Rank the following gases in order of their speed of diffusion through a membrane, and calculate the ratio of their diffusion rates: HCl, F2, Ar.

Verified step by step guidance

1. Identify the molar masses of each gas: HCl, F2, and Ar. You can find these values on the periodic table or in a chemical database.
2. Use Graham's Law of Effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The formula is: Rate of Effusion \( \propto \frac{1}{\sqrt{M}} \), where \( M \) is the molar mass of the gas.
3. Calculate the square root of the molar mass for each gas. This will help in comparing their rates of diffusion.
4. Rank the gases based on the inverse of the square roots calculated. The gas with the smallest square root of molar mass will diffuse the fastest.
5. To find the ratio of their diffusion rates, compare the rates using the formula: \( \frac{Rate_{\text{Gas 1}}}{Rate_{\text{Gas 2}}} = \sqrt{\frac{M_{\text{Gas 2}}}{M_{\text{Gas 1}}}} \). Apply this formula for each pair of gases to find the ratios.

Key Concepts

Graham's Law of Effusion

Graham's Law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass. This means lighter gases diffuse faster than heavier gases. For example, if you compare hydrogen (H2) and oxygen (O2), hydrogen will diffuse more quickly due to its lower molar mass.

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 determining the speed of diffusion, as gases with lower molar masses will diffuse more rapidly than those with higher molar masses. In this question, the molar masses of HCl, F2, and Ar will be essential for calculating their diffusion rates.

Diffusion

Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration. In the context of gases, diffusion occurs through a membrane, and the rate can be influenced by factors such as temperature, pressure, and the nature of the gas. Understanding diffusion is crucial for ranking the gases based on their speeds in this scenario.