The potential of the following cell is 0.34 V at `25^(@)C` calculate the standard reduction potential of the copper half cell
`Pt|H_(2)(1 atm)| H^(+)(1 M)||Cu^(2+)(1 M)|Cu`

Options

A. `-3.4 V`
B. `+3.4 V`
C. `-0.34 V`
D. `+0.34 V`

Explanation

To calculate the standard reduction potential of the copper half-cell in the given electrochemical cell, we can follow these steps:

### Step 1: Identify the components of the cell
The cell is represented as:
\[ \text{Pt} | \text{H}_2 (1 \text{ atm}) | \text{H}^+ (1 \text{ M}) || \text{Cu}^{2+} (1 \text{ M}) | \text{Cu} \]

Here, the left side (anode) is the hydrogen half-cell, and the right side (cathode) is the copper half-cell.

### Step 2: Understand the cell potential
The overall cell potential (\(E_{\text{cell}}\)) is given as 0.34 V at standard conditions (1 M concentration for ions and 1 atm pressure for gases).

### Step 3: Write the formula for cell potential
The cell potential can be expressed using the standard reduction potentials of the cathode and anode:
\[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \]

### Step 4: Identify the anode and cathode
- **Anode (oxidation)**: Hydrogen half-cell, where the standard reduction potential (\(E_{\text{anode}}\)) for the hydrogen electrode is defined as 0 V.
- **Cathode (reduction)**: Copper half-cell, where we need to find the standard reduction potential (\(E_{\text{cathode}}\)).

### Step 5: Substitute known values into the equation
Substituting the known values into the equation:
\[ 0.34 \, \text{V} = E_{\text{copper}} - 0 \, \text{V} \]

### Step 6: Solve for the standard reduction potential of copper
From the equation:
\[ E_{\text{copper}} = 0.34 \, \text{V} \]

### Conclusion
The standard reduction potential of the copper half-cell is:
\[ E_{\text{copper}} = 0.34 \, \text{V} \]

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