Question

The compressibility factor for $1$ mole of a Van der Waal's gas at $t^0$C and $p$ atm pressure is found to be $Z$. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, $a$.

• A. $VRT$ $(1-z)$
• B. $VRT$ $(1+z)$
• C. $VRT/$$(1-z)$
• D. none of these

Answer 1

The correct option is A $VRT$ $(1-z)$

Let us consider the problem.

$=\frac{PV}{nRT}$

implies that

$\left(P+\frac{a}{v^2}\right)\left(V-b\right)=RTfor1mol$

Since, the volume of molecules is neglligible

therefore,

$p+\frac{a}{{}^{v^2}}\left(v-0\right)=RT$

Implies that

$\left(p+\frac{a}{v^2}\right)V=RT$

Implies that

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

Implies that

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

Implies that

$\frac{pv}{RT}+\frac{A}{VRT}=1$

Implies that

$a=\left(1-\frac{pv}{RT}\right)VRT-\left(1\right)$

For 1 mole

Put $z$ value in equation (1)

$a=VRT\left(1-z\right)$