One mole of an ideal gas is confined in a frictionless
CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance
Problem
One mole of an ideal gas is confined in a frictionless, piston–cylinder apparatus. Initially the gas is at 300 K, 1.20 atm, and occupies a volume V₁. The gas undergoes the following two-step process:
• Step I: The gas is compressed isothermally to one-half of its original volume.
• Step II: With the piston locked in place (constant volume), the gas is heated from 300 K to 450 K.
Assume no gas escapes during either step.
(a) Calculate the pressure of the gas at the end of Step I.
(b) Calculate the pressure of the gas at the end of Step II.
(c) Determine the overall factor by which the pressure has changed after both steps relative to the initial pressure. Express your answer as Pfinal/Pinitial.
(d) Explain, with reference to molecular motion and collision frequency, why the pressure change in Step II differs from that in Step I even though the amount of gas remains the same.