Computation of the Standard Cell Potential

Compute the standard cell potential and the equilibrium constant for the reaction
$Cu ^{2+}( aq )+ Zn ( s ) \rightarrow Cu ( s )+ Zn ^{2+}( aq )$

Question

Computation of the Standard Cell Potential

Compute the standard cell potential and the equilibrium constant for the reaction

[latex]Cu ^{2+}( aq )+ Zn ( s ) \rightarrow Cu ( s )+ Zn ^{2+}( aq )[/latex]

Accepted Answer

The reaction above is the sum of the two half-cell reactions

[latex]Cu ^{2+}( aq )+2 e^{-} ightarrow Cu ( s ) \quad ext { half-cell standard potential }=+0.34 V[/latex]

[latex]Zn ( s ) ightarrow Zn ^{2+}( aq )+2 e^{-} \quad ext { half-cell standard potential }=-(-0.76 V )=+0.76 V[/latex]

where the negative of the reported half-cell standard potential has been used for the second reaction, since its direction is opposite to that given in the table. Therefore, the standard cell potential for the overall reaction is

[latex]E^{\circ}=+0.34+0.76=+1.10 V[/latex]

The equilibrium constant for this reaction is then

[latex]\ln K_{a}=\frac{n F E^{\circ}}{R T}=\frac{2 imes 9.6485 imes 10^{4} \frac{ C }{ mol } imes 1.10 V }{8.314 \frac{ J }{ mol K } imes 298.15 K imes 1 \frac{ C V }{ mol }}=85.6[/latex]

or

[latex]K_{a}=1.5 imes 10^{37}[/latex]

or equivalently,

[latex]\ln K_{a}=\frac{n F E^{\circ}}{R T}=\frac{n E^{\circ}}{\left(\frac{R T}{F} ight)}=\frac{2 imes 1.10 V imes \frac{1000 mV }{ V }}{25.7 mV }=85.6[/latex]

or

[latex]K_{a}=1.5 imes 10^{37}[/latex]

Question 14.6.1: Computation of the Standard Cell Potential Compute the stand...

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