Unit 7: Formula Mass and % Composition

The Formula Mass (also sometimes called the molecular mass) is the mass of an entire compound. It is determined by adding together the total atomic masses of each element involved in a compound. Each element’s mass is measured in Atomic Mass Units (amu), which is defined as 1/12 of the mass of an atom of Carbon – 12 (which has six protons and six neutrons in its nucleus). The atomic mass, then, is the average mass of the atoms of an element, based on the relative abundance of the element’s isotopes. If you look on the chart and find Carbon, its atomic mass is listed as 12.01, not 12.00, because all of the isotopes of Carbon have been averaged together based on its isotopes. Since some of Carbon’s isotopes have more than six neutrons, that’s where the 12.01 is coming from. Here’s a chart that I like to use because the elements are in alphabetical order. But the Periodic Table you downloaded should have atomic masses too.

Table of Atomic Masses

Ex: Let’s find the formula mass of the compound: H₂SO₄ (that’s sulfuric acid – the stuff in your vehicle’s battery right now. Sometimes, sulfuric acid is referred to as “battery acid”)

Here’s how we do it:

There are 2 hydrogen atoms, 1 sulfur atom, and four oxygen atoms in sulfuric acid, right?

Hydrogen = 1.008 amu x 2 = 2.016
Sulfur = 32.06 amu x 1 = 32.06
Oxygen = 16.00 amu x 4 = 64.00

Add those numbers together: 2.016 + 32.06 + 64 = 98.076
So, the formula mass of sulfuric acid is 98.076

Ex: what’s the formula mass of sodium hydroxide? NaOH

Sodium = 22.99 x 1 = 22.99
Oxygen = 16.00 x 1 = 16.00
Hydrogen = 1.008 x 1 = 1.008

Add those numbers together: 22.99 + 16.00 + 1.008 = 39.998
The formula mass of sodium hydroxide is 39.998

Ex: What’s the formula mass of copper sulfate pentahydrate? Copper what??? Copper sulfate pentahydrate has the formula: CuSO₄•5H₂O

Now, if this was a math class and you saw that dot in the middle, you’d be thinking that you would multiply the two parts of this formula together – but that’s not what we do in chemistry! In chemistry, we just add everything together. That dot followed by a certain number of water molecules in a compound formula means that there are water molecules associated with the first part of the compound. So in this case it means that there are 5 water molecules associated with the cupric sulfate. The entire formula, including the 5 waters, is what we want the mass for. Add it all up!

Copper = 63.55 x 1 = 63.55
Sulfur = 32.06 x 1 = 32.06
Oxygen = 16.00 x 4 = 64.00
(that takes care of the cupric sulfate part)

Hydrogen = 1.008 x 10 = 10.08 (there are 5 water molecules and each molecule has 2 H atoms)
Oxygen = 16.00 x 5 = 80.00 (there are 5 water molecules and each molecule has 1 O atom)
(that takes care of the 5 waters)

63.55 + 32.06 + 64.00 + 10.08 + 80.00 = 249.69
The formula mass of cupric sulfate pentahydrate is 249.69

Ex: What do you do when you’re dealing with a formula that includes one of those darn parentheses? Ammonium Phosphate had the formula: (NH₄)₃PO₄

Nitrogen = 14.01 x 3 = 42.03 (we multiply the N x 3 because everything inside the parenthesis is multiplied times the subscript on the outside of the parenthesis. There is 1 N so 1 x 3 = 3)
Hydrogen = 1.008 x 12 = 12.096 (There are 4 H inside the parenthesis so 4 x 3 = 12)
Phosphorus = 30.97 x 1 = 30.97
Oxygen = 16.00 x 4 = 64.00

42.03 + 12.096 + 30.97 + 64.00 = 149.096
The formula mass of ammonium phosphate is 149.096

Percent Composition

The Percent Composition of a compound tells us the percent by mass of each element in a compound. It’s just a step beyond what we’ve already been doing with formula mass!

To calculate the percent composition of a compound:

• Calculate the total mass of each element present in the formula of the compound
• Calculate the formula mass of the compound (just like we’ve been doing)
• Calculate the percent composition:
  % by mass of element = (total mass of element present ÷ formula mass) x 100

Ex: What is the percent composition of Iron(III) oxide?

Iron(III) oxide has the formula: Fe₂O₃

Iron = 55.85 x 2 = 111.70
Oxygen = 16.00 x 3 = 48.00
111.70 + 48.00 = 159.70 (Formula mass of Iron(III) oxide is 159.70)

So, to calculate the percent iron in this compound by mass:
111.70 ÷ 159.70 = 0.6994 x 100 = 69.94% iron

To calculate the percent oxygen in this compound by mass:
48.00 ÷ 159.70 = 0.3006 x 100 = 30.06% oxygen

When you add the percentages, they should be right at 100 (a hair over or under is most likely a rounding issue and is not a big deal!)

Sometimes you just need to know the percent of a single element in a compound.

Ex: What is the percent nitrogen in Ammonium nitrate?

The formula for ammonium nitrate is: NH₄NO₃ (note that there are 2 nitrogen atoms in this compound! We might as well take care of both of them when we calculate the total mass of N)

Nitrogen = 14.01 x 2 = 28.02
Hydrogen = 1.008 x 4 = 4.032
Oxygen = 16.00 x 3 = 48.00
28.02 + 4.032 + 48.00 = 80.052 (Formula mass of ammonium nitrate = 80.052)

So, to calculate the percent nitrogen in ammonium nitrate:
28.02 ÷ 80.052 = 0.35 x 100 = 35% nitrogen