Which of the following colligative properties of colloidal solutions is used to determine the molecular mass?

Options

A. Relative lowering of vapour pressure
B. Elevation in boiling point
C. Depression in freezing point
D. Osmotic pressure

Answer

To determine the molecular mass of a colloidal solution using colligative properties, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Colligative Properties**:
The four colligative properties are:
- Relative lowering of vapor pressure
- Elevation in boiling point
- Depression in freezing point
- Osmotic pressure

2. **Determine the Relevant Property**:
Among these properties, osmotic pressure is the only one that can be used to determine the molecular mass of the dispersed phase in a colloidal solution.

3. **Apply the Formula for Osmotic Pressure**:
The formula for osmotic pressure (π) is given by:
\[ \pi = CRT \]
where:
- \(C\) = concentration of the solution in moles per liter (mol/L)
- \(R\) = universal gas constant
- \(T\) = temperature in Kelvin

4. **Relate Concentration to Moles**:
The concentration \(C\) can be expressed in terms of the number of moles \(n\) and the volume \(V\) of the solution:
\[ C = \frac{n}{V} \]

5. **Express Moles in Terms of Mass**:
The number of moles \(n\) can be expressed as:
\[ n = \frac{W_2}{M_2} \]
where:
- \(W_2\) = mass of the solute (dispersed phase)
- \(M_2\) = molar mass of the solute

6. **Substitute into the Osmotic Pressure Formula**:
Substituting \(C\) into the osmotic pressure equation gives:
\[ \pi = \left(\frac{W_2}{M_2 V}\right)RT \]

7. **Rearrange to Solve for Molar Mass**:
Rearranging the equation to solve for \(M_2\) (molar mass) yields:
\[ M_2 = \frac{W_2RT}{\pi V} \]

8. **Conclusion**:
Thus, the molecular mass of the dispersed phase in a colloidal solution can be determined using osmotic pressure. Therefore, the correct answer is:
**Osmotic Pressure (Option 4)**.