1. Chapter 10 The Mole Molar Mass
Mole Relationships in Chemical Equations
Mass Calculations for Reactions
Molar Volume
Percentage Composition
Empirical and Molecular Formulas

2. THE MOLE CONCEPT
A sensitive balance can weight to the nearest g, but a typical atom has a mass of only g
Is it possible to keep track of atoms by counting them? Yes, but not directly. We count them in groups. That is we count atoms in the same way we count eggs by the dozen (12), pencils by the gross (144), pop by the case (24), and sheets of paper by the ream (500).
 The relative mass of an atom is compared to a reference atom using an instrument called a mass spectrometer. Carbon-12 has been chosen as a reference and it is assigned a mass of exactly 12 amu. The masses of other atoms are compared relative to carbon-12.

3. Experiments have shown that 12. 01 g of carbon contains 6
Experiments have shown that g of carbon contains 6.02 x 1023 atoms of carbon.
In fact, the gram atomic mass of each element contains 6.02x1023 atoms of that element.
AVOGADRO’S Number:
Number of atoms in grams of carbon
6.02 x1023 atoms

4. MOLE:
Amount of a substance containing 6.02x1023 representative particles 
Why do we need this tool (the mole)?
Chemists and many others need to know relative amounts of substances.

5. A Moles of Particles Contains 6.02 x 1023 particles
1 mole C = x 1023 C atoms
1 mole H2O = x 1023 H2O molecules
1 mole NaCl = x 1023 Na+ ions and
6.02 x 1023 Cl– ions

6. Examples of Moles Moles of elements 1 mole Mg = 6.02 x 1023 Mg atoms
1 mole Au = x 1023 Au atoms
Moles of compounds
1 mole NH3 = x 1023 NH3 molecules
1 mole C9H8O4 = x 1023 aspirin molecules

7. Avogadro’s Number
6.02 x 1023 particles
1 mole or
1 mole

8. MOLAR MASS:
Mass in grams of one mole of any substance, element, or compound
Has the same numerical value as formula mass.
Molar mass of any element = the gram atomic mass (gam) of that element
Example:
1 mole H = 1.01g H
1 mole Ca = 40.1g Ca
1 mole O = 16.0g O
1 mole C = 12.0g C

9. Molar Mass Number of grams in 1 mole
Equal to the numerical value of the atomic mass
1 mole of C atoms = g
1 mole of Mg atoms = 24.3 g
1 mole of Cu atoms = 63.5 g

10. Learning Check Give the molar mass to 0.1 g
A. 1 mole of Br atoms = ________
B. 1 mole of Sn atoms = ________

11. Solution Give the molar mass to 0.1 g
A. 1 mole of Br atoms = 79.9 g/mole
B. 1 mole of Sn atoms = g/mole

12. Problems What is the molar mass for the following elements? Na Cl FeHg

13. FORMULA MASS: (Molar Mass)
The sum of the atomic masses, for each element, found in the compound
Exp: Calculate the formula mass of H2O
2 hydrogen amu
1 oxygen amu
= amu
One molecule of water has a mass of amu

14. 2 atoms H x atomic mass 1.0g = 2.0 g/mole
Example: H2S
2 atoms H x atomic mass 1.0g = g/mole
1 atom S x atomic mass 32.1g = 32.1 g/mole
(Molar mass) = 34.1 g/mole
2(1.0) = 34.1 g/mole
1 mole = 6.02 x 1023 (how many) = molar mass (grams)

15. Molar Mass of Compounds
Mass in grams of 1 mole equal numerically to the sum of the atomic masses
1 mole of CaCl2 = g/mole
1 mole Ca x 40.1 g/mole = 40.1 g/mole
+ 2 moles Cl x 35.5 g/mole = 71.0 g/mole
1 mole of N2O4 = 74.0 g/mole
2 moles N x 14.0 g/mole = 28.0 g/mole
+ 4 moles O x 16.0 g/mole = 64.0 g/mole

16. Learning Check A. 1 mole of K2O = ______g
B. 1 mole of antacid Al(OH)3 = ______g

17. Solution A. 1 mole of K2O = 94.2 g/mole
2 atoms K x 39.1 g/mole + 1 atom O x 16.0 g/mole
B. 1 mole of antacid Al(OH)3 = g/mole
1 atom Al x 27.0 g/mole + 3 atoms O x 16.0 g/mole
+ 3 atoms x 1.0 g/mole

18. Learning Check
Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of
1) g/mole
2) 262 g/mole
3) 309 g/mole

19. Solution
Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of
3) 309 g/mole
17 atoms C (12.0) + 18 atoms H (1.0) + 3 atoms F (19.0) + 1 atom N (14.0) + 1atom O (16.0)

20. Problems
State how many moles and calculate the molar mass of each substance.
2 Cu
5.00 NaCl
2.5 H2SO4

21. Molar Mass Factors
Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors.
Molar mass of CH4 = g
16.0 g CH and mole CH4
1 mole CH g CH4

22. Learning Check
Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole.
1 mole of acetic acid = ____________
1 mole acetic acid or g acetic acid
g acetic acid mole acetic acid

23. Solution
Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole.
1 mole of acetic acid = g acetic acid
1 mole acetic acid or g acetic acid
60.0 g acetic acid 1 mole acetic acid

24. Problems
The formula of sodium hydrogen carbonate (baking soda) is NaHCO3. What is its formula mass?
Answer the following:
Write the formula for Magnesium Acetate.
Determine its formula mass.
Determine the molar mass for the following:
NaCl
CaCO3
H2SO4

25. Calculations with Molar Mass
Grams Moles
1 mole = molar mass

26. Moles and Grams 3.00 moles Al ? g Al
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

27. Known: Given: 3.00 Al Molar mass of Al 1 mole Al = 27.0 g Al
Conversion factors for Al
27.0g Al or mol Al
1 mol Al g Al

28. Unknown: ? g Al M(mass) = n(moles) x molar mass or
n(moles) = M(mass) / molar mass
Setup: M(mass) = n(moles) x molar mass

29. Solution 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

30. Learning Check
The artificial sweetener aspartame (Nutri-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?

31. Solution 1. Molar mass of Aspartame C14H18N2O5
(14 x 12.0) + (18 x 1.01) + (2 x 14.0) + (5 x 16.0) = 294 g/mole
2. Setup
225 g aspartame x 1 mole aspartame
294 g aspartame
= mole aspartame

32. Calculations with Molar Volume
Liter Moles
1 mole = 22.4L

33. RELATE MOLES TO PARTICLES AND PARTICLES TO MOLES
Factor Label Method: unit needed = given x conversion factor
Determine the given and unit needed.
Find relationship between given unit and needed unit that is your conversion factor.
Substitute into factor label equation.
Unit that are identical cancel out.

34. How many H2 molecules are there in 0.025 moles of H2?
Known:
Given = moles of H2
1 mole H2 = 6.022x1023 molecules H2
Unknown:
unit needed = H2 molecules
Setup: molecules of H2 =

35. Learning Check 1. Number of atoms in 0.500 mole of Al 1) 500 Al atoms
2) x 1023 Al atoms
3) x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024 S atoms
1) mole S atoms
2) mole S atoms
3) x 1048 mole S atoms

36. Solution 1. Number of atoms in 0.500 mol of Al 3) 3.01 x 1023 Al atoms
0.500 mol Al x x 1023 Al atoms
1 mol Al
2. Number of moles of S if a sample of S contains 4.50 x 1024 S atoms
2) mole S atoms
4.50 x 1024 S atoms x mol S
6.02 x 1023 S atoms

37. Percent Composition
The percent composition is a list of the mass percent of each element in a compound.
Percent Composition of a Compound =
Mass of the element Mass of the compound x 100

38. Calculate the percent composition of proply chloride (C3H7Cl)
First, calculate the molar mass for the compound by adding up the masses of all the elements:
3 carbons at 12.01amu each = amu
7 hydrogen at 1.01amu each= 7.07 amu
1 chlorine atom at amu
Summing these values yield:
= amu = formula mass of C3H7Cl

39. Second, for each element found in the compound set up ratio of its mass over the total mass times 100 to convert to percent.
Carbon (36.03 / 78.55) x 100 = 45.87% Carbon
Hydrogen (7.07 / 78.55) x 100 = 9.00% Hydrogen
Chlorine (35.45 / 78.55) x 100 = 45.13% Chlorine
These values add up to a hundred percent (100%).

40. Learning Check
What is the percent carbon in C5H8NO4 (MSG monosodium glutamate), a compound used to flavor foods and tenderize meats?
1) %C
2) %C
3) %C

41. Solution Molar mass = 146.0 g/mole % = total g C x 100
total g compound
= g C x 100 = 41.1% C
146.0 g MSG

42. Empirical formula Simplest formula for a compound; it is the smallest whole-number ratio of the atoms present.
Molecular formula Expression of the formula for a compound; it shows the actual number of atoms of each element present in one molecule of the compound.

43. Calculating Empirical Formulas
Steps:
Change % to g (change signs).
Convert to Moles.
Divide the mass by 1 mol/atomic mass of each element.
Find mole ratio.
Divide each by the lowest moles.
If ratio is not a whole number multiple by a number that converts the fraction to a whole number.

44. Calculate the empirical formula for a compound composed of 26
Calculate the empirical formula for a compound composed of 26.6% potassium, 35.4% chromium, and 38.1% oxygen.
Percent means a fraction of 100. Thus, if we assume 100 grams of sample we can then use the percent values as grams of each element. From grams we find moles of each element in the formula.

45. Find moles potassium.
Next find moles of chromium.
Then find moles oxygen.

46. Next, set up a mole ratio that relates the moles of each element to the moles of the element that is least present.
Because a chemical formula must have only whole numbers we multiply by 2 to yield: K2Cr2O7 as the empirical formula.

47. Calculating Molecular Formulas
Molecular mass must be known before a molecular formula can be determined.
Molecular mass is a whole-number multiple of the empirical formula mass.
(empirical formula mass)x = molecular mass

48. Molecular formulas Solve for x.
Multiply empirical formula by whatever is x.
Examples: (CH4)x
(CH4 mass)x = 16
{ (1.0)}x = 16
(16.0)x = 16
x = 16.0
16.0
x = 1 (CH4)x (CH4)1 = CH4

49. (HO)x
(HO mass)x = 34.0
( )x = 34.0
(17.0)x = 34.0
x = 34.0
17.0
x = 2
(HO)x (HO)2 = H2O2

50. Problems
A certain hydrocarbon compound is found by analysis to have the empirical formula CH3. Its molecular weight is What is the molecular formula?
A compound is found by analysis to consist of 40.1% S and 59.9% O. Its molecular weight is (Change % to g, just change the signs)
What is its empirical formula?
What is its molecular formula?
What is the name of the compound?

51. A compound of nitrogen and sulfur is found by analysis to have the empirical formula NS2. Its molecular weight is
What is its molecular formula?
What is the name of the compound?