Return to dimensional analysis THE MOLE Return to dimensional analysis

THE MOLE What 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 MOLE Just 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 THESE If you have 3.5 moles of copper, how many copper atoms do you have? If you have 0.0235 moles of water, how many water molecules do you have? If you have 3.31 x 1024 atoms of potassium, how many moles do you have?

ANSWER 2.11 X 1024 atoms of copper 1.41 x 1022 molecules of water 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 MASS Before 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 value Molar mass: the mass in grams of one mole of any pure substance. For example 1 mole of Lithium = 6.94g/mole 1 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 CCl4 NaBr Pb(SO4)2 AgNO3

SOLUTIONS 153.81 g/mole CCl4 102.89 g/mole NaBr 399.32 g/mole Pb(SO4)2 169.88 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?

EXAMPLE 22.0g 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 B 1.23 x 10 24 atoms of B

TRY THESE If you have 13.8g of lithium, how many moles is this? How many atoms? If you have 88.5g of chlorine, how many moles is this? How many atoms?

ANSWERS 1.99 moles; 1.20 x 1024 atoms of Li 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

EXAMPLE Everyone 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: manganese (IV) oxide = MnO2 1 Mn = 54.94 g/mole 2 O = 2(16 g/mole) = 32 g/mole Molar mass = 54.94g/mole + 32 g/mole 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 You start with 361g of MgSO4. How many molecules of magnesium sulfate do you have? You start with 370.5g of Ca(OH)2. How many molecules of calcium hydroxide do you have in this sample?

SOLUTION 1.81 x 1024 molecules MgSO4 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/volume Grams/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 Write down what you start with 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 density Molecules/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 THESE 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? You have 3.5 moles of mercury. What volume does this take up if the density of mercury is 13.6 g/mL? 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?

SOLUTION 2.67 moles of H2O 52 mL of Hg 0.0958 mL of ethyl alcohol