   Chapter 16, Problem 120IP Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
ISBN: 9781305079243

Solutions

Chapter
Section Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
ISBN: 9781305079243
Textbook Problem

What is the pH of a 0. 125-M solution of the weak base B if ∆H°= −28.0 kJ and ∆S°= −175 J/K for the following equilibrium reaction at 25°C? B ( a q ) + H 2 O ( l ) ⇌ BH + ( a q ) + OH - ( a q )

Interpretation Introduction

Interpretation: The reaction between B and H2O , the value of ΔH°,ΔS° and volume of the weak base B is given. The pH value of this weak base is to be calculated at a given temperature.

Concept introduction: The expression for free energy change is,

ΔG°=ΔH°TΔS°=RTln(Kb)

The relation between pH and pOH is,

pH+pOH=14

Explanation

Given

The value of ΔH° is 28.0kJ .

The value of ΔS° is 175J/K .

Temperature is 25°C .

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence,

The conversion of 25°C into Kelvin is,

T(K)=T(°C)+273T(K)=(25+273)K=298K

The conversion of kilo-joule (kJ) into joule (J) is done as,

1kJ=103J

Hence,

The conversion of 28.0kJ into joule is,

28.0kJ=(28.0×103)J=28.0×103J

Formula

The formula of ΔG° is,

ΔG°=ΔH°TΔS°

Where,

• ΔH° is the standard enthalpy of reaction.
• ΔG° is the free energy change.
• T is the given temperature.
• ΔS° is the standard entropy of reaction.

Substitute the values of T,ΔH° and ΔS° in the above equation.

ΔG°=ΔH°TΔS°=28.0×103J[(298K)(175J/K)]=24150J_

The value of ΔG° is 24150J .

Temperature is 298K .

Formula

The expression for free energy change is,

ΔG°=RTln(Kb)

Where,

• ΔG° is the standard free energy change.
• R is the gas law constant (8.3145J/Kmol) .
• T is the absolute temperature.
• Kb is the base dissociation constant.

Substitute the values of R,ΔG° and T in the above expression.

ΔG°=RTln(Kb)24150J=(8.3145J/K)(298K)ln(Kb)Kb=5.8×105_

The stated reaction is,

B(g)+H2O(l)BH+(aq)+OH(aq)

The change in concentration of OH(aq) is assumed to be x

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