Chapter 18, Problem 18.34QP

Interpretation Introduction

Interpretation:

Using the given data, the emf of a cell has to be calculated.

Concept introduction:

Electro motive force (emf) of the reaction can be calculated by Nernst equation:

${\text{E}}_{\text{cell}}{\text{= E}}^{\text{o}}{}_{\text{cell}}\text{-}\frac{\text{RT}}{\text{nF}}\text{lnQ}$

E^o_cell = standard potential of a cell

${\text{E}}^{\text{o}}{}_{\text{cell}}{\text{= E}}^{\text{o}}{}_{{\text{H}}^{\text{+}}{\text{/H}}^{\text{2}}}{\text{-E}}^{\text{o}}{}_{{\text{Pb/Pb}}^{\text{2+}}}$

R = universal gas constant (8.31 J mole^-1 K^-1)

T = Absolute temperature in Kelvin

F = Faraday constant, number of coulombs per mole of electron (96845 C/mole)

n = Number of electrons transferred in the cell reaction

Q = Reaction quotient

Since the cell reaction takes place at room temperature (298K), so the Nernst equation was simplified as

${\text{E}}_{\text{cell}}{\text{= E}}^{\text{o}}{}_{\text{cell}}\text{-(}\frac{\text{0}\text{.0257}}{\text{n}}\text{)lnQ}$

Further the above equation can be written in terms of log₁₀

${\text{E}}_{\text{cell}}{\text{= E}}^{\text{o}}{}_{\text{cell}}\text{-(}\frac{\text{0}\text{.0592}}{\text{n}}\text{)logQ}$