THE MOLEReturn to dimensional analysis

THE MOLEWhat is a mole?

Not a furry animal that burrows in the ground

What it is? . . . A unit of measure that tells how much of something you have

THE MOLE Examples:

1 dozen eggs is how many eggs? A couple of dollars is how many

dollars? 1 score of people is how many people?

The mole is another example of a word that describes a number of something

THE MOLE How much is a mole?

REMEMBER: In chemistry, we are talking about atoms and there are a LOT of atoms

Therefore the mole is a VERY BIG number 1 mole of stuff is 6.02 x 1023 items of

the thing For example if you have 1 mole of

pennies this equals 6.02 x 1023 pennies

THE MOLE Where did we get this number?

6.02 x 1023

Discovered by a scientist by the name of Avagadro.

Therefore, it is called AVAGADRO’S NUMBER

He discovered how many atoms made up 12 grams of carbon.

Became the basis for the number of any number of particles in 1 mole

THE MOLEJust how big is the mole?

If you had 1 mole of pennies (6.02 x 1023 pennies), then you could cover the entire earth with pennies 100 feet deep.

Let’s look at some other examples

THE MOLE Now that we have the mole as a

measurement, we can now find the number of particles in a sample

For example: 1 mole of a compound is 6.02 x 1023

molecules 1 mole of an element is 6.02 x 1023

atoms

EXAMPLE If you have 2 moles of iron, how many

iron atoms do you have? (We will continue to use dimensional analysis)

1 mole = 6.02 x 1023 atoms

2 moles | 6.02 x 1023 atoms = 1.20 x 1024

atoms

| 1 mole

TRY THESE1. If you have 3.5 moles of copper, how

many copper atoms do you have?

2. If you have 0.0235 moles of water, how many water molecules do you have?

3. If you have 3.31 x 1024 atoms of potassium, how many moles do you have?

ANSWER1. 2.11 X 1024 atoms of copper

2. 1.41 x 1022 molecules of water

3. 5.5 moles of potassium

MOLAR MASS Yay! We get to use the periodic table

again. We talked earlier in the year about the

mass number The number located at the bottom of each

element For example:

Mass number of Lithium is 6.94 Mass number of Bromine is 79.90

MOLAR MASSBefore the mass number was

the measure of the number of protons + neutrons

It also accounted for all the isotopes (that’s why some numbers have decimals)

MOLAR MASS It turns out the molar mass has

another valueMolar mass: the mass in grams of

one mole of any pure substance.For example1 mole of Lithium = 6.94g/mole1 mole of Bromine = 79.90g/mole

WHAT HAPPENS WHEN YOU HAVE A COMPOUND?

How do we find the molar mass of water (H2O)?

TRY IT

SOLUTION To find the molar mass, you add the molar

mass of ALL the elements in the compound H2O

You have 2 H 2 (1.01 g/mole) = 2.02g/mole

You have 1 O 16.0 g/mole Total molar mass = 16.0 g/mole + 2.02

g/mole Therefore the molar mass of water is:

18.02 g/mole H2O

TRY THESE – Be careful of the subscript numbers

1. CCl4

2. NaBr

3. Pb(SO4)2

4. AgNO3

SOLUTIONS1. 153.81 g/mole CCl42. 102.89 g/mole NaBr3. 399.32 g/mole Pb(SO4)2

4. 169.88 g/mole AgNO3

NOTICE: The units for molar mass are g/mole (this is a conversion unit)

HOW TO USE MOLAR MASS

We can now measure the mass of substances and determine how many moles and how many particles we have?

For example: You measure 22.0g of boron (B), what is the number of moles you have? What is the number of boron atoms you have?

EXAMPLE22.0g of B | 1 mole of B = 2.04 moles of

B

|10.81 g of B

2.04 moles of B | 6.02x1023 atoms of B =

| 1 mole of B1.23 x 10 24 atoms of B

TRY THESE

1. If you have 13.8g of lithium, how many moles is this? How many atoms?

2. If you have 88.5g of chlorine, how many moles is this? How many atoms?

ANSWERS

1. 1.99 moles; 1.20 x 1024 atoms of Li

2. 2.50 moles; 1.50 x 1024 atoms of Cl

FINDING THE MOLES FOR A COMPOND

Now that we know how to find the molar mass of a compound, we can calculate the number of moles and the number of molecules of a compound

The procedure is just like an element, except you have to calculate the molar mass first.

YOU MUST ALSO KNOW HOW TO NAME COMPOUNDS

EXAMPLEEveryone try this out:

You start with 261 g of manganese (IV) oxide. What is the molar mass of manganese (IV) oxide? How many moles is this? How many molecules is this?

SOLUTION To find the molar mass, you need to

use the periodic table:1. manganese (IV) oxide = MnO2

2. 1 Mn = 54.94 g/mole3. 2 O = 2(16 g/mole) = 32 g/mole

4. Molar mass = 54.94g/mole + 32 g/mole

5. Total molar mass = 86.94 g/mole

SOLUTION (CONT) Starting mass: 261g Molar mass: 86.94g/mole

261g of MnO2 | 1 mole = | 86.49 g of MnO

3.02 moles of MnO2

SOLUTION (CONT) 3.02 moles | 6.02 molecules =

| 1 mole

1.82 x1024 molecules of MnO2

TRY THESE – You can do dimensional analysis all at once

1. You start with 361g of MgSO4. How many molecules of magnesium sulfate do you have?

2. You start with 370.5g of Ca(OH)2. How many molecules of calcium hydroxide do you have in this sample?

SOLUTION

1. 1.81 x 1024 molecules MgSO4

2. 3.010 x 1024 molecules Ca(OH)2

LET’S BRING IN DENSITY We know that density is a conversion

factor between mass and volume Density has the following units:

Mass/volumeGrams/milliliter (g/mL)Grams/cubic centimeter (g/cm3)Kilograms/liter (kg/L)etc . . .

DENSITY As long as we know that density is a

conversion factor, now we can convert number of molecules to volume or volume to number of molecules

Molecules Moles Mass Volume

(atoms)avagadro’s # molar mass density

EXAMPLE You have a sample of iron that

contains 3.00 x 1025 atoms. If the density of iron is 7.87g/mL, what is the volume that the iron takes up?

To do this, it’s just like any other dimensional analysis problem

1. Write down what you start with2. Cancel out the stinking units

EXAMPLE Step 1:

You begin with 3.00 x 1025 iron atoms. What is the next thing we have to get to

head towards volume?

Molecules/Atoms Moles 3.00 x 1025 atoms | 1 mole_______

6.02 x 1023 atoms

EXAMPLE Step 2

After you get to moles where is the next stop on your way to volume?

Molecules/Atoms Moles Mass You need the molar mass of iron (Fe)

55.85 g/mole 3.00 x 1025 atoms | 1 mole_____| 55.85 g__

| 6.02 x 1023 atom | 1 mole

EXAMPLE Step 3

The final conversion we need is densityMolecules/Atoms Moles Mass

Volume Density of iron is 7.87 g/mL (you will not be

able to do the problem unless density is given

3.00 x 1025 atoms | 1 mole_____| 55.85 g_| 1mL__

| 6.02 x 1023 atom | 1 mole | 7.87 g

SOLUTION 353 mL

NOTICE: Each time we needed to do a conversion,

we made sure the units cancelled out You have to follow the correct pathway to

get from the unit you start with to the unit you are trying to find.

TRY THESE1. You start with 48.1 mL of H2O. The

density of water is 1.00g/mL. What is the number of moles of water you have?

2. You have 3.5 moles of mercury. What volume does this take up if the density of mercury is 13.6 g/mL?

3. You start with 9.90 x 1020 molecules of ethyl alcohol (C2H6O). If the density of ethyl alcohol is 0.791 g/mL, what volume does this take up?

SOLUTION1. 2.67 moles of H2O

2. 52 mL of Hg

3. 0.0958 mL of ethyl alcohol