Which of the following colligative property can provide molar mass of proteins (or polymers or colloids) with greatest precision?

Options

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

Explanation

To determine which colligative property can provide the molar mass of proteins (or polymers or colloids) with the greatest precision, we can analyze each of the colligative properties mentioned in the question: osmotic pressure, elevation in boiling point, depression in freezing point, and relative lowering of vapor pressure.

### Step-by-Step Solution:

1. **Understand Colligative Properties**:
- Colligative properties depend on the number of solute particles in a solution, not on the identity of the solute. The main colligative properties are:
- Osmotic pressure
- Elevation in boiling point
- Depression in freezing point
- Relative lowering of vapor pressure

2. **Analyze Each Property**:
- **Osmotic Pressure (π)**: The formula for osmotic pressure is given by:
\[ \pi = iCRT \]
where \(i\) is the van 't Hoff factor, \(C\) is the molar concentration, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. This property can provide very precise measurements as it can yield values up to four significant figures.

- **Elevation in Boiling Point (ΔTb)**: The formula is:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where \(K_b\) is the ebullioscopic constant and \(m\) is the molality. This method can give a good estimate but is less precise compared to osmotic pressure.

- **Depression in Freezing Point (ΔTf)**: The formula is:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where \(K_f\) is the cryoscopic constant. Similar to boiling point elevation, it provides reasonable estimates but lacks the precision of osmotic pressure.

- **Relative Lowering of Vapor Pressure (ΔP)**: The formula is:
\[ \Delta P = P_0 - P = \frac{n_a}{n_a + n_b} P_0 \]
where \(P_0\) is the vapor pressure of the pure solvent, and \(n_a\) and \(n_b\) are the number of moles of solute and solvent, respectively. This method also provides less precision than osmotic pressure.

3. **Conclusion**:
- Among the four colligative properties, osmotic pressure provides the greatest precision for determining the molar mass of proteins, polymers, or colloids. This is due to its ability to yield results with up to four significant figures, making it a reliable method for precise measurements.

### Final Answer:
**Osmotic Pressure** is the colligative property that can provide the molar mass of proteins (or polymers or colloids) with the greatest precision.