Find out the `E_("cell")^(@)` from the given data
(a) `Zn|Zn^(+2)|| Cu^(+2)| Cu, E_("cell")^(@) = 1.10V`
(b) `Cu| Cu^(+2)|| Ag^(+)|Ag, E_("cell")^(@) = 0.46V`
( c) `Zn|Zn^(+2)||Ag^(+) | Ag, E_("cell")^(@) = ?`
(Given `E_(Cu^(+2)//Cu)^(@) = 0.34V`)

Options

A. `-0.04V`
B. `+0.04V`
C. `+0.30V`
D. `+1.56V`

Answer

To find the standard cell potential \( E^\circ_{\text{cell}} \) for the cell reaction \( \text{Zn} | \text{Zn}^{2+} || \text{Ag}^+ | \text{Ag} \), we will use the provided data from the other two cell reactions.

### Step-by-Step Solution:

1. **Identify the Reactions:**
- For reaction (a):
\[ \text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu}, \quad E^\circ_{\text{cell}} = 1.10 \, \text{V} \]
- For reaction (b):
\[ \text{Cu} + \text{Ag}^+ \rightarrow \text{Cu}^{2+} + 2\text{Ag}, \quad E^\circ_{\text{cell}} = 0.46 \, \text{V} \]

2. **Write the Standard Reduction Potentials:**
- Given:
\[ E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \]
- For the reaction (b), we can deduce:
\[ E^\circ_{\text{Ag}^+/\text{Ag}} = E^\circ_{\text{Cu}^{2+}/\text{Cu}} - E^\circ_{\text{cell}} = 0.34 \, \text{V} - 0.46 \, \text{V} = -0.12 \, \text{V} \]

3. **Combine Reactions:**
- The overall reaction for (c) can be obtained by combining reactions (a) and (b):
\[ \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]

4. **Calculate \( E^\circ_{\text{cell}} \) for the Combined Reaction:**
- Since the overall cell potential is the sum of the potentials of the individual half-reactions:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{Zn}^{2+}/\text{Zn}} + E^\circ_{\text{Ag}^+/\text{Ag}} \]
- From reaction (a), we know:
\[ E^\circ_{\text{Zn}^{2+}/\text{Zn}} = 1.10 \, \text{V} \]
- From our earlier calculation, we have:
\[ E^\circ_{\text{Ag}^+/\text{Ag}} = 0.80 \, \text{V} \]
- Therefore:
\[ E^\circ_{\text{cell}} = 1.10 \, \text{V} + 0.80 \, \text{V} = 1.56 \, \text{V} \]

5. **Final Answer:**
\[ E^\circ_{\text{cell}} = 1.56 \, \text{V} \]