A 1.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 25.0 °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 g/mL.)

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Calculate the mass of liquid nitrogen using its density and the volume of the container: \( \text{mass} = \text{density} \times \text{volume} \).

Convert the mass of liquid nitrogen to moles using the molar mass of nitrogen (N2), which is approximately 28.02 g/mol.

Use the ideal gas law \( PV = nRT \) to find the volume of nitrogen gas at 25.0 °C and 1.0 atm. Remember to convert the temperature to Kelvin by adding 273.15.

Calculate the volume of the closet in liters: \( \text{volume} = \text{length} \times \text{width} \times \text{height} \).

Determine the percent of air displaced by dividing the volume of nitrogen gas by the volume of the closet and multiplying by 100 to get the percentage.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under varying conditions and is crucial for calculating the volume of nitrogen gas produced when liquid nitrogen evaporates.

Density and Volume Conversion

Density is defined as mass per unit volume (density = mass/volume). In this problem, knowing the density of liquid nitrogen allows us to convert its mass into volume, which is necessary to determine how much nitrogen gas will occupy the space when it evaporates.

Displacement of Air

When a substance is placed in a container, it displaces an equivalent volume of the fluid (or gas) that was previously in that space. In this scenario, calculating the volume of nitrogen gas produced will help determine the volume of air displaced in the closet, which is essential for finding the percent of air displaced.