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 potential (E_cell). The cell potential can be calculated using the Nernst equation:

\[ E_{cell} = E^{\circ}_{cell} - \frac{0.0591}{n} \log Q \]

where:
- \( E^{\circ}_{cell} \) is the standard cell potential,
- \( n \) is the number of moles of electrons transferred in the reaction,
- \( Q \) is the reaction quotient.

### Step-by-Step Solution:

1. **Identify the Reaction Quotient (Q)**:
The reaction quotient \( Q \) for the given reaction is defined as:
\[ Q = \frac{[\text{Cu}^{2+}]}{[\text{Ag}^+]^2} \]
Here, \( [\text{Cu}^{2+}] \) is the concentration of copper ions, and \( [\text{Ag}^+] \) is the concentration of silver ions.

2. **Analyze the Effect of Concentrations**:
- Increasing the concentration of \( \text{Cu}^{2+} \) will increase \( Q \), which will increase the value of \( \log Q \). Since \( E_{cell} \) has a negative sign in front of the log term, this will decrease \( E_{cell} \).
- Increasing the concentration of \( \text{Ag}^+ \) will decrease \( Q \) (since \( [\text{Ag}^+] \) is in the denominator squared). This will decrease the value of \( \log Q \), thus increasing \( E_{cell} \).

3. **Consider the Dimensions of Electrodes**:
The dimensions of the electrodes do not affect the voltage of the cell directly. The voltage is dependent on the concentrations of the reactants and products in the Nernst equation.

4. **Conclusion**:
To increase the voltage of the cell, we should increase the concentration of \( \text{Ag}^+ \). This will decrease the value of \( \log Q \) and consequently increase \( E_{cell} \).

### Final Answer:
Increasing the concentration of \( \text{Ag}^+ \) will increase the voltage of the cell.

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