Question

The critical volume of a gas is 0.036 $lit.mo{l}^{-1}$. The radius of the molecule will be (in cm):
(Avogadro Number = $6\times {10}^{23}$)

• A. ${(\frac{9}{4\pi }\times {10}^{-23})}^{\frac{1}{3}}$
• B. ${(\frac{8\pi }{3}\times {10}^{-23})}^{\frac{1}{3}}$
• C. ${(\frac{3}{8\pi }\times {10}^{-23})}^{\frac{1}{3}}$
• D. none of these

Answer 1

The correct option is C ${(\frac{3}{8\pi }\times {10}^{-23})}^{\frac{1}{3}}$

Critical volume of gas=3b [for 1 molecule]

For 1 mole, critical volume=0.036 liters

$⟹0.036\times {10}^3{cm}^3=3\left(\frac{4}{3}\pi r^3\right)\times N_A⟹r={(\frac{36}{24\pi }\times {10}^{-23})}^{\frac{1}{3}}={(\frac{3}{8\pi }\times {10}^{-23})}^{\frac{1}{3}}$