# Atomic Mass: Definition, Units & How To Calculate

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Everything you interact with on a daily basis is ultimately made up of atoms. A 200-mL glass of water, for example, contains about 6.7 × 1024 molecules, and since the number of atoms in each molecule is three, in total there are about 2 × 1025 atoms in just that one glass. That’s 20 million billion billion – a number so big you can’t even really picture it – and that’s just in a fairly small glass of water. Understanding these tiny constituents of matter is a crucial step to understanding the macroscopic properties we’re familiar with on a day-to-day basis.

But how can you even calculate something like the number of atoms in a glass of water? The trick in this specific case was using the ​molar mass​ of water, and the known number of atoms in a mole of any substance. But molar mass, in turn, depends on the ​atomic mass unit​, which is absolutely crucial to understand for any student of physics or chemistry. Thankfully, this is really a simplification of the actual mass of an atom of any substance, which essentially tells you the relative mass in comparison to a single neutron or proton.

## Atomic Structure

Atoms have three major components: protons, neutrons and electrons. The protons and neutrons exist inside the nucleus, which is a compact arrangement of matter that sits at the center of the atom, and the electrons exist as a “fuzzy cloud” around the outside of it. There is a huge amount of space between the nucleus and even the closest electron. The nucleus has a positive charge, because the protons are positively charged and the neutrons are neutral, while the cloud of electrons carries a negative charge that balances that from the neutron.

The nucleus contains the bulk of the mass of the atom, because the neutrons and protons are much, much heavier than electrons. In fact, either protons or neutrons are about 1,800 times bigger than electrons, so much bigger that in many cases you can safely neglect the mass of an electron when you’re thinking about atomic mass more generally.

## Atomic Number

The periodic table lists all of the elements (i.e., types of atom) found in nature, starting with the simplest, which is the hydrogen atom. The ​atomic number​ of an atom (given the symbol ​Z​) tells you how many protons the atom for the element has in its nucleus, and it is the upper number on the relevant block in the periodic table. Because this carries the positive charge, and the number of electrons (which is an essential piece of information when you’re thinking about atomic bonding) has to be equal to this to main overall electrical neutrality, this number really characterizes the element.

There can be different ​isotopes​ of the same element, however, which have the same number of protons (and so can be reasonably thought of as the same element), but a different number of neutrons. These may or may not be stable, which is an interesting topic on its own, but the important thing to note for now is that different isotopes have different masses but the same overall properties in most other ways.

Although atoms in their ordinary form are electrically neutral, some atoms are prone to gaining or losing electrons, which can give them a net electric charge. Atoms that have undergone one of these processes are called ions.

## Atomic Mass

The atomic mass is generally defined in terms of atomic mass units (amu). The official definition is that 1 amu is 1/12 of the mass of a carbon-12 atom. Here, carbon-12 is the standard way of saying “the isotope of carbon with six protons and six neutrons,” so you can ultimately think about an atomic mass unit as being the mass of either a proton or a neutron. So, in a way, the atomic mass number is the number of protons and neutrons in the nucleus, and this means it isn’t the same as the atomic number, ​Z​.

It’s important to note that, for the reasons explained in the last section, the mass of the electrons in the atom is neglected when you’re talking about atomic mass in most situations. Another interesting note is that the mass of an atom is actually slightly less than the mass of all of the components combined, because of the “binding energy” it takes to hold the nucleus together. However, this is another complication that you don’t really need to consider in most situations.

The lower number on an element’s block on the periodic table is the average atomic mass, which is also different from the mass expressed in atomic mass units. This is essentially a weighted average of the masses of different isotopes of an element, accounting for their relative abundance on Earth. So in a sense this is the most accurate “overall” measure of an element’s mass, but in practice the atomic mass of any particular isotope will be a whole number in atomic mass units. On simpler periodic tables, this “atomic mass number” (​A​) is used instead of the average atomic mass.

## Molecular Mass

The ​molecular mass​ (or, to use a less accurate but also common term, “molecular weight”) is the mass of a molecule of a substance in atomic mass units. Working this out is really simple: You find the chemical formula for the substance in question, and then add together the atomic masses of the constituent atoms. For example, methane is composed of one carbon atom and four hydrogen atoms, and so it has the mass of these components combined. One carbon-12 atom has an atomic mass of 12, and each hydrogen atom has an atomic mass of 1, so the total molecular mass of a methane molecule is 16 amu.

## Molar Mass

The molar mass of a substance is the mass of one mole of the substance. This is based on Avogadro’s number, which tells you the number of atoms or molecules in one mole of a substance, and the definition of a mole. A mole is the amount of a substance that makes its mass in grams the same as its atomic mass number. So for carbon-12, for example, one mole has a mass of 12 g.

Avogadro’s number is 6.022 × 1023, and so 12 g of carbon-12 contains this many atoms, and likewise, 4 g of helium contains this many atoms too. It’s important to remember that if the substance in question is a molecule (i.e., something composed of more than one atom) then Avogadro’s number tells you the number of ​molecules​ rather than the number of atoms.

This gives you everything you need to know to go through an example like that of the glass of water in the introduction. The glass contained 200 mL, which corresponds to 200 g in terms of mass, and one water molecule (chemical formula H2O) has two hydrogen atoms and one oxygen atom, for a molecular mass of 18 amu and a molar mass of 18 g. So to find the number of atoms, you simply divide the mass by the mass of a mole to find the number of moles, and then multiply by Avogadro’s number to find the number of molecules. Finally, noting that each molecule has three atoms, you multiply by three to find the number of individual atoms.

\begin{aligned} \text{Number of moles} &= \frac{200 \text{ g}}{18 \text{ g/mol}} \\ &= 11.111 \text{ mol} \\ \text{Number of molecules} &= 11.111 \text{ mol} × 6.022 × 10^{23} \text{ molecules/mol} \\ &= 6.7 × 10^{24} \text{ molecules} \\ \text{Number of atoms} &= 6.7 × 10^{24} \text{ molecules} × 3 \text{ atoms/molecule} \\ &= 2 × 10^{25} \text{ atoms} \end{aligned}

## Examples – the Mass of Carbon

Working through more examples can help you understand the key concepts about atomic mass. The simplest example is working out the mass of a simple element like carbon-12. The process is really straightforward if you’re solely thinking in terms of amu, but you can also convert amu to kg pretty easily to get a more standardized measurement of the mass of carbon.

You should be able to calculate the mass of an atom of carbon in amu based on what you’ve already learned from the article, and noting that there are six protons and six neutrons in each atom. So what is the mass of a carbon atom in amu? Of course, it’s 12 amu. You add the six protons to the six neutrons and find the answer, since both types of particle have a mass of 1 amu.

Converting amu to kg is pretty simple from this point too: 1 amu = 1.66 × 1027 kg, so

12\text{ amu} = 12\text{ amu}\times 1.66 \times 10^{−27}\text{ kg/amu} = 1.99 \times 10^{−26}\text{ kg}

This is a ​really​ tiny mass (and that’s why atomic mass is usually measured in amu instead), but it’s worth noting that an electron’s mass is about 9 × 1031, so it’s clear that even adding in all 12 of the electrons to the mass of the carbon atom wouldn’t have made a notable difference.

## Examples – Molecular Weight

Molecular weight is a little bit more complicated than just working out the mass of an atom, but all you have to do is look at the chemical formula of the molecule and combine the masses of the individual atoms to find the total. For example, try to calculate the mass of benzene, which has the chemical formula: C6H6, noting that they are carbon-12 atoms and it’s the ordinary isotope of hydrogen rather than deuterium or tritium.

The key is noticing that you have six atoms of carbon-12 and six of hydrogen, so the mass of the molecule is:

\begin{aligned} \text{Molecular mass} &= (6 × 12 \text{ amu}) + (6 × 1 \text{ amu}) \\ &= 72 \text{ amu} + 6 \text{ amu} \\ &= 78 \text{ amu} \end{aligned}

The process of finding the molecular weight can get a little bit more complicated for bigger molecules, but it always follows this same process.

## Examples – Calculating Average Atomic Mass

Finding the average atomic mass of an element involves considering both the atomic mass ​and​ the relative abundance of the specific isotope on Earth. Carbon is a good example for this because 98.9 percent of all the carbon on Earth is carbon-12, with 1.1 percent being carbon-13 and a ​very​ small percentage being carbon-14, which can be safely neglected.

The process for working this out is actually pretty straightforward: Multiply the proportion of the isotope by the mass of the isotope in amu, and then add the two together. Carbon-12 is the most common isotope of carbon, so you’d expect the result to be very close to 12 amu. Remember to convert the percentages to decimals (divide them by 100) before calculating and you’ll come out with the correct answer:

(12 \text{ amu} × 0.989) + (13 \text{ amu}× 0.011) = 12.011 \text{ amu}

This result is exactly what you’ll find on a periodic table that lists the average atomic mass rather than the mass of the most common isotope.

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