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 find the standard EMF of the half-cell \( Y^+ // Y \) given the standard EMF of the half-cell \( Y^{2+} // Y^+ \) and the standard EMF of the full cell. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
We have:
- Standard EMF of the half-cell \( Y^{2+} // Y^+ \) is \( E_1 = 0.15 \, V \).
- Standard EMF of the full cell \( E_{cell} = 0.34 \, V \).
- We need to find the standard EMF of the half-cell \( Y^+ // Y \), denoted as \( E_2 \).

### Step 2: Write the Cell Reaction
The overall cell reaction can be represented as:
\[ Y^{2+} + 2e^- \rightarrow Y \]
This reaction involves two electrons being transferred.

### Step 3: Use the Relationship of EMFs
The standard EMF of the full cell can be expressed in terms of the EMFs of the half-cells:
\[ E_{cell} = E_1 + E_2 \]
Where:
- \( E_1 \) is the EMF of the half-cell \( Y^{2+} // Y^+ \).
- \( E_2 \) is the EMF of the half-cell \( Y^+ // Y \).

### Step 4: Substitute the Known Values
Substituting the known values into the equation:
\[ 0.34 \, V = 0.15 \, V + E_2 \]

### Step 5: Solve for \( E_2 \)
Rearranging the equation to solve for \( E_2 \):
\[ E_2 = 0.34 \, V - 0.15 \, V \]
\[ E_2 = 0.19 \, V \]

### Step 6: Conclusion
The standard EMF of the half-cell \( Y^+ // Y \) is \( 0.19 \, V \).