If standard emf `(E^(@))` of a half -cell `Y^(2+)//Y^(+)` is 0.15 V, the standard emf of the half cell `Y^(+)//Y` will be ? Given that the standard emf of cell of full cell is 0.34V.

Options

A. `0.19V`
B. `0.53V`
C. `0.49V`
D. `0.64V`

Explanation

To solve the problem, we need to determine the standard EMF of the half-cell \( Y^{+} // Y \) given the standard EMF of the half-cell \( Y^{2+} // Y^{+} \) is 0.15 V and the standard EMF of the full cell is 0.34 V.

### Step-by-Step Solution:

1. **Identify the Half-Cells:**
- We have two half-cells:
- Half-cell 1: \( Y^{2+} + 2e^- \leftrightarrow Y^{+} \) with \( E^\circ_1 = 0.15 \, \text{V} \)
- Half-cell 2: \( Y^{+} + e^- \leftrightarrow Y \) (we need to find \( E^\circ_2 \))

2. **Write the Full Cell Reaction:**
- The overall cell reaction can be represented as:
\[ Y^{2+} + 2e^- \rightarrow Y^{+} \quad (E^\circ_1 = 0.15 \, \text{V}) \]
\[ Y^{+} + e^- \rightarrow Y \quad (E^\circ_2 \, \text{unknown}) \]
- The total cell reaction is:
\[ Y^{2+} + 2e^- \rightarrow Y \quad (E^\circ_{\text{cell}} = 0.34 \, \text{V}) \]

3. **Use the Relationship Between Cell EMF and Half-Cell EMFs:**
- The standard EMF of the full cell is given by the equation:
\[ E^\circ_{\text{cell}} = E^\circ_1 - E^\circ_2 \]
- Rearranging gives:
\[ E^\circ_2 = E^\circ_1 - E^\circ_{\text{cell}} \]

4. **Substituting the Known Values:**
- Substitute \( E^\circ_1 = 0.15 \, \text{V} \) and \( E^\circ_{\text{cell}} = 0.34 \, \text{V} \):
\[ E^\circ_2 = 0.15 \, \text{V} - 0.34 \, \text{V} \]
\[ E^\circ_2 = -0.19 \, \text{V} \]

5. **Conclusion:**
- The standard EMF of the half-cell \( Y^{+} // Y \) is \( -0.19 \, \text{V} \).

### Final Answer:
The standard EMF of the half-cell \( Y^{+} // Y \) is \( -0.19 \, \text{V} \).