Question

The critical volume of a gas is $0.072lit.mo{l}^{-1}$. The radius of the molecule will be, in cm:

• A. $(\frac{3}{4\pi }\times {10}^{-23}{)}^{\frac{1}{3}}$
• B. $(\frac{4\pi }{3}\times {10}^{-23}{)}^{\frac{1}{3}}$
• C. $(\frac{3\pi }{4}\times {10}^{-23}{)}^{\frac{1}{3}}$
• D. $(\frac{4}{3\pi }\times {10}^{-23}{)}^{\frac{1}{3}}$

Answer 1

The correct option is A $(\frac{3}{4\pi }\times {10}^{-23}{)}^{\frac{1}{3}}$

The critical volume is three times the Van der Waals constant 'b'.
$b=\frac{16}{3}\pi r^3{N}_A;V_c=3b=0.072lit.mo{l}^{-1}$

The expression for the magnitude of the Van der Waals constant, b, for the gas is $b=\frac{16}{3}\pi r^3{N}_A$

Thus $3b=\frac{16}{3}\pi r^3{N}_A\times 3$

Substitute values in the above expression,

$0.072\times 1000=\frac{16}{3}\times 6.023\times {10}^{23}\times \pi \times r^3\times 3$

Thus $r=(\frac{3}{4\pi }\times {10}^{-23}{)}^{\frac{1}{3}}cm$.