   Chapter 15, Problem 26PS

Chapter
Section
Textbook Problem

Relationship of Kc and Kp: (a) The equilibrium constant, Kc, for the following reaction at 25 °C is 170. What is the value of Kp? N2O4(g) ⇄ 2 NO2(g) (b) Kc for the decomposition of ammonium hydrogen sulfide is 1.8 × 10−4 at 25 °C. What is the value of Kp? NH4HS(s) ⇄ NH3(g) + H2S(g)

(a)

Interpretation Introduction

Interpretation: The value of Kp for the given reaction has to be calculated using the relationship between Kc and Kp.

Concept introduction:

• Equilibrium constant: It is the ratio of products to reactants has a constant value when the reaction is in equilibrium at a certain temperature. And it is represented by the letter K.

For a reaction,

aA+bBcC+dD

The equilibrium constant is,K=[C]c[D]d[A]a[B]b,where, a, b, c and d are the stoichiometric coefficients of reactant and product in the reactions.

• Kc is the equilibrium constant of a reaction at equilibrium which is expressed in terms of concentration of gaseous reactants and products. Whereas Kp is the equilibrium constant of a reaction at equilibrium which is expressed in terms of partial pressure of gaseous reactants and products in a closed system.

Kp=Kc(RT)Δn where,Δn is difference between the sum of stoichiometric coefficients of products and reactants.

Explanation

Kc for the given equation is calculated as,

Given,

R=0.08206L.atm K1mol1T=250C=(25+273)K=298KKp=170

The balanced chemical equation for the reaction is,

N2O4(g)2NO

(b)

Interpretation Introduction

Interpretation: The value of Kc for the given reaction has to be calculated using the relationship between Kc and Kp.

Concept introduction:

• Equilibrium constant: It is the ratio of products to reactants has a constant value when the reaction is in equilibrium at a certain temperature. And it is represented by the letter K.

For a reaction,

aA+bBcC+dD

The equilibrium constant is,K=[C]c[D]d[A]a[B]b,where, a, b, c and d are the stoichiometric coefficients of reactant and product in the reactions.

• Kc is the equilibrium constant of a reaction at equilibrium which is expressed in terms of concentration of gaseous reactants and products. Whereas Kp is the equilibrium constant of a reaction at equilibrium which is expressed in terms of partial pressure of gaseous reactants and products in a closed system.

Kp=Kc(RT)Δn where,Δn is difference between the sum of stoichiometric coefficients of products and reactants.

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