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Question

The Henry's law constant for gas A in a particular solvent is $K_H$.  If the partial pressure of A above the solution is doubled, what happens to the mole fraction of A in the solution?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Henry's Law
 **Related Topics**: Gas solubility, partial pressure, mole fraction
 **Prerequisites**: Understanding of proportionality and Henry's Law.
## SOLUTION PATHWAY
**Given Information**:
  $K_H$ = Henry's law constant for gas A
  Initial partial pressure of A = $P_A$
  Final partial pressure of A = $2P_A$
  [Important conditions] Henry's law applies.
**Method & Steps**:
 1. State Henry's Law:
  Reasoning: Henry's law states that the partial pressure of a gas above a solution is directly proportional to the mole fraction of the gas in the solution.
  Formula/Rule: $P_A = K_H x_A$, where $P_A$ is the partial pressure of gas A and $x_A$ is the mole fraction of A in the solution.
 2. Analyze the effect of doubling the partial pressure:
  Working: Initially, $P_A = K_H x_{A1}$ (where $x_{A1}$ is the initial mole fraction).  If the partial pressure is doubled, then $2P_A = K_H x_{A2}$ (where $x_{A2}$ is the final mole fraction). 
  Key Point:  Since $K_H$ is a constant for a given gas and solvent at a specific temperature, the only variable that changes is the mole fraction.
 3. Determine the relationship between initial and final mole fractions:
  Result: Dividing the second equation by the first, we get: $\frac{2P_A}{P_A} = \frac{K_H x_{A2}}{K_H x_{A1}}$, which simplifies to $2 = \frac{x_{A2}}{x_{A1}}$. Therefore, $x_{A2} = 2x_{A1}$.
  Verification: Doubling the partial pressure doubles the mole fraction, consistent with Henry's Law.
 ## OPTION ANALYSIS
A :x: Halving the mole fraction is incorrect; it should increase with increasing partial pressure.
B :x: The mole fraction is directly proportional to partial pressure; it will change.
C ✓: Doubling the partial pressure doubles the mole fraction according to Henry's Law.
D :x: Quadrupling the mole fraction is incorrect; it's a direct, not quadratic, relationship.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing direct and inverse proportionality: Remember that Henry's law describes a direct proportionality between partial pressure and mole fraction.
  2.Ignoring the constant:  $K_H$ is constant for a given system at a given temperature. Do not treat it as a variable.
 **Quick Tips**:
  1.Visualize the relationship graphically: A plot of $P_A$ vs $x_A$ will be a straight line passing through the origin with a slope equal to $K_H$.
  2.Remember the direct proportionality:  Higher partial pressure means higher solubility (higher mole fraction).

Mr. S M HUSSAIN · Answer

It halves.

Mr. S M HUSSAIN · Answer

It remains the same.

Mr. S M HUSSAIN · Answer

The correct Option is "It doubles."

Mr. S M HUSSAIN · Answer

It quadruples.

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