Question

The compressiblity factor for a real gas at high pressure is:

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

Answer 1

Answer: (C)

$1+\frac{Pb}{RT}$

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

At high pressure, $\frac{a}{V^2}$ term can be neglected, since P is large.

$PV-Pb=RT$
or $PV=RT+Pb$

$\frac{PV}{RT}=1+\frac{Pb}{RT}$

$Z$$=$$1+\frac{Pb}{RT}$