The standard potential `E^(@)` for the half reactions are as `:`
`Zn rarr Zn^(2+) + 2e^(-), E^(@) = 0.76V`
`Cu rarr Cu^(2+) +2e^(-) , E^(@) = -0.34 V `
The standard cell voltage for the cell reaction is ?
`Zn +Cu^(2) rarr Zn ^(2+) +Cu`

Options

A. 0.42V
B. `-0.42 v `
C. `-1.1V`
D. 1.10V

Answer

To find the standard cell voltage for the reaction \( \text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu} \), we can follow these steps:

### Step 1: Identify the half-reactions
The given half-reactions are:
1. **Zinc oxidation**:
\[ \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^{-} \]
The standard reduction potential \( E^\circ \) for this half-reaction is \( +0.76 \, \text{V} \).

2. **Copper reduction**:
\[ \text{Cu}^{2+} + 2e^{-} \rightarrow \text{Cu} \]
The standard reduction potential \( E^\circ \) for this half-reaction is \( -0.34 \, \text{V} \).

### Step 2: Determine the anode and cathode
- In this cell reaction, zinc is oxidized (loses electrons) and acts as the anode.
- Copper is reduced (gains electrons) and acts as the cathode.

### Step 3: Write the standard cell potential formula
The standard cell potential \( E^\circ_{\text{cell}} \) can be calculated using the formula:
\[ E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \]

### Step 4: Substitute the values
From the half-reactions:
- The standard reduction potential for the cathode (copper) is \( -0.34 \, \text{V} \).
- The standard reduction potential for the anode (zinc) is \( +0.76 \, \text{V} \).

Now substituting these values into the formula:
\[ E^\circ_{\text{cell}} = (-0.34 \, \text{V}) - (0.76 \, \text{V}) \]

### Step 5: Calculate the cell potential
\[ E^\circ_{\text{cell}} = -0.34 \, \text{V} - 0.76 \, \text{V} = -1.10 \, \text{V} \]

### Step 6: Final result
The standard cell voltage for the cell reaction is:
\[ E^\circ_{\text{cell}} = 1.10 \, \text{V} \]