Question

For Van Der Waals equation

(P + a/V2)(V - b) = nRT

How can you find the values of "a" and "b" using an experiment? Please explain the method of the experiment too

Answer 1

The constants ' a '& ' b' in van der Waals equation represent pressure and volume correction with respect to ideal gas behaviour. The values of these two constants depend on the nature of the gas and , therefore is different for different gases. So far as experimental determinations of these values are concerned ,it can be determined by knowing P, V, & T of a gaseous system under two different conditions.

The value of the constant 'a ' is calculated using relation : a = pV² / n² ;

where , p is determined by the force of attraction between two molecules of the gases (A) striking the wall of the container and the molecule (B) pulling it inward .

The constant 'b' represents volume correction which is closely related to to the van der Waal's radius. It is the individual volume occupied by an atom ( or molecule ) of a gas. The van derWaals volume may be calculated if the van der Waals radii of an atom ( and for molecules , the inter atomic distances and angles ) are known. For a spherical single atom its volume is given by -

V_w   = 4/3 pi r_w³  

The van der Waals volume of an atom or molecule can also be determined by experimental measurements on different gases from polarizability and molar refractivity considerations of the concrned gas. All the measurements are made on macroscopic or molar quantities. To find the van der Waals volume of a single atom or molecule it would be necessary to to divide these values by Avagadro's No. N_A   

Thus, b = Volume / n

So far as the method of experiment to determine these constants is concerned a single method is not known. Actually , it is the compilation of attractive , repulsive forces , polarizability ,refractivity properties of the gas molecules to be applied separately for calculations to find out the desired constants.