   Chapter 14, Problem 126E

Chapter
Section
Textbook Problem

# A 0.20-M sodium chlorobenzoate (NaC7H4ClO2) solution has a pH of 8.65. Calculate the pH of a 0.20-M chlorobenzoic acid (HC7H4ClO2) solution.

Interpretation Introduction

Interpretation: A 0.20M solution of the salt NaC7H4ClO2 is given to have a pH value of 8.65 . The pH of a 0.20M solution of HC7H4ClO2 is to be calculated.

Concept introduction: The pH of a solution is define as a figure that expresses the acidity of the alkalinity of a given solution.

The pH of a solution is calculated by the formula, pH=log[H+]

The sum, pH+pOH=14

The equilibrium constant for water is denoted by Kw and is expressed as,

Kw=[H+][OH]

The value of Kw is calculated by the formula,

Kw=KaKb

Explanation

Explanation

To determine: The pH of a 0.20M solution of HC7H4ClO2 .

The pOH of the given NaC7H4ClO2 salt is 5.35_ .

The given value of pH is 8.65 .

The sum, pH+pOH=14

The value of pOH is calculated by the formula,

pOH=14pH

Substitute the value of pH in the above expression.

pOH=148.65=5.35_

The [OH] is 4.467×10-6M_ .

The pOH of a solution is calculated by the formula,

pOH=log[OH]

Rearrange the above expression to calculate the value of [OH] .

[OH]=10pOH

Substitute the value of pOH in the above expression.

[OH]=105.35=4.467×10-6M_

The equilibrium constant expression for the given reaction is, Kb=[HC7H4ClO2][OH][C7H4ClO2]

The dominant equilibrium reaction is,

NaC7H4ClO2(aq)HC7H4ClO2(aq)+OH(aq)

At equilibrium, the equilibrium constant expression is expressed by the formula,

Kb=ConcentrationofproductsConcentrationofreactants

Where,

• Kb is the base ionization constant.

The equilibrium constant expression for the given reaction is,

Kb=[HC7H4ClO2][OH][C7H4ClO2] (1)

The Kb value is 3.99×10-10_ .

The change in concentration of C7H4ClO2 is assumed to be x .

The liquid components do not affect the value of the rate constant.

The ICE table for the stated reaction is,

C7H4ClO2(aq)HC7H4ClO2(aq)+OH(aq)Inititialconcentration0.2000Changex+x+xEquilibriumconcentration0.20xxx

The equilibrium concentration of [C7H4ClO2] is (0.20x)M .

The equilibrium concentration of [HC7H4ClO2] is xM .

The equilibrium concentration of [OH] is xM .

Substitute the value of [C7H4ClO2] , [HC7H4ClO2] and [OH] in equation (1).

Kb=[x][x][0.20x]Kb=[x]2[0.20x]

The value of [OH] that is equal to the value of x is 4.467×106M .

Substitute the value of x in the above expression.

Kb=[4.467×106]2[0.050(4.467×106)]Kb=3.99×10-10_

The Ka value is 2

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