PHYSICAL CHEMISTRY In physical chemistry, it is shown that the pressure P of a gas is rela...

PHYSICAL CHEMISTRY In physical chemistry, it is shown that the pressure P of a gas is related to the volume V and temperature T by van der

Waals’ equation:

where a, b, n, and R are constants. The critical temperature Tc of the gas is the highest temperature at which the gaseous and liquid phases can exist as separate phases.

a. When T =Tc, the pressure P is given as a function P(V)of volume alone. Sketch the graph of P(V).

b. The critical volume Vc is the volume for which P'(Vc) = 0 and P"(Vc) = 0. Show that Vc = 3b.

c. Find the critical pressure Pc =P(Vc)and then express Tc in terms of a, b, n, and R.