1. Unit E: The Mole
6.02 X 1023

2. Learning Objectives Identify Avogadro’s Number
Distinguish between counting numbers and mass/volume numbers
Calculate the number of particles in a mole
Calculate the number of moles in a quantity

3. STOICHIOMETRY
the study of the quantitative aspects of chemical reactions.
Stoich = element
Metry = study of (think: geometry)

4. Avogadro's Number (the Mole)
A counting unit
Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000
6.02 X 1023 (in scientific notation)
This number is named in honor of Amedeo _________ (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present in a given volume

5. Just How Big is a Mole?
Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.
If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.
If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.
In other words: a LOT.

6. Everybody Has Avogadro’s Number! But Where Did it Come From?
It was NOT just picked! It was MEASURED.
One of the better methods of measuring this number was the Millikan Oil Drop Experiment
Since then we have found even better ways of measuring using x-ray technology

7. Try it yourself…
Suppose we invented a new collection unit called a rapp. One rapp contains 8 objects.
1. How many paper clips in 1 rapp?
a) 1 b) 4 c) 8
2. How many oranges in 2.0 rapp?
a) 4 b) 8 c) 16
3. How many rapps contain 40 gummy bears?
a) 5 b) 10 c) 20

8. The Mole 1 dozen cookies = 12 cookies
1 mole of cookies = 6.02 X 1023 cookies
1 dozen cars = 12 cars
1 mole of cars = 6.02 X 1023 cars
1 dozen Al atoms = 12 Al atoms
1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same, but the MASS is very different! (a mole of cars will probably weigh more than a mole of cookies!)
Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

9. A Mole of Particles Contains 6.02 x 1023 particles
= x 1023 C atoms
= x 1023 H2O molecules
= x 1023 NaCl “molecules”
(technically, ionic compounds are ratios not molecules so they are called formula units)
6.02 x 1023 Na+ ions and
6.02 x 1023 Cl– ions
1 mole C
1 mole H2O
1 mole NaCl

10. Avogadro’s Number as Conversion Factor
6.02 x 1023 particles
1 mole or
1 mole
Note that a particle could be an atom OR a molecule!

11. Learning Check 1. Number of atoms in 0.500 mole of Al a) 500 Al atoms
b) x 1023 Al atoms
c) x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) mole S atoms
b) mole S atoms
c) x 1048 mole S atoms

12. Part 2: Molar Mass Describe what molar mass is
Distinguish between gram molecular mass and gram formula mass
Find the molar mass of elements and compounds

13. Molar Mass
The mass (in grams) of 6.02 x 1023 particles (1 mole) of a substance
Equal to the average atomic mass (mass number) on the periodic table
1 mole of C atoms = g
1 mole of Mg atoms = 24.3 g
1 mole of Cu atoms = 63.5 g

14. The Unit
We express molar mass using the unit g/mol(grams per mole)
Similar to density (g/mL)

15. Formula/Atomic/Molecular Mass
Gram atomic mass (gam) is the mass of 1 mole of atoms
Gram Molecular Mass (gmm) is the mass of 1 mole of molecules (covalent only!)
Gram Formula Mass (gfm) is the mass of 1 mole of ionic compounds
These are all examples of the same thing: molar mass!

16. Other Names Related to Molar Mass
Molecular Mass/Molecular Weight: If you have a single molecule, mass is measured in amu’s instead of grams. But, the molecular mass/weight is the same numerical value as 1 mole of molecules. Only the units are different. (This is the beauty of Avogadro’s Number!)
Formula Mass/Formula Weight: Same goes for compounds. But again, the numerical value is the same. Only the units are different.
THE POINT: You may hear all of these terms which mean the SAME NUMBER… just different units

17. Learning Check! = 79.9 g/mole 1 mole of Br atoms 1 mole of Sn atoms
Find the molar mass (usually we round to the tenths place)
= 79.9 g/mole
1 mole of Br atoms
1 mole of Sn atoms
= g/mole

18. Molar Mass of Molecules and Compounds
Mass in grams of 1 mole equal numerically to the sum of the atomic masses
1 mole of CaCl2 = g/mol
1 mole Ca x 40.1 g/mol
+ 2 moles Cl x 35.5 g/mol = g/mol CaCl2
1 mole of N2O4 = 92.0 g/mol

19. 94. 2 g/mol 78.0 g/mol Learning Check!
Molar Mass of K2O = ? Grams/mole
B. Molar Mass of antacid Al(OH)3 = ? Grams/mole
94. 2 g/mol
78.0 g/mol

20. Challenge
Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. Find its molar mass.

21. Calculations with Molar Mass
Grams Moles
Moles to Grams/Grams to Moles
Particles to Grams/Grams to Particles
Volume

22. Converting Moles and Grams
Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al?
3.00 moles Al ? g Al

23. 1. Molar mass of Al 1 mole Al = 27.0 g Al
2. Conversion factors for Al
27.0g Al or mol Al
1 mol Al g Al
3. Setup 3.00 moles Al x g Al
1 mole Al
Answer = g Al

24. Learning Check!
After leaving his bike out all night, Mr. Pinson collected a 36g sample of Iron (II) Oxide from his wheel. How many moles of rust were formed?

25. Challenge!
The artificial sweetener aspartame (Nutra-Sweet) formula C14H18N2O5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 g of aspartame?

26. Atoms/Molecules and Grams
Since 6.02 X 1023 particles = 1 mole AND 1 mole = molar mass (grams)….
You can convert atoms/molecules to moles and then moles to grams! (Two step process)

27. …But!!
You can’t go directly from atoms to grams!!!! You MUST go thru MOLES.
That’s like asking 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert to dozen first!

28. Everything must go through Moles!!!
Calculations
molar mass Avogadro’s number Grams Moles particles
Everything must go through Moles!!!

29. Atoms/Molecules and Grams
How many atoms of Cu are present in 35.4 g of Cu?
35.4 g Cu mol Cu X 1023 atoms Cu g Cu mol Cu
= 3.4 X 1023 atoms Cu

30. Learning Check!
How many atoms of K are present in 78.4 g of K?

31. Learning Check!
What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?

32. Learning Check! How many atoms of O are present in 78.1 g of oxygen?
78.1 g O2 1 mol O X 1023 molecules O2 2 atoms O g O mol O molecule O2

33. Volume of a Mole
Through experimentation, scientists have discovered that 1 mole of any gas will occupy the same volume: 22.4 L
They will still have different molar masses, however, and so their densities will be different

34. Example 56 L 2.5 moles x 22.4 L = mole
How much space will 2.5 moles of N2 gas occupy?
2.5 moles x 22.4 L =
mole
56 L

35. Example 2 1.54 Moles CH3 34.5 L x 1 mole = 22.4 L
How many moles are in 34.5 L of methane gas?
1.54 Moles CH3
34.5 L x 1 mole =
22.4 L

36. Try it yourself 1.34 moles ozone = ? L 13 L of mustard gas = ? Moles
230 L of Helium gas = ? Moles
5.6 moles Nitrogen gas = ? L

37. Percent Composition
What is the percent carbon in C5H8NO4 (the glutamic acid used to make MSG monosodium glutamate), a compound used to flavor foods and tenderize meats?
a) %C
b) %C
c) %C

38. Chemical Formulas of Compounds
Formulas give the relative numbers of atoms or moles of each element in a formula unit - always a whole number ratio (the law of definite proportions).
NO atoms of O for every 1 atom of N
1 mole of NO2 : 2 moles of O atoms to every 1 mole of N atoms
If we know or can determine the relative number of moles of each element in a compound, we can determine a formula for the compound.

39. Types of Formulas
Empirical
Molecular (true)

40. Empirical Formula
The formula of a compound that expresses the smallest whole number ratio of the atoms present.
Ionic formula are always empirical formulas

41. Molecular Formula (true formula)
The formula that states the actual number of each kind of atom found in one molecule of the compound.

42. Examples
Empirical Formula
Molecular Formula CH
C2H2
CH2O
C6H12O6
NaCl
CH4N
C2H8N2

43. To obtain an Empirical Formula
1. Convert % to grams, if necessary
2. Calculate the number of moles of each element.
3. Divide each by the smallest number of moles to obtain the simplest whole number ratio.
If whole numbers are not obtained* in step 3), multiply through by the smallest number that will give all whole numbers
* Be careful! Do not round off numbers prematurely

44. 1. Convert grams to moles 2.34g N x 1 mole N = 0.167 14g mol
A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.
1. Convert grams to moles
2.34g N x 1 mole N = 0.167
14g mol
5.34g O x 1 mole O = mol 16g

45. 2. Divide by smallest mol number 0.167 mol N ___________ 0.167
A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.
2. Divide by smallest mol number
0.167 mol N
0.333 mol O
___________
0.167
___________
0.167
= About 1
= About 2

46. NO2 3. Assign ratio numbers to formula 1 mole N for every 2 moles O =
A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.
3. Assign ratio numbers to formula
1 mole N for every 2 moles O =
NO2
Note: This is an empirical formula, NOT a molecular formula! The compound is not necessarily Nitrogen Dioxide!

47. Empirical Formula Song
% to Grams
Grams to Moles
Divide by the Smallest
Multiply to Whole!

48. Empirical Formula from % Composition
A substance has the following composition by mass: % Na ; % B ; % H
What is the empirical formula of the substance?
Consider a sample size of 100 grams
This will contain 60.8g of Na, grams of B and grams H
Note: Because % Composition is a constant, you could use ANY sample size to find empirical formula…but 100g is the easiest

49. 1. Convert grams to moles 60.8g Na x 1 mole Na = 2.65 mol 23g
28.60g B x 1 mole B = 2.65 mol
10.8g
10.60g H x 1 mole H = 10.6 mol 1g

50. 2. Divide by smallest mole
2.65 mol Na
2.65 mol B
10.60 mol H
__________
2.65
__________
2.65
__________
2.65 =1
= 1
= 4
Ratio = 1:1:4

51. 3. Assign ratio to elements in formula
1:1:4 = NaBH4

52. Practice: Empirical Formula
94.1% O, 5.9% H
79.8% C, 20.2% H
67.6% Hg, 10.8% S, 21.6% O
27.59% C, 1.15% H, 16.09% N, 55.17% O OH
CH3
HgSO4
C2HNO3

53. Multiply to Whole You cannot round anything more than .1
To convert to whole numbers, multiply the whole problem by 2, 3, or 4
1.5 x 2 = x 4 = 5
1.3 x 3 = (4)

54. Example w/ Multiply to Whole
A sample contains 70% iron, 30% oxygen. What is its empirical formula?
70% = 70g Fe
30% = 30g O
1. % to grams
70g x 1mole = 1.25
55.8g
2. Grams to moles
____
1.25
= 1
3. Divide by the Smallest
30g x 1 mole = 1.875
16g
____
1.25
= 1.5

55. 4. Multiply to Whole ( )
FeO1.5
= Fe2O3 2

56. Calculation of the Molecular Formula
A compound has an empirical formula of NO2. The colourless liquid, used in rocket engines has a molar mass of 92.0 g/mole. What is the molecular formula of this substance?

57. 1. Find molar mass of Empirical Formula (efm)
Element
# of Atoms
Mass per Atom
Total Mass N 1 14 O 2 16 32
= 46g

58. 2. Divide molar mass of compound by empirical formula mass
92g 46g
= 2

59. 3. Multiply the answer by the formula subscripts
NO2 x 2 =
N2O4
=The compound is Dinitrogen Tetroxide

60. Practice: Molecular Formula
Ethylene glycol (CH3O), used in antifreeze, with a molar mass of 62g/mol
P-dichlorobenzene (C3H2Cl), makes up mothballs with molar mass of 147g/mol
C2H6O2
C6H4Cl2