Question

If the critical constants for a hypothetical gas are $V_c=150c{m}^{3}mo{l}^{-1},P_c=50atm$ and $T_c=300K$. Then the radius of the molecule is: [Take $R=\frac{1}{12}{\text{L atm mol}}^{-1}{K}^{-1}$]

• A. ${\left(\frac{75}{2\pi N_A}\right)}^{1/3}$
• B. ${\left(\frac{75}{8\pi N_A}\right)}^{1/3}$
• C. ${\left(\frac{3}{\pi N_A}\right)}^{1/3}$
• D. ${\left(\frac{3}{256\pi N_A}\right)}^{1/3}$

Answer 1

The correct option is D

${\left(\frac{3}{256\pi N_A}\right)}^{1/3}$

$P_c=\frac{a}{27b^2},T_c=\frac{8a}{27Rb}$

$\frac{P_c}{T_c}=\frac{R}{8b}\Rightarrow b=\frac{300\times \left(\frac{1}{12}\right)}{8\times 50}=\frac{1}{16}$

$b=4\times \frac{4}{3}\pi r^3.N_A$

$r={\left(\frac{3}{256\pi N_A}\right)}^{1/3}$