The indoor concentration of ozone above 300 mg/m³ is considered to be unhealthy. What mass of ozone in grams is present in a room measuring 3.2 m × 2.8 m × 4.1 m?

Verified step by step guidance

Calculate the volume of the room by multiplying its dimensions: $3.2 \, \text{m} \times 2.8 \, \text{m} \times 4.1 \, \text{m}$.

Convert the volume from cubic meters to cubic decimeters (liters) since 1 m³ = 1000 dm³.

Use the given concentration of ozone, 300 mg/m³, to find the total mass of ozone in milligrams by multiplying the concentration by the volume of the room in cubic meters.

Convert the mass of ozone from milligrams to grams by dividing by 1000, since 1 g = 1000 mg.

Summarize the steps to ensure the mass of ozone in grams is calculated correctly based on the room's volume and the given concentration.

Key Concepts

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

Volume Calculation

To determine the mass of ozone in the room, we first need to calculate the room's volume. The volume of a rectangular room can be found using the formula: Volume = length × width × height. In this case, the dimensions are given in meters, so the volume will be in cubic meters (m³).

Density and Mass Relationship

The relationship between mass, volume, and density is crucial for this problem. Density is defined as mass per unit volume (density = mass/volume). By rearranging this formula, we can find the mass of ozone by multiplying its concentration (in mg/m³) by the volume of the room (in m³).

Unit Conversion

Since the concentration of ozone is given in milligrams per cubic meter (mg/m³) and we need the mass in grams, unit conversion is necessary. There are 1000 mg in 1 gram, so we must convert the final mass from milligrams to grams to provide the answer in the required unit.

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