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. What is the mass difference between the two?

Video transcript

Hi everyone here, we have a question asking us, what are the mass of hydrogen and a hydrogen filled balloon and the mass of helium in a helium filled balloon? If the volume of the balloon is 2944 mL with the total pressure of 200 P. S. I. At 27 degrees Celsius. And what is the mass difference between the two? So density equals mass over volume density also equals pressure times molar mass over r gas constant times our temperature, which means our mass is going to equal pressure times molar mass times volume, divided by r gas constant times our temperature. And we know that our pressure is P. S. I. And we want to change that to atmosphere. So we're going to multiply by one atmosphere Divided by 14. p. s. i. And r P. S. S are going to cancel out leaving us with .6091 atmospheres And we know that our volume equals 2944 ml. We want to change that to leader. So we're going to multiply by one leader Over ml And our middle leaders are going to cancel out leaving us with 2. L. And our temperature is 27°C. And we want that in Kelvin. So we're gonna add 273. And that equals 300 . Kelvin. So our massive helium Is going to equal .6091 atmospheres times 4. g per mole. That's the molar mass of helium, which is found on the periodic table Times 2. L. Yeah, over 0. times 300 .15 Kelvin. And that equals 6.5115 g. And now we can calculate the mass of hydrogen That's going to equal 13.6091 atmospheres and its molar mass. But because it is a di atomic molecule, it will be multiplied by two. So 2.16 g Permal Times 2.94, 4 L. Over zero . Times 300.15 Kelvin And that equals 3. g. And now we need to calculate our mass difference So that is going to equal 6. -3.2794. And that equals 3. g. So those are our three answers. Thank you for watching. Bye