A voltaic cell is based upon the half-reactions below. $\begin{array}{lccc}
\mathrm{Pb}^{2+}(a q)+2 e^{-} \rightarrow \mathrm{Pb}(s) & E^{\circ}=-0.127 \mathrm{~V}\
\mathrm{Cd}^{2+}(a q)+2 e^{-} \rightarrow \mathrm{Cd}(s) & E^{\circ}=-0.402 \mathrm{~V} \
\end{array}$

Calculate the equilibrium constant for the overall chemical reaction at 25°C.(R = 8.31 J/K?mol,F = 96480 C/mol e?)

Question

A voltaic cell is based upon the half-reactions below. $\begin{array}{lccc}
\mathrm{Pb}^{2+}(a q)+2 e^{-} \rightarrow \mathrm{Pb}(s) &  E^{\circ}=-0.127 \mathrm{~V}\
\mathrm{Cd}^{2+}(a q)+2 e^{-} \rightarrow \mathrm{Cd}(s) & E^{\circ}=-0.402 \mathrm{~V} \
\end{array}$

Calculate the equilibrium constant for the overall chemical reaction at 25°C.(R = 8.31 J/K?mol,F = 96480 C/mol e?)

Quizplus · Accepted Answer

The equilibrium constant for the overall cell reaction can be calculated using the Nernst equation: 
$$E_{cell}=E^{\circ}_{cell}-\frac{RT}{nF}\ln Q$$
where $E_{cell}$ is the cell potential, $E^{\circ}_{cell}$ is the standard cell potential, $R$ is the gas constant, $T$ is the temperature in Kelvin, $n$ is the number of electrons transferred in the balanced equation, $F$ is the Faraday constant, and $Q$ is the reaction quotient.

In this case, the balanced equation for the cell reaction is: 
$$\mathrm{Pb}^{2+}(aq)+\mathrm{Cd}(s)ightarrow \mathrm{Cd}^{2+}(aq)+\mathrm{Pb}(s)$$
with $n=2$.

The standard cell potential is given by: 
$$E^{\circ}_{cell}=E^{\circ}_{\mathrm{reductant}}-E^{\circ}_{\mathrm{oxidant}}=-0.402-(-0.127)=-0.275~\mathrm{V}$$

At equilibrium, the cell potential is zero, so we can set $E_{cell}=0$ in the Nernst equation: 
$$0=-0.275-\frac{RT}{2F}\ln Q$$
$$\ln Q=\frac{-2FE^{\circ}_{cell}}{RT}=19.2$$

Finally, the equilibrium constant can be calculated from the expression: 
$$\Delta G^{\circ}=-RT\ln K$$
where $\Delta G^{\circ}=-nFE^{\circ}_{cell}$ is the standard Gibbs free energy change for the reaction.

Substituting the values: 
$$-nFE^{\circ}_{cell}=-2	imes 96480~\mathrm{C/mol} 	imes (-0.275~\mathrm{V})=53179~\mathrm{J/mol}$$

Therefore, 
$$K=e^{-\Delta G^{\circ}/(RT)}=2.0	imes 10^{19}$$

The correct answer is choice C.

A Voltaic Cell Is Based Upon the Half-Reactions Below Calculate the Equilibrium Constant for the Overall Chemical Reaction at q)+2