What is the standard free energy change for the cell, having following cell reaction? \(\text{2 Ag\(^+\)(aq) + Cd(s) $\longrightarrow$ 2 Ag(s) + Cd\(^{2+}\)(aq), E\(_{\text{cell}}\) = 1.20 V} \)
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To calculate standard free energy change, use the formula \(\Delta G^\circ = -nFE_{\text{cell}}\), where \(n\) is the number of electrons transferred, \(F\) is Faraday’s constant, and \(E_{\text{cell}}\) is the cell potential.
Step 1: Applying the Nernst equation.
The standard free energy change \(\Delta G^\circ\) can be calculated using the relation:
\[
\Delta G^\circ = -nFE_{\text{cell}}
\]
where \(n\) is the number of moles of electrons transferred, \(F\) is Faraday's constant (96,485 C/mol), and \(E_{\text{cell}}\) is the cell potential. In this reaction, 2 moles of electrons are transferred. Therefore,
\[
\Delta G^\circ = -2 \times 96,485 \times 1.20 = -231.6 \, \text{kJ}
\]
Step 2: Conclusion.
The standard free energy change is (A) -231.6 kJ.
