Physical Chemistry Third Edition

7.2 Reactions Involving Gases and Pure Solids or Liquids 313

Kexp

⎡

⎣− 130900 J mol

− 1

(

8 .3145 J K−^1 mol−^1

)

(298.15 K)

⎤

⎦

 1. 17 × 10 −^23

Peq(CO 2 )

(

P◦

)(

1. 17 × 10 −^23

)

 1. 17 × 10 −^23 bar 1. 15 × 10 −^23 atm

This equilibrium constant is strongly temperature-dependent and becomes much larger

at higher temperatures. At high temperatures this reaction is used to make CaO(s)

(“quicklime”) commercially from limestone.

Reactions that appear to proceed to completion are not fundamentally different from

other reactions. They just have very large equilibrium constants.

EXAMPLE 7.5

a.Write the activity quotient for the combustion of propane at 298.15 K.

b.Find the value of the equilibrium constant for this reaction.

Solution

a.The reaction equation is

0 3CO 2 (g)+4H 2 O(l)−C 3 H 8 (g)−5O 2 (g)

Q

(P(CO 2 ))/P◦)^3 ( 1 )^4

(P(C 3 H 8 )/P◦)(P(O 2 ))/P◦)^5

b.

∆G◦ 3 ∆fG◦(CO 2 )+ 4 ∆fG◦(H 2 O)− 1 ∆fG◦(C 3 H 8 )

+(−5)∆fG◦(O 2 )

(3)(− 394 .389 kJ mol−^1 )+(4)(− 237 .141 kJ mol−^1 )

+(−1)(− 23 .27 kJ mol−^1 )−5(0)

− 2108 .46 kJ mol−^1

Kexp

⎡

⎣ 2108460 J mol

− 1

(

8 .3145 J K−^1 mol−^1

)

( 298 .15 K)

⎤

⎦

e^850.^5  2 × 10369

Exercise 7.4

a.Find the final partial pressure of propane and oxygen if a stoichiometric mixture of propane

and oxygen comes to equilibrium at 298.15 K and a total pressure of 760.0 torr.

b.Find the volume containing one molecule of propane at the equilibrium of part a. Comment

on the magnitude of your result.