A 1.0 L container of liquid nitrogen is kept in a closet...

A $1.0 \mathrm{~L}$ container of liquid nitrogen is kept in a closet measuring $1.0 \mathrm{~m}$ by $1.0 \mathrm{~m}$ by $2.0 \mathrm{~m}$. Assuming that the container is completely full, that the temperature is $25.0{ }^{\circ} \mathrm{C}$, and that the atmospheric pressure is $1.0$ atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of $0.807 \mathrm{~g} / \mathrm{mL}$.)

Key Concepts

Density and Mass Conversion

This concept involves using the density of a substance to convert its volume into mass. For a liquid, knowing its density allows one to determine how much mass is present in a given volume, which is a crucial step in calculating the number of moles of a substance before any further thermodynamic analysis.

Phase Transition

Phase transition refers to the change from one state of matter to another, such as liquid to gas. In this context, the evaporation of liquid nitrogen involves a significant increase in volume because the gaseous phase occupies much more space than the liquid phase, under the same conditions of temperature and pressure.

Ideal Gas Law Application

The ideal gas law (PV = nRT) is a fundamental relation that connects the pressure, volume, temperature, and number of moles of a gas. It is used to estimate the volume occupied by the nitrogen gas after evaporation, provided the temperature and pressure remain constant.

Volume Displacement in Constrained Spaces

This concept deals with calculating how much space a gas occupies in an enclosed environment and how the introduction of the gas displaces the air present. Understanding volume displacement is important when assessing the impact of gas expansion in confined spaces, such as a closet, and determining the proportion of space that is affected.

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