Suppose a helium-filled balloon used to carry scientific...

Suppose a helium-filled balloon used to carry scientific instru- ments into the atmosphere has a volume of $1.00 \times 10^6 \mathrm{~L}$ at $25^{\circ} \mathrm{C}$ and a pressure of 752 mm Hg at the time it is launched. What will be the volume of the balloon, in liters, when, at a height of 37 km , it encounters a temperature of $-33^{\circ} \mathrm{C}$ and a pressure of 75.0 mm Hg ?

Key Concepts

Combined Gas Law

The combined gas law relates the pressure, volume, and temperature of a fixed amount of gas when it undergoes a change from one set of conditions to another. It is expressed as (P?V?/T?) = (P?V?/T?), and it allows you to solve for an unknown variable when the others change, making it essential for problems involving simultaneous changes in temperature, pressure, and volume.

Absolute Temperature Scale (Kelvin)

In gas law calculations, temperature must always be expressed in Kelvin, the absolute temperature scale. Converting Celsius to Kelvin (by adding 273.15) is necessary because the gas laws are based on the behavior of an ideal gas at absolute zero, ensuring that temperature values are always positive and the relationships hold true.

Unit Conversion

Consistent unit conversion is crucial in applying any gas law correctly. This involves converting all initial and final measurements to a consistent set of units (such as converting pressure to a common unit and temperature to Kelvin) so that the mathematical relationships between the variables remain valid across different conditions.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, encapsulates the fundamental relationship between pressure, volume, temperature, and the amount of gas. It serves as the foundation for deriving other related gas laws, including the combined gas law, and helps in understanding how gases respond to changes in external conditions.

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