For a dilute solution containing a nonvolatile solute, the molar mass of solute evaluated from the elevation of boiling point is given by the experssion:

Options

A. `M_(2) = (DeltaT_(b))/(K_(b)) (m_(1))/(m_(2))`
B. `M_(2)=(DeltaT_(b))/(K_(b))(m_(2))/(m_(1))`
C. `M_(2) =(K_(b))/(DeltaT_(b)) (m_(2))/(m_(1))`
D. `M_(2) = (K_(b))/(DeltaT_(b)) (m_(1))/(m_(2))`

Explanation

To find the molar mass of a non-volatile solute from the elevation of boiling point, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Boiling Point Elevation**:
- The boiling point of a solution is higher than that of the pure solvent when a non-volatile solute is added. This phenomenon is known as boiling point elevation (ΔTb).

2. **Define the Boiling Point Elevation**:
- The elevation in boiling point can be expressed as:
\[ \Delta T_b = T_b - T_{b0} \]
- Where \(T_b\) is the boiling point of the solution and \(T_{b0}\) is the boiling point of the pure solvent.

3. **Use the Formula for Boiling Point Elevation**:
- The relationship between the elevation in boiling point and molality (m) of the solution is given by:
\[ \Delta T_b = K_b \cdot m \]
- Where \(K_b\) is the ebullioscopic constant of the solvent.

4. **Define Molality**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \]

5. **Express Moles of Solute**:
- If \(m_2\) is the mass of the solute and \(M_2\) is the molar mass of the solute, the number of moles of solute can be expressed as:
\[ \text{moles of solute} = \frac{m_2}{M_2} \]

6. **Substitute Molality into the Boiling Point Elevation Formula**:
- Substitute the expression for molality into the boiling point elevation formula:
\[ \Delta T_b = K_b \cdot \frac{m_2/M_2}{m_1} \]
- Here, \(m_1\) is the mass of the solvent in kg.

7. **Rearranging the Equation**:
- Rearranging the equation to solve for the molar mass \(M_2\):
\[ M_2 = \frac{K_b \cdot m_2}{\Delta T_b \cdot m_1} \]

8. **Final Expression for Molar Mass**:
- The final expression for the molar mass of the solute in terms of boiling point elevation is:
\[ M_2 = \frac{K_b}{\Delta T_b} \cdot \frac{m_2}{m_1} \]

9. **Check Against Given Options**:
- Verify which option matches the derived expression.