For a silute solution containing a nonvolatile solute, the molar mass of solute evaluated from the osmotic pressure measurement is given as:

Options

A. `M_(2) = (m_(2))/(V)(RT)/(pi)`
B. `M_(2) = (m_(2))/(V)(pi)/(RT)`
C. `M_(2) = m_(2)(RT)/(pi)`
D. `M_(2) = m_(2)(pi)/(RT)`

Explanation

To derive the expression for the molar mass of a nonvolatile solute in a dilute solution using osmotic pressure measurements, we can follow these steps:

### Step-by-Step Solution

1. **Understand Osmotic Pressure**:
Osmotic pressure (\( \pi \)) is defined as the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. The formula for osmotic pressure is given by:
\[ \pi = C \cdot R \cdot T \]
where \( C \) is the concentration of the solute in moles per liter (mol/L), \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

2. **Relate Concentration to Moles**:
The concentration \( C \) can also be expressed in terms of the number of moles of solute (\( n \)) and the volume of the solution (\( V \)):
\[ C = \frac{n}{V} \]
where \( n = \frac{m}{M} \) (with \( m \) being the mass of the solute and \( M \) being the molar mass of the solute).

3. **Substituting for Moles**:
Substitute \( n \) in the osmotic pressure equation:
\[ \pi = \frac{m}{M \cdot V} \cdot R \cdot T \]

4. **Rearranging the Equation**:
To find the molar mass \( M \) of the solute, rearrange the equation:
\[ M = \frac{m \cdot R \cdot T}{\pi \cdot V} \]

5. **Final Expression**:
Thus, the expression for the molar mass of the solute evaluated from the osmotic pressure measurement is:
\[ M = \frac{m \cdot R \cdot T}{\pi \cdot V} \]