# Unit 6: Quantifying Chemical Reactions—Stoichiometry and Moles

## Section 4: Avogadro's Number and Atomic Mass

Early chemists defined the mole as the number of hydrogen atoms in one gram of hydrogen because that was the most accurate measurement they could make at the time. Later, because it was easier to obtain the ratio of atomic masses for most elements with oxygen than it was with hydrogen (for technical reasons), many people used oxygen as the standard for atomic masses. One mole was defined as the number of atoms in 16 grams of oxygen. The current standard for Avogadro's number was set in the 1960s to be the most precise one agreed on by chemists and physicists. We now define a mole in terms of carbon-12, the most common isotope of carbon, which has six protons and six neutrons in its nucleus. (We will cover more about isotopes of various elements in Unit 4 and Unit 12). One mole is the number of carbon-12 atoms in exactly 12 grams of carbon-12. From this new standard, precise measurements of all the atomic masses can be made and then extended out for compounds, as we will see in the next section.

If we remember, a dozen is a good metaphor for the mole; so let's consider a dozen eggs. One dozen chicken eggs and one dozen quail eggs—both have twelve eggs, but very different masses. For example, a dozen chicken eggs has a mass of 720 grams, while a dozen quail eggs has a mass of 96 grams. We can extend this to the mole. One mole of carbon-12 atoms has a mass of exactly 12 grams, but another type of atom will have a very different mass if we count out a mole of them. For example, a mole of gold atoms would have a mass of 197 grams.

### Figure 6-4. Finding the Atomic Mass on the Periodic Table of Elements

On the periodic table, the elements are ordered by their atomic numbers, which is the number of protons that particular atom has in the nucleus. Atomic mass is the average mass of atoms of an element, calculated using the relative abundance of isotopes in a naturally occurring element. In the case of helium, it is designated as 4.003 and is shown in the bottom right-hand corner.

© Science Media Group.

Avogadro's number makes it possible for us to convert an almost uncountable number of atoms or molecules into measurable amounts that can be determined as a mass by a scale. Since chemists have established that a mole of carbon-12 atoms has 6.02214179 × 10^{23} atoms and an atomic mass of 12 grams, they calibrate mass spectrometers (instruments used to measure the very precise masses and relative amounts of atoms and molecules) to the mass of carbon-12. A mole of any other substance also contains 6.02 x 10^{23} atoms, but has a mass of more or less than 12 grams.

As we saw in Unit 4, each element in the periodic table has an atomic mass in the lower right corner, which represents the average atomic mass of all of the isotopes of that element. (Figure 6-4) Helium's atomic mass, or the average mass of a single atom of helium, is 4.003. Normally in chemistry, we make sure to write the units next to any numerical value we want to talk about. So, why is there not a unit next to the 4.003 for helium? Because there are actually two different ways to interpret that number, both of which are linked to the mole and Avogadro's number.

So the number 4.003 technically means that if a carbon-12 atom has a mass of exactly 12, then a helium atom (on average) has a mass of 4.033. One way to interpret that number is in atomic mass units (abbreviated as u). An atomic mass unit is a very small unit of mass, about 1.66 x 10^{-27} kilograms. But talking about the masses of individual atoms is not very useful for trying to quantify chemical reactions. The other way to interpret that number on the periodic table is to say that it has units of grams per mole or g/mol. This means that on average a mole of helium atoms has a mass of 4.003 grams.