For a cell given below:
`Ag|Ag^(+)||Cu^(2+)|Cu`
`Ag^(+)+e^(-)toAg,E^(@)=x`
`Cu^(2+)+2e^(-)toCu,,E^(@)=y` ltbr. The value of `E_(cell)^(@)` is

Options

A. `x+2y`
B. `2x+y`
C. `y-x`
D. `y-2x`

Explanation

To solve the problem, we need to determine the standard cell potential \( E_{\text{cell}}^{\circ} \) for the electrochemical cell given by the half-reactions:

1. \( \text{Ag}^+ + e^- \rightarrow \text{Ag}, \quad E^{\circ} = x \)
2. \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}, \quad E^{\circ} = y \)

### Step-by-Step Solution:

**Step 1: Identify the Anode and Cathode**
- In the given cell notation \( \text{Ag} | \text{Ag}^+ || \text{Cu}^{2+} | \text{Cu} \), the left side represents the anode and the right side represents the cathode.
- The anode is where oxidation occurs, and the cathode is where reduction occurs.

**Step 2: Determine the Half-Reactions**
- At the anode (oxidation):
\[ \text{Ag} \rightarrow \text{Ag}^+ + e^- \]
The standard reduction potential for this reaction is \( x \), but since it is oxidation, we take it as \( -x \).

- At the cathode (reduction):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]
The standard reduction potential for this reaction is \( y \).

**Step 3: Write the Cell Potential Formula**
- The standard cell potential \( E_{\text{cell}}^{\circ} \) can be calculated using the formula:
\[ E_{\text{cell}}^{\circ} = E_{\text{cathode}}^{\circ} - E_{\text{anode}}^{\circ} \]

**Step 4: Substitute the Values**
- Substitute the values of the potentials into the formula:
\[ E_{\text{cell}}^{\circ} = y - (-x) = y + x \]

**Step 5: Final Result**
- Therefore, the value of \( E_{\text{cell}}^{\circ} \) is:
\[ E_{\text{cell}}^{\circ} = y + x \]