Question

A gas obeys the Van der Waals equation. The approximate value of the constants 'a' and 'b' for this gas are:

• A. $1.88\times {10}^{6}c{c}^{2}atm/mol{e}^2,120cc/mole$
• B. $3.16\times {10}^{6}c{c}^{2}atm/mol{e}^2,30cc/mole$
• C. $3.16\times {10}^{6}c{c}^{2}atm/mol{e}^2,50cc/mole$
• D. $0.86\times {10}^{5}c{c}^{2}atm/mol{e}^2,30cc/mole$

Answer 1

The correct option is B $3.16\times {10}^{6}c{c}^{2}atm/mol{e}^2,30cc/mole$

Since, calculation requires approximation, at critical point. let,
$P_c=130atm$ and $V_c=90c{m}^3/mole$ and $T_c=380K$
$V_c=3b,P_c=\frac{a}{27b^2}$
$90=3b$ ..........(i)
$130=\frac{a}{27b^2}$..........(ii)
$\therefore b=\frac{90}{3}=30cc/mole$
Substituting b in equation (ii)
$a=3.16\times {10}^{6}c{c}^2$ $atm/mol{e}^2$