Chapter 20.1, Problem 7PP

Interpretation Introduction

Interpretation:

The half cell reaction of a given balanced overall reaction is to be written and the cell potential is to be determined.

Concept introduction:

The half cell reactions are the reactions which occur at anode and cathode electrode. The difference between the electrode potential of the two electrodes consisting an electrochemical cell is known as cell potential

Answer to Problem 7PP

The half cell reaction at anode

${\text{2Hg}}^{\text{+2}}\left(\text{aq}\right){\text{+2e}}^{\text{-}}\to {\text{Hg}}_{\text{2}}{}^{\text{+2}}$

The half cell reaction at cathode is

${\text{Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+4H}}_{\text{2}}\text{O}\to {\text{MnO}}_{\text{4}}{}^{\text{-}}{\text{+8H}}^{\text{+}}{\text{+5e}}^{\text{-}}$

$\begin{array}{l}\text{The}\text{balanced}\text{over}\text{all}\text{reaction}\text{is}\\ {\text{2Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+8H}}_{\text{2}}\text{O }\left(\text{l}\right){\text{+ 10Hg}}^{\text{+2}}\left(\text{g}\right)\to {\text{2MnO}}_{\text{4}}{}^{\text{-1}}{\text{+16H}}^{\text{+}}{\text{+ 5Hg}}_{\text{2}}{}^{\text{+2}}\left(\text{aq}\right)\\ \text{The}\text{cell}\text{reprsentation}\text{of}\text{this}\text{over}\text{}\text{all}\text{reaction}\text{is}\\ {\text{Hg}}^{\text{+2}}|{\text{Hg}}_{\text{2}}{}^{\text{+2}}\Vert {\text{Mn}}^{\text{+2}}|{\text{MnO}}_{\text{4}}{}^{\text{-}}\\ \text{The oxidation is occur at Hg electrode or anode and reduction is occurs at }\\ \text{Mn electrode or cathode}\text{.}\\ \text{The cell potental of the reaction is calculated as}\\ {\text{E°}}_{\text{cell}}{\text{=E°}}_{\text{cathode}}{\text{-E°}}_{\text{anode}}\\ \text{=}\left(\text{1}\text{.507}\right)\text{-}\left(\text{0}\text{.920}\right)\\ \text{= 0}\text{.587 V}\\ \text{The cell potential is 0}\text{.587 V}\end{array}$

Explanation of Solution

Given information:

$\begin{array}{l}\text{The}\text{standard}\text{potential}{\text{2Hg}}^{\text{+2}}\left(\text{aq}\right){\text{+2e}}^{\text{-}}\to {\text{Hg}}_{\text{2}}{}^{\text{+2}}\text{=0}\text{.920}\text{V}\\ \text{The standard}\text{potential}\text{of}{\text{Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+4H}}_{\text{2}}\text{O}\to {\text{MnO}}_{\text{4}}{}^{\text{-}}{\text{+8H}}^{\text{+}}{\text{+5e}}^{\text{-}}\text{=1}\text{.507}\text{V}\end{array}$

The half cell reaction at anode

${\text{2Hg}}^{\text{+2}}\left(\text{aq}\right){\text{+2e}}^{\text{-}}\to {\text{Hg}}_{\text{2}}{}^{\text{+2}}$

The half cell reaction at cathode is

${\text{Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+4H}}_{\text{2}}\text{O}\to {\text{MnO}}_{\text{4}}{}^{\text{-}}{\text{+8H}}^{\text{+}}{\text{+5e}}^{\text{-}}$

$\begin{array}{l}\text{The}\text{balanced}\text{over}\text{all}\text{reaction}\text{is}\\ {\text{2Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+8H}}_{\text{2}}\text{O }\left(\text{l}\right){\text{+ 10Hg}}^{\text{+2}}\left(\text{g}\right)\to {\text{2MnO}}_{\text{4}}{}^{\text{-1}}{\text{+16H}}^{\text{+}}{\text{+ 5Hg}}_{\text{2}}{}^{\text{+2}}\left(\text{aq}\right)\\ \text{The}\text{cell}\text{reprsentation}\text{of}\text{this}\text{over}\text{}\text{all}\text{reaction}\text{is}\\ {\text{Hg}}^{\text{+2}}|{\text{Hg}}_{\text{2}}{}^{\text{+2}}\Vert {\text{Mn}}^{\text{+2}}|{\text{MnO}}_{\text{4}}{}^{\text{-}}\\ \text{The oxidation is occur at Hg electrode or anode and reduction is occurs at }\\ \text{Mn electrode or cathode}\text{.}\\ \text{The cell potental of the reaction is calculated as}\\ {\text{E°}}_{\text{cell}}{\text{=E°}}_{\text{cathode}}{\text{-E°}}_{\text{anode}}\\ \text{=}\left(\text{1}\text{.507}\right)\text{-}\left(\text{0}\text{.920}\right)\\ \text{= 0}\text{.587 V}\\ \text{The cell potential is 0}\text{.587 V}\end{array}$

Conclusion

$\begin{array}{l}\text{The}\text{balanced}\text{over}\text{all}\text{reaction}\text{is}\\ {\text{2Mn}}^{\text{+2}}\left(\text{aq}\right){\text{+8H}}_{\text{2}}\text{O }\left(\text{l}\right){\text{+ 10Hg}}^{\text{+2}}\left(\text{g}\right)\to {\text{2MnO}}_{\text{4}}{}^{\text{-1}}{\text{+16H}}^{\text{+}}{\text{+ 5Hg}}_{\text{2}}{}^{\text{+2}}\left(\text{aq}\right)\\ \text{The}\text{cell}\text{reprsentation}\text{of}\text{this}\text{over}\text{}\text{all}\text{reaction}\text{is}\\ {\text{Hg}}^{\text{+2}}|{\text{Hg}}_{\text{2}}{}^{\text{+2}}\Vert {\text{Mn}}^{\text{+2}}|{\text{MnO}}_{\text{4}}{}^{\text{-}}\\ \text{The oxidation is occur at Hg electrode or anode and reduction is occurs at }\\ \text{Mn electrode or cathode}\text{.}\\ \text{The cell potental of the reaction is calculated as}\\ {\text{E°}}_{\text{cell}}{\text{=E°}}_{\text{cathode}}{\text{-E°}}_{\text{anode}}\\ \text{=}\left(\text{1}\text{.507}\right)\text{-}\left(\text{0}\text{.920}\right)\\ \text{= 0}\text{.587 V}\\ \text{The cell potential is 0}\text{.587 V}\end{array}$