For diatomic carbon dioxide gas (CO2, molar mass 44.0 g/mol) at T = 300 K, calculate (c) the root-mean-square speed v_rms.

Video transcript

Hey everyone in this problem, we have nitrogen which is a di atomic gas and we're told it's Mueller masses 28.01 g per mole were asked what is its root mean square speed at room temperature. So 298 Calvin. Okay, so let's recall that we can write the root mean square speed V R M. S as the square root Of three R. T. Over big R. Is the gas constant. M is a molar mass. T. Is the temperature. So we know all of those things. We can go ahead and substitute them. So in this case we're gonna have The square root of three Times are which is 8.314. Again, that's the gas constant that you can look up. The unit here is jewels per more Calvin And then we're multiplying by the temperature, which is 298 Kelvin. We're going to divide that by the molar mass. Now the molar mass we're given is in grams per mole. We want to make that kilograms per mole. Okay, so that our units are consistent. So this is going to be 0.0 to a 01 kilogram two more and just be careful with your molar mass when you're working with di atomic gasses. Okay? In this case we were given the molar mass, but if you needed to look it up in your periodic table, you would need to double it. Okay, It would give you something like it would give you around 14 for nitrogen k. So that's one atom instead of the di atomic molecules. Okay so you would need to double it. So just be careful when you're working with your molar masses if you're getting them from the periodic table. Alright so simplifying this a bit. We're going to have the square root. Um Let's look at units first. Okay? The unit of Calvin. We have Calvin divided by Calvin. That's gonna cancel. And we have a unit of per mole in the numerator, per mole in the denominator. So those will also cancel. Okay, we're gonna be left with 7432.716. Okay. We have jewels. Another way we can write jewel is kilogram meter squared per second squared. And then we're dividing by 0.0 to 801 kg. Okay so the unit of kilogram will cancer. We're gonna be left with meter squared per second squared. So when we take the square root we're going to get meters per second. Which is the unit for speed that we want. So the units check out here. Okay, we're going to get the R. M. S. Taking the square root. It's gonna be 515. m/s. Okay, so that is our root mean square speed Of nitrogen at room temperature. That's going to correspond with answer. B 515 m/s. That's it for this one. Thanks everyone for watching. I hope this video helped