Why do we use moles in chemistry

The mole is a concept that you'll see everywhere in chemistry, from GCSE through A level. Although this is the case, it can be very easy to lose sight of what it actually is and why we use it, as your teacher may explain it briefly and then never do so again. It has an exact definition, which you probably will only need to learn exactly if you're an A level student: the mass of substance that contains the same number of particles as there are atoms in exactly 12.000 g of 12C. This is a complicated way of saying that the mole is a standard number of particles across any compound or element. For example, one mole of hydrogen will contain the same number of particles as one mole of lead, despite them weighing very different amounts. The mole is especially useful when writing chemical equations, because it lets us compare the ratio in which particles react rather than ratio of masses. For example: C + O2 = CO2 shows that one mole of carbon reacts with one mole of oxygen to form one mole of carbon dioxide. This is much more helpful than knowing 1 gram of carbon reacts with 2.7 grams of oxygen to form one mole of carbon dioxide. In case you are asked how many particles or 'fundamental units' are in a compound, you should be familiar with the Avogadro Constant: 6.02 x 10^23 mol^-1. This means that there are that many particles in one mole of substance! If you multiple the number of moles of substance you have by the Avogadro constant, you'll find out how many particles you have.

Simply speaking, because it's an appropriate unit to use.

Let's imagine I wanted to measure the length of a rope. What would be an appropriate length to use? Inches? Centimeters? Feet, maybe? It would really be awkward to express it as 0.000189393 miles, or as 304,800,000 nanometers.

(Note: if you can't see why these units are awkward, take any page discussing things like this (e.g. biomass of certain species) and change all the units so that they're nonsense like this. Then put it away for a week and try to read it later.)

Now let's say I've changed my mind and I'd like to measure all the rope created in the world in a year. Now an appropriate unit is almost certainly miles or kilometers, and not inches or centimeters.

Let's consider something else: so far, I've been using length to measure ropes. Would it make sense to measure their combined mass instead? Maybe not for small amounts, since I think I would throttle you if you told me to cut off half a pound of rope, but for global-scale things, tons or metric tons may make sense.

On the other hand, using measurements like the average density of the rope or the combined diameters of all the ropes really wouldn't be much use at all.

What we've seen here is that when we're measuring things, there are measures that make sense (for rope, length, maybe weight) and some measures that really don't (color, average diameter, etc.). In those measures, there are units that are convenient (inches, feet), and some that aren't (nanometers).

This is exactly the problem with chemical units, but much more magnified. When I measure the energy released on hydrolysis of a sample, I'm not measuring the energy of one bond, or two bonds, or a thousand bonds, or even a million. I'm measuring a collection of so insanely many molecules that there's really no number in common language for it.

What is an appropriate way to measure things in these molecules? If I'm only interested in how much I have and not what's in it, per gram or per volume is often a good way to do it. Since when I'm measuring the temperature change of something, I don't particularly care what it's made of, measures of this (specific heat, for instance) are done in units of something per gram.

On the other hand, if I do care what my sample is made of, then I need a better way to measure it. For example, sodium chloride and calcium chloride look similar, but will have very different energies since there's three ions in a $\ce{CaCl2}$ unit and only two in an $\ce{NaCl}$ unit.

Since you can't have half a molecule, the simplest way to do it is to count the darn things. Unfortunately, measuring things per atom is a really awkward way to do things because of the problems I described above. The energy it takes to melt ice is 0.000000000000000000001029 J/molecule.

What we need then, is some count of molecules that's convenient. We could go by 1000 molecules, or a million molecules, but it's a pain in the butt to convert between that and macroscopic units (how much does 1 million calcium atoms weigh?) Now it just so happens that $6.022 \times 10^{23}$ atoms of carbon-12 weigh 12 grams, and a single carbon-12 weighs 12 amu. A single molecule of water weighs roughly 18 amu, $6.022 \times 10^{23}$ molecules of water weigh 18 grams.

Let's take a look at what using $6.022 \times 10^{23}$ molecules offers us over other units:

• It is appropriate. $6.022 \times 10^{23}$ molecules will typically
  fall in the gram to kilogram range of substance, which can easily be measured out on a balance. It's also within the range of what you'd usually use in a lab.
• It allows for easy conversion. You can easily tell when you have $6.022 \times 10^{23}$ molecules because your atomic mass is equal to your macroscopic mass.
• It makes sense. Intuitively, we'd like to measure things per atom or per molecule, but doing so leads to some ugly units. Instead, if we measure per $6.022 \times 10^{23}$ molecules, we still are doing a counting-based measurement, but the numbers themselves are a lot

  nicer.

You probably know this already, but we call $6.022 \times 10^{23}$ molecules a mole. These are the advantages of using the mole as a unit, and not for backwards-compatibility. I am of the opinion that if we shed all our units today and started from scratch, we would start off with grams and liters, but we would probably start using the measure of a mole again within a year. It's just a very powerful, useful way to measure things.

P.S. This is much longer than I was initially intending and was not written while I was in the most awake state of mind. Please let me know in the comments if you think this answer is unclear, or stupid, or just plain wrong.

The Mole concept

Chemists need the mole concept to bridge the gap between the microscopic world of atoms to the macroscopic world of humans. As you know, the molecular level consists of particles that are invisible to us. Because of this, chemists can’t count or weigh these individual particles on a scale.

So, how do chemists get around this problem?

To solve this problem, chemists introduced the mole concept. The mole is the unit for the SI base quantity the Amount of Substance. And the mole concept connects the macroscopic to the atomic or molecular level. Let use the following model to illustrate:

What’s the Amount of Substance?

The Amount of substance is a quantity that measures the size of a pile (collection) of particles. These particles can be electrons, atoms, molecules, ions, or formula units. The amount of substance is an SI measured quantity that has a symbol n, and a base unit of mole, which is often written in a short way as mol.

What’s a Mole?

A mole is the size of a pile of particles (amount of substance) that contains as many particles (electrons, atoms, molecules, ions, or formula units) as there are atoms in 12 grams of carbon-12 (an isotope of carbon). Therefore, a mole or

1 mole of carbon-12 = 12 grams of carbon-12

What amount of substance can have the same number of particles as in 12g of carbon-12? The amount of substance that can have the same number of particles include:

1. atomic mass of an element expressed in grams
2. molecular mass of molecular compounds expressed in grams
3. formula mass of ionic compounds expressed in grams

What do we mean by the atomic mass expressed in grams?

It means that we take the relative atomic mass values of all the elements on the periodic table and attach grams to them. Once we do that, we can now weigh 1 mole of any element by simply weighing its exact atomic mass in grams. Similarly, since atoms combine to make molecules, we can find the molecular mass of any molecule by simply finding the sum of all the atomic masses in the chemical formula. The following table shows how to transition from atomic mass (amu) to molar mass (g/mol).

Why is it that 1 mole of any element has the same number of particles as in 1 mole of carbon-12?

They do because of Avogadro’s hypothesis, and recall that it was his hypothesis that helped scientists determine the relative atomic masses of the elements.

Now, how many particles (atoms, molecules, or ions) are in 1 mole of a chemical substance? There are 6.02 x 1022 particles in 1 mole of any chemical substance. As you can see, this number is so huge that it has a special name called the Avogadro’s number in honor of Avogadro; The Italian mathematician who contributed to our understanding of the mole concept.

Mathematically, we can write a relationship between 1 mole, Avogadro’s number, and atomic mass in grams.  For example, we can write that 1 mole of carbon is equal to 12 g of carbon and in this 12 g there are 6.02 x 1022 atoms of carbon. If we translate that to a mathematical expression, we will get;

• 1 mole = 12 g = 6.02 x 1022 atoms of carbon.

If we divide through by 1 mole, we will get two ratios:

• 12 g/1mole
• 6.02 x 1022 atoms of carbon/1mole.

The ratio 12 g/1 mole or 12 g/mol (read as grams per mol) has a special name called Molar Mass. So, the molar mass is simply the mass of 1 mol of a substance in grams. As a result, the only number that will keep changing from substance to substance is the mass of 1 mole of substance (see text in bold). Now, if you need to convert some certain grams of carbon to atoms of carbon or atoms of carbon to grams of carbon, the two ratios, or conversion factors we just derived are the ones we will use.

Here is a model that shows the relationship between Mass, Mole, and Avogadro’s number

How is the mole related to the dozen?

We can relate the mole to the counting unit: Dozen. We buy eggs by the dozen, we buy soda by the dozen, we buy many things by the dozen, and we know that a dozen always contains 12 things. However, as we buy a dozen of this and a dozen of that, the only number that keeps changing is the mass of the items in the dozen. As a result, we can write a mathematical expression similar to the mole one. Let’s say if a dozen eggs weigh 10 g, then we can write something like this: 10 g = 1 Dozen = 12 eggs. If we divide through by 1 Dozen, we will get two ratios:

• 10 g/1Dozen and
• 12eggs/1Dozen,

These ratios are the ones we will use to convert from grams of eggs to Dozen of eggs to number of eggs and in reverse order.

Once you understand how grams of substance relate to moles, how moles of substance relate to Avogadro’s number and vice versa, you will always find mole problems easy to solve. Here is a diagram summarizing these relationships.

If you want to learn how to calculate the number of atoms in an element, click here

Check you understanding

1. If you have a sample of 10 mol of carbon dioxide (CO2), how many molecules of CO2 are in the sample?
2. Calculate the molar mass of sulfuric acid (H2SO4)
3. If you have a sample of 5.0 g of sulfuric acid, how many mol of sulfuric acid are in the sample?

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