A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the second gas.

Video transcript

Alright, folks, so, the rates of diffusion of oxygen to an unknown gas have a ratio of 1.488. Okay, so we have a ratio of rates of the fusion of two gasses. We need to determine the identity of the other gas. So, when we're comparing two different gasses, we use this equation right, For a fusion of gasses. So, we have rate of one Um gas. Or so we're gonna put oxygen on top of 02. Right? Because here we have rates of diffusion of oxygen oxygen to and another gas. And then a rate of the other gas on the bottom. We're gonna call us um gas X. Right? And that's going to equal to the square root of their molar masses. But in verse. So this is going to be a molar mass of X Over Mueller mass of 0.2. Okay, so now we're just gonna go ahead and plug in the numbers. Now, for the rates, we obviously don't know the individual rates, but we have the ratio, right? So its rate of 022 rate of X Is 1.488. So this whole left side equals to 1.488. It's just a ratio. And that's going to equal to So, if we plug in the numbers, we do know the molar mass of 02, but not of X. M. X. Is going to stay up there. And then molar mass of 02. So we know that oxygen weighs 16 g per one mole, There's two of them there. That's going to be 32 g per mole. Right? So that's the molar mass of oxygen of oxygen gas. So it's not just oxygen, but it's oxygen gas. That's why it has to be 02. So it is going to be 32 grams per mole. Now, how do we get rid of this square root here? We're just going to go ahead and take both sides. We're going to square them. Right, this whole thing. So that will get rid of the square root. So 1.488 squared will give us 2.21 41. All right, so the left side, that's right there. And then here we're just going to have Mueller mouse of X divided by grams per mole. Alright, so to find Moller mouse of X, we're just going to go ahead and multiply both sides by 32. And once you do that, You get 70. grams per mole. Now, a lot of the gasses usually are di atomic just like to write. And if you take a look at the periodic table, um you know, you can't really find anything that's 70 85. But if you divide that by two, assuming that X. Here is most likely X. To write whatever the exes, Let's just go ahead and check when you do that. That gives us 35.42 grams per mole. That's actually the smaller mass of one chlorine, just of one chlorine. So it looks like our X. Here is CL two. So we were correct in assuming that this was probably a di atomic gas, just like CO two, so X. Here, the unknown gas that we had is chlorine gas. CL two. Alright, folks, thank you so much for watching.