Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 °C. Also, assume an average molar mass for air of 28.8 g/mol. Calculate the mass of air in an air-filled tire.

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Hello everyone in this problem. We're going to be dealing with the ideal gas law equation. So first I want to read out what information we're getting just by reading the problem alone. So what we're given is first we have a volume of two 50 no leaders And then we have a pressure of 85.5 P. S. I. And then we have a temperature at 26°C. We also have that the average Mueller for air is 28 .8 g per mole. And what we're trying to find from this problem is going to be the mass of the air and the tire some mass of air. Alright, so the ideal gas equation is also known as Prevnar art. That is PV equals N. R. T. And the R. Is going to be our constant. That's going to be 0.8206 times a T. M. Times later. All over kelvin times more. Now this value is universal. It can be found in your textbook or something that your professor has provided. But regardless, this is something that you should memorize because it will appear a lot when dealing with the ideal gas law equation. So because this is our constant and any of our information that we're going to be plugging into our ideal gas law equation, it has to match the units of our constant. So let's see here we have a volume we have a pressure, we have a temperature. So temperature we want kelvin's Celsius. We'll convert that into Calvin's and for pressure we want a tm here we have the P. S. I. And then volume we want leaders. But we have millions. So we have some conversion work to do. Starting off with my volume. We are given the 1250 ml converting that into leaders. We know that every leader has 1000 ml. You can see here that the Millers will cancel out and they fine answer will be given in letters plugging that into my calculator. I'll get 1.250 L. Next we will have our pressure. So we're given the 85.5 P. S. I. And to convert that into A. T. M. New murder. We have won A. T. M. Denominator will be 14.696 P. S. I. Again we can see here that the P. S. I will cancel. No Putting that into my calculator. I'll get 5.8179 A. Yeah. Alright next will be my temperature. So we're given the 26.0°C. Let's go ahead and add to 73.15 because that's how we get our unit to be converted to Calvin's. So putting that into my calculator, I would get to 99.15 calvins. Alright, now that we have all the given data and the correct units. We're gonna go ahead and plug into the ideal gas law equation. We can see here that we're solving for end value. I want to go ahead and make my life a little bit easier, divide your side by RT to isolate our end. So artie's will cancel. Let's go ahead and move down here. Have a little bit more room. Sorry. N is going to be equal to PV over R. T. Alright moving down. All right. So, and it goes pressure. That's going to be 5.8179 a. T. M. The volume which we just calculated is 1. L. It's going to be all divided by first our gas law constant 0.08206 A. T. M. Times leader all over kelvin's times mold. And then we need to multiply Our calculated temperature which is 20 or 299.15 Kelvin's. I can see here that the ATMs will cancel. Leaders will cancel and Calvin's will cancel. So, plugging that into my calculator. My value that I get. It's going to be 0.29625. And my unit is going to be in moles. Alright. Now, final step is utilizing this which in the problem says is the average more error. And we want the massive air. And so because we have this here we go ahead and actually cancel with this leaving us with the massive air in grams. So let's go handle it. So We just offer end value. So the more value which is 0.29625 moles. And then we want to use the given information, which in the denominator will be one More. And in the know Mary numerator is going to be 28.8 g. So you can see here the moles will cancel it nicely, leaving us with just two g, putting that into my calculator. I'll get the final value as eight 0. 3g. And it's going to be my final answer for this problem. Thank you all so much for watching.

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Key Concepts

Ideal Gas Law

Molar Mass

Gas Density