1. Mole, Avogadro’s Number Mass percent composition
Molar Mass
Mass percent composition
Empirical Formula

2. Why is Knowledge of Composition Important?
Everything in nature is either chemically or physically combined with other substances
Some Applications:
the amount of sodium in NaCl for diet
the amount of iron in iron ore for steel production
the amount of carbon in fossil fuel in terms of green house effect

3. Counting Pennies by Weight
What if a person doesn’t have bills but pounds of pennies when he wants to buy a $10 pizza?
Seinfeld: Kramer’s attempt to buy calzone with pennies
Assuming each penny weighs exactly the same (2.500 g), we can count pennies by weight the total weight of pennies…

4. Counting Pennies by Weight
Kramer brought 2,500. g (ca. 5.5 lbs) of new pennies to the Italian restaurant. Do you think he can buy three calzones ($10.0 total)? Each new penny weighs g.

5. Counting Coins by Weight
What if Kramer bought a different coin?
Would the mass of single dime be g?
Would there be $10.00 in 2,500. g dimes?
How would this affect the weight-dollar conversion factors?

6. Mass of atoms Atoms of the same element have on average the same mass.
Mass of atom in amu (atomic mass unit):
1 amu = ×10-27 kg
Mass of a C-12 atom = 12 (exact) amu
Mass of a gold atom on average = amu
Do I have to memorize these numbers?!

7. Counting atoms by mass
Similar to how we count the number of pennies, we can count the number of atoms using their mass
The number of atoms in a sample often is an astronomical number, so we use a big unit to account for the number of atoms. Just like 1 dozen = 12 items

8. “Chemical Dozen” – the Mole
The number of particles in 1 mole:
Avogadro’s Number = _______________ units
1 mole of any atomic element has x 1023 atoms
1 mole of oxygen gas has x 1023 O2 molecules
1 mole of NaCl solid has x 1023 Na+ ions and x 1023 Cl- ions

9. Avogadro’s Number as Conversion Factor
Given number of Moles  number of Units
Given number of Units  Mole #
Mole =
#Units

10. 1 mole Ag atoms = 6.022 x 1023 Ag atoms
Example: A silver ring contains moles of silver. How many silver atoms silver are in the ring?
Information
Given: moles of Ag atoms
Find: ? number of Ag atoms
1 mole Ag atoms = x 1023 Ag atoms
2.5 x 1022 Ag atoms (2 sig. figs)

11. Example: How many moles of water are in 1.234 x 1020 water molecules?
Information
Given: x 1020 water molecules
Find: ? moles of water molecules
1 mole water = x 1023 water molecules
2.049 x 10-4 moles water (4 sig. figs)

12. Mole, Atomic Mass, Mass
The mass of exactly one mole of any element equals the Atomic Mass in grams.
Example:
Exactly 1 mole He = _______ g
Exactly 1 mole Li = _______ g
If given the mass of a particular number of atoms, we can determine the number of atoms in any mass of the element!

13. The Mass of one mole substance depends on the Element

14. Molar Mass
The mass of one mole of atoms is called the Molar mass. Unit as g/mole or g/mol.
The molar mass of an element, in grams, is numerically equal to the element’s atomic mass.
Example:
Molar mass of Sodium = ___________

15. Molar Mass as Conversion Factor
Example: molar mass He = g
So 1 mole He = gram He
Given number of Moles  Mass
Mass (gram) = _________________
Given Mass  Mole
Mole = ___________________

16. Example: Calculate the number of moles of sulfur in 57.8 g of sulfur
Information
Given: 57.8 g S
Find: ? moles S
Conv. Fact.: 1 mole S = g
1.80 moles S (3 sig. figs)

17. Example: Calculate the mass of 3.34 x 10-3 mole of helium gas.
Information
Given: x 10-3 moles He
Find: ? Grams of He
Conv. Fact.: 1 mole He = 4.00 g
g He

18. Practice: #atoms, moles, molar mass
The largest uncut diamond (pure carbon) weighs 755 carat (1 carat = 0.2 grams exactly). How many moles of carbon atoms are in this diamond?
What is mass for 1.2 x 10-3 mole gold?
(optioinal) 70% of the mass of the Sun is hydrogen. The mass of the Sun is 1.99 x 1030 kg. How many moles of hydrogen atoms are in the Sun?
12.6 mol C
0.24 g mol Au
1.38 x 1033 mol H atom

19. Molar Mass and Avogadro’s Number
Since 1 mole contains Avogadro’s number of units whilst has a mass of molar mass
there is direct connection/conversion factor between Avogadro’s number and molar mass.
Example:
6.022 x 1023 Al atoms = _______ g Al

20. Example: How many aluminum atoms are in an aluminum can with a mass of 16.2 g?
Information
Given: 16.2 g Al
Find: ? atoms Al
1 mol Al = g = x 1023 Al atoms
g Al
mole Al
atoms Al
3.62 x 1023 atoms Al

21. Example: What is the mass of 1.34 x 1020 silver atoms?
Given: x 1020 Ag
Find: ? grams Ag
1 mol Ag = g Ag = x 1023 Ag atoms
SM: atoms  mol  g
g Ag

22. Practice: Mass vs. Molec/Atom
Diamond is made of pure carbon. The largest uncut diamond weighs 755 carat (1 carat = 0.2 grams exactly). How many carbon atoms are in this diamond?
What is the mass of one gold atom in grams?
7.57 x 1024 C atoms
x grams

23. Molar Mass of Compounds
Molar Mass: Mass of molecules per exactly one mole of this molecule. Unit = g/mol
Example:
1 mole of H2O = 2 moles H + 1 mole O
Molar Mass of H2O = 2(1.008 g/mol H) g/mol O
= g/mol
1 mole Al(NO3)3 = 1 mole Al + 3 mole N + 9 mole O
Molar Mass of Al(NO3)3 = 1(26.98) + 3(14.01) + 9(16.00) = g/mol

24. Practice: Find the Molar Mass
Sulfuric acid
Aluminum sulfate
Ammonium chlorite
Hydrobromic acid
Nickel(II) phosphate

25. Mass of Compound ↔ Moles of Compound

26. Example: Calculate the mass (in grams) of 1.75 mol of water
Information
Given: 1.75 mol H2O
Find: ? g H2O
C F: 1 mole H2O = g H2O
31.5 g H2O

27. Example: Calculate the mole of CO2 in 454 g dry ice (solid carbon dioxide).
Information
Given: 454 g CO2
Find: ? mol CO2
C F: 1 mole CO2 = g CO2
10.3 mol CO2

28. Mass of Compound ↔ Number of molecules

29. Example: Find the mass of 4.8 x 1024 NO2 molecules
Information
Given: 4.8 x 1024 molec NO2
Find: ? g NO2
1 mole NO g NO2
3.7 x 102 g

30. Example: How many water molecules in 1.00 mL DI water?
Information
Given: 1.00 mL H2O
Find: #H2O molecules
1 mole H2O = g H2O
Density of water = ______ g/mL
3.34 x 1022 H2O molecules

31. Practice
Online: 
How many moles of water in mL pure water if the density of water is 1.00 g/mL?
Determine the mass of 2.0 × 103 mole NaCl.

32. Chemical Formulas as Conversion Factors
1 spider  8 legs + 1 head + 1 abdomen
1 chair  4 legs + 1 seat + 1 back
1 H2O molecule  2 H atoms + 1 O atom

33. Mole Relationships in Chemical Formulas
Given:
#moles of the compound
Chemical formula of the compound
#moles of a constituent element within the compound
Moles of Compound
Moles of Constituents
1 mol NaCl
1 mole Na, 1 mole Cl
1 mol H2O
2 mol H, 1 mole O
1 mol CaCO3
1 mol Ca, 1 mol C, 3 mol O
1 mol C6H12O6
6 mol C, 12 mol H, 6 mol O

34. *Example: How many oxygen atoms are in 100. g of iron(II) phosphate.
Chemical formula: __________
Molar mass = g/mol
For exactly 1 mole compound, there are ___ mole of oxygen
mol _________
2.054 mol O
1.24 x 1024 O atoms

35. Mass Percent Composition
Mass% represents the mass of constituent element in grams per exactly 100 g of compound:
Example: mass percent of nitrogen in Al(NO3)3

36. Example: Find mass% Find Mass% of Nitrogen in Ammonium phosphate.
Formula:
Molar mass = g/mol
For exactly 1 mole compound, there are ___ mole of Nitrogen
Exactly 1 mole compound weighs ______ g
____ moles nitrogen weighs g
Mass% of Nitrogen = g/ g x 100% = 23.20%

37. Example: Use mass% to find mass of constituent element
Given the mass% of nitrogen in Ammonium phosphate (23.20%), find the mass of nitrogen in 454 g of ammonium phosphate.
Meaning of mass%: A conversion factor 
exact 100 g ammonium phosphate = g N
454 g _______ x
Mass Nitrogen = 105 g

38. Empirical Formula Chemical Formula  Mass% of each element
Mass% of each element  Chemical Formula?
Empirical Formula: The simplest, whole-number ratio of atoms in a molecule
It shows the mole ratio in the compound
It can be determined from percent composition or combining masses

39. Empirical Formula vs. Molecular Formula
Hydrogen Peroxide (in store)
Molecular Formula = H2O2
Empirical Formula = HO
Benzene (in gasoline)
Molecular Formula = C6H6
Empirical Formula = CH
Glucose (essential energy in body)
Molecular Formula = C6H12O6
Empirical Formula = CH2O

40. Finding an Empirical Formula
mass% of each element  grams of each element
skip if already grams
grams  moles of each element
use atomic mass of each element
pseudoformula w/ moles as subscripts
divide all by smallest number of moles
multiply all mole ratios by number to make all whole numbers
if ratio ?.5, multiply all by 2; if ratio ?.33 or ?.67, multiply all by 3, etc.
skip if already whole numbers

41. How to Determine Empirical Formulas. A
From the masses of constituents
mass A (g) moles A
MMA
moles A
moles B
mass B (g) moles B
MMB

42. Empirical Formula: Mass composition
One g sample of iron-oxygen compound contains g iron. Find the empirical formula of this compound.
Solution Map: g
Fe, O
mol
Fe, O
mol
ratio
empirical
formula
Atomic mass (g/mol): O 16.00, Fe 55.85
mass of O = – = g
mol Fe
mol O

43. Example: One 1. 205-g sample of iron-oxygen compound contains 0
Example: One g sample of iron-oxygen compound contains g iron. Find the empirical formula of this compound.
Find:
mol Fe, mol O
(Contd.)

44. Practice: A 1. 144-g sample of manganese ore contains 0. 320 g oxygen
Practice: A g sample of manganese ore contains g oxygen. Find its empirical formula.

45. Example: Empirical formula from mass% Find the empirical formula of aspirin with the given mass percent composition: 60.00% C, 4.48% H, 35.53% O g
C, H, O
mol
C, H, O
mol
ratio
empirical
formula

46. Example: Find the empirical formula of aspirin with the given mass percent composition.
Given: 60.00% C, 4.48% H, 35.52% O
1 mol C = g; 1 mol H = g; 1 mol O = g
Assuming 100 (exact) grams of compound aspirin, mass of each element in grams equals percentage.
Mass C = g
Mass H = 4.48 g
Mass O = g
C4.996H4.44O2.221
C9H8O4

47. From Empirical Formula to Molecular Formula
Note: Empirical formula comes from REDUCED Molecular formula
The “Molar mass” based on Empirical formula is multiplied by an integer n should give the Molecular Formula

48. Example: Find Empirical Formula and Molecular Formula
Vitamic C has the following mass percent composition: C 40.91%, H 4.58%, O 54.41%. Find the empirical formula.
Ans: C3H4O3
The molar mass of vitamin C is g/mol. Find the molecular formula of vitamin C.
Ans: solve n = 2, so molecular formula C6H8O6

49. Same Empirical Formula, Different Molecular Formula!
Name
Molecular
Formula
Empirical
Molar
Mass, g
glyceraldehyde
C3H6O3
CH2O 90
erythrose
C4H8O4
120
arabinose
C5H10O5
150
glucose
C6H12O6
180
Name
Molecular
Formula
Empirical
glyceraldehyde
C3H6O3
CH2O
erythrose
C4H8O4
arabinose
C5H10O5
glucose
C6H12O6

50. Answer key: Molar Mass (all in g/mol)
Sulfuric acid: g/mol
Aluminum sulfate: g/mol
Ammonium chlorite: g/mol
Hydrobromic acid: g/mol
Nickel(II) phosphate: g/mol

51. Example: Find the empirical formula of aspirin with the given mass percent composition.
Information
Given: g C, 4.48 g H, g O
Find: empirical formula, CxHyOz
CF: 1 mol C = g;
1 mol H = g; 1 mol O = g
SM: g C,H,O  mol C,H,O 
mol ratio  empirical formula
calculate the moles of each element

52. Apply the Solution Map:
Example: Find the empirical formula of aspirin with the given mass percent composition.
Information
Found: mol C, 4.44 mol H,
2.221 mol O
Find: empirical formula, CxHyOz
Apply the Solution Map:
write a pseudoformula
C4.996H4.44O2.221

53. Apply the Solution Map:
Example: Find the empirical formula of aspirin with the given mass percent composition.
Information
Given: C2.25H2O1
Find: pseudoempirical formula, C2.25H2O1
CF:
Apply the Solution Map:
multiply subscripts by factor to give whole number
{ } x 4
C9H8O4