What Is Dimensional Analysis in Chemistry? - Definition, Method & Practice Problems

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  • 0:01 Dimensional Analysis…
  • 0:55 Units of Measurement
  • 1:48 Conversion Factors & Prefixes
  • 4:23 Dimensional Analysis Practice
  • 8:46 Lesson Summary
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Lesson Transcript
Instructor: Sheila Morrissey

Sheila has a master's degree in geology and has taught middle school through university-level science courses.

Learn about units of measurement in chemistry and the common metric prefixes you will see used with those units. Practice converting units of measurement using Dimensional Analysis.

Dimensional Analysis in Chemistry

Dimensional Analysis is a way chemists and other scientists convert units of measurement. We can convert any unit to another unit of the same dimension. This means we can convert some number of seconds into another unit of time, such as minutes, because we know that there are always 60 seconds in one minute. Or we can convert some amount of mass from grams to kilograms, knowing that there are always 1000 grams in one kilogram. Or we can convert lengths, say, from kilometers to miles, although metric units are most frequently used in chemistry. With a known conversion factor, it is sometimes possible to convert to a new dimension. For instance, 1 kilogram of pure water is equal to 1 liter. Using that knowledge, you could convert a volume of water to a mass of water, or vice versa.

Units of Measurement

Commonly used dimensions in chemistry include time, mass, length, and volume. The standard units of measurement (those used most frequently so that they can be easily shared with other scientists) are the SI units, from the International System of Units. The SI unit of time is seconds, and its unit symbol is s. The SI unit of mass is kilogram. It is written as kg, where the k is the metric prefix meaning kilo and the g stands for gram, the base unit of mass. The SI unit of length is the meter, with the symbol m. Chemists also often use moles, an SI unit describing an amount of a substance. A mole is equal to approximately 6.022 x 10^23 particles, such as atoms or molecules. Its symbol is mol.

SI Base Units

Conversion Factors and Prefixes

In order to convert from one unit to another, we need to know how those units are related. Sometimes there is a well-established conversion factor that you can use to convert between dimensions, such as 1 kilogram of pure water equals 1 liter of pure water. You could also measure (or look up) conversion factors between metric and English units of the same dimension. For instance, 1 mile is approximately equal to 1.6 kilometers.

Most often in chemistry, your conversions will include either moles or metric units. To make your dimensional analysis life easier, it is important to work toward memorizing both an approximation of Avogadro's constant, the number of particles in a mole, and the metric prefixes. Equally important is that you have a sense of what these units mean.

We have said before that one mole is equal to approximately 6.022 x 10^23 particles (this can be anything, really, though most often it will be atoms or molecules). That's a really big number! Avogadro's constant sometimes scares new chemistry students, but it's just a number.

So if I were to ask you how many cookies are in a dozen, you'd hopefully tell me that there are 12 cookies in a dozen. And if I said I had a mole of cookies, you would know that means I have approximately 6.022 x 10^23 cookies.

Let's bring it back to chemistry. If you have 1 mole of carbon atoms, then that would mean you have approximately 6.022 x 10^23 carbon atoms. Or, if you have 1 mole of water molecules, that would be approximately 6.022 x 10^23 water molecules.

Our final step before we start practicing dimensional analysis is to learn about the metric prefixes so that we can make conversions between like base units. If we need to convert 1 kg to g, for instance, you will need to remember that g stands for grams, a unit of weight, and that the prefix k means kilo, or one thousand. So if we have 1 kg (or 1 kilogram), that means that we have one thousand grams, and our conversion is complete.

You might already recognize some of the biggest metric prefixes from your experience with computers, specifically, k (kilo), M (mega), G (giga) and T (tera). Of the prefixes smaller than 1, you might recognize deci, meaning one tenth, from the word decimal and realize that centi, one hundredth, has the same origins and meaning as the word cent. One penny, or one cent, is one one-hundredth of a dollar.

Metric Prefixes

Dimensional Analysis Practice

It's time to put our understanding of units and conversion factors to use. We will use dimensional analysis to set up and solve our unit conversion problems with known conversion factors.

Practice Problem #1

Convert 25.0 mL to L.

Practice Problem 2

First, write down your starting measurements. Here, we have 25.0 mL. Sometimes the units will have both a numerator and a denominator, like meters per second, but if not, then you can put your measurement over 1.

In order to not change our initial measurement of 25.0 mL but only change the units, we want to find a way to multiply it by a value of 1. We'll need to find a conversion factor that will cancel out the mL units we already have, since we're moving away from those units, and one that will introduce Liters, the final units we're moving towards. We already know that mL means milliliters and that the prefix milli means one thousandth. That means we'd have to have 1000 mL to equal 1 L. We'll plug in that conversion factor.

Looking at our new dimensional analysis setup, we can cancel the mL units because we have one in the numerator and one in the denominator. The only units remaining are L, which is our final destination in this unit conversion. Finally, all we need to do is to follow through with the multiplication of the numbers, and we get 0.025 L.

Practice Problem #2

Convert 5.0 kg to cg.

Practice Problem 1

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