Chapter 19, Problem 19.31QP

Interpretation Introduction

Interpretation:

Calculation of standard potential and emf of ${\text{Zn/Zn}}^{\text{2+}}$ half-cell coupled with standard hydrogen electrode (SHE).

Concept introduction:

In an electrochemical cell, current is generated by the flow of electron from one electrode to another. In the given Zn|Zn²⁺ half-cell coupled with SHE the electrons flow from Zinc and reduces H⁺_(aq) to H₂ gas.  The cell reaction was given below.

$\begin{array}{l}\text{Oxidation}{\text{Zn}}_{\text{(s)}}\stackrel{}{\to }{\text{Zn}}^{\text{2+}}{}_{\text{(aq)}}{\text{+2e}}^{\text{-}}\\ \text{Reduction}{\text{2H}}^{\text{+}}{}_{\text{(g)}}{\text{+2e}}^{\text{-}}\stackrel{}{\to }{\text{H}}_{\text{2(g)}}\\ \text{Overall}\text{Reaction}{\text{Zn}}_{\text{(s)}}{\text{+ 2H}}^{\text{+}}{}_{\text{(aq)}}\stackrel{}{\to }{\text{Zn}}^{\text{2+}}{}_{\text{(aq)}}{\text{+H}}_{\text{2(g)}}\end{array}$

Standard potential of a cell (E^o_cell) is the potential measured at 298K, 1 atm pressure with electrolyte concentration of 1 M. It can be calculated by the below equation.

${\text{E}}^{\text{o}}{}_{\text{cell}}{\text{=E}}^{\text{o}}{}_{\text{reduction}}{\text{-E}}^{\text{o}}{}_{\text{oxidation}}$

The standard potential for the reduction half (cathode) and the oxidation half (anode) were measured in relative with standard hydrogen electrode (SHE) at standard temperature and pressure with electrolyte concentration of 1M.

In our case the standard potential of the cell can be calculated by the following reaction

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

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

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

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

Further the above equation can be written in terms of log₁₀

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