Question

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

• A. $Z=1+\frac{Pb}{RT}$
• B. $Z=1-\frac{Pb}{RT}$
• C. $Z=1+\frac{RT}{Pb}$
• D. $Z=1-\frac{a}{VRT}$

Answer 1

The correct option is D $Z=1-\frac{a}{VRT}$

The van der Waals equation is as given below.

$(P+\frac{n^{2}a}{V^2})(V-nb)=nRT$

For $n=1$, the equation becomes,

$(P+\frac{a}{V^2})(V-b)=RT$

At low pressure, V > > b

Hence, the equation becomes,

$(P+\frac{a}{V^2})V=RT$

Rearrange above equation

$PV+\frac{a}{V}=RT$

$PV=RT-\frac{a}{V}$

Dividing both sides by RT

$\frac{PV}{RT}=1-\frac{a}{VRT}$

$z=1-\frac{a}{VRT}$.

Thus, if Z is a compressibility factor, van der waals equation at low pressure can be written as $Z=1-\frac{a}{VRT}$.

So, the correct option is $D$