Which one of the following condition will increase the voltage of the cell represented by the equation?
`Cu(s) + 2Ag ^(+) (aq)` `(Cu^(2+)(aq) + 2Aq(s)`

Options

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

Explanation

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

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

we need to analyze the factors that affect the cell voltage (E_cell).

### Step-by-Step Solution:

1. **Understand the Cell Reaction**:
The given cell reaction involves copper (Cu) being oxidized to copper ions (Cu²⁺) and silver ions (Ag⁺) being reduced to silver (Ag).

2. **Identify the Standard Cell Potential (E°)**:
The standard cell potential (E°) is determined by the half-reactions involved. The overall cell potential can be expressed as:
\[ E_{cell} = E_{cell}^0 - \frac{0.0591}{n} \log Q \]
where \( n \) is the number of moles of electrons transferred (which is 2 in this case), and \( Q \) is the reaction quotient.

3. **Determine the Reaction Quotient (Q)**:
For the given reaction, the reaction quotient \( Q \) is given by:
\[ Q = \frac{[\text{Cu}^{2+}]}{[\text{Ag}^+]^2} \]

4. **Analyze the Effect of Concentration**:
- **Increasing the Concentration of Cu²⁺**: If we increase the concentration of Cu²⁺, \( Q \) increases, leading to a higher value in the log term, which decreases \( E_{cell} \).
- **Increasing the Concentration of Ag⁺**: If we increase the concentration of Ag⁺, \( Q \) decreases, leading to a lower value in the log term, which increases \( E_{cell} \).

5. **Conclusion**:
The condition that will increase the voltage of the cell is:
- **Increase in concentration of Ag⁺ ions**.

### Final Answer:
The condition that will increase the voltage of the cell is **increasing the concentration of Ag⁺ ions**.

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