Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. What is the mass difference between the two? Assume that the volume of the tire is 857 , that it is filled with a total pressure of 125 psi, and that the temperature is 26 . Also, assume an average molar mass for air of 28.8 .

890

To calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire, we can use the Ideal Gas Law equation: PV = nRT.

Let's break down the process step by step:

Step 1: Convert tire volume to cubic meters
In the given information, the volume of the tire is provided in an unspecified unit. We'll assume it's in liters (L). To convert it to cubic meters (m³), we need to divide it by 1000 since 1 L equals 0.001 m³.

Given volume of the tire = 857 L
Converted volume = 857 L * 0.001 m³/L = 0.857 m³

Step 2: Calculate the amount of air in the tire
Using the Ideal Gas Law equation (PV = nRT), we can solve for n (the number of moles of gas) as follows:

P = pressure of the gas = 125 psi = 125 pounds per square inch
V = volume of the gas = 0.857 m³
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature of the gas in Kelvin (K) = 26 °C + 273.15 = 299.15 K

n = (P * V) / (R * T)

Substituting the values, we get:
n = (125 * 0.857) / (8.314 * 299.15)

Step 3: Calculate the mass of air in the tire
To find the mass of air, we need to multiply the number of moles of air (n) by the average molar mass of air.

Average molar mass of air = 28.8 g/mol (given)

Mass of air = n * average molar mass of air

Step 4: Calculate the mass of helium in the tire
To calculate the mass of helium, we follow the same process as step 3, but with the molar mass of helium instead of air.

Molar mass of helium = 4.0 g/mol

Mass of helium = n * molar mass of helium

Step 5: Calculate the mass difference between the two
To find the mass difference between the mass of air and the mass of helium, subtract the mass of helium from the mass of air.

Mass difference = Mass of air - Mass of helium

Now, you just need to substitute the values into the respective formulas and perform the calculations to get the final answers.