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` and what it is independent of, we can follow these steps:

### Step 1: Identify the Components of the Cell
The cell consists of two half-cells:
- Anode: `Zn | Zn^(2+)` where zinc is oxidized to zinc ions.
- Cathode: `Ag^(+) | Ag` where silver ions are reduced to solid silver.

### Step 2: Write the Half-Reactions
At the anode, the oxidation reaction is:
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^{-} \]

At the cathode, the reduction reaction is:
\[ \text{Ag}^{+} + e^{-} \rightarrow \text{Ag} \]

### Step 3: Write the Overall Cell Reaction
Combining the half-reactions, we get the overall reaction:
\[ \text{Zn} + 2\text{Ag}^{+} \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]

### Step 4: Understand the Nernst Equation
The emf (E) of the cell can be expressed using the Nernst equation:
\[ E = E^{\circ} - \frac{RT}{nF} \ln Q \]
Where:
- \( E^{\circ} \) is the standard emf of the cell.
- \( R \) is the universal gas constant.
- \( T \) is the temperature in Kelvin.
- \( n \) is the number of moles of electrons transferred (2 in this case).
- \( F \) is Faraday's constant.
- \( Q \) is the reaction quotient.

### Step 5: Analyze the Reaction Quotient (Q)
The reaction quotient \( Q \) for this reaction is given by:
\[ Q = \frac{[\text{Zn}^{2+}]}{[\text{Ag}^{+}]^2} \]
Since the concentration of solids (like Ag) does not appear in the expression for \( Q \), we can ignore it.

### Step 6: Identify What the EMF Depends On
From the Nernst equation, we see that the emf depends on:
- The concentrations of the ions involved (\( [\text{Zn}^{2+}] \) and \( [\text{Ag}^{+}] \)).
- The temperature (T).
- The number of electrons transferred (n).

### Step 7: Identify What the EMF is Independent Of
The emf of the cell is independent of the volume of the solution. Changes in volume do not affect the concentration of the ions in the solution directly, hence they do not affect the emf.

### Conclusion
The emf of the cell `Zn|Zn^(2+)|Ag^(+)|Ag` is independent of the volume of the solution.

---