# Chapter 3 Stoichiometry: Ratios of Combination

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1 Chapter 3 Stoichiometry: Ratios of Combination 1

2 3.1 Molecular and Formula Masses 3.2 Percent Composition of Compounds 3.3 Chemical Equations 3.4 The Mole and Molar Mass 3.5 Combustion Analysis 3.6 Calculations with Balanced Chemical Equations 3.7 Limiting Reactants 1 2

3 3.1 Molecular and Formula Masses Molecular mass - (molecular weight) The mass in amu s of the individual molecule Multiply the atomic mass for each element in a molecule by the number of atoms of that element and then total the masses Formula mass (formula weight)- The mass in amu s of an ionic compound 3

4 Calculating Molecular Mass Calculate the molecular mass (Mwt) for carbon dioxide, CO 2 Write down each element; multiply by atomic mass C = 1 x = amu O = 2 x = amu Total: = amu 4

5 Your Turn! Calculate the molecular mass or formula mass for each of the following: Sulfur trioxide Barium phosphate Sodium nitrite Acetic acid 5

6 3.2 Percent Composition of Compounds Calculated by dividing the total mass of each element in a compound by the molecular mass of the compound and multiplying by 100 6

7 % Composition Calculate the percent composition of iron in a sample of iron (III) oxide Formula: Fe 2 O 3 Calculate formula mass Fe = 2 x = amu O = 3 x = amu Total mass: = amu 7

8 % Composition % by mass = = 69.9% Fe What is the % oxygen in this sample? (hint :100%) 8

9 Glucose (C 6 H 12 O 6 ) Example What is the mass percent of each element in glucose? - For each mole of glucose, we have 6 moles of C, 12 moles H, and 6 moles O 6 C 6 x = amu 12 H 12 x = amu + 6 O 6 x = amu amu mass percent of C = C glucose = x 100 = mass %C mass percent of H = H glucose = x 100 = mass %H mass percent of O = O glucose = x 100 = mass %O 9

10 Your Turn! Calculate the percent oxygen in a sample of potassium chlorate KClO 3 10

11 3.3 Chemical Equations Chemical equations represent chemical sentences Read the following equation as a sentence NH 3 + HCl NH 4 Cl ammonia reacts with hydrochloric acid to produce ammonium chloride 11

12 Chemical Equations Reactant: any species to the left of the arrow (consumed) Product: any species to the right of the arrow (formed) State symbols: (s) solid (l) liquid (g) gas (aq) water solution 12

13 Balancing Equations Balanced: same number and kind of atoms on each side of the equation 2 H 2 (g) + O 2 (g) 2 H 2 O (I) 13

14 Balancing Equations Steps for successful balancing 1. Change coefficients for compounds before changing coefficients for elements.(never change subscripts!) 2. Treat polyatomic ions as units rather than individual elements. 3. Count carefully, being sure to recount after each coefficient change. 14

15 In chemical reaction, all atoms present in reactants must be accounted for among the products. this is the called balanced chemical equation 2 H 2 + O 2 2 H 2 O 2 Mg + O 2 2 MgO Balanced equation Balanced equation C 2 H 6 + O 2 CO 2 + H 2 O Unbalanced equation 15

16 Balancing Chemical Equations 1. Write the correct formula(s) for the reactants on the left side and the correct formula(s) for the product(s) on the right side of the equation. Ethane reacts with oxygen to form carbon dioxide and water C 2 H 6 + O 2 CO 2 + H 2 O 2. Change the numbers in front of the formulas (coefficients) to make the number of atoms of each element the same on both sides of the equation. Do not change the subscripts. 2C 2 H 6 NOT C 4 H 12 2H 2 O NOT H 4 O 2 16

17 Balancing Chemical Equations C 2 H 6 + O 2 CO 2 + H 2 O start with C or H but not O 2 carbon on left 1 carbon on right multiply CO 2 by 2 C 2 H 6 + O 2 2CO 2 + H 2 O multiply H 2 O by 3 6 hydrogen on left C 2 H 6 + O 2 2 hydrogen on right 2CO 2 + 3H 2 O 17

18 Balancing Chemical Equations C 2 H 6 + O 2 2CO 2 + 3H 2 O multiply O 2 by oxygen on left 4 oxygen (2x2) + 3 oxygen (3x1) = 7 oxygen on right C 2 H O 2 2CO 2 + 3H 2 O 2 2C 2 H 6 + 7O 2 4CO 2 + 6H 2 O remove fraction multiply both sides by 2 18

19 Double check! 2C 2 H 6 + 7O 2 4CO 2 + 6H 2 O 4 C (2 x 2) 4 C 12 H (2 x 6) 12 H (6 x 2) 14 O (7 x 2) 14 O (4 x 2 + 6) Reactants 4 C 12 H 14 O Products 4 C 12 H 14 O 19

20 Balancing Equations Balance the equation representing the combustion of hexane C 6 H 14(l) + O 2(g) CO 2(g) + H 2 O (l) (Hint: Make a list of all elements and count to keep track) 20

21 Balancing Equations Balance the equation representing the combustion of hexane C 6 H 14(l) +7/2O 2(g) 6CO 2(g) + 7H 2 O (l) Or multiply through the entire equation to eliminate fractions 2C 6 H 14(l) +7O 2(g) 12CO 2(g) + 14H 2 O (l) 21

22 Chemical Equations Equations can represent physical changes KClO 3(s) KClO 3(l) Or chemical changes Note the symbol for heat above the arrow KClO 3(s) KClO 3(l) 22

23 3.4 The Mole and Molar Masses Balanced equations tell us what is reacting and in what relative proportions on the molecular level. 23

24 The Mole The unit of measurement used by chemists in the laboratory The mole is the number equal to number of carbon atoms in exactly 12 grams of pure 12 C Avogadro has determined this number to be N A = X Particle/mole 1 mole 12 C atoms = x atoms = 12.00g 24

25 The Mole 2 H 2(g) + O 2(g) 2 H 2 O (l) 2 molecules H 2(g) + 1 molecule O 2(g) 2 molecules H 2 O (l) 2 moles H 2(g) + 1 mole O 2(g) 2 moles H 2 O (l) 25

26 Molar Mass Molar mass is the mass of 1 mole of anything in grams Carbon = 12.0 grams/mole Sodium = 22.9 grams/mole 1 mole lithium atoms = g of Li For any element atomic mass (amu) = molar mass (grams) 26

27 Molecular mass (or molecular weight) is the sum of the atomic masses (in amu) in a molecule. SO 2 1S 2O SO amu + 2 x amu amu For any molecule molecular mass (amu) = molar mass (grams) 1 molecule SO 2 = amu 1 mole SO 2 = g SO 2 27

28 Molar Mass for Compounds Calculate the molar mass for each of the following: H 2 O H 2 x 1.01 g/mol = 2.02 O 1 x g/mol = Molar mass = g/mol 28

29 Example How many atoms are in g of potassium (K)? 1 mol K = g K 1 mol K = x atoms K g K x 1 mol K g K x x 1023 atoms K 1 mol K = 8.49 x atoms K 29

30 Example How many H atoms are in 72.5 g of C 3 H 8 O? 1 mol C 3 H 8 O = (3 x 12) + (8 x 1) + 16 = 60 g C 3 H 8 O 1 mol C 3 H 8 O molecules = 8 mol H atoms 1 mol H = x atoms H 72.5 g C 3 H 8 O 1 mol C 3H 8 O x 60 g C 3 H 8 O x 8 mol H atoms 1 mol C 3 H 8 O x H atoms x = 1 mol H atoms 5.82 x atoms H 30

31 Conversions between grams, moles and atoms No of Moles = Mass (g) Molar Mass (g/mole) No of Atoms = No of Moles x x atom 1 mole 31

32 Interconverting mass, moles and number of particles Determine the number of moles in grams of sodium chlorate, NaClO 3 1 mole NaClO g NaClO mol NaClO g NaClO

33 Another Determine the number of molecules in 4.6 moles of ethanol, C 2 H 5 OH. (1 mole = x ) molecules C H OH 4.6 mol C H OH molecules 2 5 1mol C H OH

34 Another Determine how many H atoms are in 4.6 moles of ethanol molecules C 2 H 5 OH 6 H atoms 1 molecule C 2 H 5 OH atoms H 34

35 Another How many grams of oxygen are present in 5.75 moles of aluminum oxide, Al 2 O 3? Strategy: 35

36 Example Determine the number of fluorine atoms in grams of sulfur hexafluoride. 36

37 Empirical and Molecular Formulas Empirical- simplest whole-number ratio of atoms in a formula Molecular - the true ratio of atoms in a formula; often a whole-number multiple of the empirical formula We can determine empirical formulas from % composition data. 37

38 Empirical and Molecular Formulas molecular formula = (empirical formula) n [n = integer] molecular formula = C 6 H 6 = (CH) 6 empirical formula = CH If the Molar mass for any compound is known one can get the chemical or molecular formula by the following: 1- calculate empirical mass = atomic mass 1- find the multiplication factor = MM/EM 1- molecular formula = multiplication factor x EF Note: if MM = EM molecular formula = empirical formula 38

39 Example Caffeine contain % C, 5.159% H, % N, and % O by mass has a molar mass g/mol. Determine the molecular formula of caffeine. Solution Assume you have 100g of the caffeine, Then you have g C g H g N g O - Divide by the molar mass of each element g C = 4.12 mol C 5.12 mol H 2.06 mol N 1.03 mol O g/mole C Find the ratio of the moles (divide by the smallest number) C 5 H 2 N 1 O 39

40 Continue 4 C 5 H 2 N 1 O -The empirical formula is C 4 H 5 N 2 O - The empirical Atomic mass = x x x x1 = g/mol - The empirical Atomic mass = g/mol - The multiplication factor = g/mol = g/mol The molecular formula = (C 4 H 5 N 2 O) 2 = C 8 H 10 N 4 O 2 40

41 Example - lactic acid (M=90.08 g/mol) contains 40.0 mass% C, 6.71 mass% H, and 53.3 mass% O. - Determine the molecular formula Solution Assuming there are 100. g of lactic acid 40 g C 6.71 g H 12.01g C g H 53.3 g O g O 3.33 mol C 6.66 mol H 3.33 mol O g/mol g/mol CH 2 O empirical formula EM = g/mol 3 C 3 H 6 O 3 is the molecular formula 41

42 Empirical Formulas Steps for success Convert given amounts to moles Mole ratio (divide all moles by the smallest number of moles) The numbers represent subscripts. If the numbers are not whole numbers, multiply by some factor to make them whole. 42

43 Empirical Formula Determine the empirical formula for a substance that is determined to be 85.63% carbon and 14.37% hydrogen by mass. 43

44 3.5 Combustion Analysis Analysis of organic compounds (C,H and sometimes O) are carried using an apparatus like the one below Organic Compound O 2 CO 2, H 2 O 44

45 Combustion Analysis The data given allows an empirical formula determination with just a few more steps. The mass of products (carbon dioxide and water) will be known so we work our way back. 45

46 Example Vitamin C (M=176.12g/mol) is a compound of C,H, and O. When a g sample of vitamin C is placed in a combustion chamber and burned, the following data are obtained: Mass of CO 2 = 1.50 g Mass of H 2 O = 0.41 g What is the molecular formula of vitamin C? Solution There are 1 mole of C per 1 mole of CO g CO g/mol CO 2 = mole of CO 2 Moles of C = moles of CO 2 = mole Mass of C = Moles of C x Molar mass of C mole of C x g/mol = g C 46

47 Continue There are 2 mole of H per 1 mole of H 2 O Moles of H 2 O = 0.41 g g H 2 O = mole Mass of H = Mole of H x Molar mass of H mole H x g/mole = g of H Mass of O = 1 (0.409 g C g of H) = g of O Moles of H = 2 x Moles of H 2 O = 2 x = mole H g C g C g H g O = mol C = mol H = mol O g H g O C 1 H 1.3 O 1 C 3 H 4 O g/mol g = C 6 H 8 O 6 47

48 3.6 Calculations with Balanced Chemical Equations Balanced equations allow chemists and chemistry students to calculate various amounts of reactants and products. The coefficients in the equation are used as mole ratios. 48

49 Stoichiometry Stoichiometry- using balanced equations to find amounts How do the amounts compare in the reaction below? 49

50 Mole Ratios Many mole ratios can be written from the equation for the synthesis of urea Mole ratios are used as conversion factors 2 molnh 3 1mol CO 2 or 1 molco 2 2 mol NH 3 50

51 1. Write balanced chemical equation 2. Convert quantities of known substances into moles 3. Use coefficients in balanced equation to calculate the number of moles of the required quantity 4. Convert moles of required quantity into desired units 51

52 Calculations with Balanced Equations How many moles of urea could be formed from 3.5 moles of ammonia? 2NH 3(g) + CO 2(g) (NH 2 ) 2 CO (aq) + H 2 O (l) 3.5 mol NH 3 1 mol (NH 2 ) 2 CO 2 mol NH 3 = 1.8 mol (NH 2 ) 2 CO 52

53 Mass to Mass A chemist needs grams of urea, how many grams of ammonia are needed to produce this amount? Strategy: Grams moles mole ratio grams 2NH 3(g) + CO 2(g) (NH 2 ) 2 CO (aq) + H 2 O (l) g (NH 2 ) 2 CO 1 mol(nh 2 ) 2 CO g(nh 2 ) 2 CO 2 mol NH 3 1 mol (NH 2 ) 2 CO g NH 3 1mol NH 3 = g NH 3 53

54 You Try! How many grams of carbon monoxide are needed to produce 125 grams of urea? 54

55 Example Methanol burns in air according to the equation 2CH 3 OH + 3O 2 2CO 2 + 4H 2 O If 209 g of methanol are used up in the combustion, what mass of water is produced? grams CH 3 OH moles CH 3 OH moles H 2 O grams H 2 O molar mass CH 3 OH coefficients chemical equation molar mass H 2 O 209 g CH 3 OH 1 mol CH 3 OH x 32.0 g CH 3 OH x 4 mol H 2 O 2 mol CH 3 OH 18.0 g H 2 O x = 1 mol H 2 O 235 g H 2 O 55

56 3.7 Limiting Reactants Limiting reactant - the reactant that is used up first in a reaction (limits the amount of product produced) Excess reactant - the one that is left over 56

57 Limiting Reagents 2NO + 2O 2 2NO 2 NO is the limiting reagent O 2 is the excess reagent 57

58 Calculation involve limiting reactant 1. Balance the equation. 2. Convert masses to moles. 3. Determine which reactant is limiting. 4. Use moles of limiting reactant and mole ratios to find moles of desired product. 5. Convert from moles to grams. 58

59 How to calculate Limiting Reactant In one process, 124 g of Al are reacted with 601 g of Fe 2 O 3 2Al + Fe 2 O 3 Al 2 O 3 + 2Fe Calculate the mass of Al 2 O 3 formed? g Al mol Al mol Fe 2 O 3 needed g Fe 2 O 3 needed OR g Fe 2 O 3 mol Fe 2 O 3 mol Al needed g Al needed 124 g Al x 1 mol Al 27.0 g Al x 1 mol Fe 2 O 3 2 mol Al 160. g Fe 2 O 3 x = 367 g Fe 2 O 3 1 mol Fe 2 O 3 Start with 124 g Al need 367 g Fe 2 O 3 Have more Fe 2 O 3 (601 g) so Al is limiting reagent 59

60 Continue Use limiting reagent (Al) to calculate amount of product that can be formed. g Al mol Al mol Al 2 O 3 g Al 2 O 3 2Al + Fe 2 O 3 Al 2 O 3 + 2Fe 124 g Al x 1 mol Al 27.0 g Al x 1 mol Al 2 O 3 2 mol Al 102. g Al 2 O x 3 = 234 g Al 1 mol Al 2 O 2 O

61 Example When grams of nitrogen react with grams of hydrogen, how many grams of ammonia are produced? How many grams of excess reagent remain in the reaction vessel? 3H 2(g) + N 2(g) 2NH 3(g) Moles of N 2 = 35.5 g 28.01g/mol = 1.27 mole of N 2 Moles of H 2 = g 2.02g/mol = mole of H 2 61

62 3H 2(g) + N 2(g) 2NH 3(g) Continue 1.27 mole of N mole of H 2 1- Assume the N 2 is the limiting reactant 2- Calculate how many moles of H 2 needed Moles of H 2 needed = moles of N 2 3 Moles of H 2 1 Moles of N 2 3 Moles of H mole N 2 1 Moles of N 2 = 3.81 mole H 2 N 2 is the limiting reactant 62

63 Continue 3H 2(g) + N 2(g) 2NH 3(g) g N 2 moles N 2 moles NH 3 g NH 3 2 Moles of NH 3 Moles of NH 3 = 1.27 mole N 2 1 Moles of N 2 = 2.54 mole NH 3 Mass of NH 3 = 2.54 mole g/mole = g Moles of H 2 unreacted = = 8.94 moles Mass of H 2 remains = 8.94 mole 2.02 g/mole = g H 2 63

64 Reaction Yield Theoretical yield: the maximum amount of product predicted by stoichiometry Actual yield: the amount produced in a laboratory setting Percent yield: a ratio of actual to theoretical (tells efficiency of reaction) % Yield = Actual Yield Theoretical Yield x

65 Example 3.75 g of zinc (Zn) reacted with excess hydrochloric acid (HCl), 5.58 g of zinc chloride (ZnCl 2 ) were collected. What is the percent yield for this reaction? Zn (s) + 2 HCl (aq) ZnCl 2(aq) + H 2(g) g of Zn moles of Zn moles of ZnCl 2 g of ZnCl g of Zn x mole g x 1 mole of ZnCl 2 1 mole of Zn x g ZnCl 2 mole = 7.82 g of ZnCl 2 (Theoretical Yield) 65

66 Continue Theoretical yield = 7.82 g ZnCl 2 Actual yield = 5.58 g ZnCl 2 % yield = 5.58 g of ZnCl g of Zncl 2 X 100 = 71.4 % 66

67 A Few Reaction Types Combination: one product is formed Decomposition: one reactant produces more than one product Combustion: a hydrocarbon reacts with oxygen to produce carbon dioxide and water 67

68 Combination Reaction General formula: A + B AB Sodium + chlorine sodium chloride 2Na + Cl 2 2 NaCl Sulfur dioxide + water sulfurous acid SO 2 + H 2 O H 2 SO 3 68

69 Decomposition Reaction General formula: AB A + B Copper (II) carbonate decomposes with heat into copper (II) oxide and carbon dioxide CuCO 3 CuO + CO 2 Potassium bromide decomposes into its elements 2KBr 2K + Br 2 69

70 Combustion (hydrocarbons) General formula: C x H y + O 2 CO 2 + H 2 O Methane gas burns completely CH 4 + 2O 2 CO 2 + 2H 2 O Butane liquid in a lighter ignites 2C 4 H O 2 8CO H 2 O 70

71 Review Molecular mass Percent composition Chemical equations Reactants Products State symbols Balancing 71

72 Review continued Mole concept and conversions Empirical and molecular formulas Combustion analysis Stoichiometry Limiting reactant % yield Types of reactions 72

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