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Celebrate MOLE Day! October 23 rd from 6:02 a.m. till 6:02 p.m.

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IV. Relating Mass to Numbers of Atoms

1. The Mole (can be abbreviated mol, but NOT m, which is the abbreviation for meter!) - the SI unit for amount of substance. A mole is the amount of a substance that contains as many particles as there are atoms in exactly 12 grams of carbon-12.

2. Avogadro’s Number

-the number of particles in exactly one mole of a pure substance. This number was determined experimentally and its value is 6.022 X 1023, which means that 12 g of carbon-12 contains 6.022 x 1023 carbon-12 atoms.

3. Using the Mole and Avogadro’s Number

- A mole can be thought of as a counting unit just like a dozen (12), pair (2), ream (500), mole (6.022X1023 ).

OK, so How many is a mole? How large is Avogrado’s number…

Let’s get some perspective…

If every person living on Earth (6 billion people) worked to count out one mole of oranges (or anything else), and if each person counted continually at a rate of one orange per second, it would take about 4 million years for all the oranges to be counted!

If we had a mole of sand it would cover the earth 7 times over! If you had a mole of dollar bills, you could spend a million dollars every minute of your life and never spend it all!!!

Since the mole is so large, we use it to count very tiny things – like atoms. Because the mole is so large, (and we now know that we cannot count out a mole of anything), how do we know when we have a mole of anything?

- We determine the mass and relate that to the number of atoms present.

4. Molar Mass

- – The mass of one mole of a pure substance. The pure substance can be an element or a compound.
- The atomic mass is the mass of 1 atom of that element measured in amu’s.
- The atomic mass is also equal to 1 mole of atoms measured in grams it is called the molar mass!!!! What a coincidence!!!!

Mass of 1 atom of Pb = 207.2 amu

- Mass of 1 mole of Pb atoms = 207.2 g
- Mass of 1 atom of N = 14.01 amu
- Mass of 1 mole of N atoms = 14.01 g
- Mass of 1 atom of Ba = 137.33 amu
- Mass of 1 mole of Ba atoms = 137.33 g
- Mass of 1 atom of Al = 26.98 amu
- Mass of 1 mole of Al atoms = 26.98 g

3. Molar Mass for compounds

How to find the molar mass:

- Write a CORRECT formula for the compound (we’ll do this later)
- Look up the atomic mass of each element in the compound
- Multiply the atomic mass by the subscripts, if any. Add all masses of elements together and use the unit, g/mol

Example: find the molar mass of NaCl.

Na=23.0 g/mol

Cl=35.5 g/mol

58.5 g/mol

Example: find the molar mass of calcium phosphate, Ca3(PO4)2.

- Ca = 40.1 x 3 = 120.3
- P = 31.0 x 2 = 62.0
- 0 = 16.00 x 8 = 128.00
- 310.3 g/mol

Practice:

- Find the molar mass of ammonium sulfate, (NH4)2SO4
- Find the molar mass of Cl2O7
- Find the molar mass of NaCl

Let’s prove it: Determine the mass, in grams, of 6.022X1023 atoms of aluminum. Use 1amu = 1.66X10-27kg.

With this information we can write some new conversion ratio’s!!

1 mole = 6.022X1023 atoms OR molecules OR formula units

1 mole Al = 26.98 grams

1 atom Al = 26.98 amu

V. Mole Problems – When in doubt go to the mole!

- The MOLE has been defined as 6.022 x l023 atoms of a pure element or the molar mass of a substance expressed in grams. It can also be defined as 6.022 x l023 molecules of a compoundor diatomic molecule (O2, N2, H2, etc)
- THE ONLY THING HARD ABOUT UNDERSTANDING THE DEFINITION OF A MOLE IS THAT YOU UNDERSTAND THAT THE VALUE OF A MOLE IS DIFFERENT FOR EVERY DIFFERENT ELEMENT AND COMPOUND.

1. Gram/Mole conversions-how to convert moles to grams or grams to moles.

Example: 120 g Ca x 1 mole Ca = 2.99 mole Ca

40.1 g Ca

- Practice:
- How many grams of sodium are in 5.00 moles of sodium?
- How many grams of magnesium are in 0.250 moles of magnesium?
- How many moles of lead, Pb, are in 210. g of lead?
- How many moles of nitrogen are in 44.0 g of nitrogen?

2. Conversions with Avogadro’s Number

Example: How many atoms of silver, Ag, are in 4.25 moles of Ag?

4.25 moles Ag X 6.022 x 1023 atoms Ag =

1 mole Ag

Practice:

- How many atoms of Pb are in 3.80 moles of Pb?
- How many moles of Na are in 8.24 x 1024 atoms of Na?

Two-step conversions:

Ex: How many atoms of sodium, Na, are in 5.25 g of Na?

5.25 g Na x 1 mole Na x 6.022 x 1023 atoms Na =

23 g Na 1 mole Na

- Practice:
- How many atoms of potassium, K, are in 3.99 g of K?
- How many g of He are in 3.03 x 1021 atoms of He?
- 3. How many atoms of Li are in 0.755 g of Li?

Hydrates - Some compounds trap water inside their crystal structure and are known as hydrates. You will not be able to predict which compounds will form hydrates. All you have to do is to be able to name them and find their molar masses (including the water).

- CuSO4 · 5H20 is an example of a hydrate. This says that one formula unit of cupric sulfate (or copper (II) sulfate) will trap 5 molecules of water inside its crystal.

Hydrates are named by naming the ionic compound by the regular rules and then adding (as a second word) a prefix indicating the number of water molecules. You will use the word “hydrate” to indicate water. The above compound would be called cupric sulfate pentahydrate.

- To find the formula mass of a hydrate, simply find the mass of the ionic compound by itself and then ADD the mass of water molecule(s) to that mass.

Practice: What is the formula mass of barium chloride dehydrate, BaCl2 · 2H2O?

What is the formula mass of aluminum sulfate octahydrate, Al2(SO4)3 · 8H2O?

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