A sample of N2O effuses from a container in 42 seconds. How
long ...

Question

A sample of N2O effuses from a container in 42 seconds. How
long will it take the same amount of gaseous I2 to effuse from
the same container under identical conditions?

Accepted Answer

Hey there, welcome back. Alright, so if it takes 54 seconds for N20 gas diffuse from a container, how much time would it take for the same amount, but for I two gas to a fuse from the same from the same conditions. All right. Um so let's go ahead and take a look. So usually when we look at two gasses, we use this equation, right? So we have a rate of infusion of one of the gasses. So here we have and to go gas divided by rate of the other gas, which is going to be I to write and that's going to equal to the square root inverse of their molar masses. But here we don't want rates, we actually want times. So the times are going to be um inverse to they're going to be inversely proportional to the to the rate. So, the rate of effusion, basically, the faster the rate is, the less time it takes for that gas molecules to fuse. Right? So they're inversely proportional. So time or just let's say T T of And two Oh, well go on the bottom and then time for I too will go on top. Okay, and all of that is going to equal to the roots square of Mueller mouse of I two over Mueller mouse of and two. Oh, Alright, so here we're not really going to look at the rates here because they're not asking for the rate they're not giving us Indian rates. We just have the time. Okay, so these are times. Alright, so now let's go ahead and figure out the molar masses of each of these molecules of gasses and then we can solve for the time that it takes for I too, because we have the time for N20. Just 54 seconds. Alright, so we have a two And that is I dine. We have two of them here and each I dine weighs 127 g per mole. So that will be 254g. Right? and then four into and two. Oh We have nitrogen. We have two of them here and they weigh about 14 g each. So that is 28 g For oxygen. There's only one and it weighs 16 g. So go ahead and add that together and that will be 44. Just 44 g per mole. Alright, so those are the molar masses of those two gasses. So let's go ahead and plug in the numbers. So we have T. Of I. Two, which is the unknown. Now we do have the time for N 20. It is 44 seconds. 54 seconds. I'm sorry. And then plug in the molar masses. So I too 2 grams per mole And then at the bottom is grams per mole. Alright, so go ahead and find the answer to that right side. That will be 2.403. Right? So you divide the molar masses then square victims. Don't forget to square victim. And you get 2.403. Now to find T. Of I two, we just simply multiply both sides by 54 seconds. Right? So 2.4 oh three times 54 is going to give us 129.7 seconds. Alright, so that is going to be the time that it takes I two gas to a few. So the same amount of gas is going to take it way much much longer rate. So N 20. Is a lighter molecules, so it has greater infusion rate. It's suffusing faster so it doesn't take as long it took 54 seconds. But then for the same amount of I two because it is heavier, it smaller masses, way much much larger. Its rate is actually lower, but the time that it takes to fuse is going to be much much longer. Alright. Thanks so much for watching and we'll see you in the next video.

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