Question

# At low pressures, the van der Waals equation is written as $$\left [ P+\cfrac{a}{V^{2}} \right ]V= RT$$.  The compressiblity factor of the gas is:

A
[1aV]
B
[1aTV]
C
[1aRTV]
D
[1RTaV]

Solution

## The correct option is C $$\left [ 1-\cfrac{a}{RTV} \right ]$$Solution:- (C) $$\left[ 1 - \cfrac{a}{RTV} \right]$$Given that at low pressure, van der Waals equation is-$$\left[ P + \cfrac{a}{{V}^{2}} \right] V = RT$$$$\Rightarrow PV + \cfrac{a}{V} = RT$$$$\Rightarrow \cfrac{PV}{RT} + \cfrac{a}{RTV} = 1$$$$\Rightarrow \cfrac{PV}{RT} = 1 - \cfrac{a}{RTV}$$$$\Rightarrow Z = 1 - \cfrac{a}{RTV} \quad \left( \because Z = \cfrac{PV}{RT} \right)$$Hence the compressiblity factor of the gas is $$\left[ 1 - \cfrac{a}{RTV} \right]$$.Chemistry

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