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 `562 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.

Explanation

To find the molecular weight of the organic liquid `A`, we can use the given data and apply Raoult's Law and the concept of partial pressures. Here’s a step-by-step solution:

### Step 1: Understand the Given Data
- **Boiling point of the mixture:** 90°C
- **Partial vapor pressure of water (P_water):** 562 mm Hg
- **Atmospheric pressure (P_total):** 736 mm Hg
- **Weight ratio of liquid A to water (w_A:w_water):** 2.5:1

### Step 2: Calculate the Partial Vapor Pressure of Liquid A
Using the formula for total vapor pressure:
\[ P_{total} = P_{A} + P_{water} \]
Where:
- \( P_A \) is the partial vapor pressure of liquid A.

Rearranging gives:
\[ P_A = P_{total} - P_{water} \]
Substituting the values:
\[ P_A = 736 \, \text{mm Hg} - 562 \, \text{mm Hg} = 174 \, \text{mm Hg} \]

### Step 3: Use the Weight Ratio
Let:
- \( w_A = 2.5x \) (weight of liquid A)
- \( w_{water} = x \) (weight of water)

### Step 4: Apply Raoult's Law
According to Raoult's Law:
\[ \frac{w_A}{w_{water}} = \frac{M_A \cdot P_A}{M_{water} \cdot P_{water}} \]
Where:
- \( M_A \) is the molecular weight of liquid A.
- \( M_{water} = 18 \, \text{g/mol} \).

Substituting the known values:
\[ \frac{2.5x}{x} = \frac{M_A \cdot 174}{18 \cdot 562} \]

### Step 5: Simplify the Equation
This simplifies to:
\[ 2.5 = \frac{M_A \cdot 174}{18 \cdot 562} \]

### Step 6: Rearranging to Find Molecular Weight
Rearranging gives:
\[ M_A = 2.5 \cdot \frac{18 \cdot 562}{174} \]

### Step 7: Calculate the Molecular Weight
Now, calculate \( M_A \):
1. Calculate \( 18 \cdot 562 = 10116 \).
2. Divide by 174: \( \frac{10116}{174} \approx 58.2 \).
3. Multiply by 2.5: \( 2.5 \cdot 58.2 \approx 145.5 \).

Thus, the molecular weight of liquid A is approximately:
\[ M_A \approx 145.5 \, \text{g/mol} \]

### Final Answer
The molecular weight of the organic liquid A is approximately **145.5 g/mol**.

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