The van der Waals equation is



P +

an2 V2

 V n

− b



= RT, where P is the pressure of the gas, V is the volume, R is the gas constant, T is the temperature, n is the number of moles, and a and b are parameters that depend on the gas.

a. What are the units of a and b?

b. Define a new variable, the molar volume, Vm, which is equal to the volume of one mole of the gas. How would you write the van der Waals equation in terms ofVm? (Hint:
how would you write Vm in terms of V and n?)

c. Suppose you have 1 mol of argon at 300 K. Find out (by searching the web) what a and b are for argon, and write P as a function of V for argon. Plot P(V) (use any appropriate software). Be very careful with the values you use for a and

b. Your values need to be in the right units to match the other units in the equation. On the same graph plot P(V)
for an ideal gas. Comment on the differences. In particular, what are the differences between a real gas and an ideal gas at high pressures?
The answer to this part of the question can be found in Fig. 12.13.

d. In the van der Waals equation, for what values of V is P(V)
scientifically valid? Warning: this last part of the question is tricky, and is best answered only after you have drawn the two plots of P(V) for an ideal gas and a real gas.