Question

Unknown gas diffuses with CO${}_2$. Rate of diffusion of unknown gas is double than that of CO${}_2$. The molecular weight of the unknown gas is :

• A. $22$
• B. $30$
• C. $11$
• D. $44$

Answer 1

Answer: (C)

$11$

According to Graham' s Law, the rate of diffusion is inversely proportional to the square root of its molecular weight.

Let $m_1$ be the mass of the unknown gas

$m_2$ is the mass of $C{O}_2$

$r_1=$ rate of diffusion of the unknown gas

$r_2=$ rate of diffusion of $C{O}_2$

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

Given that $\frac{r_1}{r_2}=2$

thus, $2=\sqrt{\frac{44}{m_1}}$

Squaring both sides:

$4=\frac{44}{m_1}$

$m_1=11g$

Hence, option C is correct.