Ideal gas law question

laczlacylaci

2+ Year Member I chose B from P1V1=P2V2. But A was the correct answer.

The key says it is less than 20L because 200atm (P1) is greater than 10 atm, so the size of the molecules cannot be ignored. 0.1L (V1) is slightly greater than it should be for an ideal gas. Therefore the calculated V2=20: is slightly larger than it should be.

1) So in what case would C be correct? None? In other words, why is it slightly larger and not smaller?
2) when it says V1 is slightly greater than an ideal gas, what is the boundary for this "ideal" volume?
3) If 10 atm (maxima) is the boundary for pressure, is there a minima?->giving a volume larger/smaller?

lpp06

5+ Year Member
The subjects you'll want to research here are Real Gasses and van der Waals equation

As you state, the ideal gas law makes the assumption that a gas molecule's volume is negligible when compared to the space it can occupy. This holds true when the distance between the molecules is sufficient (i.e. normal pressure <10atm). When the pressure increases and forces molecules closer together, their volume must now be considered. This now means that the volume of the container which the gas is in decreases because the molecules occupy space. In the context of the question, because the gas is under high pressure - you can expect the free volume will be less than 0.1L and in turn give a volume less than the predicted 20L at 1 atm.

Breaking it down via an equation (see van der Waals; simplified here to only correct for volume)

P1(V1 -nb) = P2(V2 - nb); where nb (which accounts for the molecule's size) can be ignored on the right (the gas is now in ideal conditions so their size can be neglected)
V2 = (P1(V1-nb))/P2 ; if you plug in your values (even if you don't know nb) you will note that your end value will be slightly less than 20L