Carbon monoxide (CO) detectors sound an alarm when peak...

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 $400,000 \mu \mathrm{g}$ 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.

Key Concepts

Concentration Measurement

Concentration measurement refers to quantifying the amount of a particular substance within a given volume. Typically expressed in units such as parts per million (ppm) or micrograms per cubic meter (µg/m³), understanding concentration is crucial for assessing the intensity or dosage of a substance in an environment.

Mass Estimation

Mass estimation involves calculating the total mass of a substance present within a volume by multiplying the concentration (or density) of that substance by the volume it occupies. This requires accurate unit conversions and an understanding of the relationship between mass, volume, and concentration.

Volume Calculation

Volume calculation involves determining the space occupied by a given object or area by multiplying its dimensions. This concept is critical in many scientific applications, such as determining the amount of a substance in a container, where the overall volume is used in tandem with the density or concentration of that substance.

Unit Conversion

Unit conversion is the process of translating measurements from one system to another so that all calculations are consistent and accurate. In many problems, you have to convert dimensions (like converting feet to meters) to ensure that units match when calculating volumes or other quantities.

Transcript

00:01 So we're learning about carbon monoxide in this problem, and they're telling us they want us to figure out how much 100 parts per million of co weighs giving us this density of 400 ,000 micrograms per meter cubed.

00:15 And they're asking us if you have a room that's this volume filled with co, how much mass would have to be in that room that would register the 100 ppm on a carbon monoxide detector.

00:30 So there's two main ways to do this problem, right? so you notice that your volume is going to be probably in feet cubed, right? so if you compute this, you're going to get 1 ,728 feet cubed.

00:43 And then you have to find a way to convert from feet cube to meters cubed.

00:47 Right.

00:47 So there's two ways to do this.

00:48 One of them is probably a little more mathematically challenging, which is figuring out a unit conversion from feet cubes to meters cubed, which is what i'm going to do in this tutorial.

00:58 Another solution would be to convert all of your individual lengths into centimeters and then into meters.

01:06 So you can go from feet to inches, inches to centimeters, and then centimeters to meters, and then compute your volume after doing all of that to get to meters cubed.

01:16 Or you can figure out the unit conversion for feet cube to meters cube, which is what i'm going to do on this page just to show people and give them experience with dimensional analysis, especially if you're struggling, basically unit hopping, going from feet to inches, to centimeters to meters.

01:31 So the way that we're going to do this is we're going to start with feet.

01:33 So one foot is going to equal 12 inches, right? so you have 12 inches for each foot.

01:47 Feet are going to cancel out.

01:50 And then using the next unit, which is centimeters.

01:53 So you have 2 .54 centimeters in each inch.

01:58 I got all of these from the first chapter of the textbook.

02:02 They're all in there.

02:03 And then we're going to use, sorry, not equals.

02:05 We're going to use our prefix definition of centimeters, right? so centi is 10 to the minus second.

02:13 So when you're converting from centimeters to meters to meters, you're going to have 10 to the minus second meters is equal to one centimeter.

02:20 So centimeters will cancel out.

02:21 So when you do all of that, you're going to get that one foot is equal...