Pressurized carbon dioxide inflators can be used to inflate...

Pressurized carbon dioxide inflators can be used to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain $16.0 \mathrm{~g}$ of carbon dioxide. At $298 \mathrm{~K}$, to what pressure (in psi) can the carbon dioxide in the cartridge inflate a $3.45 \mathrm{~L}$ mountain bike tire? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is $14.7$ psi.)

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Key Concepts

Gauge Pressure

Gauge pressure is the measure of pressure relative to the ambient atmospheric pressure. It is defined as the difference between the absolute (total) pressure inside a system and the surrounding atmospheric pressure, and it is crucial in applications like tire inflation where only the excess pressure above atmospheric pressure is of interest.

Unit Conversion

Unit conversion is critical in solving problems that involve different measurement systems. When applying the ideal gas law, pressures, volumes, and temperatures must be consistent in their units, and after finding the pressure, it often needs to be converted into the specific unit required, such as psi from atmospheres or Pascals.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relationship in thermodynamics that connects the pressure, volume, temperature, and number of moles of a gas. It is used to determine one variable when the others are known and is core to many calculations involving gases, including the expansion of gases in a tire.

Molar Mass and Mole Calculation

Knowing the molar mass of a gas and its mass allows you to calculate the number of moles present. This conversion from mass to moles is essential when applying the ideal gas law, as the law requires the amount of substance in moles to compute other properties like pressure.

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