   # Calculate Δ G° and K at 25°C for the reactions in Exercises 37 and 41. ### Chemistry: An Atoms First Approach

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

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 17, Problem 75E
Textbook Problem
1 views

## Calculate ΔG° and K at 25°C for the reactions in Exercises 37 and 41.

(a)

Interpretation Introduction

Interpretation:

The equations for different chemical reactions are given. The value of ΔG° and K for different reactions is to be calculated.

Concept introduction:

The relationship between reduction potential and standard reduction potential value and activities of species present in an electrochemical cell at a given temperature is given by the Nernst equation.

The value of Ecell is calculated using Nernst formula,

E=E°(RTnF)ln(Q)

At room temperature the above equation is specifies as,

E=E°(0.0591n)log(Q)

This relation is further used to determine the relation between ΔG° and K , ΔG° and E°cell .

To determine: The value of ΔG° and K for different reactions.

### Explanation of Solution

The given cell reaction is,

Cr3+(aq)+Cl2(g)Cr2O72(aq)+Cl(aq)

The reaction taking place on cathode,

Cl2(g)+2e2Cl(aq)E°red=1.36V

The reaction taking place at anode,

2Cr3+(aq)+7H2O(l)Cr2O72(aq)+14H+(aq)+6eE°ox=1.33V

Multiply reduction half-reaction with a coefficient of 3 and then add both the reduction half and oxidation half-reaction.

Cl2(g)+2e2Cl(aq)2Cr3+(aq)+7H2O(l)Cr2O72(aq)+14H+(aq)+6e

The overall cell reaction is,

2Cr3+(aq)+7H2O(l)+3Cl2(g)Cr2O72(aq)+14H+(aq)+6Cl(aq)

The overall cell potential is calculated as,

E°cell=E°ox+E°red=1.33V+(1.36V)=0.03V_

The relationship between cell potential and Gibbs free energy change is given by the formula,

ΔG°=nFE°cell

Where,

• ΔG° is the Gibbs free energy change at the standard conditions.
• n is the number of electrons involved in the reaction.
• F is the Faraday’s constant.
• E°cell is the cell potential at the standard condition.

The number of moles of electrons involved in the reaction is 6 .

Substitute the values in above equation,

ΔG°=(6mole)(96,485Cmole-)(0.03JC)=17,367.3J=-17.36kJ_

The value of ΔG° is calculated as -17.36kJ_

The relationship between Gibbs free energy change and equilibrium constant is given by the formula,

ΔG°=RTlnK=nFE°cell

Where,

• ΔG° is the Gibbs free energy change at the standard conditions.
• R is the universal gas constant.
• T is the temperature in Kelvin.
• K is the equilibrium constant.

Rearranged equation at 25°C is obtained as,

logK=((n)(E°)0.0591)

Substitute the obtained values in above equation,

logK=((6)(0

(b)

Interpretation Introduction

Interpretation:

The equations for different chemical reactions are given. The value of ΔG° and K for different reactions is to be calculated.

Concept introduction:

The relationship between reduction potential and standard reduction potential value and activities of species present in an electrochemical cell at a given temperature is given by the Nernst equation.

The value of Ecell is calculated using Nernst formula,

E=E°(RTnF) ln(Q)

At room temperature the above equation is specifies as,

E=E°(0.0591n) log(Q)

This relation is further used to determine the relation between ΔG° and K , ΔG° and E°cell .

To determine: The standard line notation for the given cell reaction.

### 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

Find more solutions based on key concepts
To overload a muscle is never productive. T F

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

Do all chordates have backbones?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin

The fundamental frequency of an open organ pipe corresponds to middle C (261.6 Hz on the chromatic musical scal...

Physics for Scientists and Engineers, Technology Update (No access codes included) 