Lesson Video: Formula Mass Chemistry

Video Transcript

In this video, we will learn about formula masses and molecular masses and learn how to calculate them from atomic masses. We’ll also look at the difference between masses and relative masses.

Before we can explore formula masses, we need to recall what an atomic mass is. Atoms really are tiny, so they have very, very small masses. The smallest atom, an atom of hydrogen, is composed of a single electron bound to a single proton. If we measure the mass of a hydrogen atom in grams, the value would be minuscule. Instead, we have a much more convenient system.

Imagine you’re loading a delivery van with some fruit. Each type of fruit weighs a different amount. And you could use grams. So, an apple is 80 grams, a banana is 120 grams, and a watermelon is 8000 grams or eight kilograms. However, to make things easier to manage, we could come up with our own special mass unit, which we’ll call “the apple”, which is 80 grams. Our apple has a mass of one “apple”, the banana has a mass of 1.5 “apples”, and our watermelon has a mass of 100 “apples”.

These numbers are relative masses. They are relative to the apple. These numbers are much easier to compare. We know when we’re loading our van that each watermelon is going to weigh as much as 100 apples. Instead of using the incredibly tiny gram masses of individual atoms, we define the apple equivalent for atoms. For complicated reasons that I won’t go into here, chemists chose their atom apple to be an atom of carbon-12. That’s an atom consisting of six protons and six neutrons in the nucleus and six electrons in the electron cloud. The full definition is a little bit more complex, but we’re not going to look at that here.

Using carbon-12, we can start to talk about the masses of other atoms in more sensible numbers. Here, my examples are atoms of hydrogen-1 and bromine-79. Now, we could just use the whole of the carbon atom as our reference point. And on that scale, a carbon-12 atom would have a mass of one. And our hydrogen and bromine atoms would have relative masses of about a twelfth and about 6.6.

However, chemists came up with a more convenient way of doing it. Electrons don’t have much mass compared to protons and neutrons, but protons and neutrons weigh about the same. So, instead, chemists use a system where the number of protons plus the number of neutrons is very close to the relative mass. While it may sound complicated, it does make things a lot easier. These small, easy to handle numbers can be used in calculations. And we can measure the mass of a carbon-12 atom more easily than we can the mass of an individual proton or an individual neutron.

So, for our purposes, relative mass is the mass of something on a scale where the mass of a carbon-12 atom is exactly 12. Relative masses in chemistry are great as long as you remember what they are relative to. To make things easier, there’s a unit called the unified atomic mass unit with symbol u. It’s very similar to the atomic mass unit, amu, but I’ll use u throughout.

One unified atomic mass unit is equal to one twelfth of the mass of the carbon-12 atom. So, it’s defined in a very similar way to relative mass. Unified atomic mass units are particularly useful when you want to convert to grams because one unified atomic mass unit is approximately equal to 1.66 times 10 to the negative 24 grams.

So, how do we use measuring mass in fractions of a carbon atom into use? If you look at all the atoms and ions in the universe, you’ll be able to identify many different varieties. We first group them together based on the number of protons in their nuclei. These are the elements of which carbon is an example. However, nuclei of an element can have different numbers of neutrons. So, we have another layer of grouping, which are the isotopes.

On Earth, we need to know the average mass of atoms of an element to do calculations. So, we analyze samples and work out how common each isotope is. You have the benefit of years of research in the form of the periodic table, where you can see the average atomic masses of many of the elements.

Let’s look at carbon as an example. We can read the number at the bottom as an average atomic mass and add the units of unified atomic mass units. Or we can take it as a relative atomic mass. We define the average atomic mass of an element as the average mass of an atom of that element in unified atomic mass units. The average atomic mass of carbon is 12.011 unified atomic mass units, a little more on average than a carbon-12 atom because there is some carbon-13 in samples on Earth.

Of course, you can use relative atomic mass or RAM instead, which is simply the average mass of the atom on a scale where an atom of carbon-12 has a mass of 12. Some elements don’t have standardized atomic masses because they are too rare for accurate measurements to be made, often because they are unstable and undergo radioactive decay to form other elements.

Now that we know how to find how heavy atoms of different elements are on average, we should be able to work out how much molecules and compounds weigh.

Let’s imagine you want to weigh out specific amounts of chemicals in the lab, but the atoms are bonded together, like in a water molecule. A water molecule is made of two atoms of hydrogen and one atom of oxygen. We don’t know for sure which isotopes are in this particular molecule. But we do know, on average, that each atom of hydrogen has a mass of 1.008 unified atomic mass units from the periodic table and each atom of oxygen has a mass of 15.999 unified atomic mass units.

To work out the mass of the average water molecule, all we need to do is add the masses of the atoms together, giving us 18.015 unified atomic mass units. Remember, this is an average for all water molecules. Some water molecules might be a little bit lighter because they’re made of lighter isotopes of oxygen and hydrogen. And, of course, some may be heavier. We’re not trying to work out the actual mass of individual molecules. We’re just working out averages so we can do calculations for the lab.

For water, we call this the formula mass. This is because we can look at the chemical formula of water H2O, see there are two hydrogen atoms and one oxygen atom, and add the average masses of those atoms together. So, the formula mass is simply the sum of the average atomic masses of the components of a formula. The relative formula mass is simply the equivalent with relative atomic masses.

Formula mass is a general term. For lattices, the chemical formula is the simplest ratio of the elements that make it up. For instance, sodium chloride is made up of alternating sodium ions and chloride ions. Since the crystal could theoretically go on forever, there isn’t a simple way to write the formula. So, we write the empirical formula NaCl. And we do the same for metals like magnesium or covalent lattices like silicon dioxide.

To work out the formula mass for sodium chloride, we simply take the average atomic mass of sodium and add it to that of chlorine, giving us 58.44 unified atomic mass units. For magnesium, the formula mass is exactly the same as the average atomic mass of magnesium.

For molecules, the chemical formula can be different to the empirical formula. This is a molecule of hydrogen peroxide made of two oxygen atoms and two hydrogen atoms. The empirical formula of hydrogen peroxide is just HO because the hydrogen and oxygen atoms are in a ratio of one to one. But the molecular formula accounts for all the atoms in a single molecule H2O2. It’s the molecular formula we use when we’re working out the formula mass for a molecular substance. So, we call that, specifically, the molecular mass to be clear.

Molecular mass is simply the formula mass of a molecule based on its molecular formula. Now, we’re going to have a look at how we’d calculate the formula mass for various types of substance.

For an atom or an ion, the formula mass is simply the atomic mass of the element. For ions, we generally ignore any mass changes due to the gain or loss of electrons. For lattices like sodium chloride, magnesium, or silicon dioxide, we start by separating the formula into the individual elements, keeping track of how many atoms or ions there are for each one. Then, we look up the average atomic masses for those elements on the periodic table. We then multiply those average atomic masses by the number of atoms or ions in the formula and then add them altogether.

Molecules can be drawn in a variety of ways, so you might have to figure out the molecular formula from a diagram. Once you’ve counted up all the atoms of each element, you then do exactly the same process as with the lattice. Separate out formula, find the average atomic masses, and multiply and sum them together.

So, we’ve looked at how formula masses apply to atoms, ions, lattices, and molecules. Let’s have some practice.

The atomic mass unit, u, is defined as one twelfth of the mass of an atom of carbon-12. What is the mass of a silicon-30 atom in atomic mass units?

Sometimes, you may see unified dropped from unified atomic mass unit. That’s fine as long as you’re using the symbol u. The symbol amu is sometimes used interchangeably, but they’re actually defined slightly differently. But it’s perfectly okay because we actually have the definition in the question, one twelfth of the mass of an atom of carbon-12.

Carbon is an element we can find on the periodic table. The atomic number for carbon is six. The atomic number of an element is the number of protons we find in atoms or ions of that element. So, in an atom of carbon-12, we know that there are six protons in the nucleus. In the naming of isotopes like carbon-12, we put the mass number at the end. Atomic number tells us the number of protons in the nucleus. And mass number tells us the number of protons plus the number of neutrons.

What this tells us is that in our nucleus of carbon-12, we have six protons and enough neutrons that when you sum them together, you get 12. 12 minus six is six. So, we have six neutrons. And since we’re dealing with atoms, which must be neutral, we must have six electrons to balance out the positive charge of the protons.

The next thing we have to do is work out the mass of a silicon-30 atom in atomic mass units. Silicon is the element just below carbon in the periodic table with an atomic number of 14. So, we know in our atom of silicon-30, there must be 14 protons in the nucleus. But of course, silicon-30 is an isotope of silicon where the nuclei contain a strict number of neutrons and the number of protons plus the number of neutrons is 30.

So, our atom of silicon-30 also contains 16 neutrons. Just like with the atom of carbon, we’re dealing with a neutral combination of protons and electrons. So, we need 14 electrons to balance out the charge of the 14 protons. The first thing we need to understand is that an atom of carbon-12 has a mass of exactly 12 unified atomic mass units. We know that because from the definition, we know one unified atomic mass unit is the mass of a carbon-12 atom divided by 12.

The next thing we need to know is that the mass of a proton and the mass of a neutron are about the same. And electrons have much less mass than protons or neutrons. So, for the purposes of this question, we can ignore them. Protons and neutrons are known collectively as nucleons. So, the question is, if 12 nucleons together have a mass of 12 unified atomic mass units, what will be the mass of 30 nucleons? And the answer is 30 unified atomic mass units.

Now, bear in mind this is only approximate because when neutrons and protons bond together, there is a slight change in their mass and things are a bit more complicated. You may have noticed that I steered clear of the average atomic mass for silicon, which is 32.06. This represents the average mass for a silicon atom on Earth based on the abundance of different silicon isotopes.

Our estimate of 30 unified atomic mass units for an atom of silicon 30 is the best we can do with the figures we have available.

Now, let’s have a look at a formula-mass calculation.

A substance has a formula unit AB2. What is the relative formula mass of this substance in terms of Ar(A) and Ar(B), the relative atomic masses of A and B?

This one’s a little bit tricky because we haven’t been told what elements are involved. We’ve just got one A, whatever that is, and two of B. We’ve been asked for the relative formula mass of this substance, which means we need to work out the relative mass on a scale where an atom of carbon-12 would have a mass of 12.

To make things easier, let’s actually imagine a number line. We’d read an atom of carbon-12 as having a mass of 12. And what we’ve been given are some symbols for the relative atomic masses of A and B. I’m just going to imagine that the relative atomic mass of A is about four and that the relative atomic mass of B is about five. These numbers don’t actually matter. It’s just useful to draw it out.

To work out the relative formula mass, what we need to do is sum together the relative atomic masses of the constituents of the formula. With the formula AB2, we have one of A and two of B. Therefore, our relative formula mass, or RFM, is equal to one of the relative atomic mass of A plus two of the relative atomic mass of B.

We can imagine that on our diagram, where we’re getting gradually heavier as we move to the right. We have one of the relative atomic mass of A and two of the relative atomic mass of B. Since we’ll multiply the relative atomic mass of A by one, we can just remove the one and simplify our answer to the relative formula mass is equal to the relative atomic mass of A plus two times the relative atomic mass of B.

Now, it’s time to go over the key points. Whether we’re doing things relatively or directly, we’re comparing the masses of atoms, ions, and formulas with the mass of the carbon-12 atom. The unified atomic mass unit is equivalent to a twelfth of the mass of a carbon-12 atom. The average atomic mass of an element is the average mass of one atom of that element in unified atomic mass units. For carbon, the average atomic mass is 12.011 unified atomic mass units. If you want the relative atomic mass, you just have to drop the units of u.

A formula mass is the mass of a single unit of a formula in unified atomic mass units. We can calculate the formula mass by summing together the average atomic masses of the constituents. Or we can get the relative formula mass by summing together the relative atomic masses.

And lastly, the molecular mass is simply the formula mass as applied to a molecule. So, it’s the mass of a single molecule in unified atomic mass units. The calculation is identical. And at the end, you can remove the units of u to produce the relative molecular mass. And you may see these terms abbreviated.