The RIGHT Way To Think About Moles in Chemistry
One of the big ideas that Chemistry students are introduced to pretty early in the class is the concept of the mole. A significant percentage of the calculations in Chemistry class depend on this concept, so a clear understanding of moles is really helpful not just for its own sake, but for understanding large portions of the rest of the class as a whole.
If you are reading this, maybe you are learning about moles in Chemistry class for the first time. Or maybe you never quite fully understood moles when your teacher or professor introduced it, and now you are discovering that this is getting in the way of your understanding of subsequent parts of Chemistry. Either way, you have come to the right place! I will discuss moles in this blog post in a way that is easy to understand.
What is a mole, anyway?
At its core, the mole is actually a pretty simple idea. A mole is just a word that represents a certain number of things.
Note that a mole is not a unit, like meters or grams. It represents a certain number of things. What things? Well, in principle it could be anything, as long as the things are separate objects that can be counted.
If that seems strange, consider the fact that we have words to mean a certain number of things already. For instance, we have the word “dozen” which refers to twelve things. The things could be anything: a dozen eggs, a dozen donuts, a dozen muffins. When Abraham Lincoln wrote the Emancipation Proclamation, he started it with “Four score and seven years ago,” by which he meant 87. So a “score” is twenty of something.
So a mole is conceptually no different. The only real difference is that a mole refers to a VERY large number of things. Specifically, it refers to
6.02214076 × 1023
things. (If you are not familiar with scientific notation as a way of expressing numbers, you can learn more about it here.) For practical purposes, we don’t usually use so many digits, and just report the number as 6.022 × 1023.
Isn’t that a large number?
That is a VERY large number. Just to compare:
- The number of cells in the human body is roughly estimated at about only 30 trillion (3 × 1013), which is much smaller than a mole. In fact, you would have to gather the combined cells from about 2 billion people to get a mole of cells.
- There are an estimated 10 quintillion (1 × 1019) insects on the Earth at any given time. You would need about 60,000 identical Earths in order to accumulate a mole of insects.
- There have only been about 436 quadrillion (4.36 × 1017) seconds since the Big Bang that started the universe. So a mole of seconds has not yet elapsed since the universe began.
Significance of the mole
So why on earth would we ever need such a large number? This is the significance of the mole:
One mole of protons (or neutrons) has a mass of 1 gram.
Before I get lots of comments about this, let me say: I know this is not the official definition. If you are interested in such things, you can read more about the official definition of the mole here. I am using the above working definition because it is easier to understand and make calculations with.
So if I somehow got a mole of protons and laid them out in a row, like this:
that row would have a mass of 1 gram..
What would be the mass of a mole of hydrogen atoms?
A hydrogen atom is composed of just one proton and one electron. The electron is very tiny compared to the proton — it is only about 1/2000 of the mass of the proton. So we can essentially ignore the electrons for purposes of deciding on the mass. In that case, there is essentially no difference in mass between a mole of protons and a mole of hydrogen atoms, and so the latter also has a mass of 1 gram.
What about a mole of helium-4 atoms? Remember that the 4 indicates that the atoms all have a mass number of 4, that is, the number of protons and neutrons added together is 4..
The helium-4 atom consists of two protons and two neutrons, and two electrons as well, but for the same reasons as above we will ignore the electrons. Note that we could line up the helium atoms in a row also:
We could then split up each helium atoms into individual protons and neutrons, and end up with two rows of protons and two rows of neutrons as follows:
We know that each row has a mass of 1 gram, so the combination of all four rows must have a mass of 4 grams!
And we can use the same reasoning to conclude that a mole of any single-isotope atom has a mass in grams equal to its mass number:
- A mole of carbon-12 atoms has a mass of 12 grams
- A mole of oxygen-16 atoms has a mass of 16 grams
- A mole of silicon-28 atoms has a mass of 28 grams
Now, what if we collected a mole of water molecules? Let’s assume for the moment that we managed to get all the water molecules to be constructed from oxygen-16 atoms and hydrogen-1 atoms.
Just like with the helium atoms, we could line up the mole of water molecules in a row, with the oxygen atoms depicted in red and the hydrogen atoms in white, like so:
We could then split up each water molecule into an oxygen atoms and two hydrogen atoms, so we would end up with a row containing one mole of oxygen-16 atoms, and two rows each containing one mole of hydrogen atoms:
We know the mass of the first row is 16 grams, and the mass of each of the other two rows is 1 gram. So the total mass of the row of water molecules has to be 18 grams. Note that we essentially got this number by multiplying the mass of one mole of each type of atom by the number of times that atom is repeated in the molecule:
(16 g per mole of O-16 atoms) (1 O atom per molecule) +
(1 g per mole of H-1 atoms) ( 2 H atoms per molecule) = 18 g
How about a mole of glucose molecules?
Glucose has the chemical formula C6H12O6; that is, each molecule has six carbon atoms, twelve hydrogen atoms, and six oxygen atoms. If we again assume that all the carbon atoms are carbon-12, all the oxygen atoms are oxygen-16, and all the hydrogen atoms as hydrogen-1, then a mole of glucose molecules would have a mass of
(12 g per mole of C-12 atoms)(6 C atoms per molecule) +
(1 g per mole of H-1 atoms)(12 H atoms per molecule) +
(16 g per mole of O-16 atoms)(6 O atoms per molecule) = 180 g
If this is starting to look just too simple, I will admit to you that it is … in a way.
Using atomic mass instead of mass number
As you probably have already learned in your Chemistry class, a real sample of carbon in nature doesn’t just consist of carbon-12. All the atoms would have to have six protons, otherwise they wouldn’t be carbon anymore, but they could (and in practice will) have differing numbers of neutrons and therefore different mass numbers. Your Chemistry teacher or professor may have told you that atoms with the same number of protons but different numbers of neutrons are called isotopes. If not, you can read more about isotopes here.
What it means in practice is that, in any real life sample of carbon, the carbon atoms are not all carbon-12 (6 protons and 6 neutrons). Most of them are carbon-12, but there is a small fraction of them that are actually carbon-13 (6 protons and 7 neutrons), and depending on the sample, perhaps a tiny percentage of them that are carbon-14 (6 protons and 8 neutrons). We wouldn’t want to use a mass number of 12 for all of them, since that doesn’t represent the carbon-13 and carbon-14 atoms adequately. So what we do in practice is to take an average over the many many atoms in the sample. Since most of them are carbon-12, the average will be very close to 12, but not exactly since we are averaging the other two isotopes in also. For carbon, the average mass number is closer to 12.011.
We could compute a similar average for every element on the Periodic Table, and this averaged mass number is known as the atomic mass for that element. The atomic mass for each element is given on the Periodic Table:
When the atoms all had the same mass number, we determined that one mole of those atoms had a mass in grams equal to its mass number. With a real-life sample of atoms of mixed mass numbers, one mole of these atoms now has a mass in grams equal to the average mass number, or the atomic number. So a mole of real-life carbon atoms has a mass of 12.011 grams, since that is the same as the atomic number. When we talk about this number in the context of a mole of the substance, we now refer to the number as the molar mass.
So in practice, if we want to compute the mass of one mole of real glucose molecules, we would use the molar mass of each element, which is more representative of the average over all the isotopes of each element:
(12.011 g per mole of carbon atoms)(6 C atoms per molecule) +
(1.008 g per mole of hydrogen atoms)(12 H atoms per molecule) +
(15.999 g per mole of oxygen atoms)(6 O atoms per molecule) = 180.156 g
Since it is based on the average mass numbers for all the elements, this number is also considered a molar mass (of glucose). Note that it is not that different from the result we got using mass numbers, so we can sometimes get away with using mass numbers if we want a quick estimate and don’t need too much accuracy. If you want to see what we use the molar mass for, please check out my blog entry on solving stoichiometry problems.
I hope you find my post helpful! If you would like more help in Chemistry, I would love to work with you on 1:1 tutoring. Please see my website at https://andrewjeungtutoring.com .