2. LO 1.2: The student is able to select and apply mathematical routines to mass data to identify or infer the composition of pure substances and/or mixtures. (Sec 3.7)
LO 1.3: The student is able to select and apply mathematical relationships to mass data in order to justify a claim regarding the identity and/or estimated purity of a substance. (Sec 3.6)
LO 1.4: The student is able to connect the number of particles, moles, mass, and volume of substances to one another, both qualitatively and quantitatively. (Sec )
LO 1.14: The student is able to use data from mass spectrometry to identify the elements and the masses of individual atoms of a specific element. (Sec 3.2)
LO 1.17: The student is able to express the law of conservation of mass quantitatively and qualitatively using symbolic representations and particular drawings. (Sec )
LO 1.18: The student is able to apply conservation of atoms to the rearrangements of atoms in various processes. (Sec )

3. LO 1.19: The student can design, and/or interpret data from, an experiment that uses gravimetric analysis to determine the concentration of an analyte in a solution. (Sec 3.10)
LO 3.1: Students can translate among macroscopic observations of change, chemical equations and particle views. (Sec 3.8)
LO 3.3: The student is able to use stoichiometric calculations to predict the results of performing a reaction in the laboratory and/or to analyze deviations from the expected results. (Sec 3.11)
LO 3.4: The student is able to relate quantities (measured mass of substances, volumes of solutions, or volumes and pressures of gases) to identify stoichiometric relationships for a reaction, including situations involving limiting reactants and situations in which the reaction has not gone to completion. (Sec 3.11)
LO 3.6: The student is able to use data from synthesis or decomposition of a compound to confirm the conservation of matter and the law of definite proportions. (Sec 3.7)

4. Chemical Stoichiometry
Stoichiometry – The study of quantities of materials consumed and produced in chemical reactions.
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Objects behave as though they were all identical.
Atoms are too small to count.
Need average mass of the object.
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6. Copyright © Cengage Learning. All rights reserved
EXERCISE!
A pile of marbles weigh g. 10 marbles weigh g. How many marbles are in the pile?
Average mass of one marble = g / 10 marbles = 3.76 g / marble
g / 3.76 g = 105 marbles
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7. AP Learning Objectives, Margin Notes and References
LO 1.14: The student is able to use data from mass spectrometry to identify the elements and the masses of individual atoms of a specific element.

8. The masses of all other atoms are given relative to this standard.
12C is the standard for atomic mass, with a mass of exactly 12 atomic mass units (u).
The masses of all other atoms are given relative to this standard.
Elements occur in nature as mixtures of isotopes.
Carbon = % 12C
1.11% 13C
< 0.01% 14C
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9. Average Atomic Mass for Carbon
98.89% of 12 u % of u =
exact number
(0.9889)(12 u) + (0.0111)( u) =
12.01 u
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10. Average Atomic Mass for Carbon
Even though natural carbon does not contain a single atom with mass 12.01, for stoichiometric purposes, we can consider carbon to be composed of only one type of atom with a mass of
This enables us to count atoms of natural carbon by weighing a sample of carbon.
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11. Schematic Diagram of a Mass Spectrometer
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12. Calculate the average atomic mass and identify the element.
EXERCISE!
An element consists of 62.60% of an isotope with mass u and 37.40% of an isotope with mass u.
Calculate the average atomic mass and identify the element.
186.2 u
Rhenium (Re)
Average Atomic Mass = (0.6260)( u) + (0.3740)( u) = u
The element is rhenium (Re).
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13. AP Learning Objectives, Margin Notes and References
LO 1.4: The student is able to connect the number of particles, moles, mass, and volume of substances to one another, both qualitatively and quantitatively.

14. The number equal to the number of carbon atoms in exactly 12 grams of pure 12C.
1 mole of something consists of × 1023 units of that substance (Avogadro’s number).
1 mole C = × 1023 C atoms = g C
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15. EXERCISE!
Calculate the number of iron atoms in a 4.48 mole sample of iron. 2.70×1024 Fe atoms
(4.48 mol Fe) × (6.022×1023 Fe atoms / 1 mol Fe) = 2.70×1024 Fe atoms.
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16. AP Learning Objectives, Margin Notes and References
LO 1.4: The student is able to connect the number of particles, moles, mass, and volume of substances to one another, both qualitatively and quantitatively.

17. Molar Mass of Ba(NO3)2 = 261.35 g/mol
Mass in grams of one mole of the substance:
Molar Mass of N = g/mol
Molar Mass of H2O = g/mol
(2 × g) g
Molar Mass of Ba(NO3)2 = g/mol
g + (2 × g) + (6 × g)
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18. CONCEPT CHECK!
Which of the following is closest to the average mass of one atom of copper?
a) g
b) g
c) g
d) g
e) x g
The correct answer is “e”. The mass of one atom of copper is going to be extremely small, so only letter “e” makes sense. The calculated solution is (1 Cu atom) × (1 mol Cu/6.022×1023 Cu atoms) × (63.55 g Cu/1 mol Cu).
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19. CONCEPT CHECK!
Calculate the number of copper atoms in a g sample of copper ×1023 Cu atoms
6.022×1023 Cu atoms; g of Cu is 1 mole of Cu, which is equal to Avogadro’s number.
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20. CONCEPT CHECK!
Which of the following g samples contains the greatest number of atoms?
Magnesium
Zinc
Silver
The correct answer is “a”. Magnesium has the smallest average atomic mass (24.31 u). Since magnesium is lighter than zinc and silver, it will take more atoms to reach g.
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21. Rank the following according to number of atoms (greatest to least):
EXERCISE!
Rank the following according to number of atoms (greatest to least):
107.9 g of silver
70.0 g of zinc
21.0 g of magnesium
b) a) c)
b, a, c; The greater the number of moles, the greater the number of atoms present. Zinc contains 1.07 mol, Ag contains mol, and Mg contains mol.
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22. Consider separate 100.0 gram samples of each of the following:
EXERCISE!
Consider separate gram samples of each of the following: 
H2O, N2O, C3H6O2, CO2
Rank them from greatest to least number of oxygen atoms.
H2O, CO2, C3H6O2, N2O
H2O, CO2, C3H6O2, N2O; The number of oxygen atoms in each is:
H2O = 3.343×1024
CO2 = 2.737×1024
C3H6O2 = 1.626×1024
N2O = 1.368×1024
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23. Conceptual Problem Solving
Where are we going?
Read the problem and decide on the final goal.
How do we get there?
Work backwards from the final goal to decide where to start.
Reality check.
Does my answer make sense? Is it reasonable?
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24. AP Learning Objectives, Margin Notes and References
LO 1.3: The student is able to select and apply mathematical relationships to mass data in order to justify a claim regarding the identity and/or estimated purity of a substance.

25. Mass percent of an element:
For iron in iron(III) oxide, (Fe2O3):
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26. Consider separate 100.0 gram samples of each of the following:
EXERCISE!
Consider separate gram samples of each of the following: 
H2O, N2O, C3H6O2, CO2
Rank them from highest to lowest percent oxygen by mass.
H2O, CO2, C3H6O2, N2O
H2O, CO2, C3H6O2, N2O; The percent oxygen by mass in each is:
H2O = 88.81%
CO2 = 72.71%
C3H6O2 = 43.20%
N2O = 36.35%
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27. AP Learning Objectives, Margin Notes and References
LO 1.2: The student is able to select and apply mathematical routines to mass data to identify or infer the composition of pure substances and/or mixtures.
Additional AP References
LO 3.6 (see APEC Lab 7, " Hydrates and Thermal Decomposition")

28. Formulas Empirical formula = CH Simplest whole-number ratio
Molecular formula = (empirical formula)n [n = integer]
Molecular formula = C6H6 = (CH)6
Actual formula of the compound
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29. Analyzing for Carbon and Hydrogen
Device used to determine the mass percent of each element in a compound.
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30. What is the empirical formula? C3H5O2 What is the molecular formula?
EXERCISE!
The composition of adipic acid is 49.3% C, 6.9% H, and 43.8% O (by mass). The molar mass of the compound is about 146 g/mol.
What is the empirical formula?
C3H5O2
What is the molecular formula?
C6H10O4
Assume 100.0g g of carbon is mol C (49.3/12.01) g of hydrogen is mol H (6.9/1.008) g of oxygen is mol O (43.8/16.00). The ratio of C:H:O is 1.5:2.5:1 (C: 4.105/ = 1.5; H: 6.845/ = 2.5). Multiplying each by 2 to get a whole number becomes a ratio of 3:5:2. The empirical formula is therefore C3H5O2. The molar mass of the empirical formula is g/mol, which goes into the molar mass of the molecular formula 2 times (146/73.07). The molecular formula is therefore C6H10O4.
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31. C2H5OH + 3O2 2CO2 + 3H2O A representation of a chemical reaction:
reactants products
Reactants are only placed on the left side of the arrow, products are only placed on the right side of the arrow.
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32. AP Learning Objectives, Margin Notes and References
LO 1.18: The student is able to apply conservation of atoms to the rearrangements of atoms in various processes.
LO 3.1: Students can translate among macroscopic observations of change, chemical equations and particle views.

33. The equation is balanced.
C2H5OH + 3O CO H2O
The equation is balanced.
All atoms present in the reactants are accounted for in the products.
1 mole of ethanol reacts with 3 moles of oxygen to produce 2 moles of carbon dioxide and 3 moles of water.
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34. The balanced equation represents an overall ratio of reactants and products, not what actually “happens” during a reaction.
Use the coefficients in the balanced equation to decide the amount of each reactant that is used, and the amount of each product that is formed.
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35. AP Learning Objectives, Margin Notes and References
LO 1.17: The student is able to express the law of conservation of mass quantitatively and qualitatively using symbolic representations and particular drawings.
LO 1.18: The student is able to apply conservation of atoms to the rearrangements of atoms in various processes.

36. Writing and Balancing the Equation for a Chemical Reaction
Determine what reaction is occurring. What are the reactants, the products, and the physical states involved?
Write the unbalanced equation that summarizes the reaction described in step 1.
Balance the equation by inspection, starting with the most complicated molecule(s). The same number of each type of atom needs to appear on both reactant and product sides. Do NOT change the formulas of any of the reactants or products.
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38. I. CaO2 + 3C CaC2 + CO2 II. 2CaO + 5C 2CaC2 + CO2
EXERCISE!
Which of the following correctly balances the chemical equation given below? There may be more than one correct balanced equation. If a balanced equation is incorrect, explain what is incorrect about it.
CaO + C CaC2 + CO2
I. CaO2 + 3C CaC2 + CO2
II. 2CaO + 5C CaC2 + CO2
III. CaO + (2.5)C CaC2 + (0.5)CO2
IV. 4CaO + 10C CaC2 + 2CO2
II, III, and IV are correct. I is not correct because you cannot use subscripts to balance a chemical equation.
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39. CONCEPT CHECK!
Which of the following are true concerning balanced chemical equations? There may be more than one true statement. I. The number of molecules is conserved. II. The coefficients tell you how much of each substance you have. III. Atoms are neither created nor destroyed. IV. The coefficients indicate the mass ratios of the substances used. V. The sum of the coefficients on the reactant side equals the sum of the coefficients on the product side.
Only III is correct.
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40. Notice
The number of atoms of each type of element must be the same on both sides of a balanced equation.
Subscripts must not be changed to balance an equation.
A balanced equation tells us the ratio of the number of molecules which react and are produced in a chemical reaction.
Coefficients can be fractions, although they are usually given as lowest integer multiples.
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41. AP Learning Objectives, Margin Notes and References
LO 1.17 The student is able to express the law of conservation of mass quantitatively and qualitatively using symbolic representations and particulate drawings.
Additional AP References
LO 1.19 (see APEC #3, “Gravimetric Analysis of a Sulfate Mixture”)

42. Stoichiometric Calculations
Chemical equations can be used to relate the masses of reacting chemicals.
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43. Calculating Masses of Reactants and Products in Reactions
1. Balance the equation for the reaction. 2. Convert the known mass of the reactant or product to moles of that substance. 3. Use the balanced equation to set up the appropriate mole ratios. 4. Use the appropriate mole ratios to calculate the number of moles of the desired reactant or product. 5. Convert from moles back to grams if required by the problem.
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44. Calculating Masses of Reactants and Products in Reactions
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45. EXERCISE!
Consider the following reaction: If 6.25 g of phosphorus is burned, what mass of oxygen does it combine with? 8.07 g O2
(6.25 g P4)(1 mol P4 / g P4)(5 mol O2 / 1 mol P4)(32.00 g O2 / 1 mol O2) = 8.07 g O2
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46. Write balanced equations for each of these reactions.
EXERCISE!
(Part I)
Methane (CH4) reacts with the oxygen in the air to produce carbon dioxide and water.
Ammonia (NH3) reacts with the oxygen in the air to produce nitrogen monoxide and water.
Write balanced equations for each of these reactions.
CH4 + 2O2  CO2 + 2H2O
4NH3 + 5O2  4NO + 6H2O
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47. EXERCISE!
(Part II)
Methane (CH4) reacts with the oxygen in the air to produce carbon dioxide and water.
Ammonia (NH3) reacts with the oxygen in the air to produce nitrogen monoxide and water.
What mass of ammonia would produce the same amount of water as 1.00 g of methane reacting with excess oxygen?
1.42 g of ammonia is required. Use the balanced equations from the previous exercise to start this problem. Determine the amount of water produced from 1.00 g of methane (which is moles of water). Use the moles of water and the balanced equation to determine the amount of ammonia needed.
See the “Let’s Think About It” slide next to get the students going.
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48. Let’s Think About It Where are we going?
To find the mass of ammonia that would produce the same amount of water as 1.00 g of methane reacting with excess oxygen.
How do we get there?
We need to know:
How much water is produced from 1.00 g of methane and excess oxygen.
How much ammonia is needed to produce the amount of water calculated above.
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49. AP Learning Objectives, Margin Notes and References
LO 1.17 The student is able to express the law of conservation of mass quantitatively and qualitatively using symbolic representations and particulate drawings.
LO 3.3: The student is able to use stoichiometric calculations to predict the results of performing a reaction in the laboratory and/or to analyze deviations from the expected results.
LO 3.4: The student is able to relate quantities (measured mass of substances, volumes of solutions, or volumes and pressures of gases) to identify stoichiometric relationships for a reaction, including situations involving limiting reactants and situations in which the reaction has not gone to completion.

50. Limiting Reactants
Limiting reactant – the reactant that runs out first and thus limits the amounts of products that can be formed.
Determine which reactant is limiting to calculate correctly the amounts of products that will be formed.
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51. Limiting Reactants To play movie you must be in Slide Show Mode
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52. A. The Concept of Limiting Reactants
Stoichiometric mixture
N2(g) + 3H2(g) NH3(g)

53. A. The Concept of Limiting Reactants
Limiting reactant mixture
N2(g) + 3H2(g)  2NH3(g)

54. A. The Concept of Limiting Reactants
Limiting reactant mixture
N2(g) + 3H2(g) NH3(g)
Limiting reactant is the reactant that runs out first. H2

55. Limiting Reactants
The amount of products that can form is limited by the hydrogen.
Hydrogen is the limiting reactant.
Nitrogen is in excess.
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56. CONCEPT CHECK!
Which of the following reaction mixtures could produce the greatest amount of product? Each involves the reaction symbolized by the equation:
2H2 + O H2O
a) 2 moles of H2 and 2 moles of O2
2 moles of H2 and 3 moles of O2
2 moles of H2 and 1 mole of O2
d) 3 moles of H2 and 1 mole of O2
e) Each produce the same amount of product.
The correct answer is “e”. All of these reaction mixtures would produce two moles of water.
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57. Notice
We cannot simply add the total moles of all the reactants to decide which reactant mixture makes the most product. We must always think about how much product can be formed by using what we are given, and the ratio in the balanced equation.
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58. CONCEPT CHECK!
You know that chemical A reacts with chemical B. You react 10.0 g of A with 10.0 g of B.
What information do you need to know in order to determine the mass of product that will be produced?
See the “Let’s Think About It” slide next to get the students going.
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59. Let’s Think About It Where are we going?
To determine the mass of product that will be produced when you react 10.0 g of A with 10.0 g of B.
How do we get there?
We need to know:
The mole ratio between A, B, and the product they form. In other words, we need to know the balanced reaction equation.
The molar masses of A, B, and the product they form.
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60. EXERCISE!
You react 10.0 g of A with 10.0 g of B. What mass of product will be produced given that the molar mass of A is 10.0 g/mol, B is 20.0 g/mol, and C is 25.0 g/mol? They react according to the equation: A + 3B 2C
8.33 g of C is produced.
Note: Use the box animations to assist in explaining how to solve the problem.
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61. Percent Yield
An important indicator of the efficiency of a particular laboratory or industrial reaction.
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62. Consider the following reaction: P4(s) + 6F2(g) 4PF3(g)
EXERCISE!
Consider the following reaction:
P4(s) + 6F2(g) 4PF3(g)
What mass of P4 is needed to produce 85.0 g of PF3 if the reaction has a 64.9% yield?
46.1 g P4
64.9% = (85.0 g PF3 / x)(100); x = g PF3
( g PF3)(1 mol PF3 / g PF3)(1 mol P4 / 4 mol PF3)( g P4 / 1 mol P4) = 46.1 g of P4 needed
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