Question

The compressiblity factor (Z) for 1 mole of a real gas at low pressure can be written as:

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

Answer 1

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

Compressibility factor $\left(Z\right)=\frac{PV}{RT}$
(For one mole of real gas)

van der Waals' equation for 1 mole of a real gas is
$(P+\frac{a}{V^2})(V-b)=RT$

At low pressures, the volume is very large and hence correction term b can be neglected.
i.e, $V-b\approx V$

$(P+\frac{a}{V^2})V=RT$;
$PV+\frac{a}{V}=RT$;
$PV=RT-\frac{a}{V}$;
$\frac{PV}{RT}=1-\frac{a}{VRT}$
Hence, $Z=1-\frac{a}{VRT}$