Department

Chemistry

Course Code

CHEM1006

Professor

Reeves Valerie

Lecture 2

Unit analysis is a form of proportional reasoning where a given measurement can be multiplied

by a known proportion or ratio to give a result having a different unit or dimension.

Algebraically, we know that any number multiplied by one will be unchanged.

If the number has units, and we multiply it by a ratio containing units, the units in the number

will multiply and divide by the units of the ratio, giving the original number but with different

units.

This method can be generalized as: multiply or divide a given number by a known ratio to find

your answer.

The ratios used are based upon the units and are set up so that the units in the denominator of

the ratio match the numerator units of the given and the units in the numerator of the ratio

match those in either the next ratio or the final answer.

When these are multiplied, the given number will now have the correct units for your answer.

Say you were trying to convert 3.41 grams of He to a number of atoms of He. You would

identify 3.41 grams as the given.

The first step is always to place the given out front of your equation.

Then find a ratio that will help you convert the units of grams to atoms.

As you probably have already guessed, you need to use a couple of ratios to help you in this

problem.

The ratio that 4.002 g of He = 1 mole will help you in this problem.

Avogadro's number, 6.022 x 1023 atoms = 1 mole, will also help you in this problem.

Then you set up your ratios so that your units will cancel successfully.

As always, your final answer should contain the correct number of sig figs and the correct units.

If you had a sample of a substance with a mass of 0.0034 grams, and you wanted to express

that mass in mg, you could use the following dimensional analysis.

The given quantity is the mass of 0.0034 grams.

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