Question

The rate of effusion of an unknown gas $\left(X\right)$ through a pinhole is found to be $0.279$ times the rate of effusion of hydrogen through the same pinhole, if both are at STP. What is the molecular mass of the unknown gas?

• A. 12.85
• B. 25.7
• C. 15
• D. 30

Answer 1

The correct option is B 25.7

Thomas Graham studied the rates of effusion of different gases and formulated Graham’s law of effusion: The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles:
Using Graham's law of diffusion
$\frac{rateofeffusionofX}{rateofeffusionofhydrogen}$ =$\sqrt{\frac{M_H}{M_X}}$
$\frac{r_X}{r_{H_2}}=\sqrt{\frac{2}{M_X}}$
0.279 = $\sqrt{\frac{2}{M_X}}$
$(0.279{)}^2=\frac{2}{M}$
M =$\frac{2}{0.077841}$
$M=25.69=25.7$