Physical Chemistry Third Edition

7.1 Gibbs Energy Changes and the Equilibrium Constant 309

Exercise 7.2

Carry out the steps to obtain Eqs. (7.1-16) and (7.1-17).

If it is possible to keep the activity of every substance fixed during a chemical

reaction, the value ofQis fixed and the change in Gibbs energy for 1 mol of reaction

can be written

∆G(fixed composition)

(

∂G

∂ξ

)

T,P

∣

∣

∣

∣

∣

f ixed comp



∫ 1

0

∆G◦+RTln(Q)dξ

∆G◦+RTln(Q)

∫ 1

0

dξ

∆G(fixed composition)∆G◦+RTln(Q) (7.1-18)

EXAMPLE 7.2

Calculate the value of∆G(fixed composition) at 298.15 K for the reaction of Exercise 7.1 if

the partial pressure of PCl 5 is maintained equal to 0.0100 bar, the partial pressure of PCl 3

is maintained equal to 0.00600 bar, and the partial pressure of Cl 2 is maintained equal to

0.00300 bar. Assume that the gases are ideal.

Solution

Q

a(PCl 3 )a(Cl 2 )

a(PCl 5 )



(0.00600)(0.00300)

(0.0100)

 0. 00180

(

∂G

∂ξ

)

T,P

 20 .661 kJ mol−^1 +(8.3145 J K−^1 mol−^1 )(298.15 K) ln(0.00180)

 20 .661 kJ mol−^1 +(−15667 J mol−^1 )

4994 J mol−^1  4 .994 kJ mol−^1

Exercise 7.3

Repeat the calculation of the previous example if the partial pressure of PCl 5 is maintained equal

to 0.00600 bar, the partial pressure of PCl 3 is maintained equal to 0.0100 bar, and the partial

pressure of Cl 2 is maintained equal to 0.00300 bar.

At equilibrium, (∂G/∂ξ)T,P0, and Eq. (7.1-16) becomes

0 ∆G◦+RTln(Qeq) (7.1-19)