Question

The van der Waal gas constant 'a' is given by which of the following relations?

• A. $\frac{V_c}{3}$
• B. $\frac{R{T}_c}{8P_c}$
• C. $9R{T}_c{V}_c$
• D. $3P_c{V}_c^2$

Answer 1

The correct option is D $3P_c{V}_c^2$

$T_c=\frac{8a}{27Rb}$ - $i$
$P_c=\frac{a}{27b^2}$ - $ii$
$V_c=3b$ - $iii$
We can get 'a' from:
$i^2÷ii$
$\frac{T_c^2}{P_c}=\frac{64a}{27R^2}$;
$a=\frac{27T_c^2{R}^2}{64P_c}$
And also from $ii\times ii{i}^2$
$P_c{V}_c^2=\frac{a}{3}$;
$a=3P_c{V}_c^2$