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798 | Thermodynamics

EXAMPLE 16–1 Equilibrium Constant of a Dissociation Process

Using Eq. 16–14 and the Gibbs function data, determine the equilibrium

constant KPfor the dissociation process N 2 →2N at 25°C. Compare your

result to the KPvalue listed in Table A–28.

Solution The equilibrium constant of the reaction N 2 →2N is listed in

Table A–28 at different temperatures. It is to be verified using Gibbs func-

tion data.

Assumptions 1 The constituents of the mixture are ideal gases. 2 The equi-

librium mixture consists of N 2 and N only.

Properties The equilibrium constant of this reaction at 298 K is ln KP

367.5 (Table A–28). The Gibbs function of formation at 25°C and 1 atm is

O for N 2 and 455,510 kJ/kmol for N (Table A–26).

Analysis In the absence of KPtables, KPcan be determined from the Gibbs

function data and Eq. 16–14,

where, from Eq. 16–11,

Substituting, we find

or

The calculated KPvalue is in agreement with the value listed in Table A–28.

The KPvalue for this reaction is practically zero, indicating that this reaction

will not occur at this temperature.

Discussion Note that this reaction involves one product (N) and one reactant

(N 2 ), and the stoichiometric coefficients for this reaction are nN 2 and

nN 2 1. Also note that the Gibbs function of all stable elements (such as N 2 )

is assigned a value of zero at the standard reference state of 25°C and 1 atm.

The Gibbs function values at other temperatures can be calculated from the

enthalpy and absolute entropy data by using the definition of the Gibbs func-

tion, , where .g* 1 T 2 h 1 T 2 Ts* 1 T 2 h 1 T 2 h*fhTh298 K

KP
 2 
 10 ^160

367.5

ln KP

911,020 kJ>kmol

1 8.314 kJ>kmol # K 21 298.15 K 2

911,020 kJ>kmol

 1221 455,510 kJ>kmol 2  0

¢G* 1 T 2 nNgN* 1 T 2 nN 2 gN* 21 T 2

KPe¢G*^1 T2>RuT

EXAMPLE 16–2 Dissociation Temperature of Hydrogen

Determine the temperature at which 10 percent of diatomic hydrogen (H 2 )

dissociates into monatomic hydrogen (H) at a pressure of 10 atm.

Solution The temperature at which 10 percent of H 2 dissociates into 2H is

to be determined.

Assumptions 1 The constituents of the mixture are ideal gases. 2 The equi-

librium mixture consists of H 2 and H only.

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