An organic liquid, `A` is immiscible with water. When boiled together with water, the boiling point is `90^(@)C` which the partial vapour pressure of water is `256 mm Hg`. The superincumbent (atmospheric) pressure is `736 mm Hg`. The weight ratio of the liqid water collected `2.5:1`. What is the molecular weight of the liquid.

Answer

To solve the problem, we will use the relation between the weights of the liquid and water collected, their molecular weights, and their partial vapor pressures.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Boiling point of the mixture = \(90^\circ C\)
- Partial vapor pressure of water (\(P_w\)) = \(256 \, \text{mm Hg}\)
- Atmospheric pressure (\(P_{atm}\)) = \(736 \, \text{mm Hg}\)
- Weight ratio of liquid to water = \(2.5:1\)

2. **Calculate the Partial Vapor Pressure of the Liquid:**
The partial vapor pressure of the liquid (\(P_A\)) can be calculated using the formula:
\[ P_A = P_{atm} - P_w \]
Substituting the values:
\[ P_A = 736 \, \text{mm Hg} - 256 \, \text{mm Hg} = 480 \, \text{mm Hg} \]

3. **Set Up the Weight Ratio Equation:**
The weight ratio of the liquid (\(w_1\)) to water (\(w_2\)) is given as:
\[ \frac{w_1}{w_2} = \frac{2.5}{1} \]
Therefore, we can express \(w_1\) in terms of \(w_2\):
\[ w_1 = 2.5 \, w_2 \]

4. **Use the Formula Relating Weights and Partial Pressures:**
The relation between the weights of the liquid and water, their molecular weights (\(M_A\) for the liquid and \(M_w\) for water), and their partial pressures is given by:
\[ \frac{w_1}{w_2} = \frac{M_A \cdot P_A}{M_w \cdot P_w} \]
Substituting \(w_1\) and \(w_2\):
\[ \frac{2.5 \, w_2}{w_2} = \frac{M_A \cdot 480}{18 \cdot 256} \]
This simplifies to:
\[ 2.5 = \frac{M_A \cdot 480}{18 \cdot 256} \]

5. **Solve for the Molecular Weight of the Liquid:**
Rearranging the equation to solve for \(M_A\):
\[ M_A = \frac{2.5 \cdot 18 \cdot 256}{480} \]
Now, calculate \(M_A\):
\[ M_A = \frac{2.5 \cdot 18 \cdot 256}{480} = \frac{11520}{480} = 24 \, \text{g/mol} \]

### Final Answer:
The molecular weight of the liquid \(A\) is \(24 \, \text{g/mol}\).