BuyFindarrow_forward

Chemistry: An Atoms First Approach

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

Solutions

Chapter
Section
BuyFindarrow_forward

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

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 16 Solutions

Show all chapter solutions add

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Match the molecular model with the correct chemical formula: CH3OH, NH3, KCl, H2O.

General Chemistry - Standalone book (MindTap Course List)

Water balance is governed by the a. liver b. kidneys c. brain d. b and c

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

How are granules and super granules related? How do they differ?

Horizons: Exploring the Universe (MindTap Course List)

The main obstacle to nursing multiples is milk supply. __ True __ False

Nutrition Through the Life Cycle (MindTap Course List)