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The Mole (and M&M’s)

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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?

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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?

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Let’s try to come up with a way to count the number of M&M’s in a large bag of M&M’s 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?

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Counting by Weighing

Weight of 10 M&M’s _____ g

Average weight of one M&M _____ g

Weight of M&M’s in bag _____ g

Weight of M&M’s in bag _____ (g) 1 M&M = _____ M&M’s in a bag

____ (g)

8.660.87

357.2

357.2

411

0.87

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 M&M’s were all exactly the same we would only have to weigh one and not take the average of ten!

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Counting by Weighing

What was the key information needed to determine the number of M&M’s in any bag of M&M’s without counting them all?

The average mass of ONE M&M

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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 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 has 6 protons

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

electron = 9.11 x 10-28g Carbon has 6 electrons

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Mass of one Carbon Atom

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Applying “Counting by Weighing” to Atoms So one atom of Carbon-12 weighs 2.0 x 10-23 g.

Now to determine the relationship between mass and # of Carbon atoms. How many grams of carbon should we use? (like the total mass of a M&M’s bag).

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

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

Let’s use dimensional analysis 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!!

(Who is this guy?)

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

number of atomsParticles 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?

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The Mole 6.0 x 1023 is a pretty special number. “Mole” represents 6.0 x 1023 of anything. Like 1 dozen = 12 of anything Using other means scientists have determined

that

One Mole = 6.022 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 mass of a

chemical and calculate the number of atoms present in that mass!

One mole of M&M’s is 6.02 x 1023 M&M’s.

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“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.

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The Mole 6.022 x 1023 atoms of carbon is 12.00 grams, and

6.022 x 1023 atoms oxygen 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 any element.

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

= =

1 mole of carbon = 12.00g carbon = 6.02 x 1023 atoms of C 1 mole of chlorine = 35.45g chlorine = 6.02 x 1023 atoms of Cl 1 mole of barium = 137.3g barium = 6.02 x 1023 atoms of Ba

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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 Pentium 1 GHz CPU, it will still take about 2,243,506 years to finish this task.

One mole of M&M’s would cover the earth 25 miles thick!!

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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

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Bad Mole Jokes

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The Original Wack-a-Mole

A small furry mammal walks into a bar and orders a drink. The bartender says, "Sorry, our maximum occupancy is only 6.00 x 1023. We can't serve a mole."

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"Do you have mole problems? If so, call Avogadro at 555 - 602 - 1023."

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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 = 1.7x1023Molecules Cl2

1 mole Cl2

How many grams of oxygen gas are in 0.625 moles of O2 ?

0.625 mol O2 32.00g O2 = 20.0g O2

1 mole O2

END

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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!!

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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 = 1.7x1023Molecules Cl2 1 mole Cl2

How many grams of oxygen gas are in 0.625 moles of O2 ?

0.625 mole O2 32.00g O2 = 20.0g O2

1 mole O2