Question

A gas diffuses four times quickly as oxygen. The molecular mass of gas is:

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is A $2$

According to Graham's law, rate of diffusion is incresely proportional to the square roots of its molecule weight.

Let m be the mass of the unknown gas

$m_2$ is the mass of oxygen

$r_1$ = rate of diffusion of the unknown gas

$r_2$ = rate of diffusion of oxygen

$\frac{r_1}{r_2}=\sqrt{\frac{m_2}{m_1}}$

Given $\frac{r_1}{r_2}=4$

thus $4=\sqrt{\frac{32}{m_1}}$

Squaring boil sides

$16=\frac{32}{m}$

$m_1=2g$