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Question

A mixture of two volatile liquids A and B follows Raoult's law. At a certain temperature, the partial pressures of A and B above the solution are 200 mmHg and 300 mmHg respectively. If the mole fraction of A in the liquid phase is 0.4, what is the vapor pressure of pure A at this temperature?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A (500 mmHg)
## CONCEPT FRAMEWORK
 **Primary Concept**: Raoult's Law
 **Related Topics**: Partial pressures, mole fractions, vapor pressure
 **Prerequisites**: Understanding of ideal solutions and Raoult's Law.
## SOLUTION PATHWAY
**Given Information**:
  * Partial pressure of A ($P_A$) = 200 mmHg
  * Partial pressure of B ($P_B$) = 300 mmHg
  * Mole fraction of A in the liquid phase ($x_A$) = 0.4
  * Raoult's Law applies.
**Method & Steps**:
 1. Apply Raoult's Law:
  Reasoning: Raoult's Law states that the partial pressure of a component in a solution is equal to the product of its mole fraction in the liquid phase and its vapor pressure in the pure state.
  Formula/Rule: $P_A = x_A P_A^*$, where $P_A^*$ is the vapor pressure of pure A.
 2. Solve for $P_A^*$: 
  Working: We have $P_A = 200$ mmHg and $x_A = 0.4$. Substituting into Raoult's Law:
  $200 \, mmHg = 0.4 	imes P_A^*$
  $P_A^* = \frac{200 \, mmHg}{0.4} = 500 \, mmHg$
  Key Point:  The total pressure is the sum of the partial pressures, but this information is not needed to solve for the vapor pressure of pure A.
 3. Final Result:
  Result: The vapor pressure of pure A at this temperature is 500 mmHg.
  Verification: Substitute $P_A^* = 500$ mmHg back into Raoult's Law: $0.4 	imes 500 \, mmHg = 200 \, mmHg$, which matches the given partial pressure of A.
 ## OPTION ANALYSIS
A ✓: 500 mmHg is the correct vapor pressure of pure A as calculated using Raoult's Law.
B :x: 600 mmHg is incorrect; it's not consistent with Raoult's Law and the given data.
C :x: 750 mmHg is incorrect; it's not consistent with Raoult's Law and the given data.
D :x: 1000 mmHg is incorrect; it's not consistent with Raoult's Law and the given data.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing mole fractions in the liquid and gas phases: Remember Raoult's Law uses the liquid phase mole fraction.
  2.Incorrectly applying the formula: Make sure to correctly substitute the given values into the Raoult's Law equation.
 **Quick Tips**:
  1.Always clearly identify the liquid phase mole fraction when applying Raoult's Law.
  2.Double-check your calculations to avoid arithmetic errors.

Mr. S M HUSSAIN · Answer

The correct Option is "500 mmHg"

Mr. S M HUSSAIN · Answer

600 mmHg

Mr. S M HUSSAIN · Answer

750 mmHg

Mr. S M HUSSAIN · Answer

1000 mmHg

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