Chapter 19, Problem 84GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# A voltaic cell is set up utilizing the reactionCu(s) + 2 Ag+(aq) → Cu2+(aq) + 2 Ag(s)Cu(s) | Cu2+(aq, 1.0 M) || Ag+(aq, 0.001 M)|Ag(s)Under standard conditions, the expected potential is 0 45 V predict whether the potential for the voltaic cell will be higher, lower, or the same as the standard potential. Verify your prediction by calculating the new cell potential.

Interpretation Introduction

Interpretation:

It has to be predicted whether the potential for the voltaic cell will be higher, lower or same as the standard potential and the verification of the prediction also has to be done.

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

The relation between solubility product Ksp and equilibrium constant is as follows.

Ksp= e+lnK

Explanation

The given over all reaction is as follows.

Cu(s)Â +Â 2Ag+(aq)Â â†’Cu2+(aq)Â +Â 2Ag(s)

At standard conditions, the ions in solution are at concentrations of 1.0Â M. In the above reaction, Ag+ is at a concentration of 0.001Â M. Ag+ is a reactant in the above reaction.

Because there is less of a reactant that is needed to drive the reaction., the measure potential will be lower than the standard potential.

Letâ€™s calculate the reduction potential of voltaic cell:

lnKÂ =Â nE00.0257Â atÂ 298K

Rearrange the above formula as follows.

EÂ =Â E0Â -Â 0

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