Question

At low pressure, the van der Waals equation is reduced to

• A. $Z=\frac{P{V}_m}{RT}=1-\frac{ap}{RT}$
• B. $Z=\frac{P{V}_m}{RT}=1+\frac{b}{RT}P$
• C. $p{V}_m=RT$
• D. $Z=\frac{P{V}_m}{RT}=1-\frac{a}{RT}$

Answer 1

Answer: (A)

When pressure is low
$\left[P+\frac{a}{V^2}\right]\left(V-b\right)=RT$
or $PV=RT+Pb-\frac{a}{V}+\frac{ab}{V^2}$ or $\frac{PV}{RT}=1-\frac{a}{VRT}$
$Z=-\frac{a}{VRT}\left(\because \frac{PV}{RT}=Z\right)$