1. Chapter 10 Chemical Quantities
10.1 The Mole: A Measurement of Matter
10.2 Mole-Mass and Mole-Volume Relationships
10.3 Percent Composition and Chemical Formulas
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2. What does the percent composition of a compound tell you?
CHEMISTRY & YOU
What does the percent composition of a compound tell you?
A tag sewn into the seam of a shirt usually tells you what fibers were used to make the cloth and the percent of each.
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3. Percent Composition of a Compound
How do you calculate the percent composition of a compound?
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4. Percent Composition of a Compound
The relative amounts of the elements in a compound are expressed as the percent composition or the percent by mass of each element in the compound.
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5. Percent Composition of a Compound
The percent composition of potassium chromate, K2CrO4, is:
K = 40.3%
Cr = 26.8%
O = 32.9%
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6. Percent Composition of a Compound
These percents must total 100%.
K = 40.3%
Cr = 26.8%
+ O = 32.9%
100%
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7. Percent Composition of a Compound
These percents must total 100%.
The percent composition of a compound is always the same.
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8. Percent Composition of a Compound
Percent Composition from Mass Data
If you know the relative masses of each element in a compound, you can calculate the percent composition of the compound.
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9. Percent Composition of a Compound
Percent Composition from Mass Data
The percent by mass of an element in a compound is the number of grams of the element divided by the mass in grams of the compound, multiplied by 100%.
% by mass of element =
× 100%
mass of element
mass of compound
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10. Calculating Percent Composition from Mass Data
Sample Problem 10.9
Calculating Percent Composition from Mass Data
When a g sample of a compound containing only magnesium and oxygen is decomposed, 5.40 g of oxygen is obtained. What is the percent composition of this compound?
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11. Analyze List the knowns and the unknowns.
Sample Problem 10.9
Analyze List the knowns and the unknowns. 1
The percent by mass of an element in a compound is the mass of that element divided by the mass of the compound multiplied by 100%.
KNOWNS mass of compound = g mass of oxygen = 5.40 g O mass of magnesium = g – 5.40 g O = 8.20 g Mg
UNKNOWNS percent by mass of Mg = ?% Mg percent by mass of O = ?% O
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12. Calculate Solve for the unknowns.
Sample Problem 10.9
Calculate Solve for the unknowns. 2
Determine the percent by mass of Mg in the compound.
% Mg =
mass of Mg
mass of compound
× 100%
= 60.3% Mg =
8.20 g
13.60 g
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13. Calculate Solve for the unknowns.
Sample Problem 10.9
Calculate Solve for the unknowns. 2
Determine the percent by mass of O in the compound.
% O =
mass of O
mass of compound
× 100%
5.40 g
= 39.7% O =
13.60 g
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14. Evaluate Does the result make sense?
Sample Problem 10.9
Evaluate Does the result make sense? 3
The percents of the elements add up to 100%.
60.3% % = 100%
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15. Practice Problem: A compound is formed when 9
Practice Problem: A compound is formed when 9.03 g of Mg combines completely with 3.48 g of N. What is the percentage composition of each element in this compound?
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16. Total Mass of Compound = 9.03 + 3.48 = 12.51 g
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17. Determine the percent by mass of Mg in the compound.
mass of compound
× 100%
= 72.2% Mg =
9.03 g
12.51g
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18. Determine the percent by mass of N in the compound.
mass of compound
× 100%
3.48 g
= 27.8% N =
12.51 g
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19. Percent Composition of a Compound
Percent Composition from the Chemical Formula
You can also calculate the percent composition of a compound using its chemical formula.
The subscripts in the formula are used to calculate the mass of each element in a mole of that compound.
Using the individual masses of the elements and the molar mass, you can calculate the percent by mass of each element.
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20. Percent Composition of a Compound
Percent Composition from the Chemical Formula
You can also calculate the percent composition of a compound using its chemical formula.
% by mass of element
× 100% =
mass of element
mass of compound
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21. Calculating Percent Composition from a Formula
Sample Problem 10.10
Calculating Percent Composition from a Formula
Propane (C3H8), the fuel commonly used in gas grills, is one of the compounds obtained from petroleum. Calculate the percent composition of propane.
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22. Analyze List the knowns and the unknowns.
Sample Problem 10.10
Analyze List the knowns and the unknowns. 1
Calculate the percent by mass of each element by dividing the mass of that element in one mole of the compound by the molar mass of the compound and multiplying by 100%.
KNOWNS mass of C in 1 mol C3H8 = 3 mol × 12.0 g/mol = 36.0 g mass of H in 1 mol C3H8 = 8 mol × 1.0 g/mol = 8.0 g molar mass of C3H8 = 36.0 g/mol g/mol = 44.0 g/mol UNKNOWNS percent by mass of C = ?% C percent by mass of H = ?% H
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23. Calculate Solve for the unknowns.
Sample Problem 10.10
Calculate Solve for the unknowns. 2
Determine the percent by mass of C in C3H8.
% C =
mass of C in 1 mol C3H8
molar mass of C3H8
× 100%
= 81.8% C =
36.0 g
44.0 g
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24. Calculate Solve for the unknowns.
Sample Problem 10.10
Calculate Solve for the unknowns. 2
Determine the percent by mass of H in C3H8.
% H =
mass of H in 1 mol C3H8
molar mass of C3H8
× 100%
= 18% H =
8.0 g
44.0 g
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25. Evaluate Does the result make sense?
Sample Problem 10.10
Evaluate Does the result make sense? 3
The percents of the elements add up to 100% when the answers are expressed to two significant figures (82% + 18% = 100%).
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26. Calculate the percentage by mass of nitrogen in these compounds: NH3
NH4NO3
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27. % of Nitrogen in NH3 mass of N in 1 mol NH3 × 100% % N =
molar mass of NH3
× 100%
= 82.4% N =
14.0 g
17.0 g
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28. % of Nitrogen in NH4NO3 mass of N in 1 mol NH4NO3 × 100% % N =
molar mass of NH4NO3
× 100%
= 27.8% N =
28.0 g
80.0 g
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29. Percent Composition of a Compound
Percent Composition as a Conversion Factor
You can use percent composition to calculate the number of grams of any element in a specific mass of a compound.
To do this, multiply the mass of the compound by a conversion factor based on the percent composition of the element in the compound.
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30. Percent Composition of a Compound
Percent Composition as a Conversion Factor
Propane is 81.8% carbon and 18% hydrogen.
You can use the following conversion factors to solve for the mass of carbon or hydrogen contained in a specific amount of propane.
81.8 g C
100 g C3H8
and
18 g H
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31. CHEMISTRY & YOU
What information can you get from the percent composition of a compound?
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32. CHEMISTRY & YOU
What information can you get from the percent composition of a compound?
You can use percent composition to determine the mass of an element in a sample of a compound of a given size. You can also determine the empirical formula of the compound.
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33. Sample Problem 10.11
Calculating the Mass of an Element in a Compound Using Percent Composition
Calculate the mass of carbon and the mass of hydrogen in 82.0 g of propane (C3H8).
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34. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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35. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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36. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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37. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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38. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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39. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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40. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol H g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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41. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol C g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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42. To calculate the mass of H:
Sample Problem 10.11
To calculate the mass of H:
82.3 g C3H8 1 mol C3H8 8 mol H g H
44 g C3H8 1 mol C3H8 1 mol H
= g
To calculate the mass of C:
82.3 g C3H8 1 mol C3H8 3 mol C g C
44 g C3H8 1 mol C3H8 1 mol C
= g
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43. Evaluate Does the result make sense?
Sample Problem 10.11
Evaluate Does the result make sense?
The sum of the two masses equals 82 g, the sample size, to two significant figures (67.34 g C g H = 82.3 g C3H8).
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44. Calculate the grams of hydrogen in each of the following compounds.
350 g ethane (C2H6)
20.2 g Sodium hydrogen sulfate
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45. To calculate the mass of H in 350 g of C2H6 :
Sample Problem 10.11
To calculate the mass of H in 350 g of C2H6 :
350 g C2H6 1 mol C2H6 6 mol H g H
30 g C2H6 1 mol C2H6 1 mol H
= 70 g H in C2H6
To calculate the mass of H in 20.2 g of NaHSO4 :
20.2 g NaHSO4 1 mol NaHSO mol H g H
g NaHSO4 1 mol NaHSO4 1 mol H
= .168 g of H in NaHSO4
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46. To calculate the mass of H in 350 g of C2H6 :
Sample Problem 10.11
To calculate the mass of H in 350 g of C2H6 :
350 g C2H6 1 mol C2H6 6 mol H g H
30 g C2H6 1 mol C2H6 1 mol H
= 70 g H in C2H6
To calculate the mass of H in 20.2 g of NaHSO4 :
20.2 g NaHSO4 1 mol NaHSO mol H g H
g NaHSO4 1 mol NaHSO4 1 mol H
= .168 g of H in NaHSO4
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47. To calculate the mass of H in 350 g of C2H6 :
Sample Problem 10.11
To calculate the mass of H in 350 g of C2H6 :
350 g C2H6 1 mol C2H6 6 mol H g H
30 g C2H6 1 mol C2H6 1 mol H
= 70 g H in C2H6
To calculate the mass of H in 20.2 g of NaHSO4 :
20.2 g NaHSO4 1 mol NaHSO mol H g H
g NaHSO4 1 mol NaHSO4 1 mol H
= .168 g of H in NaHSO4
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48. To calculate the mass of H in 350 g of C2H6 :
Sample Problem 10.11
To calculate the mass of H in 350 g of C2H6 :
350 g C2H6 1 mol C2H6 6 mol H g H
30 g C2H6 1 mol C2H6 1 mol H
= 70 g H in C2H6
To calculate the mass of H in 20.2 g of NaHSO4 :
20.2 g NaHSO4 1 mol NaHSO mol H g H
g NaHSO4 1 mol NaHSO4 1 mol H
= .168 g of H in NaHSO4
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49. What data can you use to calculate percent composition?
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50. What data can you use to calculate percent composition?
You can calculate percent composition if you know the mass of a compound and the masses of the elements contained in the compound, or if you know the chemical formula, the molar mass of the compound, and the atomic weights of the elements contained in the compound.
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51. How can you calculate the empirical formula of a compound?
Empirical Formulas
Empirical Formulas
How can you calculate the empirical formula of a compound?
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52. Empirical Formulas
The empirical formula of a compound gives the lowest whole-number ratio of the atoms or moles of the elements in a compound.
An empirical formula may or may not be the same as a molecular formula.
For example, the lowest ratio of hydrogen to oxygen in hydrogen peroxide is 1:1. Thus, the empirical formula of hydrogen peroxide is HO.
The molecular formula, H2O2, has twice the number of atoms as the empirical formula.
Notice that the ratio of hydrogen to oxygen is still the same, 1:1.
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53. For carbon dioxide, the empirical and molecular formulas are the same—
Empirical Formulas
For carbon dioxide, the empirical and molecular
formulas
are the
same—
CO2.
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54. Empirical Formulas
The figure below shows two compounds of carbon and hydrogen having the same empirical formula (CH) but different molecular formulas.
Ethyne (C2H2), also called acetylene, is a gas used in welders’ torches.
Styrene (C8H8) is used in making polystyrene.
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55. Empirical Formulas
The percent composition of a compound can be used to calculate the empirical formula of that compound.
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56. Empirical Formulas
The percent composition of a compound can be used to calculate the empirical formula of that compound.
The percent composition tells the ratio of masses of the elements in a compound.
The ratio of masses can be changed to ratio of moles by using conversion factors based on the molar mass of each element.
The mole ratio is then reduced to the lowest whole-number ratio to obtain the empirical formula of the compound.
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57. A formula that gives the simplest whole-number ratio of the atoms is called an empirical formula.

58. `
To determine the empirical formula from % composition, use the following guidelines for solving empirical formula problems.

59. Assume you have a 100 gram sample.
Divide each mass percentage by the molar mass of the element to obtain the number of moles of the element in the 100 gram sample.

60. Divide each molar amount by whichever amount is the smallest.
If some results from the previous step are far from integers, multiply by a common factor that converts all molar amounts to integers or near-integers.
Round off each molar number to the nearest integer.

61. Sample Problem: Given the following mass percent composition, determine the empirical formula.
49.5% C, 5.2% H, 28.8% N, 16.5% O
Assume 100 g sample :
49.5g C, 5.2g H, 28.8g N, 16.5g O

62. Divide each mass number by the molar mass:
49.5 g C
= mol C
g/mol C
5.2 g H
= mol H
1.008 g/mol H
28.8 g N
= mol N
g/mol N
16.5 g O
= mol O
g/mol O

63. Divide each molar amount by smallest amount :
4.121 mol C
= mol C
1.031 mol O
5.159 mol H
= mol H
2.056 mol N
= mol N
= mol O

64. Empirical Formula is then C4H5N2O

65. Molecular Formulas
Molecular Formulas
How does the molecular formula of a compound compare with the empirical formula?
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66. Comparison of Empirical and Molecular Formulas
Interpret Data
Ethyne and benzene have the same empirical formula—CH.
Comparison of Empirical and Molecular Formulas
Formula (name)
Classification of formula
Molar mass (g/mol) CH
Empirical 13
C2H2 (ethyne)
Molecular
26 (2 × 13)
C6H6 (benzene)
78 (6 × 13)
CH2O (methanol)
Empirical and molecular 30
C2H4O2 (ethanoic acid)
60 (2 × 30)
C6H12O6 (glucose)
180 (6 × 30)
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67. Comparison of Empirical and Molecular Formulas
Interpret Data
Methanal, ethanoic acid, and glucose have the same empirical formula—CH2O.
Comparison of Empirical and Molecular Formulas
Formula (name)
Classification of formula
Molar mass (g/mol) CH
Empirical 13
C2H2 (ethyne)
Molecular
26 (2 × 13)
C6H6 (benzene)
78 (6 × 13)
CH2O (methanal)
Empirical and molecular 30
C2H4O2 (ethanoic acid)
60 (2 × 30)
C6H12O6 (glucose)
180 (6 × 30)
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68. Comparison of Empirical and Molecular Formulas
Interpret Data
Notice that the molar masses of the compounds in these two groups are simple whole-number multiples of the molar masses of the empirical formulas, CH and CH2O.
Comparison of Empirical and Molecular Formulas
Formula (name)
Classification of formula
Molar mass (g/mol) CH
Empirical 13
C2H2 (ethyne)
Molecular
26 (2 × 13)
C6H6 (benzene)
78 (6 × 13)
CH2O (methanal)
Empirical and molecular 30
C2H4O2 (ethanoic acid)
60 (2 × 30)
C6H12O6 (glucose)
180 (6 × 30)
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69. Molecular Formulas
Methanal (formaldehyde), ethanoic acid (acetic acid), and glucose have the same empirical formula—CH2O.
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70. Molecular Formulas
The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula.
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71. Molecular Formulas
The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole-number multiple of its empirical formula.
Once you have determined the empirical formula of a compound, you can determine its molecular formula, if you know the compound’s molar mass.
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72. Molecular Formulas
You can calculate the empirical formula mass (efm) of a compound from its empirical formula.
This is simply the molar mass of the empirical formula.
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73. Molecular Formulas
You can calculate the empirical formula mass (efm) of a compound from its empirical formula.
Then you can divide the experimentally determined molar mass by the empirical formula mass.
This quotient gives the number of empirical formula units in a molecule of the compound and is the multiplier to convert the empirical formula to the molecular formula.
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74. Finding the Molecular Formula of a Compound
Sample Problem 10.13
Finding the Molecular Formula of a Compound
Calculate the molecular formula of a compound whose molar mass is 60.0 g/mol and empirical formula is CH4N.
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75. Analyze List the knowns and the unknown.
Sample Problem 10.13
Analyze List the knowns and the unknown. 1
Divide the molar mass by the empirical formula mass to obtain a whole number.
Multiply the empirical formula subscripts by this value to get the molecular formula.
KNOWNS empirical formula = CH4N molar mass = 60.0 g/mol
UNKNOWN molecular formula = C?H?N?
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76. Calculate Solve for the unknown.
Sample Problem 10.13
Calculate Solve for the unknown. 2
First calculate the empirical formula mass.
efm of CH4N = 12.0 g/mol + 4(1.0 g/mol) g/mol
= 30.0 g/mol
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77. Calculate Solve for the unknown.
Sample Problem 10.13
Calculate Solve for the unknown. 2
Divide the molar mass by the empirical formula mass.
molar mass
efm =
60.0 g/mol
30.0 g/mol
= 2
Multiply the formula subscripts by this value.
(CH4N) × 2 = C2H8N2
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78. Evaluate Does the result make sense?
Sample Problem 10.13
Evaluate Does the result make sense? 3
The molecular formula has the molar mass of the compound.
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79. What information, in addition to empirical formula, is necessary to determine the molecular formula of a compound?
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80. What information, in addition to empirical formula, is necessary to determine the molecular formula of a compound?
Molecular formula can be determined if the empirical formula and the molecular mass of a compound are known.
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81. Key Concepts
The percent by mass of an element in a compound is the number of grams of the element divided by the mass in grams of the compound, multiplied by 100%.
The percent composition of a compound can be used to calculate the empirical formula of that compound.
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82. Key Concepts and Key Equations
The molecular formula of a compound is either the same as its experimentally determined formula, or it is a simple whole-number multiple of its empirical formula.
% by mass of element
mass of element
mass of compound
= × 100%
% by mass of element
mass of element in 1 mol compound
molar mass of compound
× 100% =
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83. percent composition: the percent by mass of each element in a compound
Glossary Terms
percent composition: the percent by mass of each element in a compound
empirical formula: a formula with the lowest whole-number ratio of elements in a compound; the empirical formula of hydrogen peroxide (H2O2) is HO
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84. The Mole and Quantifying Matter
BIG IDEA
The Mole and Quantifying Matter
The molecular formula of a compound can be determined by first finding the percent composition of the compound and determining the empirical formula.
Using the empirical formula mass and the molar mass of the compound, the molecular formula can be determined.
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85. END OF 10.3
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