Unit Conversions

Not all calculations in chemistry are unit conversions, some calculations require a formula. Unit conversions (aka dimensional analysis) are used when an identity can be used to switch from one unit to another. An example would be if you are given a volume in milliliters, but the problem requires that you are working in liters. The identity used is the fact that there are 1000ml in 1 liter.

Example: You are given that there a gas occupies a volume of 500 ml. You need this in liters.

500 ml * 1 liter/1000 ml = .5 liter

The given number is written first and then multiplied by the identity. In this case, the identity is written with liters in the numerator because that is the unit you want to end up in. The ml is in the denominator so that it will cancel the ml in the given number.

I will be making the operation signs (addition, multiplication, etc) red so that you can tell the difference more easily between an identity and a calculation.

Many conversions can be done in a long string without having to press enter on your calculator until the very end.

Example: You have 4.3 kg of a substance that has a density of 2.7 g/ml (2.7g = 1 ml) and you need to know the volume in liters.

4.3 kg * 1000 g/1 kg * 1 ml/2.7 g * 1 liter/1000 ml = 1.6 liters

In this case, the 2.7 g/1 ml identity was written upside down so that the g would be in the denominator to cancel the g that was in the numerator from the previous identity.

For figuring the significant figures for your answer, use the rules for multiplying and dividing from before. Exact conversions like 1000 ml/1 liter and 12 in/1 ft have unlimited significant figures so you don't look at them when you are determining the least number of significant figures for your calculation.

There are some identities that you should have memorized. We will be adding to this list, but for now, they are:

1000 ml = 1 liter

100 cm = 1 m

1 ml = 1 cm^3

1000 g = 1 kg

 

Unit Conversions Quiz

Make the following conversions, using the correct significant figures:

1. 4.5 liters to ml
2. 36 cm to meters
3. 45 kg/litre to g/ml

Answers are on the answer page.

If you would like a little more information or practice, go to this web page on dimensional analysis.

When finished, return to the introduction page for a new topic.