Van der Waals Graph

Procrastinate

For an assignment, I am graphing using the Van der Waals equation. I am meant to find graph PV (y-axis) over (P). However, I am not sure why. On the internet, most other graphs also use these axes. Why do you use PV though?

I am getting a graph that generally similar to those on the internet. Mine goes into a bit of a trough at then it escalates upwards. Could someone please also tell me what the trough indicates? i was thinking it had something to do with liquefying but I am not sure if that is true.

arkofnoah

you mean this?



For an ideal gas, PV is constant. That's Boyle's law. You can use either PV or PV/RT for the y-axis, since the RT is constant given constant temperature. According to the PV=nRT equation, PV/RT = n which is a constant and has a value of 1 when you use one mole of gas.

For ideal gases, the PV against P graph is a horizontal line. This line is used as a benchmark for comparison. All real gases deviate from this line, and the extent of deviation from this line indicates how far a gas deviates from ideal gas behaviour. Implicitly, this means how strong the intermolecular forces are between the gas molecules - the greater the deviation, the stronger the intermolecular forces. (Recall: Ideal gases have negligible intermolecular forces.)

As the external pressure increases, the moleculars are more closely packed and therefore the intermolecular forces of attraction increases. The gas molecules pull one another closer due to attraction and therefore the gas appears to "shrink" (loosely speaking). Volume decreases more than increase in pressure and hence there is a net decrease in PV.

As the external pressure increases further, there will be a point where the gas cannot be compressed anymore and will start to push against the container wall. The pressure in the container therefore increase more than the decrease in volume and hence there is a net increase in PV.

Procrastinate

Yes, this certainly clarifies a few things for me. Thanks for the time you put into the answer.

However, how come PV/P is used instead of volume? Wouldn't that have the same effect?

arkofnoah

I don't know the exact reason pressure is used instead of volume but I'm quite sure it has some practical reasons. This graph is plotted out empirically, i.e. with measurements at different pressure range. Pressure is more direct to measure than volume, with a pressure gauge rather than measuring the dimensions of the container separately and then doing some calculations depending on whether the container is spherical, cylinder and what not.