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

A $1.0$ - 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 $1.0 \mathrm{~atm}$, calculate the percent (by volume) of air that would be displaced if all of the liquid nitrogen evaporated. (Liquid nitrogen has a density of $0.807 \mathrm{~g} / \mathrm{mL}$.)

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Key Concepts

Density

Density is defined as the mass per unit volume of a substance. It allows one to convert between the volume of a material and its mass, which is essential when determining the amount of substance present in a given liquid volume.

Phase Change and Gas Expansion

Phase change refers to the transformation of a substance from one state of matter to another, such as from liquid to gas. This transition generally involves a significant increase in volume due to the decrease in density and the larger intermolecular spacing in the gaseous state.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation that relates the pressure, volume, temperature, and number of moles of a gas. It is used to predict the behavior of gases under various conditions and is crucial for calculating the volume that a gas will occupy after a phase change.

Percentage Volume Displacement

Percentage volume displacement quantifies the proportion of a container or space that is occupied by a substance relative to the total available volume. It is calculated by comparing the volume of the substance to the total volume and expressing this ratio as a percentage, which is important for understanding how much space is affected by a process like evaporation.

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