Question

Carbon monoxide (CO) detectors sound an alarm when peak levels of carbon monoxide reach 100 parts per million (ppm). This level roughly corresponds to a composition of air that contains \(400,000\) \mug carbon monoxide per cubic meter of air \(\left(400,000 \mu \mathrm{g} / \mathrm{m}^{3}\right) .\) Assuming the dimensions of a room are 18 \(\mathrm{ft} \times 12 \mathrm{ft} \times 8 \mathrm{ft}\) , estimate the mass of carbon monoxide in the room that would register 100 \(\mathrm{ppm}\) on a carbon monoxide detector.

Short answer

The mass of carbon monoxide in the room that would register 100 ppm on a carbon monoxide detector is approximately 19.54 grams.

Step-by-step solution

Convert room dimensions to meters

To convert the room dimensions from feet to meters, we will use the conversion factor: 1 ft ≈ 0.3048 m. Therefore, the room dimensions are as follows: Length: 18 ft × 0.3048 ≈ 5.4864 m Width: 12 ft × 0.3048 ≈ 3.6576 m Height: 8 ft × 0.3048 ≈ 2.4384 m

Calculate the room volume

Now that we have the room dimensions in meters, we can calculate the volume of the room by multiplying the length, width, and height: Volume = Length × Width × Height Volume = 5.4864 m × 3.6576 m × 2.4384 m ≈ 48.8562 m³

Calculate the mass of CO at 100 ppm in the room

We are given that 100 ppm corresponds to 400,000 µg/m³ of CO. To estimate the mass of CO in the room that would register 100 ppm, we must multiply this concentration by the volume of the room: Mass of CO = Concentration × Room Volume Mass of CO = 400,000 µg/m³ × 48.8562 m³ ≈ 19,542,480 µg Finally, convert the mass of CO into grams (1 g = 1,000,000 µg): Mass of CO ≈ 19,542,480 µg × (1 g/1,000,000 µg) ≈ 19.54 g So, the mass of carbon monoxide in the room that would register 100 ppm on a carbon monoxide detector is approximately 19.54 grams.

Key concepts

Carbon Monoxide Detection

Carbon monoxide is a colorless, odorless, and poisonous gas. It is produced by incomplete combustion of carbon-containing fuels. Because of these properties, it's crucial to have a carbon monoxide detector in homes and enclosed spaces. Detectors are designed to measure the concentration of CO in the air and sound an alarm when dangerous levels are reached. This is vital in preventing CO poisoning, which can cause symptoms ranging from headaches to dangerously affecting oxygen transport in the blood. In typical detectors, the alarm is usually set to go off at a concentration of around 100 parts per million (ppm). This allows occupants to take necessary actions to ventilate the area or evacuate if needed.

Units Conversion

Understanding units conversion is essential to accurately measure and communicate physical quantities. In our exercise, we began by converting room dimensions from feet to meters. This was achieved using the conversion factor, where 1 foot is approximately equal to 0.3048 meters.
Here are the steps that were taken:

• Multiply the length in feet by the conversion factor for meters.
• Repeat the process for the width and height.

This conversion is crucial for calculating the room volume in cubic meters, necessary for analyzing the concentration of substances like carbon monoxide. Converting units ensures accurate measurements, comparisons, and calculations.

Volume Calculation

Calculating the volume of a space involves multiplying its three-dimensional measurements: length, width, and height. For this exercise, the dimensions of the room were first converted into meters. After converting, we determined the room's cubic meter volume using the formula:\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]Using the dimensions

• Length: 5.4864 meters
• Width: 3.6576 meters
• Height: 2.4384 meters

the volume was calculated to be approximately 48.8562 cubic meters.
This measurement is vital for understanding the capacity of air the room holds, directly affecting the concentration of carbon monoxide or any other substances.

Air Quality Measurement

Measuring air quality is essential for health and safety, especially indoors. In our exercise, we estimated the mass of carbon monoxide in the room by relating it to air quality standards like parts per million (ppm). The concentration of 1 ppm denotes one part gas per every million parts of the air by volume. Carbon monoxide at 100 ppm corresponds to 400,000 micrograms per cubic meter. To find out the mass of carbon monoxide contributing to this concentration in a room, you multiply the concentration by the room's volume. Finally, we converted the total mass from micrograms to grams for convenience. Remember:

• Sum of pollutants impacts air quality; it's important to know the levels of gases like CO.
• Regular monitoring ensures air remains safe and healthy to breathe.

This kind of understanding equips us to mitigate risks and ensure a safe living or working environment.