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 helium in a helium-filled tire.

Verified step by step guidance

1. Convert the volume of the tire from milliliters to liters by dividing by 1000.
2. Convert the pressure from psi to atm using the conversion factor: 1 atm = 14.696 psi.
3. Convert the temperature from Celsius to Kelvin by adding 273.15.
4. Use the ideal gas law, PV = nRT, to calculate the number of moles (n) of gas in the tire. Use R = 0.0821 L·atm/mol·K.
5. Calculate the mass of the gas by multiplying the number of moles by the molar mass of the gas (28.8 g/mol for air and 4.00 g/mol for helium).

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the amount of gas in a tire, as it allows us to determine the number of moles based on the given pressure, volume, and temperature. Understanding this relationship is crucial for solving the problem of mass calculation for both air and helium.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In this question, the average molar mass of air is given as 28.8 g/mol, which is necessary for converting the number of moles of air calculated from the Ideal Gas Law into mass. Similarly, knowing the molar mass of helium (approximately 4.00 g/mol) is vital for determining the mass of helium in the tire.

Pressure Conversion

Pressure conversion is the process of changing pressure units to facilitate calculations. In this scenario, the pressure is given in psi (pounds per square inch), which may need to be converted to atmospheres (atm) or pascals (Pa) for use in the Ideal Gas Law. Understanding how to convert between these units is essential for accurately applying the law and obtaining the correct mass values.