43.5k views
4 votes
Olympic cyclists fill their tires with helium to make them lighter. Assume that the volume of the tire is 860 mL , that it is filled to a total pressure of 120 psi , and that the temperature is 26°C. Also, assume an average molar mass for air of 28.8 g/mol.

Calculate the mass of air in an air filled tire.
Calculate the mas of helium in a helium-filled tire.
What is the mass difference between the two?

2 Answers

7 votes

Final answer:

To calculate the mass of air in an air-filled tire, you can use the ideal gas law equation PV = nRT. The mass of air in the tire is 142.57 g. To calculate the mass of helium in a helium-filled tire, use the same equation and the molar mass of helium. The mass of helium in the tire is 19.84 g. The mass difference between the two is -122.73 g, indicating that the helium-filled tire is lighter than the air-filled tire.

Step-by-step explanation:

To calculate the mass of air in an air-filled tire, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the volume from mL to L and the temperature from Celsius to Kelvin. So, the volume is 0.860 L, and the temperature is 26 + 273 = 299 K.

Next, we rearrange the ideal gas law equation to solve for n, the number of moles: n = PV / RT. Substituting the values, we get n = (120 psi x 0.860 L) / (0.0821 L.atm/mol.K x 299 K) = 4.96 moles.

The molar mass of air is given as 28.8 g/mol, so the mass of air in the tire is 4.96 moles x 28.8 g/mol = 142.57 g.

To calculate the mass of helium in a helium-filled tire, we can follow the same steps as above, but use the molar mass of helium (4 g/mol) instead. Substituting the values, we get n = (120 psi x 0.860 L) / (0.0821 L.atm/mol.K x 299 K) = 4.96 moles.

So, the mass of helium in the tire is 4.96 moles x 4 g/mol = 19.84 g.

To find the mass difference between the two, we subtract the mass of air from the mass of helium: 19.84 g - 142.57 g = -122.73 g. The negative sign indicates that the helium-filled tire is lighter than the air-filled tire by 122.73 g.

User Mohd Alomar
by
4.5k points
4 votes

Answer:

The mass of air is 8.245 g

The mass of helium is 1.145 g

The difference is 7.1 g

Step-by-step explanation:

Total mass (air and helium) = PVM/RT

P is total pressure in the tire = 120 Psi = 120/14.696 = 8.17 atm

V is volume of the tire = 860 mL = 860 cm^3

M is the total molar mass of air and helium = 28.8 + 4= 32.8 g/mol

R is gas constant = 82.057 cm^3.atm/mol.K

T is temperature = 26°C = 26+273 = 299 K

Total mass = 8.17×860×32.8/82.057×299 = 9.39 g

Mass of air = mass fraction of air × total mass = 28.8/32.8 × 9.39 = 8.245 g

Mass of helium = total mass - mass of air = 9.39 - 8.245 = 1.145 g

Difference = 8.245 - 1.145 = 7.1 g

User Kyaw Tun
by
4.5k points