The vapour pressure of the solution of two liquids A`(P^@=80mm)`and B`(P^@=120mm)`is found to `100mm` when `x_(A)=0.4` .The
result shows that

Options

A. solution exhibits ideal behaviour
B. solution shows positive deviations
C. solution shows negative deviations
D. solution will show postive deviations for lower concentration and negative deviations for higher concentrations.

Answer

To solve the problem, we will use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial pressures of each component in the solution. The partial pressure of each component can be calculated using the formula:

\[ P_{total} = P^0_A \cdot x_A + P^0_B \cdot x_B \]

Where:
- \( P_{total} \) is the total vapor pressure of the solution.
- \( P^0_A \) and \( P^0_B \) are the vapor pressures of pure components A and B, respectively.
- \( x_A \) and \( x_B \) are the mole fractions of components A and B in the solution.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- \( P^0_A = 80 \, \text{mmHg} \)
- \( P^0_B = 120 \, \text{mmHg} \)
- \( P_{total} = 100 \, \text{mmHg} \)
- \( x_A = 0.4 \)

2. **Calculate the Mole Fraction of Component B:**
- Since \( x_A + x_B = 1 \), we can find \( x_B \):
\[ x_B = 1 - x_A = 1 - 0.4 = 0.6 \]

3. **Apply Raoult's Law:**
- Substitute the known values into the Raoult's Law equation:
\[ P_{total} = P^0_A \cdot x_A + P^0_B \cdot x_B \]
\[ P_{total} = (80 \, \text{mmHg} \cdot 0.4) + (120 \, \text{mmHg} \cdot 0.6) \]

4. **Calculate the Partial Pressures:**
- Calculate the contribution of component A:
\[ P_A = 80 \cdot 0.4 = 32 \, \text{mmHg} \]
- Calculate the contribution of component B:
\[ P_B = 120 \cdot 0.6 = 72 \, \text{mmHg} \]

5. **Calculate the Total Vapor Pressure:**
- Now, add the partial pressures:
\[ P_{total} = P_A + P_B = 32 \, \text{mmHg} + 72 \, \text{mmHg} = 104 \, \text{mmHg} \]

6. **Compare Theoretical and Observed Pressures:**
- The theoretical vapor pressure calculated is \( 104 \, \text{mmHg} \), while the observed vapor pressure is \( 100 \, \text{mmHg} \).
- Since \( 104 \, \text{mmHg} > 100 \, \text{mmHg} \), this indicates a negative deviation from Raoult's Law.

### Conclusion:
The result shows that the solution exhibits a negative deviation from ideal behavior.