PHYSICAL CHEMISTRY IN BRIEF

CHAP. 11: ELECTROCHEMISTRY [CONTENTS] 399

The following relation applies between electrical work and a change in the Gibbs energy
during reaction at a given temperature and pressure, see equation (3.15)

∆rG=Wel=−zFE , [T, p,reversible process]. (11.109)

Example

The following reaction proceeds at the electrodes in a Daniell cell

Zn = Zn2++ 2 e−, Cu2++ 2 e−= Cu.

The equilibrium potential of the cell is 1 V.

a) Calculate the work doneby the cell at one mole of reaction turnovers.

b) Calculate the work doneby the cell at one mole of reaction turnovers if the reaction is written

in the form

1

2

Zn =

1

2

Zn2++ e−,

1

2

Cu2++ e−=

1

2

Cu.

Solution

a) From the reactions record it follows thatz= 2. By substituting into (11.108) we obtain

Wel=− 2 × 96485. 3 ×1 =−192 970. 6 J mol−^1.

The work done has an opposite sign and it is equal to 192 970.6 J mol−^1.

b) From the reactions record it follows thatz= 1. The work done is half, 96 485.3 J/mol.

11.8.4 Nernst equation

Let the following overall chemical reaction proceed in a galvanic cell

aA +bB.. .=sS +tT... (11.110)

By combining equations (8.10) and (11.109) we obtain for the cell potential

E=E◦−

RT

zF

ln

asSatT...

aaAabB...

, (11.111)