Copyright © 2012, The McGraw-Hill Compaies, Inc. Permission required for reproduction or display. Chemistry Third Edition Julia Burdge Lecture PowerPoints Chapter 3 Stoichiometry: Ratios of Combination

CHAPTER 3 Stoichiometry: Ratios of Combination 2 3.1Molecular and Formula Masses 3.2Percent Composition of Compounds 3.3Chemical Equations 3.4The Mole and Molar Masses 3.5Combustion Analysis 3.6Calculations with Balanced Chemical Equations 3.7Limiting Reactants

Topics 3.1Molecular and Formula Masses 3

3.1Molecular and Formula Masses 4 Using atomic masses from the periodic table and a molecular formula, we can determine the molecular mass, which is the mass in atomic mass units (amu) of an individual molecule. molecular mass of H 2 O = 2(atomic mass of H) + atomic mass of O = 2(1.008 amu) amu = amu

3.1Molecular and Formula Masses 5 Although an ionic compound does not have a molecular mass, we can use its empirical formula to determine its formula mass.

SAMPLE PROBLEM Calculate the molecular mass or the formula mass, as appropriate, for each of the following compounds: (a)propane, (C 3 H 8 ) (b)lithium hydroxide, (LiOH) (c)barium acetate, [Ba(C 2 H 3 O 2 ) 2 ]

SAMPLE PROBLEM Calculate the molecular mass or the formula mass, as appropriate, for each of the following compounds: (a)propane, (C 3 H 8 ) (b)lithium hydroxide, (LiOH) (c)barium acetate, [Ba(C 2 H 3 O 2 ) 2 ] Solution (a)3(12.01 amu) + 8(1.008 amu) = amu (b)6.941 amu amu amu = amu (c)137.3 amu + 4(12.01 amu) + 6(1.008 amu) + 4(16.00 amu) = amu

Topics 3.2Percent Composition of Compounds 8

3.2Percent Composition of Compounds 9 A list of the percent by mass of each element in a compound is known as the compound’s percent composition by mass.

SAMPLE PROBLEM Calculate the percent composition by mass of lithium carbonate (Li 2 CO 3 ). Setup The formula mass of Li 2 CO 3 is 2(6.941 amu) amu + 3(16.00 amu) = amu

SAMPLE PROBLEM Calculate the percent composition by mass of lithium carbonate (Li 2 CO 3 ). Solution

Topics 3.3Chemical Equations 12 Interpreting and Writing Chemical Equations Balancing Chemical Equations

3.3Chemical Equations Interpreting and Writing Chemical Equations 13 A chemical reaction, as described in the third hypothesis of Dalton’s atomic theory, is the rearrangement of atoms in a sample of matter. Examples include the rusting of iron and the explosive combination of hydrogen and oxygen gases to produce water. A chemical equation uses chemical symbols to denote what occurs in a chemical reaction.

3.3Chemical Equations Interpreting and Writing Chemical Equations 14 “Ammonia and hydrogen chloride react to produce ammonium chloride.” “Calcium carbonate reacts to produce calcium oxide and carbon dioxide.”

3.3Chemical Equations Interpreting and Writing Chemical Equations 15 Each chemical species that appears to the left of the arrow is called a reactant. Reactants are those substances that are consumed in the course of a chemical reaction. Each species that appears to the right of the arrow is called a product.

3.3Chemical Equations Interpreting and Writing Chemical Equations 16 Indicating physical state:

3.3Chemical Equations Interpreting and Writing Chemical Equations 17 Allotropes:

3.3Chemical Equations Balancing Chemical Equations 18

3.3Chemical Equations Balancing Chemical Equations 19 Balancing a chemical equation requires something of a trial- and-error approach. In general, it will facilitate the balancing process if you do the following: 1.Change the coefficients of compounds (e.g., CO 2 ) before changing the coefficients of elements (e.g., O 2 ).

3.3Chemical Equations Balancing Chemical Equations 20 2.Treat polyatomic ions that appear on both sides of the equation (e.g., CO 3 2– ) as units, rather than counting their constituent atoms individually. 3.Count atoms and/or polyatomic ions carefully, and track their numbers each time you change a coefficient.

3.3Chemical Equations Balancing Chemical Equations 21 Combustion refers to burning in the presence of oxygen.

3.3Chemical Equations Balancing Chemical Equations 22

3.3Chemical Equations Balancing Chemical Equations 23

SAMPLE PROBLEM Write and balance the chemical equation for the aqueous reaction of barium hydroxide and perchloric acid to produce aqueous barium perchlorate and water. Setup

SAMPLE PROBLEM Write and balance the chemical equation for the aqueous reaction of barium hydroxide and perchloric acid to produce aqueous barium perchlorate and water. Solution (not including O atoms in ClO 4 – ions)

SAMPLE PROBLEM Solution

SAMPLE PROBLEM Solution

SAMPLE PROBLEM Assuming that the only products are CO 2 and H 2 O, write and balance the equation for the metabolism of butyric acid, C 4 H 8 O 2. Setup

SAMPLE PROBLEM Solution

Topics 3.4The Mole and Molar Masses 30 The Mole Determining Molar Mass Interconverting Mass, Moles, and Numbers of Particles Empirical Formula from Percent Composition

3.4The Mole and Molar Masses The Mole 31 1 “pair” objects2 objects 1 “dozen” objects12 objects 1 “gross” objects144 objects 1 “million” objects1,000,000 objects 1 “trillion” objects10 12 objects 1 “mole” objects6.023 × objects People use a variety of counting groups to conveniently indicate the number of objects in some set:

3.4The Mole and Molar Masses The Mole 32 A “mole” is a counting group, defined as the number of atoms in exactly 12 g of carbon-12. This number of atoms in 12 g of carbon-12 is known as Avogadro’s Number (N A ): N A = × objects If you order one dozen doughnut, you are asking for 12 doughnuts. If you order one mole of doughnuts, you are asking for × doughnuts!

3.4The Mole and Molar Masses The Mole 33 Conversion factors for moles of objects and number of objects: 1 mol objects = × objects

SAMPLE PROBLEM A typical human body contains roughly 30 moles of calcium. Determine (a) the number of Ca atoms in moles of calcium and (b) the number of moles of calcium in a sample containing 1.00 × Ca atoms. Setup

SAMPLE PROBLEM Solution

3.4The Mole and Molar Masses Determining Molar Mass 36 Chemists determine how many moles there are of a substance by measuring its mass (usually in grams). The molar mass of the substance is then used to convert from grams to moles. The molar mass ( M ) of a substance is the mass in grams of 1 mole of the substance.

3.4The Mole and Molar Masses Determining Molar Mass 37 By definition, the mass of a mole of carbon-12 is exactly 12 g. Note that the molar mass of carbon is numerically equal to its atomic mass. Likewise, the atomic mass of calcium is amu and its molar mass is g, the atomic mass of sodium is amu and its molar mass is g, etc.

3.4The Mole and Molar Masses Determining Molar Mass 38 In effect, there is 1 mole of atomic mass units in 1 gram. So, the molar mass (in grams) of any compound is numerically equal to its molecular or formula mass (in amu).

3.4The Mole and Molar Masses Interconverting Mass, Moles, and Numbers of Particles 39

SAMPLE PROBLEM Determine (a) the number of moles of C in g of naturally occurring carbon and (b) the mass of mole of sodium chloride. Setup The molar mass of carbon is g/mol. The molar mass of a compound is numerically equal to its formula mass. The molar mass of sodium chloride (NaCl) is g/mol.

SAMPLE PROBLEM Solution

SAMPLE PROBLEM (a)Determine the number of water molecules and the numbers of H and O atoms in 3.26 g of water. (b)Determine the mass of 7.92 × carbon dioxide molecules.

SAMPLE PROBLEM Solution (a)

SAMPLE PROBLEM Solution (b)

3.4The Mole and Molar Masses Empirical Formula from Percent Composition 45 With the concepts of the mole and molar mass, we can now use the experimentally determined percent composition to determine the empirical formula of a compound.

SAMPLE PROBLEM Determine the empirical formula of a compound that is percent nitrogen and percent oxygen by mass. Strategy Assume a 100-g sample so that the mass percentages of nitrogen and oxygen given in the problem statement correspond to the masses of N and O in the compound. Then, using the appropriate molar masses, convert the grams of each element to moles.

SAMPLE PROBLEM Setup The empirical formula of a compound consisting of N and O is N x O y. The molar masses of N and O are and g/mol, respectively. One hundred grams of a compound that is percent nitrogen and percent oxygen by mass contains g N and g O.

SAMPLE PROBLEM Solution

Topics 3.5Combustion Analysis 49 Determination of Empirical Formula Determination of Molecular Formula

3.5Combustion Analysis Determination of Empirical Formula 50 Knowing the mass of each element contained in a sample of a substance enables us to determine the empirical formula of the substance. One common, practical use of this ability is the experimental determination of empirical formula by combustion analysis.

3.5Combustion Analysis Determination of Empirical Formula 51

3.5Combustion Analysis Determination of Empirical Formula 52 When a compound such as glucose is burned in a combustion analysis apparatus, carbon dioxide (CO 2 ) and water (H 2 O) are produced. Because only oxygen gas is added to the reaction, the carbon and hydrogen present in the products must have come from the glucose. The oxygen in the products may have come from the glucose, but it may also have come from the added oxygen.

3.5Combustion Analysis Determination of Empirical Formula 53 Suppose that in one such experiment the combustion of 18.8 g of glucose produced 27.6 g of CO 2 and 11.3 g of H 2 O. We can calculate the mass of carbon and hydrogen in the original 18.8-g sample of glucose as follows:

3.5Combustion Analysis Determination of Empirical Formula 54 Thus, 18.8 g of glucose contains 7.53 g of carbon and 1.26 g of hydrogen. The remaining mass [18.8 g – (7.53 g g) = 10.0 g] is oxygen.

3.5Combustion Analysis Determination of Empirical Formula 55

3.5Combustion Analysis Determination of Empirical Formula 56

3.5Combustion Analysis Determination of Molecular Formula 57 The molar mass of glucose is about 180 g. The empirical-formula mass of CH 2 O is about 30 g [12.01 g + 2(1.008 g) g]. To determine the molecular formula, first divide the molar mass by the empirical-formula mass: 180 g/30 g = 6. This tells us that there are six empirical-formula units per molecule in glucose.

3.5Combustion Analysis Determination of Molecular Formula 58 Multiplying each subscript by 6 (recall that when none is shown, the subscript is understood to be a 1) gives the molecular formula, C 6 H 12 O 6.

SAMPLE PROBLEM Combustion of a 5.50-g sample of benzene produces g CO 2 and 3.81 g H 2 O. Determine the empirical formula and the molecular formula of benzene, given that its molar mass is approximately 78 g/mol. Setup The necessary molar masses are CO 2, g/mol; H 2 O, g/mol; C, g/mol; H, g/mol; and O, g/mol.

SAMPLE PROBLEM Solution The total mass of products is g g = g. Because the combined masses of C and H account for the entire mass of the original sample (5.499 g  5.50 g), this compound must not contain O.

SAMPLE PROBLEM Solution

Topics 3.6Calculations with Balanced Chemical Equations 62 Moles of Reactants and Products Mass of Reactants and Products

3.6Calculations with Balanced Chemical Equations Moles of Reactants and Products 63 In stoichiometric calculations, we say that 2 moles of CO are equivalent to 2 moles of CO 2, which can be represented as

3.6Calculations with Balanced Chemical Equations Moles of Reactants and Products 64 Stoichiometric conversion factors:

3.6Calculations with Balanced Chemical Equations Moles of Reactants and Products 65 Consider the complete reaction of 3.82 moles of CO to form CO 2. We can determine the stoichiometric amount of O 2 (how many moles of O 2 are needed to react with 3.82 moles of CO):

SAMPLE PROBLEM Urea can be synthesized in the laboratory by the combination of ammonia and carbon dioxide according to the equation (a)Calculate the amount of urea that will be produced by the complete reaction of 5.25 moles of ammonia. (b)Determine the stoichiometric amount of carbon dioxide required to react with 5.25 moles of ammonia.

SAMPLE PROBLEM Setup

SAMPLE PROBLEM Solution (a) (b)

3.6Calculations with Balanced Chemical Equations Mass of Reactants and Products 69 Balanced chemical equations give us the relative amounts of reactants and products in terms of moles. However, because we measure reactants and products in the laboratory by weighing them, most often such calculations start with mass rather than the number of moles.

SAMPLE PROBLEM Nitrous oxide (N 2 O) is commonly used as an anesthetic in dentistry. It is manufactured by heating ammonium nitrate. The balanced equation is (a)Calculate the mass of ammonium nitrate that must be heated in order to produce 10.0 g of nitrous oxide. (b)Determine the corresponding mass of water produced in the reaction.

SAMPLE PROBLEM Setup The molar masses are as follows: g/mol for NH 4 NO 3, g/mol for N 2 O, and g/mol for H 2 O.

SAMPLE PROBLEM Solution (a) Thus, 18.2 g of ammonium nitrate must be heated in order to produce 10.0 g of nitrous oxide.

SAMPLE PROBLEM Solution (b) Therefore, 8.18 g of water will also be produced in the reaction.

Topics 3.7Limiting Reactants 74 Determining the Limiting Reactant Reaction Yield Types of Chemical Reactions

3.7Limiting Reactants Determining the Limiting Reactant 75 The reactant used up first in a reaction is called the limiting reactant, because the amount of this reactant limits the amount of product that can form. When all the limiting reactant has been consumed, no more product can be formed. Excess reactants are those present in quantities greater than necessary to react with the quantity of the limiting reactant.

3.7Limiting Reactants Determining the Limiting Reactant 76 Suppose that initially we have 5 moles of CO and 8 moles of H 2 :

3.7Limiting Reactants Determining the Limiting Reactant 77 Because there are only 8 moles of H 2 available, there is insufficient H 2 to react with all the CO. Therefore, H 2 is the limiting reactant and CO is the excess reactant.

3.7Limiting Reactants Determining the Limiting Reactant 78 To determine how much CO will be left over when the reaction is complete, we must first calculate the amount of CO that will react with all 8 moles of H 2 : Thus, there will be 4 moles of CO consumed and 1 mole (5 mol – 4 mol) left over.

SAMPLE PROBLEM Alka-Seltzer tablets contain aspirin, sodium bicarbonate, and citric acid. When they come into contact with water, the sodium bicarbonate (NaHCO 3 ) and citric acid (H 3 C 6 H 5 O 7 ) react to form carbon dioxide gas, among other products.

SAMPLE PROBLEM An Alka- Seltzer tablet contains g of sodium bicarbonate and g of citric acid. Determine, for a single tablet dissolved in water, (a)which ingredient is the limiting reactant, (b)what mass of the excess reactant is left over when the reaction is complete, and (c)what mass of CO 2 forms.

SAMPLE PROBLEM Setup

SAMPLE PROBLEM Solution (a) The amount of H 3 C 6 H 5 O 7 required to react with mol of NaHCO 3 is more than a tablet contains. Therefore, citric acid is the limiting reactant

SAMPLE PROBLEM Solution (b) Thus, mol of NaHCO 3 will be consumed, leaving mol unreacted.

SAMPLE PROBLEM Solution (c) To summarize the results: (a) citric acid is the limiting reactant, (b) g sodium bicarbonate remains unreacted, and (c) g carbon dioxide is produced.

3.7Limiting Reactants Reaction Yield 85 When you use stoichiometry to calculate the amount of product formed in a reaction, you are calculating the theoretical yield of the reaction. The theoretical yield is the amount of product that forms when all the limiting reactant reacts to form the desired product. It is the maximum obtainable yield, predicted by the balanced equation.

3.7Limiting Reactants Reaction Yield 86 In practice, the actual yield—the amount of product actually obtained from a reaction—is almost always less than the theoretical yield. The percent yield tells what percentage the actual yield is of the theoretical yield.

SAMPLE PROBLEM Aspirin, acetylsalicylic acid (C 9 H 8 O 4 ), is produced by the reaction of salicylic acid (C 7 H 6 O 3 ) and acetic anhydride (C 4 H 6 O 3 ) according to the following equation: In a certain aspirin synthesis, g of salicylic acid and g of acetic anhydride are combined. Calculate the percent yield of the reaction if g of aspirin are produced.

SAMPLE PROBLEM Setup The necessary molar masses are g/mol for salicylic acid, g/mol for acetic anhydride, and g/mol for aspirin. Solution Salicylic acid is the limiting reactant.

SAMPLE PROBLEM Solution Therefore, the theoretical yield of aspirin is mol. Thus, the theoretical yield is g.

3.7Limiting Reactants Types of Chemical Reactions 90 Combination. A reaction in which two or more reactants combine to form a single product is known as a combination reaction.

3.7Limiting Reactants Types of Chemical Reactions 91 Decomposition. A reaction in which two or more products form from a single reactant is known as a decomposition reaction.

3.7Limiting Reactants Types of Chemical Reactions 92 Combustion. A combustion reaction is one in which a substance burns in the presence of oxygen. Combustion of a compound that contains C and H (or C, H, and O) produces carbon dioxide gas and water. By convention, we will consider the water produced in a combustion reaction to be liquid water.

SAMPLE PROBLEM Determine whether each of the following equations represents a combination reaction, a decomposition reaction, or a combustion reaction:

SAMPLE PROBLEM Determine whether each of the following equations represents a combination reaction, a decomposition reaction, or a combustion reaction: Solution (a)combination (b)combustion (c)decomposition