Question

Unknown gas diffuses with ${\mathrm{CO}}_2$ .The rate of diffusion of an unknown gas is double than that of ${\mathrm{CO}}_2$. The molecular weight of the unknown gas is ?

Answer 1

Step 1: Graham's law:

• “According to Graham's law, the rate of diffusion is inversely proportional to the square root of its molecular weight.”
• It is expressed as:
• $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}}$

Step 2: Given Information:

• Let ${\mathrm{m}}_1$ be the mass of unknown gas.
• ${\mathrm{m}}_2$ be the mass of carbon dioxide i.e. $44\mathrm{g}$
• ${\mathrm{r}}_1$ is the rate of diffusion of the unknown gas.
• ${\mathrm{r}}_2$ is the rate of diffusion of carbon dioxide gas.
• $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=2$

Step 3: Substituting the values:

$$\begin{gathered} \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\sqrt{\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}} \\ \frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=2\left(\mathrm{Given}\right) \\ 2=\sqrt{\frac{44}{{\mathrm{m}}_1}} \\ 4=\frac{44}{{\mathrm{m}}_1} \\ {\mathrm{m}}_1=11\mathrm{g} \end{gathered}$$

Thus, the molecular weight of unknown gas is $11\mathrm{g}$