Question

Use critical temperature and pressure for oxygen gas to determine critical molar volume assuming
a) ideal gas  L/mole
b) van der Waals gas  L/mole
c) Redlich-Kwong gas  L/mole

Answer 1

Critical temperature is the temperature above which the gas cannot be liquefied.

For oxygen gas,

Critical pressure is the pressure required to liquefy a gas at its critical temperature.

For oxygen,

Critical molar volume of a gas is its volume of a mole of gas at its critical temperature and pressure.

Hence, it is the ratio of Volume and number of moles at critical temperature and pressure

Molar Volume =

a) Ideal Gas Scenario

The ideal gas equation is:

Replacing the value of P and T by the critical values for oxygen gas.

b) van der Waals Gas scenario

The van der Waal's gas equation is given as

where a and b are constants for a particular gas.

For oxygen,

  

Hence, putting all the values and solving for

c) Redlich- Kwong gas Scenario

The Redlich-Kwong gas equation is given as

Where a and b are calculated from the critical temperature and pressures of a particular gas

Hence, for oxygen

similarly b is given by

Putting the values back in the Redlich Kwong equation

Putting the values and solving for we get

note: use a mathematical software to calculate the roots of the equation involving V_m. It is very complicated to do it by hand.