QJEEM14Chb52e: JEE Main 2014 Chemistry - Class 11 JEEM14Chb52e Solution: If Z is a compressibility factor, van der Waals equation at low …

Question

Verified Solution • 2025–26 Session moderate

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

Accepted Answer

Compressibility factor

\left( Z \right) = {{PV} \over {RT}}

(For one mole of real gas)

van der Waals equation

\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT

At low pressure, volume is very large and hence correction term

b

can be neglected in comparison to very large volume of

V.

i.e.

\,\,\,V - b \approx V

\left( {P + {a \over {{V^2}}}} \right)V = RT;

PV + {a \over V} = RT

PV = RT - {a \over V};

{{PV} \over {RT}} = 1 - {a \over {VRT}}

Hence,

\,\,\,z = 1 - {a \over {VRT}}

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