A solution contains non-volatile solute of molecular mass`M_(2)`which of the following can be used to calculate the molecular mass of solute in terms of osmotic pressure?
(`m_(2)` =mass of solute,V=volume of solution,`pi` =osmotic pressure)

Options

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

Explanation

To calculate the molecular mass of a non-volatile solute in terms of osmotic pressure, we can use the formula for osmotic pressure, which is given by:

\[ \pi = CRT \]

Where:
- \(\pi\) = osmotic pressure
- \(C\) = concentration of the solution (in moles per liter)
- \(R\) = gas constant
- \(T\) = temperature in Kelvin

### Step 1: Express Concentration in Terms of Moles and Volume
The concentration \(C\) can be expressed in terms of the mass of the solute and its molecular mass:

\[ C = \frac{\text{moles of solute}}{\text{volume of solution}} = \frac{\frac{m_2}{M_2}}{V} \]

Where:
- \(m_2\) = mass of the solute
- \(M_2\) = molecular mass of the solute
- \(V\) = volume of the solution

### Step 2: Substitute Concentration into the Osmotic Pressure Formula
Substituting the expression for concentration \(C\) into the osmotic pressure formula:

\[ \pi = \left(\frac{m_2}{M_2 V}\right)RT \]

### Step 3: Rearranging the Equation to Solve for Molecular Mass
Rearranging the equation to solve for the molecular mass \(M_2\):

\[ \pi = \frac{m_2 RT}{M_2 V} \]

Multiplying both sides by \(M_2 V\):

\[ \pi M_2 V = m_2 RT \]

Now, isolating \(M_2\):

\[ M_2 = \frac{m_2 RT}{\pi V} \]

### Conclusion
Thus, the molecular mass \(M_2\) of the solute can be calculated using the formula:

\[ M_2 = \frac{m_2 RT}{\pi V} \]