Olympic cyclists fill their tires with helium to make them...

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. What is the mass difference between the two? Assume that the volume of the tire is 855 $\mathrm{mL}$, that it is filled to a total pressure of $125 \mathrm{psi}$, and that the temperature is $25^{\circ} \mathrm{C}$. Also, assume an average molar mass for air of $28.8 \mathrm{~g} / \mathrm{mol}$.

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Key Concepts

Ideal Gas Law

This is a fundamental equation (PV = nRT) that relates the pressure, volume, temperature, and number of moles of a gas. It allows you to determine how many moles of gas are present under given conditions, and it is essential for calculating the mass of gas in a container when combined with the concept of molar mass.

Molar Mass

Molar mass is the mass of one mole of a substance. It is used to convert the number of moles (obtained from the ideal gas law) into an actual mass. Differences in molar mass, such as between air and helium, are crucial since they directly affect the weight of gas contained in the same volume at the same temperature and pressure.

Unit Conversion

Converting units is critical in ensuring that all variables in the equations are consistent. For instance, pressure may need to be converted from psi to pascals and volume from milliliters to liters to properly apply the ideal gas law. Accurate unit conversion underpins reliable calculations.

Gas Density and Composition

The density of a gas is determined by its molar mass and the state variables as described by the ideal gas law. Even under identical conditions, a gas like helium, with a lower molar mass, will have a lower density compared to air. This concept is essential when comparing the relative masses of different gases in similar volumes.

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