The air in a bicycle tire is bubbled through water and...

The air in a bicycle tire is bubbled through water and collected at $25^{\circ} \mathrm{C}$ . If the total volume of gas collected is 5.45 $\mathrm{L}$ at a temperature of $25^{\circ} \mathrm{C}$ and a pressure of 745 torr, how many moles of gas were in the bicycle tire?

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and moles of an ideal gas. It provides the fundamental relationship that allows one to calculate any one of these variables if the other three are known. In problems like this, once the correct pressure, volume, and temperature units are used, the gas constant R is applied to determine the number of moles present.

Unit Conversions

Accurate calculations using the ideal gas law depend on correct unit measurements. This involves converting pressure into atmospheres or pascals if necessary, temperature into Kelvin, and confirming that the volume is expressed in liters (or cubic meters) as required by the gas constant used. These conversions are critical to obtaining a proper and consistent input for the equation.

Gas Collection Over Water

When a gas is collected over water, the measured pressure includes contributions from both the gas and the water vapor, which is a result of water's volatilization. In such scenarios, it is important to correct the measured pressure to obtain the pressure of the dry gas alone by accounting for the vapor pressure of water at the collection temperature. This adjustment ensures that the ideal gas law is applied accurately to the dry gas component.

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