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 $755 \mathrm{mm}$ Hg. What amount of helium is in the balloon? (Remember that gauge pressure $=$ total pressure - barometric pressure. See page $550 .)$

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Key Concepts

Unit Conversion

Appropriate unit conversion, such as for pressure (e.g., mm Hg to atmospheres or Pascals) and volume (e.g., mL to liters), is necessary so that all components in the ideal gas equation are consistent with the gas constant and each other. This step is critical for avoiding calculation errors and obtaining correct results.

Temperature Conversion

Temperature must be expressed in an absolute scale, typically Kelvin, when used in thermodynamic equations like the ideal gas law. Converting from Celsius to Kelvin is done by adding 273.15, which is essential for ensuring the accuracy of the calculations.

Gauge Pressure vs Absolute Pressure

Gauge pressure is the pressure measured relative to the ambient atmospheric pressure, while absolute pressure is the total pressure including the atmospheric component. Understanding the distinction is crucial when applying the ideal gas law, as calculations must use absolute pressure.

Ideal Gas Law

This principle, represented by the equation PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is fundamental in determining the amount of gas present in a system when other state variables are known, making it a cornerstone of thermodynamics and physical chemistry.

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