Chemistry Gases ETEA 2023
PMDC Verified Question 23 of 65
The volume of a given mass of an ideal gas at certain pressure is x at constant temperature. What will be its volume when the pressure is reduced to half?
A
\( \frac{x}{2} \)
B
\( 2x \)
C
\( 4x \)
D
\( \frac{x}{4} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 2x \)
Concept:

This problem is a direct application of Boyle's Law, which states that the volume of an ideal gas is inversely proportional to its pressure when temperature and mass remain constant.

Formula:

$$ P_1 V_1 = P_2 V_2 $$

Solution:

  • Let the initial volume \( V_1 = x \) and initial pressure \( P_1 = P \).


  • The new pressure is reduced to half, so \( P_2 = \frac{P}{2} \).


  • Substitute these into Boyle's Law: \( P \times x = \left(\frac{P}{2}\right) \times V_2 \).


  • To solve for \( V_2 \), multiply both sides by 2 and divide by P.


  • \( V_2 = \frac{2Px}{P} = 2x \).


  • Because pressure and volume are inversely proportional, halving the pressure precisely doubles the volume.


Why other options are incorrect:

  • Option A: This would happen if volume and pressure were directly proportional.
  • Options C & D: These represent quadruple or quarter changes, which do not align with a simple 1/2 change in pressure.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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