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 \( E_{\text{cell}}^\circ \) for the cell \( \text{Zn} | \text{Zn}^{2+} || \text{Ag}^+ | \text{Ag} \), we can use the data provided from the two other cells.

### Step-by-Step Solution:

1. **Identify the Reactions and Their Standard Potentials:**
- For the cell \( \text{Zn} | \text{Zn}^{2+} || \text{Cu}^{2+} | \text{Cu} \):
- Oxidation: \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \)
- Reduction: \( \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \)
- Standard cell potential \( E_{\text{cell}}^\circ = 1.10 \, \text{V} \)

- For the cell \( \text{Cu} | \text{Cu}^{2+} || \text{Ag}^+ | \text{Ag} \):
- Oxidation: \( \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \)
- Reduction: \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \)
- Standard cell potential \( E_{\text{cell}}^\circ = 0.46 \, \text{V} \)

2. **Write the Half-Reactions:**
- From the given data, we know:
- \( E^\circ_{\text{Cu}^{2+}/\text{Cu}} = 0.34 \, \text{V} \) (reduction potential)
- Therefore, the oxidation potential for copper is:
\[ E^\circ_{\text{Cu}/\text{Cu}^{2+}} = -0.34 \, \text{V} \]

3. **Combine the Reactions:**
- We need to find the standard cell potential for the reaction involving zinc and silver:
- The overall reaction can be derived from combining the two previous reactions:
\[ \text{Zn} + 2\text{Ag}^+ \rightarrow \text{Zn}^{2+} + 2\text{Ag} \]

4. **Calculate the Standard Cell Potential:**
- The standard cell potential for the combined reaction can be calculated by adding the potentials of the two half-reactions:
- For the zinc oxidation:
\[ E^\circ_{\text{Zn}/\text{Zn}^{2+}} = 0.76 \, \text{V} \quad (\text{from } 1.10 \, \text{V}) \]
- For the silver reduction:
\[ E^\circ_{\text{Ag}^+/\text{Ag}} = 0.80 \, \text{V} \quad (\text{from } 0.46 \, \text{V}) \]
- Therefore, the total standard cell potential is:
\[ E_{\text{cell}}^\circ = E^\circ_{\text{Zn}/\text{Zn}^{2+}} + E^\circ_{\text{Ag}^+/\text{Ag}} = 0.76 + 0.80 = 1.56 \, \text{V} \]

### Final Answer:
The standard cell potential \( E_{\text{cell}}^\circ \) for the cell \( \text{Zn} | \text{Zn}^{2+} || \text{Ag}^+ | \text{Ag} \) is \( 1.56 \, \text{V} \).

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