Page 195 - Physical chemistry understanding our chemical world

162 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Aside

A further complication arises from the G term in Equation (4.49). The diagram above
is clearer than the derivation: in reality, the differential quantity ∂G/∂ξ only corresponds
to the change in Gibbs function G under certain, well defined, and precisely controlled
experimental conditions.
This partial differential is called the reaction affinity in older texts and in newer texts
is called the reaction free energy.

Why does the concentration of product stop
changing?

The van’t Hoff isotherm

It would be beneficial if we could increase the yield of a chem-
Becauseweonlyever ical reaction by just leaving it to react longer. Unfortunately, the
write K (rather than concentrations of reactant and product remain constant at the end
Q) at equilibrium, it is
tautologous but very of a reaction. In other words, the reaction quotient has reached a
constant value.
common to see K writ-
ten as K (eq) or K e . At equilibrium, when the reaction stops, we give the reaction
quotient the special name of equilibrium constant, and re-symbolize
it with the letter K. The values of K and Q are exactly the
The descriptor ‘iso- same at equilibrium when the reaction stops. The value of Q is
therm’ derives from always smaller than K before equilibrium is reached, because some
the Greek iso meaning product has yet to form. In other words, before equilibrium, the
‘same’ and thermos top line of Equation (4.48) is artificially small and the bottom is
meaning ‘temperature’.
artificially big.
Q and K only have the same value when the reaction has reached
equilibrium, i.e. when G r = 0. At this extent of reaction, the rela-
Jacobus van’t Hoff tionship between ξ and G is given by the van’t Hoff isotherm:
O
was a Dutch scientist
(1852–1911). Notice G =−RT ln K (4.55)
O
the peculiar arrange-
ment of the apostro-
where R and T have their usual thermodynamics meanings. The
phe, and small and O
capital letters in his equation shows the relationship between G and K, indicat-
surname. ing that these two parameters are interconvertible when the tem-
perature is held constant.

SAQ 4.8 Show that the van’t Hoff isotherm is dimensionally self-
consistent.

Worked Example 4.10 Consider the dissociation of ethanoic (acetic) acid in water to
form a solvated proton and a solvated ethanoate anion, CH 3 COOH + H 2 O → CH 3 COO −