1. Moles
How can we count how many atoms or molecules are in a piece of matter if we can’t see them? How can we count how many atoms or molecules are in a piece of matter if they have different masses?

2. MOLES! Moles What can we measure in the laboratory that will help us?
What is the “common currency”?
MOLES!

3. Moles Unit We will incorporate the following skills and knowledge:
metric system (esp. mass)
scientific/exponent notation
conversions and dimensional analysis
sig figs
 the most important mathematical tool in chemistry – the mole!

4. Mole (agreed upon by chemists and physicists in 1960/61
1 mole = the amount of pure substance that contains as many particles (atoms, molecules, or fundamental units) as there are atoms in exactly 12 grams of carbon-12
(agreed upon by chemists and physicists in 1960/61

5. Mole
= 6.02 x 1023 particles = Avogadro’s number

6. Moles in conversion factors
number of “particles” in 1 mole is 6.02 x 1023 particles 1 mole mass (g) in 1 mole is average atomic mass in g

7. Moles in conversion factors
number of “particles” or mass (g) both of the above conversion factors, using moles as the intermediate, or “common currency” number of atoms in a compound # atoms 1 compound

8. Math and the Mole How many fingers are there on 1 person?
(# particles/mole)
How many fingers are there on 1 person?
How many fingers are there on 1 dozen people?
3. How many fingers are there on 3 dozen people?

9. Math and the Mole (# particles/mole)
4. How many fingers are there on 1 mole of people?
5. How many fingers are there on 3.12 moles of people?

10. Math and the Mole (# particles/mole)
6. How many F atoms in 3.12 moles of F?
7. How many moles of F do you have if you have 2.45 x atoms of F?

11. Math and the Mole (continued)
Hint: If problem includes numbers of atoms or other representative particles and moles, use Avogadro’s number: 6.02 x 1023 particles If problem includes grams and moles use the periodic table to find molar mass.

12. Math and the Mole (continued)
(mass/mole) 8. How many grams of F are in 3.89 moles of F? 9. How many moles of F atoms in 45.6 g of F?

13. Math and the Mole (continued)
(# particles/mass) 10. How many F atoms are in 65.8 g F? 11. What is the mass, in grams, of 7.62 x 1024 F atoms?

14. Math and the Mole (continued)
(# atoms/compound) 12. How many F atoms are in 3.84 moles of MoF6 molecules? A: 1.39 x 1025 F atoms

15. Molar Mass
Molar mass = mass, in grams, of 1 mole of a substance (6.02 x 1023 particles) expressed in g/mol Molar mass is numerically equal to average atomic mass in amus (atomic mass units).

16. Molar Mass
So, molar mass of oxygen (O) = mass of 1 mole of O atoms = mass of 6.02 x 1023 atoms = g/mol molar mass of lead (Pb) = mass of 1 mole of Pb atoms = mass of 6.02 x 1023 atoms = g/mol

17. How do we determine the molar mass of compounds?
Add up the molar masses of all elements in the compound, taking into account the number of moles of each element.

18. How do we determine the molar mass of compounds?
e.g. What is the molar mass of Na3PO4? 3 moles of g/mol = 3 mol x g mol 1 mole of g/mol = 1 mol x g 4 moles of g/mol = 4 mol x g Add these together: = g = molar mass of Na3PO4

19. How do we use molar mass of a compound in a conversion problem?
The same way we use molar mass of an atom…

20. How do we use molar mass of a compound in a conversion problem?
(#atoms/compound and molar mass of compounds)
13. How many Na atoms are in 252 g of Na3PO4?
(A: x 1024 Na atoms)

21. Where we’ve been (today’s lab quiz; Quiz 6 – next Th/F)
# particles-mole and mole-# particles conversions
mass-mole and mole-mass conversions
# atoms-molecule/formula unit conversion
molar mass of compounds
combination of two or more of above conversions

22. Where we’ve been (today’s lab quiz; Quiz 6 – next Th/F)
Use the sample problems in your notes, Moles WS #1, your bookwork and the warmups to help you prepare for Quiz 6.
Come in for ICP (T/W lunch) for more practice.

23. Moles Where we’ve been
Use dimensional analysis, Avogadro’s number (6.02 x 1023 particles) and molar mass to convert to/from moles/grams/particles (Moles Quiz 6)

24. Where we are going next – applications of mole conversions
% composition by mass from a chemical formula (today) (Moles WS #2)
Find the empirical chemical formula from % composition data (Moles WS #3 & 4) (tomorrow)
Find the molecular formula from % composition and empirical formula (Moles WS #4)
Practice problems for all moles material (Moles WS #5)

25. Where we are going next – applications of mole conversions (after next week’s test)
Calculate molarity of a solution (Moles WS #6 & 7)
Find the mass of a solute or volume of a solution using molarity (Moles WS #6 &7)
Find the mass percent of a solution (Moles WS #7)

26. Calculations relating to Chemical Formulas
1. Determine the molar mass of a compound: - Find molar masses of all elements. - Multiply each mass taking into account the number of atoms of that element present in the formula. - Add all masses together. e.g. What is the molar mass of Pb3(PO4)2?

27. Calculations relating to Chemical Formulas
1. Determine the molar mass of a compound: - Find molar masses of all elements. - Multiply each mass taking into account the number of atoms of that element present in the formula. - Add all masses together. e.g. What is the molar mass of Pb3(PO4)2? g/mol

28. Calculations relating to Chemical Formulas
2. Determine percent composition of all elements present in a compound:
- Find the molar masses of each element in the
compound.
- Find the total molar mass.
Calculate:
% composition = molar mass of element x 100%
total molar mass of compound

29. Calculations relating to Chemical Formulas
e.g.
What is the % composition of NaCl? CaCl2?
(assume % composition by mass)
Apply % composition:
e.g. What mass of Na is present in g NaCl?

30. Calculations relating to Chemical Formulas
e.g.
What is the % composition of NaCl? CaCl2?
(assume % composition by mass)
NaCl: % Na, 60.66% Cl
CaCl2: % Ca, % Cl
Apply % composition:
e.g. What mass of Na is present in g NaCl?
200.0 g x = g Na

31. 3. Convert % composition (mass percent) empirical formula
a. Assume a 100 g sample – use same numbers as grams rather than %. b. Perform mass  mole conversions. c. Divide each result (mole) by the smallest result present (mole ratio). d. Look for whole number ratio.

32. 3. Convert % composition (mass percent) empirical formula
Rhyme to remember order of steps to convert % composition  empirical formula: Percent to mass Mass to mole Divide by small Times till whole

33. Practice
1) One of the components of fresh alkaline batteries is a black powdery compound, of 63% manganese and 37% oxygen. What is the compound’s empirical formula?

34. Practice While analyzing a dead alkaline battery,
Antonio finds a compound of 70.0% manganese and 30.0% oxygen.
What is its empirical formula?

35. Empirical vs. Molecular Formula
Compound
Empirical formula
Empirical molar mass
Molecular molar mass
Molecular formula
Formaldehyde
CH2O
30.03 g
Acetic acid
60.06 g
C2H4O2
Glucose g
C6H12O6

36. To find the molecular formula of glucose,
divide the molecular molar mass by the empirical molar mass, round to the nearest whole number. (molecular) molar mass = g = ~ 6 empirical molar mass g then multiply subscripts by 6 => C6H12O6 to get the molecular formula

37. Practice Problems – Determining molecular formula
Hydrazine is 87.42% N and 12.58% H.
The (molecular) molar mass of hydrazine is 32.0 g/mol.
a) What is its empirical formula?
b) What is its molecular formula?
(Hint: find the molar mass of the empirical formula)

38. Practice Problems – Determining molecular formula
Hydrazine is 87.42% N and 12.58% H.
The (molecular) molar mass of hydrazine is 32.0 g/mol.
a) What is its empirical formula? (NH2)
b) What is its molecular formula? (N2H4)
(Hint: find the molar mass of the empirical formula)

39. Describing solution concentration – Percent by Mass
Mass % of component = mass of component in solution x 100% total mass of solution

40. Describing solution concentration – Percent by Mass
e.g. In order to maintain a sodium chloride (NaCl) concentration similar to ocean water, an aquarium must contain 3.6 g NaCl per g of water. What is the percent by mass of NaCl in the solution?

41. Describing solution concentration – Percent by Mass
3.6 g NaCl x 100% = 3.6 g NaCl x 100%
100.0 g H2O g NaCl g total
= 3.5%

42. Describing solution concentration – Percent by Mass
e.g. A solution contains 2.7 g of CuSO4 in 75 mL of solution. Assume the density of the solution is 1.0 g/mL. What is the mass percent of the solution? 2.7 g (1 mL) x 100% = 3.6% 75 mL 1.0 g

43. Molarity (Moles WS #6) One way to measure concentration
= the # moles solute dissolved in 1 L of solution
Molarity ( M ) = moles of solute
1 liter of solution

44. Molarity Divide # moles by # liters. If the problem gives you grams,
first convert to moles by dividing by
molar mass.
Also, don't forget to convert mL to L.

45. Example
A saline solution contains 0.90 g of NaCl in mL. What is the molarity?
(Molar mass of NaCl is 58.5 g.)
Begin by converting the solute and
solution into the correct units.

46. Example
Begin by converting the solute and solution into the correct units. Solute: 0.90 g (1 mol NaCl) = mol NaCl 58.5 g NaCl Solution: mL (1 L) = L 103 mL

47. Example
Next, divide the number of moles by the volume of the solution:
Molarity = mol NaCl = M NaCl L

48. Example 100.0 mL 58.5 g NaCl 1 L OR, in one step:
0.90 g (1 mol NaCl) (103 mL) = M NaCl
100.0 mL 58.5 g NaCl L

49. Molarity If M = mol then M x L = # moles L and L = mol M
You can also use the molarity equation to calculate moles (and grams) or volumes (measured in L or mL).
If M = mol then M x L = # moles L
and L = mol M

50. Molarity
Notice that all three of the equations above are just different algebraic versions of each other.
Use them to solve the next few problems, or use standard conversion techniques:

51. Example of # moles = M x L
How many moles of CaCl2 are in 250. mL of 2.0 M CaCl2? How many grams is this? Begin with the value you are given in the problem (250. mL), then use molarity of CaCl2 (2.0 M) as a conversion factor.

52. Example of # moles = M x L 103 mL 1L molarity as conversion factor
250. mL (1 L) (2.0 mol CaCl2)
103 mL L
molarity as conversion factor
= 0.50 mol CaCl2
then
0.50 mol CaCl2 ( g CaCl2) = g CaCl2
1 mol CaCl2

53. Example of # moles = M x L = 55.0 g CaCl2 OR, all in one step:
250. mL (1 L) (2.0 mol CaCl2) ( g CaCl2) mL L mol CaCl2
= 55.0 g CaCl2
molarity as conversion factor

54. Example of : # L (or mL) = mol M
How many mL contain 6.25 g of 2.00 M CaCl2?
Begin with the value you are given in the problem (6.25 g), then use molarity of CaCl2 (2.00 M) as a conversion factor.

55. Example of # L (or mL) = mol M
6.25 g CaCl2 (1 mol CaCl2) = mol CaCl2
g CaCl2
then
mol CaCl2 (1 L ) (103 mL) = 28.4 mL
2.00 mol L
Note upside down molarity

56. Making Dilutions (Honors only)
Chemists often use concentrated (or “stock”) solutions to make dilute solutions.
**The number of moles of solute does not change when a solution is diluted.**
Number of moles before dilution = Number of moles after dilution

57. Making Dilutions
Since moles = Molarity (M) x liters ( V ), then: Mc x Vc = Md x Vd
e.g.
How would you prepare 100. mL of 0.40 M MgSO4 from a solution of 2.0 M MgSO4 ?
Mc=2.0 M Vc= ????
Md = 0.40 M Vd = mL

58. Making Dilutions
Rearrange the equation: Vc = Md x Vd Mc Vc = 0.40 M x 100. mL 2.0 M = 20. mL of the concentrated solution

59. Making Dilutions
So, you would measure out 20. mL of the original solution, then add enough water to it to bring the volume to 100. mL. Important: You can do these dilution problems in either mL or L, but the V1 and V2 must both be in the same units (either both mL or both L; don't mix them up).