Question

Under which conditions does the molar volume of a gas decrease?
at 273 K and at 2.0 atm
at 273 K and at 0.5 atm
at 409.5 K and at 1.0 atm
at 546 K and at 2.0 atm

Answer 1

For an ideal gas Vm = RT/P, so molar volume is proportional to T/P. Compared to STP (273 K, 1.0 atm, Vm ∝ 273/1 = 273):

- 273 K, 2.0 atm: T/P = 273/2 = 136.5 → smaller (Vm decreases)
- 273 K, 0.5 atm: T/P = 273/0.5 = 546 → larger (Vm increases)
- 409.5 K, 1.0 atm: T/P = 409.5/1 = 409.5 → larger (Vm increases)
- 546 K, 2.0 atm: T/P = 546/2 = 273 → equal (Vm unchanged)

So the molar volume decreases only at 273 K and 2.0 atm (relative to 273 K, 1.0 atm). In general Vm decreases when temperature decreases and/or pressure increases (i.e., when T/P falls).