Free energy and cell potential Knowledge-Based Download PDF

Questions

1. 1.

   An electrochemical cell operates with a standard cell potential of $E^\circ_{\text{cell}} = +0.34\text{ V}$. When the cell reaction reaches equilibrium ($Q = K$) at constant temperature and pressure, what are the values of the cell potential ($E_{\text{cell}}$) and the Gibbs free energy change ($\Delta G$)?

   • A) $E_{\text{cell}} = 0\text{ V}$ and $\Delta G = 0\text{ kJ}\cdot\text{mol}^{-1}$
   • B) $E_{\text{cell}} = +0.34\text{ V}$ and $\Delta G = 0\text{ kJ}\cdot\text{mol}^{-1}$
   • C) $E_{\text{cell}} = 0\text{ V}$ and $\Delta G < 0\text{ kJ}\cdot\text{mol}^{-1}$
   • D) $E_{\text{cell}} = +0.34\text{ V}$ and $\Delta G < 0\text{ kJ}\cdot\text{mol}^{-1}$
2. 2.

   Which combination of thermodynamic quantities correctly represents a redox reaction that is spontaneous in the forward direction under standard-state conditions?

   • A) $E^\circ_{\text{cell}} < 0$, $\Delta G^\circ < 0$, and $K > 1$
   • B) $E^\circ_{\text{cell}} > 0$, $\Delta G^\circ < 0$, and $K > 1$
   • C) $E^\circ_{\text{cell}} > 0$, $\Delta G^\circ > 0$, and $K < 1$
   • D) $E^\circ_{\text{cell}} < 0$, $\Delta G^\circ > 0$, and $K > 1$
3. 3.

   When the stoichiometric coefficients of a balanced redox reaction are multiplied by a factor of 2, how are its standard Gibbs free energy change ($\Delta G^\circ$) and standard cell potential ($E^\circ_{\text{cell}}$) affected?

   • A) $\Delta G^\circ$ is multiplied by 2, whereas $E^\circ_{\text{cell}}$ remains unchanged.
   • B) Both $\Delta G^\circ$ and $E^\circ_{\text{cell}}$ are multiplied by 2.
   • C) $E^\circ_{\text{cell}}$ is multiplied by 2, whereas $\Delta G^\circ$ remains unchanged.
   • D) Neither $\Delta G^\circ$ nor $E^\circ_{\text{cell}}$ changes because the standard states of the species are unaffected.
4. 4.

   A galvanic cell operates via the reaction $\text{Ni}(s) + 2\text{Ag}^+(aq) \rightarrow \text{Ni}^{2+}(aq) + 2\text{Ag}(s)$ with a standard cell potential of $E^\circ_{\text{cell}} = +1.05\text{ V}$ at $298\text{ K}$. Using Faraday's constant $F = 96{,}500\text{ C}\cdot\text{mol}^{-1}$, what is the standard Gibbs free energy change ($\Delta G^\circ$) for this reaction?

   • A) $+101\text{ kJ}\cdot\text{mol}^{-1}$
   • B) $-101\text{ kJ}\cdot\text{mol}^{-1}$
   • C) $+203\text{ kJ}\cdot\text{mol}^{-1}$
   • D) $-203\text{ kJ}\cdot\text{mol}^{-1}$