A balloon at the circus is filled with helium gas to a gauge...

A balloon at the circus is filled with helium gas to a gauge pressure of $22 \mathrm{mm}$ Hg at $25^{\circ} \mathrm{C}$. The volume of the gas is $305 \mathrm{mL},$ and the barometric pressure is 755 mm Hg. What amount of helium is in the balloon? (Remember that gauge pressure = total pressure barometric pressure. See page $517 .)$

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is a fundamental equation that relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. It allows for the calculation of any one variable when the others are known, assuming that the gas behaves ideally.

Gauge Pressure versus Absolute Pressure

Gauge pressure represents the pressure measured relative to the surrounding atmospheric pressure. In scenarios where absolute pressure is needed—such as in calculations using the ideal gas law—the atmospheric (barometric) pressure must be added to the gauge pressure to obtain the total absolute pressure.

Unit Conversions

For accurate application of the ideal gas law, measurements must be in consistent units. This often requires converting quantities such as pressure from mm Hg to atmospheres or pascals, volume from milliliters to liters, and temperature from degrees Celsius to Kelvin. These conversions are crucial to ensure the correctness of the calculation.

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