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.

Recommended video:

Guided course

01:56

Conversion Factors

Related Practice

Textbook Question

(a) If an electric car is capable of going 225 km on a single charge, how many charges will it need to travel from Seattle, Washington, to San Diego, California, a distance of 1257 mi, assuming that the trip begins with a full charge?

views

Textbook Question

(d) In March 1989, the Exxon Valdez ran aground and spilled 240,000 barrels of crude petroleum off the coast of Alaska. One barrel of petroleum is equal to 42 gal. How many liters of petroleum were spilled?

views

Textbook Question

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?

views

Textbook Question

Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 30 m x 25 m ceiling with gold leaf that is twelve-millionths of a centimeter thick. The density of gold is 19.32 g/cm³, and gold costs $1654 per troy ounce (1 troy ounce = 31.1034768 g). How much will it cost the architect to buy the necessary gold?

views

Textbook Question

A copper refinery produces a copper ingot weighing 70 kg. If the copper is drawn into wire whose diameter is 7.50 mm, how many meters of copper can be obtained from the ingot? The density of copper is 8.94 g/cm³. (Assume that the wire is a cylinder whose volume V = πr²h, where r is its radius and h is its height or length.)

Textbook Question

Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: (a) a leaf (b) a 999 gold bar

108

views