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Question

A mixture of 1 mol of He and 1 mol of CO$_2$ is contained in a vessel of volume V at 20°C. If the mixture behaves ideally, what is the pressure exerted by He?

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Dalton's Law of Partial Pressures
 **Related Topics**: Ideal Gas Law, Mole Fraction
 **Prerequisites**: Understanding of partial pressures and ideal gas behavior.
## SOLUTION PATHWAY
**Given Information**:
  * 1 mol of He
  * 1 mol of CO$_2$
  * Total volume = V
  * Temperature = 20°C (This is not needed for this specific question)
  * Ideal gas behavior
**Method & Steps**:
 1. Apply Dalton's Law of Partial Pressures: The total pressure of a mixture of ideal gases is the sum of the partial pressures of the individual gases.
  Reasoning:  Each gas in an ideal mixture behaves independently and exerts a pressure as if it were alone in the container.  The partial pressure of a gas is the pressure that gas would exert if it occupied the entire volume alone.
  Formula/Rule: $P_{total} = P_{He} + P_{CO_2}$ 
 2. Determine the mole fraction of He:
  Working: The total number of moles is 1 mol He + 1 mol CO$_2$ = 2 mol. The mole fraction of He is: $X_{He} = \frac{moles \,of\, He}{total \,moles} = \frac{1 \,mol}{2 \,mol} = 0.5$
  Key Point: The mole fraction represents the proportion of each gas in the mixture.
 3. Relate partial pressure to mole fraction:
  Reasoning: For an ideal gas mixture, the partial pressure of a gas is equal to its mole fraction multiplied by the total pressure: $P_i = X_i P_{total}$ where $P_i$ is the partial pressure of gas i, $X_i$ is the mole fraction of gas i, and $P_{total}$ is the total pressure.
  Result: $P_{He} = X_{He} P_{total} = 0.5 P_{total}$ 
  Verification: This confirms that the pressure exerted by He is half of the total pressure.
 ## OPTION ANALYSIS
A ✓: Half of the total pressure. This is the correct answer derived from Dalton's Law and the mole fraction calculation.
B :x: Equal to the total pressure. This would only be true if He were the only gas present.
C :x: One-third of the total pressure. This is incorrect; the mole fraction of He is 0.5, not 1/3.
D :x: Twice the total pressure. This is impossible; the partial pressure of a gas cannot exceed the total pressure.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Ignoring Dalton's Law:  Students might try to calculate the pressure of He without considering the presence of CO$_2$.
  2.Incorrectly calculating mole fraction:  Errors in calculating the total number of moles or the ratio of moles of He to total moles can lead to an incorrect partial pressure.
 **Quick Tips**:
  1.Remember that the sum of partial pressures equals the total pressure.
  2.Always calculate the mole fraction to determine the partial pressure of a gas in a mixture.

Mr. S M HUSSAIN · Answer

The correct Option is "Half of the total pressure"

Mr. S M HUSSAIN · Answer

Equal to the total pressure

Mr. S M HUSSAIN · Answer

One-third of the total pressure

Mr. S M HUSSAIN · Answer

Twice the total pressure

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