The pressure of two pure liquid A and B which form an ideal solutions are 400 mm Hg and 800 mm Hg respectively at temperature T.A liquid containing 3:1 molar composition pressure can be varied.The solutions is slowly vapourized at temperature T by decreasing the applied pressure starting with a pressure of 760 mm Hg.A pressure gauge (in mm) Hg is connected which give the reading of pressure applied.
The reading of pressure Gauge at bubble point is

Options

A. 500
B. 600
C. 700
D. None

Explanation

To solve the problem, we need to determine the pressure gauge reading at the bubble point of a solution containing two liquids A and B that form an ideal solution. Here are the steps to arrive at the solution:

### Step-by-Step Solution:

1. **Identify Given Data:**
- Vapor pressure of pure liquid A, \( P^0_A = 400 \, \text{mm Hg} \)
- Vapor pressure of pure liquid B, \( P^0_B = 800 \, \text{mm Hg} \)
- Molar composition of the solution: \( n_A : n_B = 3 : 1 \)

2. **Calculate Mole Fractions:**
- The total moles in the solution can be expressed as \( n_A + n_B = 3 + 1 = 4 \).
- Mole fraction of A, \( x_A = \frac{n_A}{n_A + n_B} = \frac{3}{4} = 0.75 \).
- Mole fraction of B, \( x_B = \frac{n_B}{n_A + n_B} = \frac{1}{4} = 0.25 \).

3. **Apply Raoult's Law:**
- According to Raoult's Law, the total vapor pressure \( P \) of the solution can be calculated using:
\[ P = P^0_A \cdot x_A + P^0_B \cdot x_B \]
- Substituting the values:
\[ P = (400 \, \text{mm Hg} \cdot 0.75) + (800 \, \text{mm Hg} \cdot 0.25) \]

4. **Calculate Total Pressure:**
- Calculate each term:
\[ P = 300 \, \text{mm Hg} + 200 \, \text{mm Hg} = 500 \, \text{mm Hg} \]

5. **Determine the Bubble Point Pressure:**
- The bubble point is the pressure at which the first bubble of vapor forms. This occurs at the total vapor pressure calculated above.
- Therefore, the reading of the pressure gauge at the bubble point is:
\[ \text{Pressure at bubble point} = 500 \, \text{mm Hg} \]

### Final Answer:
The reading of the pressure gauge at the bubble point is **500 mm Hg**.