Graham's Law of Diffusion states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass. The formula for Graham's Law is: $$\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$$ where: • $\text{Rate}_1$ and $\text{Rate}_2$ are the rates of diffusion of gas 1 and gas 2, respectively. • $M_1$ and $M_2$ are the molar masses of gas 1 and gas 2, respectively. Example Problem: Compare the rate of diffusion of ammonia ($\text{NH}_3$) to that of hydrogen chloride ($\text{HCl}$) gas. Step 1: Determine the molar masses of the two gases. • Molar mass of $\text{NH}_3$ ($M_1$): Nitrogen (N) = $14.01 \text{ g/mol}$ Hydrogen (H) = $1.01 \text{ g/mol}$ $M_1 = 14.01 + (3 \times 1.01) = 14.01 + 3.03 = 17.04 \text{ g/mol}$ • Molar mass of $\text{HCl}$ ($M_2$): Hydrogen (H) = $1.01 \text{ g/mol}$ Chlorine (Cl) = $35.45 \text{ g/mol}$ $M_2 = 1.01 + 35.45 = 36.46 \text{ g/mol}$ Step 2: Apply Graham's Law formula. Let $\text{Rate}_1$ be the rate of $\text{NH}_3$ and $\text{Rate}_2$ be the rate of $\text{HCl}$. $$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}} = \sqrt{\frac{M_{\text{HCl}}}{M_{\text{NH}_3}}}$$ Step 3: Substitute the molar masses into the formula and calculate the ratio. $$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}} = \sqrt{\frac{36.46 \text{ g/mol}}{17.04 \text{ g/mol}}}$$ $$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}} = \sqrt{2.1396}$$ $$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}} \approx 1.46$$ This means that ammonia gas diffuses approximately $1.46$ times faster than hydrogen chloride gas. The ratio of the rate of diffusion of ammonia to hydrogen chloride is approximately $\boxed{1.46}$.