Question

What is the total number of `AlF_3` molecules in a sample of `AlF_3` containing `3.01 * 10^(23)` fluoride ions ?

Answer 1

There are 1.00 × 10²³ formula units of AlF₃.

This is a problem about conversion factors.

AlF₃ is an ionic compound. Ionic compounds do not form molecules. Instead, we speak of formula units.

We see that one formula unit (FU) of AlF₃ contains three fluoride ions.

The conversion factor is either

`(1"FU AlF₃")/(3"F⁻ ions")` or `(3"F⁻ ions")/(1"FU AlF₃")`.

We can use either one, depending on our calculation. In this case, we would write

3.01 × 10²³ F⁻ ions × conversion factor → FU of AlF₃

We must choose the ratio that makes the units cancel to give "formula units" in the answer. We choose the first one.

3.01 × 10²³ F⁻ ions × `(1"FU AlF₃")/(3"F⁻ ions")` = 1.00 × 10²³ FU AlF₃

Notice how the “F⁻ ions” in the numerator and denominator cancel to give the desired units of “FU AlF₃”.

If we had used the other ratio, we would have gotten the units of “(F⁻ ions)²/FU AlF₃”. This is obviously wrong.

Always use units in your calculations. Then you can choose the correct conversion factors to get the desired units in your answers.