# Atomic mass

When looking at a single atom or molecule, it's very hard to describe its mass in kg or g due to the incredibly tiny mass they have. It's not convenient to say that a certain atom (in this case carbon-12) has the mass $1.99 \times 10^{-26} \mathrm{kg}$ or $1.99 \times 10^{-23} \mathrm{g}$. The numbers simply tell us nothing of how big the atom is.

To describe the mass of atoms or molecules, you use something called the unified atomic mass unit.

The unified atomic mass unit has the unit u. 1 u is defined as $\frac{1}{12}$ of the mass of the atom $\mathrm{ ^{12}\mathrm{C}}$. The practical thing with this unit is that we now easily can compare atoms and molecules with each other.

Using atomic mass, we can quickly determine that magnesium magnesium (atomic mass 24.305 u) is approximately twice as heavy as carbon (atomic mass 12.011 u).

# Dalton

The unit Dalton (Da) is often used to describe atomic mass in the same way as the atomic mass unit is.

Dalton is used with very large atomic masses, since you can use SI-prefixes in front of Dalton (even though it is not a SI-unit itself), which is not done with u. A protein can for example be described to have the mass 14 kDa, but not 14 ku.

To convert u to Da or the other way around, just change the unit straight off.

$1 \, \mathrm{u} = 1 \, \mathrm{Da}$

# Chemical elements and their atomic mass

If you take a look at atomic masses in the periodic table, you will see that there are many non-integer numbers present, meaning the numbers have decimals after them. This is due to three reasons.

The first reason is that the mass number for an element is not identical to its atomic mass. They will be approximately equal, since a proton and neutron weigh close to 1 u each, but not identical.

The second reason for the atomic mass of an element to diverge from integers is that there often are several isotopes of that element. When several isotopes of the same element exists, the average mass of the naturally occurring isotopes is used.

The third reason is that an atom doesn't always weigh as much as its constituents. This has to do with special relativity (E = mc2), and is not processed any further at this level of chemistry.

## Calculating the atomic mass of an element

To calculate the atomic mass of an element when you know its isotopes, you do the following:

Average atomic mass = atomic mass(isotope 1) · relative abundance(isotope 1) + atomic mass(isotope 2) · relative abundance(isotope 2) + ...

An example is chlorine. Chlorine exists in two natural isotopes. Chlorine-35 (mass number 35, 34.97 u) with 76% abundance, and chlorine-37 (mass number 37, 36.97 u) with 24% abundance.  The average atomic mass for chlorine is:

$35.97 u \cdot 0.76 + 36.97 \cdot 0.24 = 35.45 u$

Individual atomic masses of isotopes are usually not included in the periodic system. It is possible to make a rough estimate of an isotope mass by using the mass number of the atom and translate is directly to u.