# Avogadro’s number

Avogadro’s number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.022140857 × 10^{23}. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction

Avogadro's number is the number of particles found in one mole of a substance. It is the number of atoms in exactly 12 grams of carbon-12. Thisexperimentally determined value is approximately 6.0221 x 10^{23} particles per mole.

Owing to their tiny size, atoms and molecules cannot be counted by direct observation. But much as we do when "counting" beans in a jar, we can estimate the number of particles in a sample of an element or compound if we have some idea of the volume occupied by each particle and the volume of the container.

Once this has been done, we know the number of formula units (to use the most general term for any combination of atoms we wish to define) in any arbitrary weight of the substance. The number will of course depend both on the formula of the substance and on the weight of the sample. But if we consider a weight of substance that is the same as its formula (molecular) weight expressed in grams, we have only one number to know: Avogadro's number, 6.022141527 × 10^{23} usually designated by NA.

6.02 × 10^{23} of what? Well, of anything you like: apples, stars in the sky, burritos. But the only practical use for NA is to have a more convenient way of expressing the huge numbers of the tiny particles such as atoms or molecules that we deal with in chemistry. Avogadro's number is a collective number, just like a dozen.

### Problem Example 1

**Mass ratio from atomic weights**

The atomic weights of oxygen and of carbon are 16.0 and 12.0, respectively. How much heavier is the oxygen atom in relation to carbon?

Solution:

Atomic weights represent the relative masses of different kinds of atoms. This means that the atom of oxygen has a mass that is 16/12 = 4/3 ≈ 1.33 as great as the mass of a carbon atom.

### Problem Example 2

**Mass of a single atom**

The absolute mass of a carbon atom is 12.0 unified atomic mass units (What are these?). How many grams will a single oxygen atom weigh?

Solution: The absolute mass of the carbon atom is 12.0 u,
or 12 × 1.6605 × 10^{–27} g = 19.9 × 10^{–27} kg.

The mass of the oxygen atom will be 4/3 greater, or 2.66 × 10^{–26} kg.

Alternatively: (12 g/mol) ÷ (6.022 × 1023 mol^{–1}) × (4/3) = 2.66 × 10^{–23} g.