Formula Weights

A simple but very important skill that you will be called upon to do many, many times during this course is to calculate the formula weight of a chemical based on its formula. You can do that very easily as long as you know the formula of the chemical with which you are dealing. I will present three examples (which are also shown in Example 12 in your workbook) and then have you try your hand at a few. If you are already familiar with determining formula weights, move on to the Quick Quiz on Calculating Formula Weights.

The first example is H₂O. The formula weight is the sum of the atomic weights of everything that's in that particular formula. In the case of H₂O, the formula weight of H₂O is the sum of the weights of two hydrogens and one oxygen. To get the formula weight for H₂O, you need twice the atomic weight of hydrogen and add to that the atomic weight of one oxygen. It is shown in the example that the formula weight of H₂O is 18.0.

H₂O	2 H	2 x 1.0 =	2.0
	1 O	1 x 16.0 =	16.0
		FW =	18.0

The next formula is HNO₃. The formula contains 1 hydrogen, 1 nitrogen and 3 oxygens. So the weights come out to be 1.0 plus 14.0 plus 48.0, a total of 63.0.

HNO₃	1 H	1 x 1.0 =	1.0
	1 N	1 x 14.0 =	14.0
	3 O	3 x 16.0 =	48.0
		FW =	63.0

When you are dealing with parentheses, as in Fe(NO₃)₂, that's one more factor to take into account. However, you can easily interpret the formula to see that it represents 1 iron, 2 nitrogens and 6 oxygens. Then multiply the 1, 2, and 6 by the atomic weights for iron, nitrogen, and oxygen, add all those together and you get 179.8.

Fe(NO₃)₂	1 Fe	1 x 55.8 =	55.8
	2 N	2 x 14.0 =	28.0
	6 O	6 x 16.0 =	96.0
			179.8

There is another way of doing this. That is to focus on what's in the parentheses. The NO₃ portion of that compound has its own formula weight and the formula weight of NO₃ comes out to be 62. (14.0 for the nitrogen and 3 times 16.0 gives 48.0 for the oxygen which comes to a total of 62.0.) This compound as a whole has 1 iron and 2 NO₃'s and so if you take the weight of the iron (55.8) and double the weight of the NO₃ (which is 124.0) and add those together you come up with the formula weight of 179.8 which of course is the same as what we got using the first method.

(NO₃)	1 N	1 x 14.0 =	14.0
	3 O	3 x 16.0 =	48.0
		FW of NO₃ =	63.0

Fe(NO₃)₂	1 Fe	1 x 55.8 =	55.8
	2 NO₃	2 x 62.0 =	124.0
		FW =	179.8

Something I should point out before we continue is that formula weights apply to any kind of formula. Whether you're dealing with molecular formulas or empirical formulas or whatever kind of formula you're dealing with you can calculate a formula weight for it. If you happen to be dealing with a molecular formula, the formula weight for it can also be called the molecular weight.

Practice Determining Formula Weights

Determining formula weights is very simple, straightforward, and important and I would like you to practice by determining the formula weights for the compounds in example 13 in your workbook.

So please take a moment to do that and check your answers below. (If, after completing these, you would like to try some additional problems of this type, you will find several in a "Practice Problems" page in the Wrap-Up for this lesson. Click here to go there now.)

Answers

For your answers you should have HF is 20.0; CH₄ is 16.0; C₃H₇O₂ is 75.0; Fe₂(CO₃)₃ is 291.6. If you did not get these answers, check with the instructor to figure out why before continuing. Since these are relative formula weights, we do not have units listed. However, most formula weights are listed with units of a.m.u. or g/mole; we will almost exclusively have units of g/mole for formula weights in this class. Read on to the next section for a discussion of moles.

Note: One thing that students often ask about is how many significant digits to use when calculating the formula weights. Different periodic tables will report atomic weights to different precisions - one table might only show one decimal place (like the previous examples) while another periodic table might show 5 or more decimal places! For a class at this introductory level, atomic weights are generally rounded to one or two decimal places; we used only one decimal place in the previous examples for simplicity and to get you started. From now on, for this class, I would like you to get in the habit of using two decimal places for atomic and formula weights.

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