Question:
Two galvanic cells, Cell I and Cell II, operate at the same temperature and involve two different redox systems. It is observed that at a particular value of the reaction quotient $\text{Q}_{\text{I}} = \text{Q}_{\text{II}} = \text{Q}_0$, the ratio of EMF of the two cells ($\text{E}_{\text{I}}/\text{E}_{\text{II}}$) as well as the ratio of change of Gibbs free energy for the two cells ($\Delta\text{G}_{\text{I}}/\Delta\text{G}_{\text{II}}$) are both 1/3. Assuming standard cell reactions written in the spontaneous direction and reversible operation, the pair of cells can satisfy these conditions is:
Two galvanic cells, Cell I and Cell II, operate at the same temperature and involve two different redox systems. It is observed that at a particular value of the reaction quotient $\text{Q}_{\text{I}} = \text{Q}_{\text{II}} = \text{Q}_0$, the ratio of EMF of the two cells ($\text{E}_{\text{I}}/\text{E}_{\text{II}}$) as well as the ratio of change of Gibbs free energy for the two cells ($\Delta\text{G}_{\text{I}}/\Delta\text{G}_{\text{II}}$) are both 1/3. Assuming standard cell reactions written in the spontaneous direction and reversible operation, the pair of cells can satisfy these conditions is:
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If the ratio of energy ($\Delta\text{G}$) and the ratio of driving force (E) are identical, then the scaling factor $n$ (electrons transferred) must cancel out, meaning $n$ must be equal for both processes.
Updated On: Jun 16, 2026
- Cell I: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$ and Cell II: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Cu}^{2+}\text{(aq)}|\text{Cu(s)}$
- Cell I: $\text{Ag}^+\text{(aq)}|\text{Ag(s)}||\text{Fe}^{2+}\text{(aq)}|\text{Fe}^{3+}\text{(aq)}$ and Cell II: $\text{Al(s)}|\text{Al}^{3+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$
- Cell I: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Cu}^{2+}\text{(aq)}|\text{Cu(s)}$ and Cell II: $\text{Al(s)}|\text{Al}^{3+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$
- Cell I: $\text{Fe}^{2+}\text{(aq)}|\text{Fe}^{3+}\text{(aq)}||\text{Cu}^{2+}\text{(aq)}|\text{Cu}^+\text{(aq)}$ and Cell II: $\text{Cu(s)}|\text{Cu}^{2+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question asks us to identify which pair of galvanic cells satisfies the condition that at a particular reaction quotient, both the ratio of their cell potentials ($\text{E}_{\text{I}}/\text{E}_{\text{II}}$) and the ratio of their Gibbs free energy changes ($\Delta\text{G}_{\text{I}}/\Delta\text{G}_{\text{II}}$) are exactly equal to $1/3$.
Step 2: Key Formula or Approach:
The relationship between the Gibbs free energy change ($\Delta\text{G}$) of a cell reaction and its electromotive force (EMF, E) is given by:
\[ \Delta\text{G} = -n\text{F}\text{E} \]
where $n$ is the number of moles of electrons transferred in the spontaneous cell reaction and F is Faraday's constant.
Step 3: Detailed Explanation:
• Let us express the ratio of the Gibbs free energy changes of the two cells:
\[ \frac{\Delta\text{G}_{\text{I}}}{\Delta\text{G}_{\text{II}}} = \frac{-n_{\text{I}}\text{F}\text{E}_{\text{I}}}{-n_{\text{II}}\text{F}\text{E}_{\text{II}}} = \frac{n_{\text{I}}\text{E}_{\text{I}}}{n_{\text{II}}\text{E}_{\text{II}}} \]
• We are given that at $\text{Q}_{\text{I}} = \text{Q}_{\text{II}} = \text{Q}_0$, the following ratios hold:
\[ \frac{\text{E}_{\text{I}}}{\text{E}_{\text{II}}} = \frac{1}{3} \quad \text{and} \quad \frac{\Delta\text{G}_{\text{I}}}{\Delta\text{G}_{\text{II}}} = \frac{1}{3} \]
• Substituting these values into our relation:
\[ \frac{1}{3} = \frac{n_{\text{I}}}{n_{\text{II}}} \times \frac{1}{3} \implies \frac{n_{\text{I}}}{n_{\text{II}}} = 1 \implies n_{\text{I}} = n_{\text{II}} \]
• Thus, for this condition to hold, both cell reactions must involve the transfer of the exact same number of electrons ($n_{\text{I}} = n_{\text{II}}$) when written in their balanced, spontaneous forms.
• Let us examine the cells in Option A:
itemize
• Cell I: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$
Spontaneous reaction: $\text{Zn(s)} + 2\text{Ag}^+\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + 2\text{Ag(s)}$, which involves the transfer of $n_{\text{I}} = 2$ electrons.
• Cell II: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Cu}^{2+}\text{(aq)}|\text{Cu(s)}$
Spontaneous reaction: $\text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)}$, which involves the transfer of $n_{\text{II}} = 2$ electrons.
Here, $n_{\text{I}} = n_{\text{II}} = 2$, which perfectly satisfies our condition.
Let us check the other options:
• In Option B: Cell I has $n_{\text{I}} = 1$ ($\text{Ag}^+$ to Ag and $\text{Fe}^{2+}$ to $\text{Fe}^{3+}$), and Cell II has $n_{\text{II}} = 3$ (Al to $\text{Al}^{3+}$). Here, $n_{\text{I}} \neq n_{\text{II}}$.
• In Option C: Cell I has $n_{\text{I}} = 2$, and Cell II has $n_{\text{II}} = 3$.
• In Option D: Cell I has $n_{\text{I}} = 1$ ($\text{Fe}^{2+}$ to $\text{Fe}^{3+}$ and $\text{Cu}^{2+}$ to $\text{Cu}^+$), and Cell II has $n_{\text{II}} = 2$.
itemize
Step 4: Final Answer:
Therefore, only the pair of cells in Option A satisfies the given relationship.
The question asks us to identify which pair of galvanic cells satisfies the condition that at a particular reaction quotient, both the ratio of their cell potentials ($\text{E}_{\text{I}}/\text{E}_{\text{II}}$) and the ratio of their Gibbs free energy changes ($\Delta\text{G}_{\text{I}}/\Delta\text{G}_{\text{II}}$) are exactly equal to $1/3$.
Step 2: Key Formula or Approach:
The relationship between the Gibbs free energy change ($\Delta\text{G}$) of a cell reaction and its electromotive force (EMF, E) is given by:
\[ \Delta\text{G} = -n\text{F}\text{E} \]
where $n$ is the number of moles of electrons transferred in the spontaneous cell reaction and F is Faraday's constant.
Step 3: Detailed Explanation:
• Let us express the ratio of the Gibbs free energy changes of the two cells:
\[ \frac{\Delta\text{G}_{\text{I}}}{\Delta\text{G}_{\text{II}}} = \frac{-n_{\text{I}}\text{F}\text{E}_{\text{I}}}{-n_{\text{II}}\text{F}\text{E}_{\text{II}}} = \frac{n_{\text{I}}\text{E}_{\text{I}}}{n_{\text{II}}\text{E}_{\text{II}}} \]
• We are given that at $\text{Q}_{\text{I}} = \text{Q}_{\text{II}} = \text{Q}_0$, the following ratios hold:
\[ \frac{\text{E}_{\text{I}}}{\text{E}_{\text{II}}} = \frac{1}{3} \quad \text{and} \quad \frac{\Delta\text{G}_{\text{I}}}{\Delta\text{G}_{\text{II}}} = \frac{1}{3} \]
• Substituting these values into our relation:
\[ \frac{1}{3} = \frac{n_{\text{I}}}{n_{\text{II}}} \times \frac{1}{3} \implies \frac{n_{\text{I}}}{n_{\text{II}}} = 1 \implies n_{\text{I}} = n_{\text{II}} \]
• Thus, for this condition to hold, both cell reactions must involve the transfer of the exact same number of electrons ($n_{\text{I}} = n_{\text{II}}$) when written in their balanced, spontaneous forms.
• Let us examine the cells in Option A:
itemize
• Cell I: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Ag}^+\text{(aq)}|\text{Ag(s)}$
Spontaneous reaction: $\text{Zn(s)} + 2\text{Ag}^+\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + 2\text{Ag(s)}$, which involves the transfer of $n_{\text{I}} = 2$ electrons.
• Cell II: $\text{Zn(s)}|\text{Zn}^{2+}\text{(aq)}||\text{Cu}^{2+}\text{(aq)}|\text{Cu(s)}$
Spontaneous reaction: $\text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)}$, which involves the transfer of $n_{\text{II}} = 2$ electrons.
Here, $n_{\text{I}} = n_{\text{II}} = 2$, which perfectly satisfies our condition.
Let us check the other options:
• In Option B: Cell I has $n_{\text{I}} = 1$ ($\text{Ag}^+$ to Ag and $\text{Fe}^{2+}$ to $\text{Fe}^{3+}$), and Cell II has $n_{\text{II}} = 3$ (Al to $\text{Al}^{3+}$). Here, $n_{\text{I}} \neq n_{\text{II}}$.
• In Option C: Cell I has $n_{\text{I}} = 2$, and Cell II has $n_{\text{II}} = 3$.
• In Option D: Cell I has $n_{\text{I}} = 1$ ($\text{Fe}^{2+}$ to $\text{Fe}^{3+}$ and $\text{Cu}^{2+}$ to $\text{Cu}^+$), and Cell II has $n_{\text{II}} = 2$.
itemize
Step 4: Final Answer:
Therefore, only the pair of cells in Option A satisfies the given relationship.
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