Question

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 125 psi, and that the temperature is 25∘C. Also, Calculate the mass of air in an air-filled tire. assume an average molar mass for air of 28.8 g/mol. Part B Calculate the mass of helium in a helium-filled tire. Calculate the mass of helium in a helium-filled tire. Part C What is the mass difference between the two?

Answer 1

Answer and 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 ideal gas constant, and T is the temperature.

Given:

Volume of the tire (V) = 860 mL = 0.860 L

Pressure (P) = 125 psi

Temperature (T) = 25°C = 298 K

Molar mass of air (M) = 28.8 g/mol

Using the ideal gas law, we can rearrange the equation to solve for the number of moles (n):

n = (PV) / (RT)

Substituting the values into the equation:

n = (125 psi * 0.860 L) / (0.0821 L·atm/(K·mol) * 298 K)

Calculating n, we find:

n ≈ 5.097 mol

To calculate the mass of air, we can use the equation:

Mass = n * M

Substituting the values into the equation:

Mass ≈ 5.097 mol * 28.8 g/mol

Calculating the mass, we find:

Mass ≈ 146.82 g

Therefore, the mass of air in an air-filled tire is approximately 146.82 g.

To calculate the mass of helium in a helium-filled tire, we can use the same process as above, substituting the molar mass of helium (4.0 g/mol) instead of the molar mass of air.

Given:

Molar mass of helium (M) = 4.0 g/mol

Using the same ideal gas law equation, we can calculate the number of moles of helium (n) in the tire:

n = (PV) / (RT)

Substituting the values into the equation:

n = (125 psi * 0.860 L) / (0.0821 L·atm/(K·mol) * 298 K)

Calculating n, we find:

n ≈ 5.097 mol

To calculate the mass of helium, we can use the equation:

Mass = n * M

Substituting the values into the equation:

Mass ≈ 5.097 mol * 4.0 g/mol

Calculating the mass, we find:

Mass ≈ 20.39 g

Therefore, the mass of helium in a helium-filled tire is approximately 20.39 g.

To calculate the mass difference between the two, we subtract the mass of air from the mass of helium:

Mass difference = Mass of helium - Mass of air

Substituting the values into the equation:

Mass difference = 20.39 g - 146.82 g

Calculating the mass difference, we find:

Mass difference ≈ -126.43 g

The negative sign indicates that the mass of helium is lighter than the mass of air.

Therefore, the mass difference between the two is approximately -126.43 g.