How to Count Atoms(when they are really really small)

Review:

1 12C atom = 12.0000 amu = 1.9926x 10-23 g

(from mass spectroscopy experiments)

So

1 9926 10

12 00001 6605 10

2324.

.. /

g

am ug am u

Goal: a number that is capable of expressing numbers of atoms in convenient terms.

H and O react in simple numbers of atoms to form water (H2O):

2 H : 1 O There is not a simple relation between the masses that react.

Yet – masses are what we can readily measure in a laboratory.

To get a quantity capable of expressing numbers of atoms,

Define: 1 mole = number of atoms in 12.0000 g of 12C.

We now have enough information to calculate the number of atoms in one mole of carbon:

12 001

1 9926106 022 10

12

2323 12.

..g C

atom C

gatom s C

But this is also the number of atoms in one atomic mass, expressed in grams, of any element.

This important number is known as Avogadro’s Number, NA.

Both a mole and a dozen express quantities of things by a collective number.

A dozen eggs weighs more than a dozen ping-pong balls because each individual unit is heavier.

12.0 amu

C

144.0 amu in carton

16.0 amu

O

192.0 amu in carton

Take enough cartons to have 6.02 x 1023 atomsThe total mass will be 12.0 gram

Take the same number of atomsas at the left.The total mass will be 16.0 grams

(A dozen oxygen atomsweigh more than a dozen carbon atoms)

Moral: a mole of oxygen weighs more than a mole of carbon becauseeach individual oxygen atom weighs more.

So now, atomic masses have two interpretations:

1 atom of C weighs 12.0000 amu

1 mole of C weighs 12.0000 g

Some conversion factors:

1 mole of C = 12.00 g1 mole of C = 6.02 x 1023 atoms C

Now we can calculate the mass of any atom:

1 atom of U = 238 amu

1 atom U1 m ole U

6.02x10 atom s U1.66x10 m oles U23

24

1.66x10 m oles U238 g U

1 m ole U3.95 10 g U24 22

Now we can calculate the mass of any atom:

1 atom of U = 238 amu

1 atom U1 m ole U

6.02 10 atom s U

238 g U

1 m ole U3.95 10 g

23 22

Find the number of carbon atoms in 3.0 g C.

3.0 g C1 m ole C

12.0 g C

6.02 10 atom s C

1 m ole C1.5 10 atom s C

2323

A mole road-map

Moles gramsatoms

NA

Atomic mass

This can be applied to compounds, which have a molecular mass (in amu) or a molar mass (in grams).

For instance:In one molecule of H2O, there are

2 H atoms = 2 x 1 amu = 2 amu1 O atom = 1 x 16 amu = 16 amu

18 amu

1 mole of H2O has 1 mole of O atoms and 2 moles of H atoms.

1 mole of water weighs 18 g and has 6.02 x 1023 molecules

For Ca(OH)2:

1 Ca = 40.1 amu 2 O = 32.0 amu 2 H = 2.0 amu

74.1 amu

1 mole of Ca(OH)2 has a mass of 74.1 g

Ca(OH)2 is an ionic compound so we can’t talk about molecules. Sometimes the simplest formula – which indicates only the ratio of the ions – is referred to as a formula unit.

How many atoms of O are there in 5.0 g of CO2?

5.0 g CO1 m ole CO

44 g CO

2 m oles O

1 m ole CO

6.02 10 atom s O

1 m ole O

1.4 10 atom s O

22

2 2

23

23

CO =

1 C = 12 am u

2 O = 2x16 = 32 am u

= 44 am u

2