Question

The compressibility factor $Z$ at a low-pressure range of all gases except hydrogen is:

• A. $Z=(1-\frac{Pb}{RT})$
• B. $Z=(1+\frac{a}{V_{m}RT})$
• C. $Z=(1-\frac{a}{V_{m}RT})$
• D. $Z=(1+\frac{Pb}{RT})$

Answer 1

Answer: (C)

$Z=(1-\frac{a}{V_{m}RT})$

The van der Waals equation for real gases is $(P+\frac{a}{{V_m}^2})(V_m-b)=RT$

At low pressures, neglect the $b$ term from the above equation and we get

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

$Z=\frac{P{V}_m}{RT}=(1-\frac{a}{V_{m}RT})$

Option C is correct.