   # Calculate Δ r G ° and the equilibrium constant for the following reactions. (a) Zn 2+ (aq) + Ni(s) ⇄ Zn(s) + Ni 2+ (aq) (b) Cu(s) + 2 Ag + (aq) ⇄ Cu 2+ (aq) + 2 Ag(s) ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 19, Problem 36PS
Textbook Problem
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## Calculate ΔrG° and the equilibrium constant for the following reactions. (a) Zn2+(aq) + Ni(s) ⇄ Zn(s) + Ni2+(aq) (b) Cu(s) + 2 Ag+(aq) ⇄ Cu2+(aq) + 2 Ag(s)

a)

Interpretation Introduction

Interpretation:

The ΔrGo value and the equilibrium constant for the following reaction has to be determined.

1. a) Zn2+(aq) + Ni(s)Zn(s) + Ni2+(aq)

Concept introduction:

According to the first law of thermodynamics, the change in internal energy of a system is equal ti the heat added to the sysytem minus the work done by the system.

The equation is as follows.

ΔU = Q - WΔU = Change in internal energyQ = Heat added to the systemW=Work done by the system

In voltaic cell, the maximum cell potential is directly related to the free energy difference between the reactants and products in the cell.

ΔG0= -nFE0n = Number of moles transferred per mole of reactant and productsF = Faradayconstant=96485C/mol  E0= Volts = Work(J)/Charge(C)

The relation between standard cell potential and equilibrium constant is as follows.

lnK = nE00.0257 at 298K

### Explanation of Solution

The given chemical reaction is as follows.

Zn2+(aq) + Ni(s)Zn(s) + Ni2+(aq)

Let’s write an each half cell reaction.

At anode:Oxiation : Ni(s)   Ni2+(aq) + 2eAt cathode:Reduction : Zn2+(aq) + 2eZn(s)

Let’s calculate the Ecello value of the reaction.

Ecello= ECathode0- EAnode0= -0.736 V-(-0.25 V)= -0.513 V

Let’s calculate the ΔG0 value for the reaction.

ΔG0= -nFE0n = 2F = 96485C/mol  E0= -0

(b)

Interpretation Introduction

Interpretation:

The ΔrGo value and the equilibrium constant for the following reaction has to be determined.

1. a) Cu(s) + 2Ag+(aq)Cu2+(aq) + 2Ag(s)

Concept introduction:

According to the first law of thermodynamics, the change in internal energy of a system is equal ti the heat added to the sysytem minus the work done by the system.

The equation is as follows.

ΔU = Q - WΔU = Change in internal energyQ = Heat added to the systemW=Work done by the system

In voltaic cell, the maximum cell potential is directly related to the free energy difference between the reactants and products in the cell.

ΔG0= -nFE0n = Number of moles transferred per mole of reactant and productsF = Faradayconstant=96485C/mol  E0= Volts = Work(J)/Charge(C)

The relation between standard cell potential and equilibrium constant is as follows.

lnK = nE00.0257 at 298K

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