,
with the dual effect of making the acid strong, and hence lowering the pH.
We return to the graph in Figure 4.6 of Gibbs function (as y) against extent of
reaction ξ (as x). At the position of the minimum, the amounts of free acid and
ionized products remain constant because there is no longer any energy available for
reaction, as explained in the example above.
The fundamental law of chemical equilibrium is the law of mass action, formulated in
1864 by Cato Maximilian Guldberg and Peter Waage. It has since been redefined several
times. Consider the equilibrium between the four chemical species A, B, C and D:

aA + bB = cC + dD (4.46)

where the respective stoichiometric numbers are −a, −b, c and d. The law of mass
action states that, at equilibrium, the mathematical ratio of the concentrations of
b
a
the two reactants [A] × [B] and the product of the two product concentrations
d
c
[C] × [D] , is equal. We could, therefore, define one of two possible fractions:
c
a
[A] [B] b [C] [D] d
or (4.47)
a
c
[C] [D] d [A] [B] b
This ratio of concentrations is called an equilibrium constant, and is symbolized as K.
The two ratios above are clearly related, with one being the reciprocal of the other.
Ultimately, the choice of which of these two we prefer is arbitrary, and usually relates
to the way we write Equation (4.46). In consequence, the way we write this ratio is
dictated by the sub-discipline of chemistry we practice. For example, in acid–base