   Chapter 15, Problem 20PS

Chapter
Section
Textbook Problem

Which of the following correctly relates the equilibrium constants for the two reactions shown? A + B ⇄ 2  C K 1 C ⇄ 1 2 A + 1 2 B K 2 (a) K2 = 1/(K1)1/2 (b) K2 = 1/K1 (c) K2 = K12 (d) K2 = −K11/2

Interpretation Introduction

Interpretation: The relation between the equilibrium constant for the given two reactions has to be determined from the given option.

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.

Explanation

Reason for correct option

The relation between the equilibrium constant for the given two reactions is found as K2=1(K1)1/2.

The balanced chemical equation for the first reaction is,

A+B2C

The equilibrium constant, K for the reaction is,

[C]2[A][B]=K1

The balanced chemical equation for the second reaction is,

C12A+12B

The equilibrium constant, K for the reaction is,

[A]1/2[B]1/2[C]=K2([A][B][C]2)1/2Ȁ

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