Chapter 13, Problem 5CO

Interpretation Introduction

Interpretation: to calculate cell potential under standard and non- standard condition

Conceptual Introduction: Electrode potential is the ability of the electrode to attract or to lose the electron when it is in contact with solution possessing its own (similar) ions.

There are three conditions in this:

a) When atom or ion receives no gain or loss of electrons, these are know as null electriode

b) When metal looses an electrons, these is called oxidation electrode.

c) When metal ion is reduced, this are called reduction potential.

Solutions:Cell potential in standard condition:

${\text{E}}_{\text{cell}}^{\text{0}}{\text{=E}}_{\text{cathode}}^{\text{0}}{\text{-E}}_{\text{anode}}^{\text{0}}$

${\text{E}}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}^{\text{0}}\text{=-0}\text{.76volts}$

Cell potential in non-standard condition:

${\text{E}}_{{\text{M}}^{\text{n+}}\text{/M}}{\text{=E}}_{{\text{M}}^{\text{n+}}\text{/M}}^{\text{0}}\text{-}\frac{\text{2}\text{.303T}}{\text{nF}}{\text{log}}_{\text{e}}\frac{\text{[1]}}{{\text{[M}}^{\text{n+}}\text{(aq)]}}$

Explanation of Solution

Cell potential in standard condition:

Measurement of standard electrode potential of ${\text{Zn}}^{2+}\text{/Zn}$ electrode

Electrode consisting of zinc rod is dipped in the solution of ${\text{Zn}}^{2+}$ ions of concentration 1 mol L-1 is connected to the standard hydrogen electrode. The current flows from hydrogen electrode to zinc electrode. The voltmeter records the potential difference of 0.76 volts. Electrons flow from zinc electrode to hydrogen electrode. Therefore , zinc electrode must be anode, whereas hydrogen electrode is cathode.

${\text{E}}_{\text{cell}}^{\text{0}}{\text{=E}}_{\text{cathode}}^{\text{0}}{\text{-E}}_{\text{anode}}^{\text{0}}$

$\text{0}{\text{.76 = E}}_{{\text{H}}^{\text{+}}\text{/}\frac{\text{1}}{\text{2}}{\text{H}}_{\text{2}}}^{\text{0}}{\text{-E}}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}^{\text{0}}$

$\text{0}{\text{.76 = 0-E}}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}^{\text{0}}$

${\text{E}}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}^{\text{0}}\text{=-0}\text{.76volts}$

The sign of standard electrode potential of ${\text{Zn}}^{2+}\text{/Zn}$ electrode is negative and the standard electrode potential of ${\text{Zn}}^{2+}\text{/Zn}$ electrode is- 0.76Volts

Cell potential in non-standard condition:

Nernst equation is calculated at non- standard conditions.

It connects electrode potential to the temperature of the electrode and concentration of species involved.

Nernst equation of reduction electrode is:

${\text{E=E}}^{\text{0}}\text{-}\frac{\text{RT}}{\text{nF}}{\text{Log}}_{\text{e}}\frac{\text{[reduced state]}}{\text{[oxidisedstate]}}$

E= reduction potential of electrode assembly

${\text{E}}^{\text{0}}$ = Standard reduction potential of the same electrode assembly

R = gas constant = $\text{8}{\text{.314JK}}^{\text{-1}}{\text{mol}}^{\text{-1}}$

T =temperature of electrode assembly

F = one faraday =96500 coulombs

n= Number of moles of electrons gained by one mole of the oxidised state get changed into reduced state in the process of reduction occurring at the electrode.

[Oxidised state] = concentration of the substance undergoing reduction

[Reduced state] = concentration of the substance obtained on reduction.

Consider a reaction:

${\text{M}}^{\text{n+}}{\text{(aq)+ne}}^{\text{-}}\to \text{M(s)}$

In Nernst form can be written as:

${\text{E}}_{{\text{M}}^{\text{n+}}\text{/M}}{\text{=E}}_{{\text{M}}^{\text{n+}}\text{/M}}^{\text{0}}\text{-}\frac{\text{RT}}{\text{nF}}{\text{log}}_{\text{e}}\frac{\text{[M(s)]}}{{\text{[M}}^{\text{n+}}\text{(aq)]}}$

In the above equation ${\text{M}}^{\text{n+}}\text{(aq)}$ is the oxidised state because it is undergoing reduction and M(s) is reduced state because it is obtained in reduction .

Concentration of solid is taken to be equal to unity i.e, [M (s) ]= 1

Then above equation can be written as :

${\text{E}}_{{\text{M}}^{\text{n+}}\text{/M}}{\text{=E}}_{{\text{M}}^{\text{n+}}\text{/M}}^{\text{0}}\text{-}\frac{\text{2}\text{.303T}}{\text{nF}}{\text{log}}_{\text{e}}\frac{\text{[1]}}{{\text{[M}}^{\text{n+}}\text{(aq)]}}$

This equation give the relationship between electrode reduction potential with temperature.

Conclusion

Cell potential in standard condition:

${\text{E}}_{\text{cell}}^{\text{0}}{\text{=E}}_{\text{cathode}}^{\text{0}}{\text{-E}}_{\text{anode}}^{\text{0}}$

${\text{E}}_{{\text{Zn}}^{\text{2+}}\text{/Zn}}^{\text{0}}\text{=-0}\text{.76volts}$

Cell potential in non-standard condition:

${\text{E}}_{{\text{M}}^{\text{n+}}\text{/M}}{\text{=E}}_{{\text{M}}^{\text{n+}}\text{/M}}^{\text{0}}\text{-}\frac{\text{2}\text{.303T}}{\text{nF}}{\text{log}}_{\text{e}}\frac{\text{[1]}}{{\text{[M}}^{\text{n+}}\text{(aq)]}}$