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.

Question

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.

Accepted Answer

Welcome back everyone. We need to calculate the ratio of diffusion rates and arrange the gasses in order of their speed of diffusion. And we have hydrogen bromide gas, chlorine gas and krypton gas. Our first step is to recall our formula for the rate of a fusion of a gas, Recall that a fusion is where gas particles are traveling through a smaller space. So we would recall that the rate of effusion of a gas can be calculated where we have an inverse relationship with the square root of the molar mass of that gas. So making note of our molar mass of each of our gasses, beginning with hydrogen bromide gas, according to our periodic table, we have a molar mass of 80.91 g per mole. For our molar mass of chlorine gas, we have according to our periodic table at mass of 70.90 g per mole, and for a molar mass of krypton gas, our noble gas here we have a molar mass of 83.8 g per mole, according to our periodic tables. So now, beginning with the relationship between our molar mass of hydrogen bromide gas and our molar mass of krypton, we would say that our rates of a fusion between hydrogen bromide gas and our rate of fusion between krypton gas is equal to the square root of our molar mass of krypton gas divided by our molar mass of hydrogen bromide gas. We want krypton gas and enumerators, since it's a larger value there. So what we'll have is the square root of 83.8, divided by 80.91. And this is going to simplify to 1.0177 as the rate of effusion here. Now following the same process, but comparing between our chlorine gas and now krypton gas, we're going to have that the rate of our chlorine gas to the rate of krypton gas Is equal to the square root of our molar mass of our Krypton gas, divided by our molar mass of our chlorine gas. And so, plugging in our values from our periodic table will have the square root of 83.8 divided by 70.90, which is going to yield a result of 1.08. And let's scoot this over for some more room So of 1.0872. So for our final answer, we can say that the rate of diffusion is going to be beginning with our chlorine gas, Which has a rate of 1.0872, Which is going to be diffusing faster than our second lightest gas molecule being our hydrogen bromide gas, which has a diffusion rate of 1.01 Will say eight. Rounding that up which has a greater rate of diffusion than our heaviest gas molecule, which is our krypton gas, which will say has a rate of diffusion of 1. and so for our final answer, we would say that we have the fastest diffusion associated with chlorine gas. So the fastest diffusion rate associated with chlorine gas and our slowest diffusion rate associated with krypton gash. And this entire ranking would be our final answer to complete this example. So I hope everything I reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.

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 Solution

Key Concepts

Graham's Law of Effusion

Molar Mass

Diffusion