Answer to Question #297457 in Molecular Physics | Thermodynamics for MSCA

Question

It takes 36 sec for 0.01 moles of He to effuse through a pinhole in an effusion

apparatus. It takes 72 sec for 0.01 moles of another gas to effuse through the

same system. What is the molecular weight of the unknown gas?

Answer 1

Solution;

From Graham's law of diffusion;

$\frac{t_{He}}{t_x}=\frac{n_{He}}{n_x}\sqrt{\frac{M_{He}}{M_x}}$

By direct substitution;

$\frac{36}{72}=\frac{0.01}{0.01}\sqrt{\frac{4}{M_x}}$

Simplify;

$(\frac12)^2=\frac{4}{M_x}$

$M_x=4×4=16g/mol$