Derive van der waals equation for 'n' mol of a real gas from the equation for 1 mol of the gas.

Explanation

van der waals equation for 1 mol of a real gas is given by-
`(P+(a)/(v^(2)))(v-b)=RT` . . [1]
If at a pressure P and a temperature T, the volume of 'n' moles of this gas be V, then `v=(V)/(n)`. Putting `v=(V)/(n)` in equation [1], we have
`(P+(a)/(((V)/(n))^(2)))((V)/(n)-b)=RT or (P+(n^(2)a)/(V^(2)))(V-nb)=nRT`
This is the van der waals equation for 'n' mol of real gas.