The magnitude `(` but not the sign `)` of the standard reduction potentials of two metals `X` and `Y` are `:`
`Y^(2)+2e^(-) rarr Y |E_(1)^(c-)|=0.34V`
`X^(2)+2e^(-) rarr X |E_(2)^(c-)|=0.25V`
When the two half cells of `X` and `Y `are connected to construct a cell, electrons flow from `X` to `Y`. When `X` is connected to a standard hydrogen electrode `(SHE)`,electrons flow from `X` to `SHE`.
If standard emf `(E^(c-))` of a half cell `Y^(2)|Y^(o+)` is `0.15V`, the standard emf of the half cell `Y^(o+)|Y` will be
(a)`0.19V`
(b)`0.53V`
(c)`0.49V`
(d)`0.64V`

Options

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

Explanation

To solve the problem, we need to find the standard emf of the half-cell reaction \( Y^+ \leftrightarrow Y \) given the standard emf for the half-cell reaction \( Y^{2+} + 2e^- \leftrightarrow Y \) is \( 0.34 \, V \) and the standard emf for the half-cell reaction \( Y^{2+} + e^- \leftrightarrow Y^+ \) is \( 0.15 \, V \).

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Standard reduction potential for \( Y^{2+} + 2e^- \leftrightarrow Y \) is \( E_1 = 0.34 \, V \).
- Standard reduction potential for \( Y^{2+} + e^- \leftrightarrow Y^+ \) is \( E_2 = 0.15 \, V \).

2. **Write the Half-Reactions**:
- For the first half-reaction:
\[ Y^{2+} + 2e^- \leftrightarrow Y \quad (E_1 = 0.34 \, V) \]
- For the second half-reaction:
\[ Y^{2+} + e^- \leftrightarrow Y^+ \quad (E_2 = 0.15 \, V) \]

3. **Determine the Required Half-Reaction**:
- We need to find the standard reduction potential for the half-reaction:
\[ Y^+ + e^- \leftrightarrow Y \]
- Let's denote the standard reduction potential for this half-reaction as \( E_3 \).

4. **Relate the Potentials**:
- The relationship between the potentials can be established using the following:
\[ E_1 = E_2 + E_3 \]
- Rearranging gives:
\[ E_3 = E_1 - E_2 \]

5. **Substituting the Values**:
- Substitute the known values into the equation:
\[ E_3 = 0.34 \, V - 0.15 \, V \]
- Calculate \( E_3 \):
\[ E_3 = 0.34 \, V - 0.15 \, V = 0.19 \, V \]

6. **Conclusion**:
- The standard emf of the half-cell reaction \( Y^+ \leftrightarrow Y \) is \( 0.19 \, V \).

### Final Answer:
The standard emf of the half-cell \( Y^+ \leftrightarrow Y \) is \( 0.19 \, V \).