Derive van der Waals’ equation of State for n moles of gas.'

Explanation

Ideal gases are those which follow ideal gas equation, that is, `pV = nRT" "...(i)`
Actually, almost all gases have non-ideal (real) character. For deriving Vander Waal.s equation, we will have to consider two factors as given below:
i) Volume of a molecule = b
`:.` Correct volume of gas `(V)=(V-nb)` for n moles `" " ....(ii)`
ii) Attractive intermolecular force
This intermolecular force is used in correcting the pressure term. The corrected pressure is
`p+(an^(2))/(V^(2))`.
`:.p_("corrected")=p+(an^(2))/(V^(2))" " ...(iii)`
Now by using equations (ii) and (iii) in (i), we get `(p+(an^(2))/(V^(2)))(V-nb)=nRT`
Where, V = Volume of the gas, p = Pressure of the gas
n = Number of moles of the gas, R= Universal gas constant
T= Absolute temperature
a= Constant representing the force of attraction between the molecules in a gas.
b = Constant representing effective volume of the molecules in a gas.