Solve questions on ghram law of diffusion

Question

ScanSolve AI Tutor · Accepted Answer

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.

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) = $35.45 \text{ g/mol}$ $M_2 = 1.01 + 35.45 = 36.46 \text{ g/mol}$
Apply Graham's Law formula.
Let $\text{Rate}_1$ be the rate of $\text{NH}_3$ and $\text{Rate}_2$ be the rate of $\text{HCl}$ .
$\frac{\text{Rate}_{\text{NH}_3}}{\text{Rate}_{\text{HCl}}} = \sqrt{\frac{M_{\text{HCl}}}{M_{\text{NH}_3}}}$
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 $\boxed{1.46}$ .

Answer