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Lesson · Grade 11 · Chemistry

The factor-label method: let the units guide you

  • Grade 11
  • Chemistry
  • 2 min
  • British Columbia
  • BC11-SC-21

A labelled diagram builds up step by step. It turns 2.5 h into 9.0 × 10³ s by writing each conversion factor as a fraction equal to 1 (60 min / 1 h, then 60 s / 1 min) and striking out units as they cancel, then turns 5.00 g of water into 0.277 mol using the molar mass. When the molar-mass factor is flipped upside down, the answer comes out in nonsense units (g²/mol), which shows students how to spot and fix the mistake, and the video ends on a one-line recap.

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In one sentence

The question this lesson answers

How many seconds are in 2.5 hours?

Dimensional analysis, also called the factor-label method, keeps the units in every step so they can guide you.

Transcript

What the lesson says

How many seconds are in 2.5 hours?

Dimensional analysis, also called the factor-label method, keeps the units in every step so they can guide you.

One hour is the same length of time as 60 minutes.

So 60 minutes over 1 hour equals one. This fraction is called a conversion factor.

Multiplying by one changes the units, but not the amount of time.

Hours are now on the top and on the bottom, so they cancel.

Next, 1 minute is 60 seconds, so multiply by 60 seconds over 1 minute.

Minutes cancel too, and only seconds are left.

2.5 times 60 times 60 is 9000 seconds.

2.5 has two significant figures, or meaningful digits, so we write the answer as 9.0 times 10 to the third seconds.

Chemists count particles in moles. How many moles are in 5.00 grams of water?

Water's molar mass, the mass of one mole, is 18.02 grams.

To cancel grams, put grams on the bottom: 1 mole over 18.02 grams.

Grams cancel, and 5.00 divided by 18.02 is 0.277 moles.

But what if you write the factor upside down?

Then nothing cancels, and the units come out as grams squared per mole, which makes no sense.

Nonsense units tell you to flip the factor.

Write each conversion factor so the units you don't want cancel, and only the unit you want is left.

Curriculum

Where this fits

British Columbia, Grade 11

Chemistry 11, The mole and stoichiometry: dimensional analysisBC11-SC-21

Previous: Molar mass: adding up atomic massesNext: Significant Figures: How Precise Is Your Answer?

The outcomes and strands follow the British Columbia curriculum.

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