Which will increase the voltage of the cell `Sn_((s))+2Ag_((aq))^(+)toSn_((aq))^(2+)+2Ag_((s))`

Options

A. Increase in the concentration of `Ag^(+)` ion
B. Increase in the concentration of `Sn^(2+)` ions
C. Increase in size of the silver rod none of these
D. None of these

Explanation

To determine which factor will increase the voltage of the electrochemical cell represented by the reaction:

\[ \text{Sn}_{(s)} + 2\text{Ag}^{+}_{(aq)} \rightarrow \text{Sn}^{2+}_{(aq)} + 2\text{Ag}_{(s)} \]

we will analyze the components of the cell and how changes in concentration affect the cell voltage.

### Step 1: Identify the half-reactions
The overall reaction can be broken down into two half-reactions:

1. **Oxidation at the anode**:
\[ \text{Sn}_{(s)} \rightarrow \text{Sn}^{2+}_{(aq)} + 2e^{-} \]
Here, tin (Sn) is oxidized, losing electrons.

2. **Reduction at the cathode**:
\[ 2\text{Ag}^{+}_{(aq)} + 2e^{-} \rightarrow 2\text{Ag}_{(s)} \]
Here, silver ions (Ag\(^+\)) are reduced, gaining electrons.

### Step 2: Write the Nernst equation
The Nernst equation relates the cell potential (E) to the concentrations of the reactants and products:

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

For our reaction:
- \( n = 2 \) (the number of moles of electrons transferred)
- The products are \([\text{Sn}^{2+}]\) and \([\text{Ag}]\), and the reactants are \([\text{Ag}^{+}]\).

### Step 3: Analyze the effect of concentration changes
To increase the cell voltage (E), we can manipulate the concentrations of the reactants and products:

1. **Increase in the concentration of Ag\(^+\)**:
- If we increase \([\text{Ag}^{+}]\), the term \(\log \left( \frac{[\text{products}]}{[\text{reactants}]} \right)\) will decrease, leading to an increase in E. This will increase the voltage of the cell.

2. **Increase in the concentration of Sn\(^2+\)**:
- If we increase \([\text{Sn}^{2+}]\), it will increase the value of the reactants in the logarithm, which will decrease E, thus reducing the voltage.

3. **Increase in the size of Sn\(^2+\)**:
- This does not affect the concentration and hence will not influence the voltage.

### Conclusion
The factor that will increase the voltage of the cell is the **increase in the concentration of Ag\(^+\)** ions.

### Final Answer:
**Increase in the concentration of Ag\(^+\) ions.**