   Chapter 14, Problem 124E

Chapter
Section
Textbook Problem

# Consider a solution of an unknown salt having the general formula BHCl, where B is one of the weak bases in Table 13-3. A 0.10-M solution of the unknown salt has a pH of 5.82. What is the actual formula of the salt?

Interpretation Introduction

Interpretation: The general formula of an unknown salt is given to be BHCl where B a weak base is. The pH value of a 0.10M solution of the unknown salt is 5.82 . The actual formula of the salt is to be stated.

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 actual formula of the given unknown salt.

The [H+] is 1.51×10-6M_ .

Given

pH=5.82

The pH of a solution is calculated by the formula,

pH=log[H+]

Rearrange the above expression to calculate the value of [H+] .

[H+]=10pH

Substitute the given value of pH in the above expression.

[H+]=105.82=1.51×10-6M_

The equilibrium constant expression for the given reaction is, Ka=[B][H+][BH+]

The dominant equilibrium reaction is,

BH+(aq)B(aq)+H+(aq)

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

Ka=ConcentrationofproductsConcentrationofreactants

Where,

• Ka is the acid dissociation constant.

The equilibrium constant expression for the given reaction is,

Ka=[B][H+][BH+] (1)

The Ka is 2.28×10-11_ .

The change in concentration of BH+ 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,

BH+(aq)B(aq)+H+(aq)Inititialconcentration0.1000Changex+x+xEquilibriumconcentration0

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