which of the following will increase the voltage of the cell with following cell reaction?
`Sn(s)+2Ag^(+)(aq)rarrSn^(+2)(aq)+2Ag(s)`

Options

A. Increase in the size of silver rod
B. Increase in the conc. Of `Sn^(2+)` ions
C. Increase in the concentration of `Ag^(+)` ions
D. decrease in the concentration of `Ag^(+)` ions

Explanation

To determine which option will increase the voltage of the cell for the given reaction:

**Cell Reaction:**
\[ \text{Sn(s)} + 2\text{Ag}^+(aq) \rightarrow \text{Sn}^{2+}(aq) + 2\text{Ag(s)} \]

### Step-by-Step Solution:

1. **Identify the Standard Cell Potential (E°cell):**
The standard cell potential can be calculated using the standard reduction potentials of the half-reactions involved. The half-reactions are:
- For Sn: \( \text{Sn}^{2+} + 2e^- \rightarrow \text{Sn} \) (oxidation)
- For Ag: \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \) (reduction)

The standard reduction potential for Sn is negative, while that for Ag is positive. Thus, the overall cell potential can be calculated using the formula:
\[ E°_{cell} = E°_{Ag} - E°_{Sn} \]

2. **Nernst Equation:**
The Nernst equation relates the cell potential to the concentrations of the reactants and products:
\[ E_{cell} = E°_{cell} - \frac{0.0591}{n} \log \left( \frac{[\text{Sn}^{2+}]}{[\text{Ag}^+]^2} \right) \]
where \( n \) is the number of moles of electrons transferred (which is 2 in this case).

3. **Effect of Concentration Changes:**
- **Increasing [Ag⁺]:** If the concentration of \( \text{Ag}^+ \) is increased, the term \( [\text{Ag}^+]^2 \) in the denominator of the log term will increase, leading to a decrease in the log value. This will result in an increase in \( E_{cell} \).
- **Increasing [Sn²⁺]:** If the concentration of \( \text{Sn}^{2+} \) is increased, the numerator of the log term will increase, leading to an increase in the log value, which will decrease \( E_{cell} \).
- **Decreasing Concentrations:** Decreasing either \( [Ag^+] \) or \( [Sn^{2+}] \) will lead to a decrease in \( E_{cell} \).

4. **Conclusion:**
Based on the analysis:
- Increasing the concentration of \( \text{Ag}^+ \) will increase the voltage of the cell.
- Increasing the concentration of \( \text{Sn}^{2+} \) will decrease the voltage.
- Decreasing either concentration will also decrease the voltage.

### Final Answer:
The option that will increase the voltage of the cell is **increasing the concentration of \( \text{Ag}^+ \)**.