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

The correct option is A $Z=\frac{p{V}_m}{RT}=1-\frac{ap}{RT}$

Vanderwaals equation is given as,

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

$=pv+\frac{a}{v}=RT$

$=pv+\frac{a}{v}=RT$

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

Hence the proof.