Physical Chemistry Third Edition

310 7 Chemical Equilibrium

The standard-state Gibbs energy change∆G◦depends only on temperature since the

standard-state chemical potentials depend only on temperature. The value ofQeqis

therefore equal to a constant at constant temperature. It is theequilibrium constant,

denoted byKand given by the relation

KQeq

∏c

i 1

avi,eqi e−∆G

◦/RT

(7.1-20)

whereai,eqdenotes the equilibrium value ofai. Since we have derived expressions

for the activity of any kind of a substance in Chapter 6, Eq. (7.1-20) is valid for any

kind of a reacting system. If activity coefficients are assumed equal to unity and if

concentrations or partial pressures are used for activities, Eq. (7.1-20) becomes the

familiar equilibrium constant expression of a general chemistry course.

PROBLEMS

Section 7.1: Gibbs Energy Changes and the Equilibrium
Constant

7.1A hypothetical gaseous isomerization reaction

A
B

has∆G◦− 5 .000 kJ mol−^1 at 298.15 K. Construct an

accurate graph ofG−μ∗Aas a function of the extent of

reactionξfor the case that the initial amount of A is

1.000 mol and that of B is 0. Assume that the gases are ideal.

The total pressure is kept fixed at 1.000 bar and the

temperature is kept fixed at 298.15 K. Locate the minimum

inGon the graph and calculate the equilibrium constant

from the value ofξat the minimum.

7.2Consider a hypothetical gas-phase reaction

A+B
C

for which∆G◦− 10 .00 kJ mol at 298.15 K. Assume that

the gases are ideal.

a.Find the value of

(

∂G

∂ξ

)

T,P

ifPA 1 .00 bar,

PB 0 .500 bar, andPC 0 .250 bar.

b.Find the value of the equilibrium constant.

c.If the initial partial pressures are those in part a, find the

equilibrium values of the partial pressures.

7.3A hypothetical gaseous isomerization reaction A
B has

∆G◦− 5 .000 kJ mol−^1 at 298.15 K. Consider the case

that the initial amount of A is 1.000 mol and that of B is 0.

Evaluate for

(

∂G

∂ξ

)

T,P

 0 .10 mol, 0.20 mol, 0.40 mol,

0.60 mol, 0.80 mol, and 0.90 mol. Construct an accurate

graph of this quantity. Assume that the gases are ideal.

7.2 Reactions Involving Gases and Pure Solids or Liquids

For this class of chemical reactions we will assume that all gases are ideal and that all

liquids and solids have constant volumes. We first consider reactions involving only

gases. For an ideal gas,

aiPi/P◦(ideal gas) (7.2-1)