Calculate the ratio of effusion rates for Ar and Kr.

Verified step by step guidance

1. Identify the formula for the rate of effusion, which is given by Graham's law: \( \frac{\text{Rate of effusion of gas 1}}{\text{Rate of effusion of gas 2}} = \sqrt{\frac{M_2}{M_1}} \), where \( M_1 \) and \( M_2 \) are the molar masses of the gases.
2. Assign the gases to the variables: let gas 1 be Argon (Ar) and gas 2 be Krypton (Kr).
3. Find the molar masses of Argon and Krypton. Argon (Ar) has a molar mass of approximately 39.95 g/mol, and Krypton (Kr) has a molar mass of approximately 83.80 g/mol.
4. Substitute the molar masses into Graham's law: \( \frac{\text{Rate of effusion of Ar}}{\text{Rate of effusion of Kr}} = \sqrt{\frac{83.80}{39.95}} \).
5. Simplify the expression under the square root to find the ratio of effusion rates.

Key Concepts

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases effuse faster than heavier gases. The formula can be expressed as (Rate1/Rate2) = √(Molar Mass2/Molar Mass1), allowing for the comparison of effusion rates between two different gases.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in calculating effusion rates, as it directly influences the speed at which a gas can escape through a small opening. For argon (Ar), the molar mass is approximately 40 g/mol, while for krypton (Kr), it is about 84 g/mol.

Effusion

Effusion is the process by which gas molecules escape from a container through a tiny opening into a vacuum or lower pressure area. The rate of effusion is influenced by factors such as temperature and the size of the gas molecules. Understanding effusion is essential for applying Graham's Law and comparing the behavior of different gases under similar conditions.