Which of the following condition will increase the voltage of the cell, represented by the equation-
`Cu_(s) + 2Ag_(aq)^(+) to Cu_(aq)^(2+) + 2Ag_(s)`

Options

A. Increase in the concentration of `Ag^(+)` ion
B. Increase in the concentration of `Cu^(2+)` ion
C. Increase in the dimension of silver electrode
D. Increase in the dimension of copper electrode

Explanation

To determine which condition will increase the voltage of the cell represented by the equation:

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

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

\[ E = E^\circ - \frac{0.059}{n} \log \left( \frac{[\text{Products}]}{[\text{Reactants}]} \right) \]

### Step-by-Step Solution:

1. **Identify the Components**:
- In this reaction, the products are \(\text{Cu}^{2+}\) and \(\text{Ag}_{(s)}\), while the reactants are \(\text{Cu}_{(s)}\) and \(\text{Ag}^{+}\).
- The relevant ions for the Nernst equation are \([\text{Cu}^{2+}]\) and \([\text{Ag}^{+}]\).

2. **Determine the Number of Electrons Transferred (n)**:
- In this reaction, 2 electrons are transferred, as indicated by the stoichiometry of the silver ions (\(2\text{Ag}^{+}\) being reduced to \(2\text{Ag}_{(s)}\)).
- Therefore, \(n = 2\).

3. **Write the Nernst Equation**:
- Substituting the values into the Nernst equation gives:
\[ E = E^\circ - \frac{0.059}{2} \log \left( \frac{[\text{Cu}^{2+}]}{[\text{Ag}^{+}]^2} \right) \]

4. **Analyze the Effect of Concentration Changes**:
- To increase the voltage \(E\), we need to manipulate the logarithmic term.
- If we increase the concentration of \([\text{Ag}^{+}]\), the value of \([\text{Ag}^{+}]^2\) in the denominator increases, which will decrease the overall fraction \(\frac{[\text{Cu}^{2+}]}{[\text{Ag}^{+}]^2}\) and thus decrease the logarithmic term. This will lead to an increase in the cell voltage \(E\).
- Conversely, if we increase \([\text{Cu}^{2+}]\), the fraction increases, leading to an increase in the logarithmic term, which decreases the voltage \(E\).

5. **Evaluate Other Conditions**:
- Increasing the dimensions of the silver or copper electrodes does not affect the concentration of ions in the solution and therefore does not influence the voltage.

6. **Conclusion**:
- The condition that will increase the voltage of the cell is the **increase in the concentration of \(\text{Ag}^{+}\)**.

### Final Answer:
The correct condition to increase the voltage of the cell is to **increase the concentration of \(\text{Ag}^{+}\)** ions.

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