   Chapter 18, Problem 118AE

Chapter
Section
Textbook Problem

# A standard galvanic cell is constructed so that the overall cell reaction is 2 A 1 3 + + ( a q )   +   3 M ( s )   →   3 M 2+ ( a q )   +   2 A 1 ( s ) Where M is an unknown metal. If ∆G° = −411 kJ for the overall cell reaction, identify the metal used to construct the standard cell.

Interpretation Introduction

Interpretation: The reaction taking place in a galvanic cell is given. The identity of the unknown metal used in combination with Aluminum for the construction of given galvanic cell is to be stated.

Concept introduction: The galvanic cell converts chemical energy into electrical energy while the electrolytic cell converts electrical energy into chemical energy.

The species at anode undergoes oxidation, while the species at cathode undergoes reduction and the electrons generated at the anode are transferred through wire to the cathode.

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

ΔG°=nFE°cell

To determine: The identity of the unknown metal used in combination with Aluminum for the construction of the given galvanic cell.

Explanation

Given,

The overall reaction in galvanic cell is,

2Al3+(aq)+3M(s)3M2+(aq)+2Al(s)

The value of ΔG° is 411kj .

The conversion of kJ into J is done as,

1kJ=1000J

The conversion of value of 411kj in j is represented as,

411kJ=-411×1000J=411000J

The cell reaction shows that Aluminum undergoes reduction reaction, whereas the unknown metal undergoes oxidation.

The reaction taking place at the cathode is,

Al3++3eAl   E°red=1.66 V

The reaction taking place at the anode is,

MM2++2e   E°ox=x V

Multiply the reduction half-reaction with a coefficient of 2 and the oxidation half-reaction with a coefficient of 3 and then add both the reactions,

2Al3++6e2Al 3M3M2++6e

The final equation is,

2Al3++3M3M2++2Al

The reaction involves the transfer of 6 moles of electrons.

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

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