Question

The van der Waals’ constant ‘$b$’ of helium is $24{\text{mL mol}}^{-1}$. Find the molecular diameter of helium.

• A. $1.335\times {10}^{-10}\text{cm}$
• B. $1.335\times {10}^{-8}\text{cm}$
• C. $2.670\times {10}^{-8}\text{cm}$
• D. $4.340\times {10}^{-8}\text{cm}$

Answer 1

The correct option is C $2.670\times {10}^{-8}\text{cm}$

$b=4N_A\times \frac{4}{3}\pi r^3$
$\therefore r={\left(\frac{3b}{16\pi N_A}\right)}^{\frac{1}{3}}={\left(\frac{3\times 24}{16\pi \times 6\times {10}^{23}}\right)}^{\frac{1}{3}}cm$
$\therefore r=1.33\times {10}^{-8}cm$
$\therefore \text{diameter}=2r=2.67\times {10}^{-8}cm$