Van der Waals Equation
The Van der Waals equation is an equation similar to the Real Gas Law, but includes two constants, a and b, to account for deviations from ideal behavior.
The van der Waals equation is:
[P + (n2a/V2)](V - nb) = nRT
P - pressure,
V - volume,
n - number of moles,
T - temperature,
R - ideal gas constant. If the units of P, V, n and T are atm, L, mol and K, respectively, the value of R is 0.0821
a and b - constants, which are chosen to fit experiment as closely as possible to individual gas molecule.
When the volume, temperature and the number of moles of the gas molecule are known, the pressure can be calculated:
P = [nRT/(V - nb)] - n2a/V2
To calculate Volume:
To calculate the volume of a real gas, V in term n2a/V2 can be approximated as: nR/TP
as ideal gas. Then, V can be calculated as:
V = nR3T3/(PR2T2+aP2) + nb
The van der Waals constants a and b of molecular N2 is 1.390000 and 0.039100, respectively.
To calculate Pressure:
According to the van der Waals equation,
P = nRT/(V - nb) - n2a/V2
Significance of \a/ and \b/ :
1) a measures the force of attraction between the molecules ..
2) b measure the incompressible volume of the molecules ..i.e ( the average volume excluded from the v volume of particle ) = nb and is subtracted by total volume v from the equation ...!
The main point that these constant impacts that ... In case of real gas ...the pressure is not same ..and the volume will also be not same ...Due to inter attraction and intra attraction of the molecules the pressure will increase ....and thus n^2.a/V^2
is added in the original pressure P ...and similarly to compressibility factor ..the actual volume is also not same ...and is decreased by some factor ..that factor is governed by b ..and thus volume become ( V-nb)
So ( effected pressure)(decreased volume ) = nRT
[ P + n^2.a/v^2 ] [ V-nb] = nRT
I hope now it is clear ...! If u have doubts ..ask further