1

The Mole

2

Counting Without Counting If you had to count the number of coffee beans in

this bag how would you do it? How long would it take?

3

Counting Without Counting If you had to count the number of grains of sand

in this bag how would you do it? How long would it take?

How do scientists count atoms or molecules?

4

Let’s try to come up with a way to count the number of beans in a large bag of beans without actually counting them all and without taking a long time.

Eventually we want to apply this new method of counting to counting atoms!

Any IDEAS?

5

Counting by Weighing

Weight of 10 beans _____ g

Average weight of one bean _____ g

Weight of all beans in bag _____ g

Weight of beans in bag _____ (g) 1 bean = _____ beans in a _____ (g) bag

8.510.85

453

453

533

0.85

Counting by weighing works when the items are all about the same size and mass. The closer the items are to being exactly the same, the more accurate the method is.

If the beans were all exactly the same we would only have to weigh one and not take the average of ten!

6

Counting by Weighing

What was the key information needed to determine the number of beans in any bag of beans without counting them all?

The average mass of ONE bean!

7

Applying “Counting by Weighing” to Atoms

How can we use this idea to determine the number of atoms per gram of the element carbon?

We need to know the mass of one atom of carbon! We can’t weigh an atom of carbon directly but we do

know something about the particles that make up a carbon-12 atom.

proton = 1.67 x 10-24g Carbon-12 has 6 protons

neutron = 1.67 x 10-24g Carbon–12 has 6 neutrons

electron = too small to count Carbon-12 has 6 electrons (still too small)

8

Mass of one Carbon Atom

9

Applying “Counting by Weighing” to Atoms So one atom of Carbon-12 weighs about 2.0 x 10-

23 g.

How many grams of carbon should we use? (like the total mass of an beans bag).

Weight for one carbon atom is a result of 12 particles (6p+6n). So let’s use 12 GRAMS of carbon.

(Who is this guy?)

How Many Atoms in 12 Grams of Carbon

How many atoms do you think are in 12 grams of carbon?

Let’s use dimensional analysis (canceling units) to figure it out!

12gC 1 atom C = 6.0 x 1023 atoms of carbon 2.0x10-23 gC

That’s 600,000,000,000,000,000,000,000 atoms!!

OK, Why Carbon?

10

11

Oxygen and Hydrogen Were Also Both Used as Mass Standards

Physicists used Hydrogen Chemists used Oxygen Because oxygen and Because oxygen and

hydrogen both have hydrogen both have isotopes the scales didn’t isotopes the scales didn’t agree, but the ratio of two agree, but the ratio of two elements was the same.elements was the same.

Physicists and Chemists Physicists and Chemists compromise to Carbon as compromise to Carbon as the mass standard in 1961.the mass standard in 1961.

Can you believe it took them that long to agree!!

12

The MoleNow let’s go backwards using oxygen with that 6 x 1023

number of atoms for 12 grams of carbonParticles in

O atom Mass(g) of

particle Total mass(g) of

particles

8 protons x 1.67 x 10- 24 = 1.34 x 10- 23 8 neutrons x 1.67 x 10- 24 = 1.34 x 10- 23 8 electrons x 9.108 x 10- 28 = Negligible

Total mass of Oxygen atom

2.68 x 10- 23 g

6.0 x 1023 atoms 2.68 x 10-23 g = 16 g oxygen!! oxygen 1 atom oxygen

look familiar?

13

The Mole 6.0 x 1023 is a pretty special number.

It’s called “a mole”

1 “Mole” represents 6.0 x 1023 of anything.

Like 1 dozen = 12 of anything (Other examples?)

One mole of beans is 6.0 x 1023 beans.

The mole is based on the number of

atoms in 12 grams of carbon-12

The Mole Scientists have determined that

One Mole = 6.02 x 1023

atoms. It’s important in chemistry because

its used to convert grams to atoms. Scientists want to react atoms with atoms but they can’t count out atoms directly, they’re too small.

Using The Mole scientists can weigh out a number of grams of a chemical and calculate the number of atoms present in that mass!

14

15

“The Mole” (or mol) may come from a shortening of “molecule”.

Also the word “mole” is Latin for “heap or pile”

Avogadro didn’t coin the term, he wasn’t even the first to recognize how to calculate the number.

Loschmidt, a school teacher, was the first to calculate atoms/mole and his work was based on Avogadro’s work.

Loschmidt (1865)

Avogadro (1811)

Avogadro suggested that equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

16

The Mole 6.02 x 1023 atoms of carbon-12 is 12.00 grams, and

6.02 x 1023 atoms of oxygen-16 weighs 16.00 grams …

So the mole is clearly related to an element’s atomic mass.

Let’s define one mole of any element as equal to the atomic mass (weighted average of isotopes) of that element.

What is a Mole

17

atomic mass of 1 mole of atoms 6.02 x 1023 atoms element of any element of any element

1 mole of carbon = 12.01g carbon = 6.02 x 1023 atoms C 1 mole of oxygen = 16.00g oxygen = 6.02 x 1023 atoms O 1 mole of sodium = 23.00g sodium = 6.02 x 1023 atoms Na

= =

18

How Big is a Mole (6.02 x 1023) ?

If you count out loud starting with the number "one" at the rate of one count every second, it would take you 1,909,577,942,668,696 years to finish.

Using a 2 GHz CPU, it will still take about 2,243,506 years to “count” to 1 mole.

One mole of beans would cover the earth 25 miles thick!!

19

Using “The Mole” Once you understand the concept of “The Mole” it’s

easy to use. Now that we know the mole REPRESENTS the number of particles we can use the mole directly.

Calculate the number of moles in 150.0 g of copper:

150.0 g Cu 1 mole Cu = 2.4 moles of Cu 63.55 g Cu

Calculate the number of atoms in 20.4g of carbon:

20.40 g C 1 mole C 6.02 x 1023 atoms C = 1.02x1024 atoms C

12.01 g C 1 mole C

20

Bad Mole Jokes

21

22

The Original Wack-a-Mole

23

24

25

A small furry mammal walks into a bar and orders a drink. The bartender says, "Sorry, our maximum occupancy is only 5.99 x 1023. We can't serve a mole."

26

"Do you have mole problems? If so, call Avogadro at 602-1023."

27

28

29

30

31

More Practice with the Mole

How many moles of Zinc are in 50.0g of Zinc metal?

How many particles of chlorine gas are there in 20 moles of chlorine gas?

32

More Practice with the Mole

How many moles of Zinc are in 50.0g of Zinc metal?

50.0 g Zn 1 mole Zn = 0.765 Moles Zn

65.39 g Zn

How many molecules of chlorine gas are there in 20 moles of chlorine gas?

20 moles Cl2 6.02 x 1023 molecules Cl2 = 1.2x1025 Molecules Cl2

1 mole Cl2

Even More Practice!!

How many moles of NaCl are in 50.0g of sodium chloride?

= Moles NaCl

Na = 23.00g/mole (atomic mass)

Cl = 35.45g/mole (atomic mass)

NaCl = 58.45 g/mole (molar mass)

33

50.0g NaCl58.45

1 mole NaCl g NaCl

0.855