At a constant temperature liquid `'A'` has vapour pressure of `170 mm Hg` and liquid `'B'` has vapour pressure of `280 mm Hg`. A solution of the two at the same temperature in which mole fraction of `A` is `0.7` has a total vapour pressure of `376 mm`. Identify whether the solution process is Endothermic or Exothermic ?

Explanation

To determine whether the solution process of liquids A and B is endothermic or exothermic, we can follow these steps:

### Step 1: Identify the given data
- Vapor pressure of pure liquid A, \( P^0_A = 170 \, \text{mm Hg} \)
- Vapor pressure of pure liquid B, \( P^0_B = 280 \, \text{mm Hg} \)
- Mole fraction of A in the solution, \( X_A = 0.7 \)
- Mole fraction of B in the solution, \( X_B = 1 - X_A = 0.3 \)
- Total vapor pressure of the solution, \( P_{\text{total}} = 376 \, \text{mm Hg} \)

### Step 2: Apply Raoult's Law
According to Raoult's Law, the total vapor pressure of the solution can be calculated as:
\[ P_{\text{total}} = P^0_A \cdot X_A + P^0_B \cdot X_B \]

### Step 3: Substitute the values into the equation
Substituting the known values:
\[ P_{\text{total}} = (170 \, \text{mm Hg} \cdot 0.7) + (280 \, \text{mm Hg} \cdot 0.3) \]

### Step 4: Calculate the individual contributions
Calculating each term:
- Contribution from A: \( 170 \cdot 0.7 = 119 \, \text{mm Hg} \)
- Contribution from B: \( 280 \cdot 0.3 = 84 \, \text{mm Hg} \)

### Step 5: Add the contributions to find the theoretical total pressure
Now, add these contributions:
\[ P_{\text{total}} = 119 \, \text{mm Hg} + 84 \, \text{mm Hg} = 203 \, \text{mm Hg} \]

### Step 6: Compare the calculated total pressure with the experimental total pressure
- Theoretical total pressure (from Raoult's Law) = 203 mm Hg
- Experimental total pressure = 376 mm Hg

### Step 7: Analyze the deviation
Since the experimental total pressure (376 mm Hg) is greater than the theoretical total pressure (203 mm Hg), this indicates a positive deviation from Raoult's Law.

### Step 8: Determine the nature of the solution process
In the case of positive deviation from Raoult's Law, it is known that:
- \( \Delta H > 0 \) (the enthalpy change is positive)
- This indicates that the solution process is endothermic.

### Conclusion
Thus, the solution process is **endothermic**.

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