Q.Calculate standard Gibbs energy change at 25°C for the cell reaction $Cd_{(s)} + Sn^{2+}_{(aq)} \longrightarrow Cd^{2+}_{(aq)} + Sn_{(s)}$; $E^\circ_{Cd} = -0.403V$, $E^\circ_{Sn} = -0.136V$

Electrical work done by a galvanic cell equals charge passed times cell potential, $nFE_{cell}$; Gibbs (1878) identified this with the decrease in Gibbs energy of the cell reaction, giving $\Delta G=-nFE_{cell}$ and, under standard conditions, $\Delta G^0=-nFE^0_{cell}$. Because $\Delta G^0$ is extensive (scales with reaction amount) while $n$ scales identically when the equation is multiplied by any factor, their ratio $E^0_{cell}=-\Delta G^0/nF$ stays constant — proving $E^0_{cell}$ is an intensive property. Since $\Delta G<0$ for spontaneity, $E_{cell}$ must be positive for a spontaneous cell reaction. Combining $\Delta G^0=-nFE^0_{cell}$ with the general thermodynamic relation $\Delta G^0=-RT\ln K$ gives $E^0_{cell}=\dfrac{0.0592}{n …