Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

GENERAL FORMULATION 95

wherea, b,...c, d,...are the stoichiometric coefficients of the reaction. It is still

true that

rG=

∑

G(prod)−

∑

G(react)

When equilibrium has been reached, we have

G◦=−RTlnKeq

Now the concentration quotientQtakes the form

Q=

[C]c[D]d...

[A]a[B]b...

leading to the familiar expression of the equilibrium constant as

Keq=

[C]c[D]d...

[A]a[B]b...

which is true only after the Gibbs free energy has come to a minimum and
rG=0.

The stoichiometric coefficients become exponents, and the square brackets [ ] indicate

some kind of unitless concentration variable relative to a standard state. This notation

is often used in solution chemistry to denote a concentration in moles/liter, where the

standard state of the solute in the solvent is taken for granted.

As an example of a reaction in the gas phase, the expression

G◦=−RTln

pNO^22

pN 2 O 4

can be used to find the equilibrium constant for the reaction

N 2 O 4 (g) →← 2NO 2 (g)

The standard state Gibbs chemical potential difference for this reaction is

rG◦=
G◦2(NO 2 )−
G◦N 2 O 4 =2(51.31)− 97. 89 = 4 .73 kJ mol−^1

The equilibrium constant is

Keq=e−
G

◦/RT

=e−^4730 /^8.^314 ×^298.^15 = 0. 148

which is in good agreement with the experimental value of 0.13.

It is difficult to obtain accurateKeqvalues from calorimetric determination

of
rG◦(from
rH◦and
rS◦) because of the exponential relationshipKeq=

e−
G

◦/RT

. This mathematical form brings about a large error inKeqwhen
rG◦is
in error by a small amount. To a certain degree, a “small” error or a “large” error is
in the eye of the beholder; the terms are used in the literature as influenced by the