`Y g` of non-volatile organic substance of molecular mass `M` is dissolved in `250 g` benzene. Molal elevation constant of benzene is `K_(b)`. Elevation in its boiling point is given by:s

Options

A. `(M)/(K_(b)Y)`
B. `(4K_(b)Y)/(M)`
C. `(K_(b)Y)/(4M)`
D. `(K_(b)Y)/(M)`

Answer

To solve the problem of calculating the elevation in boiling point when a non-volatile organic substance is dissolved in benzene, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Elevation in Boiling Point:**
The elevation in boiling point (\( \Delta T_b \)) is given by the formula:
\[ \Delta T_b = K_b \times \text{molality} \]
where \( K_b \) is the molal elevation constant of the solvent (benzene in this case).

2. **Define Molality:**
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:
\[ \text{molality} = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]

3. **Calculate the Number of Moles of Solute:**
The number of moles of the solute can be calculated using the formula:
\[ \text{number of moles} = \frac{\text{mass of solute (Y g)}}{\text{molar mass (M g/mol)}} \]
Therefore, the number of moles of the solute is:
\[ \text{number of moles} = \frac{Y}{M} \]

4. **Convert the Mass of Solvent to Kilograms:**
The mass of benzene is given as 250 g. To convert this to kilograms:
\[ \text{mass of solvent} = 250 \, \text{g} = 0.250 \, \text{kg} \]

5. **Calculate Molality:**
Now, substituting the number of moles and the mass of solvent into the molality formula:
\[ \text{molality} = \frac{\frac{Y}{M}}{0.250} = \frac{Y}{M \times 0.250} = \frac{Y}{0.250M} \]
Simplifying:
\[ \text{molality} = \frac{Y}{0.250M} = \frac{4Y}{M} \]

6. **Substitute Molality into the Elevation Formula:**
Now substituting the molality back into the elevation in boiling point formula:
\[ \Delta T_b = K_b \times \text{molality} = K_b \times \frac{4Y}{M} \]
Therefore, the elevation in boiling point is:
\[ \Delta T_b = \frac{4K_bY}{M} \]

### Final Answer:
The elevation in boiling point is given by:
\[ \Delta T_b = \frac{4K_bY}{M} \]