The emf of the cell, `Zn|Zn^(2+)|Ag^(+)|Ag` is independent of

Options

A. The volume of `Zn^(2+) and Ag^(+)` solution
B. The molarity of `Zn^(2oplus)` ions in solution
C. The molarity of `Ag^(+)` ions in solution
D. Temperature

Answer

To solve the question regarding the emf of the cell `Zn|Zn^(2+)|Ag^(+)|Ag`, we will analyze the components of the cell and the factors affecting its emf (electromotive force).

### Step-by-Step Solution:

1. **Identify the Components of the Cell**:
- The left side of the cell notation represents the anode, which is zinc (Zn), and the right side represents the cathode, which is silver (Ag).
- The half-reactions are:
- At the anode: \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \)
- At the cathode: \( \text{Ag}^{+} + e^- \rightarrow \text{Ag} \)

2. **Write the Overall Cell Reaction**:
- To balance the electrons, we multiply the silver half-reaction by 2:
- Overall reaction:
\[ \text{Zn} + 2 \text{Ag}^{+} \rightarrow \text{Zn}^{2+} + 2 \text{Ag} \]

3. **Understanding the Nernst Equation**:
- The Nernst equation relates the emf of the cell to the concentrations of the reactants and products:
\[ E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{RT}{nF} \ln Q \]
- Where \( Q \) is the reaction quotient, \( n \) is the number of electrons transferred, \( R \) is the gas constant, \( T \) is the temperature, and \( F \) is Faraday's constant.

4. **Determine the Reaction Quotient (Q)**:
- For the given reaction, the reaction quotient \( Q \) is:
\[ Q = \frac{[\text{Zn}^{2+}]}{[\text{Ag}^{+}]^2} \]
- Since solid zinc and solid silver do not appear in the expression for \( Q \) (they are pure solids), their concentrations are considered constant (equal to 1).

5. **Factors Affecting the emf**:
- The emf of the cell depends on:
- The concentration of \( \text{Zn}^{2+} \) ions.
- The concentration of \( \text{Ag}^{+} \) ions.
- The temperature \( T \).
- The emf does **not** depend on the volume of the solutions, as long as the concentrations remain constant.

6. **Conclusion**:
- Therefore, the emf of the cell is independent of the volume of \( \text{Zn}^{2+} \) and \( \text{Ag}^{+} \) ions.

### Final Answer:
The emf of the cell `Zn|Zn^(2+)|Ag^(+)|Ag` is independent of the volume of \( \text{Zn}^{2+} \) and \( \text{Ag}^{+} \) ions.