Unit of Van der Waals Constants

Ideal gas is a hypothetical concept which is based on the fact that the particles of the gas have no interparticle interaction. It is a gas which obeys the ideal gas equation that is given as PV=nRT where, P is the pressure of the gas , V is e volume  that the gs occupies , n denotes the number of moles f the gas , R is the –universal gas constant and T is the temperature if the gas the absolute temperature measured on kelvin while the Van der waal equation for real gases is an extension of the ideal gas equation wherein the assumptions like negligible particle size and the intermolecular interactions is taken in consideration.

Characteristics of real gas  

Ideal gas has following characteristics-

•  intermolecular force of attraction between molecules 
• Obeys (P+an2/V2)(V-nb)=nRT- vander waal equ
• definite volume
•  Non-Elastic collision between molecules
• Depends on factors like temperature ,pressure volume etc.

Difference between ideal and real gas

1. Ideal gas has no definite volume while real gas has a definite volume .
2. No force of interaction is there between the molecules in case of ideal gas but in case of real gas the intermolecular force of attraction is present .
3. Ideal gas obeys the ideal gas equation of PV=nRT while the real gas obeys the]e real gas equation r the vander waal gas equation that is (P+an2/V2)(V-nb)=nRT
4. Ideal gas is a hypothetical concept while real gas is not .
5. The ideal gas exist at high pressure while the real gas as relatively less pressure
6. Ideal gas is independent of factors like the interaction with the various pressure temperature and volume parameters but the freal gas is highly dependent on such factors .

Assumptions while deriving the ideal gas equation 

While deriving the ideal gas equation there are certain assumptions that are taken these are as follows-:

• The size of the gas is negligibly small
• There is no force of attraction between the molecules of the gas.

These assumptions are not used while deriving the real gas equation,

Van der waal equation

Van der waal equation for real gases is an extension of the ideal gas equation wherein the assumptions like negligible particle size and the intermolecular interactions is taken in consideration.

So according to the ideal gas equation

Pv=nRT

Here as the particles occupy space and hence to take into account the volume occupied  by real gas molecules  v/n is replaced by Vm-b, Vm is the molar volume and b is the volume occupied by the molecules of one mole.

Therefore , P(Vm-b)=RT

Further as the molecules of the gas interact hence the equation is further modified to take into account the extra pressure to collisions and interactions between the real gas molecules .

The value of that extra pressure is given by a/V2m  a is a constant whose value depends on the gas.

So the equation is as follows-

( P+ a/V2m)(Vm-b)=RT

This is for one mole of gas and for n moles the equation is 

 (P+ an2/V2)(V-nb)=nRT

Constants a and b

In the van der waal equation two constants a and b are used as correction factors , these factors are known as the vander waal constants and are characteristic for a given gas . These constants gave positive values . The constant a gives us the correction for intermolecular force of interaction while constant b is the measure of the volume occupied by the molecules of real gas . 

Units of the constants a and b

The constant a determines the strength of intermolecular interaction between molecules it is added in the extra pressure part .the unit for a is L2atm/mol2 as the extra pressure is given by  n2a/V2, while the constant b is taken for volume and the unit is L/mol

Conclusion

A gas which obeys the ideal gas equation  at all temperatures and  pressure is known as the ideal gas; it is a hypothetical concept . The ideal  gas equation is PV=nRT further for real gases the vander waal gas equation was formed which is the refined version of the ideal gas equation wherein the size and interactions between molecules is considered. The equation is as follows- (P+ a/V2)(V-nb)=nRT. The vanderwaal equation has two constants a and b which are basically two correction factors for the assumptions taken in ideal gas . a gives the correction for intermolecular force of attraction while b gives a correction for volume occupied by the particles since the size is now not negligible .