General Chemistry/Numbers Used to Describe Atoms

Numbers

If the red parts are protons and the green parts are neutrons, what's the atomic, neutron, and mass number of this atom? (lithium)

The Atomic number is the number of protons in the nucleus of an atom. This number determines the element type of the atom. For instance, all neon atoms have exactly ten protons. If an atom has ten protons, then it must be neon. If an atom is neon, then it must have ten protons.

The atomic number is sometimes denoted Z. Continuing with the example of neon, $Z=10$.

The Neutron number is the number of neutrons in the nucleus of an atom. Remember that neutrons have no electric charge, so they do not affect the chemistry of an element. However, they do affect the nuclear properties of the element. For instance, Carbon-12 has six neutrons, and it is stable. Carbon-14 has eight neutrons, and it happens to be radioactive. Despite these differences, both forms of carbon behave the same way when forming chemical compounds.

The neutron number is sometimes denoted N.

The Mass number is the sum of protons and neutrons in an atom. It is denoted A. To find the mass number of an atom, remember that A = Z + N. The mass number of an atom is always an integer. Because the number of neutrons can vary among different atoms of the same element, there can be different mass numbers of a given element. Look back to the example of carbon. Carbon-14 has a mass number of 14, and Carbon-12 has a mass number of 12. Every carbon atom must have six protons, so Carbon-14 has eight neutrons and Carbon-12 has six neutrons.

Isotopes of the same element have nearly identical chemical properties (because they have the same number of protons and electrons). Their only difference is the number of neutrons, which changes their nuclear properties like radioactivity.

Notation

There is a convenient way of writing the numbers that describe atoms. It is easiest to learn by examples.

Helpful Hint!
Keep in mind that any of the three numbers written around the element symbol are optional, but they should be written if it is important to the given situation. The charge number is left off if the atom has zero charge (equal number of protons and electrons). The mass number and atomic number are usually left off.

$_{\,\,9}^{19}{\text{F}}$	This is how we write fluorine-19. The atomic number is below and the mass number is above, followed by its symbol on the periodic table of the elements.
$^{12}{\text{C}}$	This example shows carbon-12. Notice how the atomic number is missing. You know which element it is because of the C, so there is no need to write the number of protons. The atomic number is rarely written because the element symbol implies how many protons there are.
$_{12}^{25}{\text{Mg}}^{+2}$	The last example shows both the atomic number and mass number, along with a charge. The charge is the difference in the number of protons compared to the number of electrons. You can read more about charge, protons, and electrons later on. From the example, you can see that this magnesium atom would have 12 protons, 13 neutrons, and 10 electrons. Its mass is 25 (12 p + 13 n) and its charge is +2 (12 p - 10 e).

Exercise for the reader!

Try writing the symbol for an atom with seven protons, seven neutrons, and eight electrons. You will need to look up its symbol on the periodic table.

Atomic Mass

The mass of an atom is measured in atomic mass units (amu). An atom's mass can be found by summing the number of protons and neutrons. By definition, 12 amu equals the atomic mass of carbon-12. Protons and neutrons have an approximate mass of 1 amu, and electrons have a negligible mass.

Usually, a pure element is made up of a number of isotopes in specific ratios. Because of this, the measured atomic mass of carbon is not exactly 12. It is an average of all the masses of all the isotopes, with the more common ones contributing more to the measured atomic mass. By convention atomic masses are given no units.

Example

Pretend that the element Wikibookium has two isotopes. The first has a mass number of 104, and the second has a mass number of 107. Considering that 75% of the naturally occurring atoms are of the first isotope, and the rest are of the second. The average atomic mass is calculated as

0.75 × 104 + 0.25 × 107 = 104.75

In this case, a bunch of Wikibookium atoms would have an average mass of 104.75 amu, but each individual atom might have a mass number of 104 or 107. Keep in mind that all of the atoms would have the same number of protons. Their masses are different because of the number of neutrons.

Moles

A mole is defined as the amount of an element whose number of particles are equal to that in 12g of C-12 carbon, also known as Avogadro's number. Avogadro's number equals 6.022 × 10²³. Moles are not very confusing: if you have a dozen atoms, you would have 12. If you have a mole of atoms, you would have 6.022 × 10²³. Why is this ridiculously large number important? It can be used to convert between atomic mass units and grams. One mole of carbon-12 is exactly 12 grams, by definition. Similarly, one mole of any element is the atomic mass of that element expressed as a weight in grams. The atomic mass is equal to the number of grams per mole of that element.

Example

There are 128.2 g of rubidium (atomic mass = 85.47 amu). How many atoms are there?

(128.2 g) / (85.47 g/mol) = 1.5 mol
(1.5 mol) × (6.022 × 10²³) = 9.03 × 10²³ atoms of rubidium

These one-liter containers each hold 0.045 moles of nitrogen-based gas. (1 L) / (22.4 L/mol) = 0.045 mol

Moles are also important because every 22.4 liters of gas contain 1 mole of gas molecules at standard temperature and pressure (STP, 0 °C and 1 atmosphere of pressure). Avogadro discovered this. (That's why it's his number.) A container filled with fluorine gas would have to be 22.4 L large to hold one mole of F₂ molecules. Knowing this fact allows you to determine the mass of a gas molecule if you know the volume of the container. This holds true for every gas.

Why every single gas? Atoms and molecules are tiny. The volume of a gas is mostly empty space, so the molecules have an insignificantly small volume. As you will eventually learn, this ensures that there is always one mole of gas atoms for every 22.4 liters at STP.