The plot on the left shows you the compressibility z = pV/nRT of a gas as a function of the pressure p over a pressure range from 0 to 1000 atm. The sliders on the bottom adjust the temperature T (in Kelvin) and the gas specific van der Waals parameters a and b, where a accounts for the attraction between molecules (given in atm L2/mol2) and b represents the excluded volume (in L/mol).

1. Ideal Gas
For an ideal gas, molecules are approximated as non-interacting mass points, so the attraction a=0 and the volume b=0 as well. These values are the preset for a and b so the initial plot upon loading of the applet shows the compressibility z for an ideal gas as a function of the pressure.
Why is the plot a simple line at z=1.0 independent of T?
2. Hydrogen
Hydrogen is a real gas with almost “ideal” behavior, as a=0.245 atm L2/mol2 and b=0.0265 L/mol, almost the smallest values for any real gas (which gas could be even more ideal?). Adjust a and b approximately to these values with the sliders.
a. Vary the temperature. At which end of the temperature scale does H2 behave even more like an ideal gas (which means that the curve is closer to the plot from 1.)
b. Why?
c. Adjust the temperature to about room temperature (300 K). Vary one of the a or b sliders over a small range around the literature value while you keep the other at its correct value for H2. Which pressure range of the compressibility curve does the attraction a and the volume b affect most?
d. Why?
e. Adjust the temperature T to a high value (say, 1000 K). Repeat your investigation from c) and compare the magnitude of the effect of a and b on the compressibility z to that at a lower temperature
3. Methane
Methane is less ideal than hydrogen, its van der Waals parameters are a=2.300 atm L2/mol2 and b=0.0430 L/mol. Adjust the sliders accordingly for about room temperature.
a. Compare the shape of the compressibility z to the plot for H2 from 2 at the same temperature. Explain.
b. Increase the temperature to 1000K. Compare the curve to the H2 plot at this temperature. Why are the differences between the two gases smaller than in a? Explain using a molecular picture.
4. Critical Temperature
Lower the temperature for the methane values of a and b to about 200-250 K. The curve seems to bend backwards such that for some values of p one could find three values of z. Does that make any sense?
a. Apparently you can no longer use the van der Waals equation in this region for this gas and expect realistic results. What is happening in reality with this gas at this set of p and T?
b. Identify the lowest temperature T that still gives you a single value for the compressibility z. This temperature is called the critical temperature, Tc, the corresponding critical pressure is pc.
Table C-14 in your text lists van der Waals parameters and critical temperatures for a number of gases. Estimate Tc for three of them using the method outlined above. Compare your results to the experimental value.

Write-up:
Please write a short report answering the questions above. Be concise. Use sketches, print-outs, or screen shots of the curves to illustrate your points. Feel free to explore additional features of the van der Waal equation either analytically or with the applet for extra credit.