Which one of the following will increase the voltage of the cell ? `(T = 298 K)`
` Sn+ 2Ag^+ rarr Sn^(2+) +2 Ag`.

Options

A. increases in the size of silver rod
B. increases in the concentration of `Sn^(+2)` ions
C. increases in the concentration of `Ag^(+)` ions
D. none of the above

Explanation

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

\[ \text{Sn} + 2 \text{Ag}^+ \rightarrow \text{Sn}^{2+} + 2 \text{Ag} \]

we will use the Nernst equation, which is given by:

\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log \left( \frac{[\text{products}]}{[\text{reactants}]} \right) \]

where:
- \( E_{\text{cell}} \) is the cell potential,
- \( E^\circ_{\text{cell}} \) is the standard cell potential,
- \( n \) is the number of moles of electrons transferred in the reaction,
- \([\text{products}]\) and \([\text{reactants}]\) are the concentrations of the products and reactants, respectively.

### Step 1: Identify the number of electrons transferred
In the given reaction, Sn is oxidized to Sn²⁺ and 2 Ag⁺ ions are reduced to Ag. Therefore, the number of electrons transferred \( n \) is 2.

### Step 2: Write the Nernst equation
Using the Nernst equation:

\[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{2} \log \left( \frac{[\text{Sn}^{2+}]}{[\text{Ag}^+]^2} \right) \]

### Step 3: Analyze the effect of changing concentrations
- **Option A: Increase in the size of the silver rod** - This does not affect the concentration of Ag⁺ ions in the solution, hence it will not change the voltage.

- **Option B: Increase in the concentration of Sn²⁺ ions** - If we increase \([\text{Sn}^{2+}]\), the fraction \(\frac{[\text{Sn}^{2+}]}{[\text{Ag}^+]^2}\) will increase, leading to an increase in the logarithm value. This will decrease \( E_{\text{cell}} \) since it is subtracted from \( E^\circ_{\text{cell}} \).

- **Option C: Increase in the concentration of Ag⁺ ions** - If we increase \([\text{Ag}^+]\), the denominator \([\text{Ag}^+]^2\) increases, which decreases the fraction \(\frac{[\text{Sn}^{2+}]}{[\text{Ag}^+]^2}\). This leads to a decrease in the logarithm value, which in turn increases \( E_{\text{cell}} \) since it is subtracted from \( E^\circ_{\text{cell}} \).

### Conclusion
The correct answer is **Option C: Increase in the concentration of Ag⁺ ions**, as this will increase the voltage of the cell.

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