In a common classroom demonstration, a balloon is filled...

In a common classroom demonstration, a balloon is filled with air and submerged in liquid nitrogen. The balloon contracts as the gases within the balloon cool. Suppose a balloon initially contains $2.95 \mathrm{~L}$ of air at a temperature of $25.0^{\circ} \mathrm{C}$ and a pressure of $0.998$ atm. Calculate the expected volume of the balloon upon cooling to $-196^{\circ} \mathrm{C}$ (the boiling point of liquid nitrogen). When the demonstration is carried out, the actual volume of the balloon decreases to $0.61 \mathrm{~L}$. How does the observed volume of the balloon compare to your calculated value? Explain the difference.

Key Concepts

Non-Ideal Gas Behavior

Non-ideal gas behavior acknowledges that real gases deviate from the predictions of the Ideal Gas Law under certain conditions, such as at high pressures or very low temperatures. At these extremes, intermolecular forces become significant and the gas molecules occupy finite volume, leading to condensation or other phenomena that cause the gas to behave differently from an idealized model. This is important for understanding discrepancies between theoretical calculations and experimental observations.

Phase Transition

Phase transition refers to the process by which a substance changes from one state of matter to another, such as from a gas to a liquid. In the context of cooling a gas to extremely low temperatures, some of the gas may condense into a liquid if the temperature falls below its condensation point. This change in the phase of some molecules results in a lower observed gas volume than what is predicted by simple gas laws that assume no phase change.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It is a fundamental concept in thermodynamics that allows us to predict how a gas will behave under changes in temperature or pressure when the amount of gas remains constant. Although useful for many calculations, it assumes that gas molecules do not interact and occupy no volume, which can cause deviations at extreme conditions such as very low temperatures.

Charles’ Law

Charles’ Law is a specific case of the Ideal Gas Law where the pressure and amount of gas are held constant. It states that the volume of a gas is directly proportional to its absolute temperature (in Kelvin). This relationship is used to predict the change in volume that occurs when a gas is cooled or heated, and it explains the contraction observed when a gas is brought from a higher temperature to a lower temperature.

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