The density of air at ordinary atmospheric pressure and25 C is 1.19 g/L. What is the mass, in kilograms, of the air ina room that measures 4.5 m * 5.0 m * 2.5 m?

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Calculate the volume of the room by multiplying its dimensions: Volume = 4.5 \text{ m} \times 5.0 \text{ m} \times 2.5 \text{ m}.

Convert the volume from cubic meters to liters, knowing that 1 \text{ m}^3 = 1000 \text{ L}.

Use the density formula $ \text{Density} = \frac{\text{Mass}}{\text{Volume}} $ to find the mass of the air, rearranging it to $ \text{Mass} = \text{Density} \times \text{Volume} $.

Substitute the given density of air (1.19 \text{ g/L}) and the calculated volume in liters into the mass formula.

Convert the mass from grams to kilograms by dividing by 1000, since 1 \text{ kg} = 1000 \text{ g}.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density

Density is defined as mass per unit volume, typically expressed in grams per liter (g/L) for gases. It indicates how much mass is contained in a given volume of a substance. In this question, the density of air is provided, which allows us to calculate the mass of air in a specified volume by rearranging the density formula: mass = density × volume.

Volume Calculation

Volume is the amount of space occupied by an object, measured in cubic units. For a rectangular room, the volume can be calculated using the formula: Volume = length × width × height. In this case, the dimensions of the room are given in meters, and the volume must be converted to liters to match the density units for accurate mass calculation.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, it is necessary to convert the volume of the room from cubic meters to liters, as the density of air is given in grams per liter. Understanding how to perform these conversions is essential for ensuring that calculations are accurate and consistent.

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