The coldest temperature recorded at ground level on Earth was -89.2 °C at the Vostok Station in Antarctica. What is the speed of a nitrogen molecule at this temperature? (LO 10.9) (a) 933 m/s (b) 40.2 m/s (c) 404 m/s (d) 12.8 m/s

Video transcript

Hey there, welcome back. Alright, so here I'm going to be calculating the root mean square speed or velocity of methane at 126 degrees Celsius. Alright, so first of all, let's go ahead and take a look at the equation for root mean square velocity. So the RMS it's going to equal to three times R T over M which is smaller mass and everything is square root, smaller mass. Guys remember is going to be in kilograms per mole instead of grams from all, We're usually used to having molar mass and grams, but for this equation is in kilograms for mole Temperature of course is in Calvin as it usually is for a lot of um equations and chemistry are here is going to be our gas constant. But remember it does have two values depending on which units were using. And so are here is going to be the one that has the jewels in it. So it's the 8.314 form of the gas constant, which is jules over more times Calvin. Now, the only thing here is that the r M S uh this square speed velocity here is in meters per second as we can see with the units of their, of our answer options. And the only way to get meters per second is actually to take uh those jewels right here, this unit of jewels. And instead of writing jules substitute kilogram or kilograms times meter squared over seconds square. So jules equals to one kg times meter squared over second squared. So instead of writing that we're going to go ahead and write this when we plug in the numbers. So let's see what we have and what we're missing or what we need to convert. So temperature, we said we need to be in degree Celsius or in the in Calvin. So we're going to go ahead and add to 73.15 to the degree sale seems to get Calvin and that will be 3 99. Calvin's. So that is the actual temperature we're going to be using um in our equation and then smaller mass here, let's go ahead and calculate molar mass of methane and then convert into kilograms. So we have carbon, one carbon and it weighs 12 g. Right? We have hydrogen. There's four of them and it weighs 1.01 each. So that will be 4.04 g. So when we add those two values together we get 16. grams per mole right? For one mole we want kilograms. So let's go ahead and convert. So graham will go on the bottom kilogram will go on top killers metric prefix gets one in front of it. So one kg is 10 to the third. So we're just dividing this 5000 essentially. And that will be point oh one 604 kilograms per mole. So that's the molar mass of methane that we're going to use. Right, so this is um Alright, so let's go ahead and plug in the numbers. So V let me go down here a little bit. So V RMS is going to equal to three times are So are we said was 8.314. So remember instead of jewels we're gonna right kilograms times meter second over seconds squared. And then of course we have more Times Calvin on the bottom there as well. That didn't go anywhere and then times the temperature which is in Calvin 3 99.15. I have not forgotten about the square root. I'm gonna close it once we are done putting everything in and then molar mass here is this number right here, point kilograms per mole. Alright, so now we're ready to close the square root. There we go. So looking at the units, let's go ahead and cancel them out. Come on. So we have kilograms right here that can cancel out with that kilogram we have the mole canceling with mole Calvin with Calvin and what do we have left? We have meters meters squared over second squared because this isn't within a square root. After you square root. This whole answer. Of course the units will just be in meters per second. Okay, so all we need to do here is of course multiply everything correctly on the top and then divided by the bottom. Then square root damage. Sure you're putting everything correctly into your calculator and V RMS here is going to equal to 787.8 meters per second. Okay, so out of the answer choices, The one that's very close as 780, so we can just obviously round us up to 788 m/s. So the correct answer here is a alright folks, I hope you thought this was easy. Let us know if you have any questions and we'll see in the next video.