Step 1: Understanding Standard Reduction Potentials
\(E^\circ_{\text{red}} (H^+/H_2) = 0.00V, E^\circ_{\text{red}} (Cu^{2+}/Cu) = 0.34V, E^\circ_{\text{red}} (Zn^{2+}/Zn) = -0.76V,\)
\(E^\circ_{\text{red}} (NO_3^-/HNO_3) = 0.97V\)
Step 2: Evaluating Statements - Statement I:
- \( H^+ \) can only oxidize a metal if its reduction potential is higher than 0.00V.
- \( Cu \) has \( 0.34V \), which is higher than \(H^+\).
- \( H^+ \) cannot oxidize \( Cu \) to \( Cu^{2+} \) . - Statement II:
- \( Zn \) has a lower reduction potential (-0.76V) than \( Cu^{2+}/Cu (0.34V) \).
- \( Zn \) is a stronger reducing agent, so it can reduce \( Cu^{2+} \) to \( Cu \).
- This statement is correct. - Statement III:
- \( NO_3^- \) has a higher reduction potential (0.97V) than \( Cu^{2+}/Cu (0.34V) \).
- \( NO_3^- \) can oxidize \( Cu \) to \( Cu^{2+} \).
- This statement is correct.
\( \Delta G^\circ \, (\text{in kJ mol}^{-1}) \text{ for the cell reaction is} \)
\( \text{Cu}^{2+}(aq) + \text{Fe}(s) \rightarrow \text{Fe}^{2+}(aq) + \text{Cu}(s) \)
\( \left[\text{Given} \, E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V}, \, E^\circ_{\text{Fe}^{2+}/\text{Fe}} = -0.44 \, \text{V} \, \text{and} \, F = 96,500 \, \text{C mol}^{-1} \right] \)