   Chapter 15, Problem 37GQ

Chapter
Section
Textbook Problem

The equilibrium constant for the butane ⇄ isobutane isomerization reaction is 2.5 at 25 °C. If 1.75 mol of butane and 1.25 mol of isobutane are mixed, is the system at equilibrium? If not, when it proceeds to equilibrium, which reagent increases in concentration? Calculate the concentrations of the two compounds when the system reaches equilibrium.

Interpretation Introduction

Interpretation: The equilibrium concentration of reactant and product has to be calculated and the given reaction is at equilibrium or not has to be checked.

Concept introduction:

• Equilibrium constant: At equilibrium the ratio of products to reactants has a constant value. And it is represented by the letter K.

For a general reaction, aA+bBcC+dD

The equilibrium constant Kc=[C]c[D]d[A]a[B]b, where a, b, c and d are the stoichiometric coefficients of reactant and product in the reaction. Concentration value for solid substance is 1.

If the value of Kc and the concentration of any of the reactant of a reaction is known then the concentration of product can be determined by multiplying Kc with the concentration of reactant.

• Reaction quotient Q expresses the relative ratio of product to reactants at a given instant. Using either the initial concentration of all components of the reaction, the progression of a reaction can easily be determined.

For a general reaction, aA+bBcC+dD

Reaction quotient Q = [C]c[D]d[A]a[B]b

When Q=K the system is at equilibrium and there is no shift to either the left or the right.

When Q<K, there are more reactants than products. Therefore some of the reactants will become products, causing the reaction to the right.

When Q>K, there are more products than reactants. To decrease the amount of products, the reaction will shift to the left and produce more reactant.

• ICE (reaction initial concentration equilibrium) table is mainly used to calculate the value of K for a reaction. This table contains the concentration of reactant and product in various stage of reaction.
Explanation

The balanced equation for the given reaction is,

ButaneIsobutane

The concentration of butane and isobutane are 1.75Mand1.25M respectively.

The reaction quotient Q for this reaction is,

Q=[Isobutane][Butane]=1.251.75 =0.714

The given value of equilibrium constant for this reaction is 2.5

When Q=K the system is at equilibrium and there is no shift to either the left or the right

But here QK

Therefore the system is not at equilibrium.

The balanced equation for the given reaction is,

ButaneIsobutane

The concentration of butane and isobutane are 1.75Mand1.25M respectively By using these concentration ICE table for this reaction can be constructed.

ButaneIsobutaneI(M)1

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