4.4 Calculations Involving the Mole Concept


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1 44 Section 43 Questions 1 Define Avogadro s constant, and explain its significance in quantitative analysis 2 Distinguish between the terms atomic mass and molar mass 3 Calculate the mass of a molecule of sucrose (sugar, C 12 ) and the mass of a mole of sucrose 4 What is the molar mass of octane, C 8 H 18(l), a component of gasoline? Making Connections 5 One mole of any gas at 0 C and 101 kpa occupies the volume 224 L Use this information and your knowledge of molar mass to determine the density (in grams per litre) of gaseous hydrogen, helium, nitrogen, oxygen, and carbon dioxide in those conditions DID YOU KNOW? Mole Day Mole Day, which is held in recognition of the mole concept, is celebrated yearly on October 23 between 6:02 am and 6:02 pm October 23 Tuesday Octobe 24 W Reflecting 6 You are learning how to calculate molar mass How do you think this skill will be useful? October 30 Tuesday O 44 Calculations Involving the Mole Concept In this section, we will apply the mole concept in a number of situations that we encounter frequently in the study of chemical reactions Chemical formulas and equations are expressed using amount in moles In a laboratory, we measure mass So we constantly need to convert amount in moles into mass and vice versa Think about the term molar mass It contains the concepts of both moles and mass We always use molar mass in connecting the two measurements of amount in moles and mass Converting Mass to Amount in Moles To calculate an amount in moles, we take the given mass in grams and divide by the molar mass Let s take an example Each mole of carbon atoms has a mass of 12 g If we have 24 g of carbon atoms, what is the amount in moles? Since 24 g is twice 12 g, we have 20 moles of carbon atoms Mathematically, when we divide the mass we are given, 24 g, by the molar mass, 12 g/mol, we get 20 mol Amount in moles mass (g) molar mass (g/mol) 24 g n c 12 g/mol 24 g 1 mol 12g n c 20 mol Quantities in Chemical Formulas 171
2 In SI symbols, the relationship of amount (n), mass (m), and molar mass (M) is expressed as n M m Sample Problem 1 Convert a mass of 15 kg of calcium carbonate to an amount in moles m CaCO3(s) 15 kg M CaCO3(s) (1 4008) + (1 1201) + (3 1600) g/mol 1 mol n CaCO3(s) 15 kg g 1 mol 1500 g g n CaCO3 15 mol A mass of 15 kg of calcium carbonate is equal to 15 mol of calcium carbonate Practice Answers mol 2 56 mol mol 4 (a) 200 mol C, 594 mol H, 100 mol O (b) 2:6:1 1 Convert a mass of 25 g of table salt (sodium chloride) to an amount in moles 2 Convert a mass of 10 kg of glucose, C 6 H 12 O 6(s), to an amount in moles 3 What is the amount in moles of 250 g of oxygen gas? 4 A clear, colourless liquid when decomposed produced 240 g of carbon atoms, 60 g of hydrogen atoms, and 160 g of oxygen atoms (a) Calculate the amount in moles of each element in the compound (b) Determine the ratio of the number of atoms of carbon to hydrogen to oxygen, that is, the mole ratio of C:H:O (c) From your answer in (b), suggest a formula for the clear, colourless liquid Converting Amount in Moles to Mass If we know the amount in moles of a reactant or a product, we can calculate the mass by using the molar mass Consider the amount of 20 mol of sodium hydroxide, NaOH (s) The molar mass of NaOH (s) is ( ) g/mol, or 4000 g/mol The mass of 20 mol of NaOH (s) would be exactly double the mass of 10 mol of NaOH (s) Therefore, the mass of 20 mol of NaOH (s) is double 40 g, which is 80 g Mathematically, in order to calculate the mass of a substance, we multiply the amount in moles by its molar mass mass m NaOH amount in moles (mol) molar mass (g/mol) 20 mol g 1 ol m 80 g 172 Chapter 4
3 44 This relationship can be represented by m nm which is simply a rearrangement of the relationship we used earlier: (a) n M m Sample Problem 2 Convert a reacting amount of 0346 mol of sodium sulfate into mass in grams (b) n Na2 SO 0346 mol 4 M Na2 SO g/mol m Na2 SO 4 m Na2 SO mol g 1 l mo 491 g The mass of 0346 mol of Na 2 SO 4(s) is 491 g Practice 5 Magnesium hydroxide is a base that is used in some antacids What is the mass in grams of 045 mol of magnesium hydroxide? 6 Ammonia is a gas that, dissolved in water, is used as a cleaning agent Convert 87 mmol of ammonia, NH 3(g), into mass in grams 7 1,4benzenedioic acid, C 8 H 6 O 4 (s), is a raw material used in the manufacture of Dacron, a synthetic fibre (Figure 1) What is the mass in grams of 6328 mol of 1,4benzenedioic acid? 8 If a patient is prescribed mol of acetylsalicylic acid (Aspirin, C 9 H 8 O 4(s) ), what mass of Aspirin should she take? Figure 1 Dacron is a type of polyester made from 1,4benzendioic acid (a) Dacron tubes reinforce a damaged artery (b) Dacron fibres are used as insulation in sleeping bags Answers 5 26 g 6 15 g kg g Calculations Involving Number of Entities We often need to know the number of entities in a sample of a substance When dealing with gases, for example, the number of atoms or molecules in a container is related to other factors, such as the temperature and the pressure of the gas We will first look at how we can convert an amount in moles into the number of entities We know there are always entities in a mole of substance If we have 20 mol of copper, then there will be copper atoms The number of entities, N, in an amount in moles is calculated by multiplying the amount in moles by ,Avogadro s constant: N nn A In the case of 20 mol of copper atoms, N Cu 20 mol atoms 1 l mo There are atoms in 20 mol of copper metal 3 Quantities in Chemical Formulas 173
4 Now let s look at calculating the number of entities in a given mass How many copper atoms do you think there are in a penny? (We ll assume our pennies are dated before 1997, since after this time they were no longer made of copper, but copperplated zinc) The calculations are similar to the preceding example; however, since we are not told the amount in moles, we need to first convert the mass into amount in moles Our strategy is first to measure the mass of the penny (Figure 2) Then we convert the mass into amount in moles Finally, we can convert the amount in moles to number of atoms Mass and number of entities are both easily converted to amount in moles, so the middle step in these conversions is always to determine the amount in moles Suppose we measured the mass of a penny and found it to be 263 g We will convert this mass to amount in moles of copper atoms M Cu(s) 6355 g/mol Figure 2 To reduce error in determining the mass of a single penny, we can find the mass of 150 pennies and divide the total mass by 150 Therefore, 1 mol n Cu(s) 263 g g n Cu(s) mol We now simply multiply the amount in moles by N A : N Cu(s) mol l mo N Cu(s) There are atoms in a copper penny Sample Problem 3 Determine the number of chloride ions in 0563 mol of calcium chloride, CaCl 2(s) n CaCl mol N CaCl mol l mo N CaCl There are formula units in 0563 mol of CaCl 2 Since each formula unit (CaCl 2 ) contains two chloride ions, there are 2 ( ), , chloride ions in 0563 mol of calcium chloride 174 Chapter 4
5 44 Sample Problem 4 How many sugar (sucrose, C 12 ) molecules are there in a 1000 kg bag of sugar? M C12 O [( ) + (22 101) + ( )] g/mol 11(s) m 1000 kg 1 mol n C12 O g g mol N C12 O mol m l o N C12 O There are sugar molecules in a 1000 kg bag of sucrose Sample Problem 5 What is the mass of one water molecule (Figure 3)? M H2 O (2 101) + (1 1600) 1802 g/mol Since there are molecules/mol, m H2 O g 1 m l o 1 ol m Figure 3 The mass of one water molecule is an unimaginable 299 x g m H2 O g The mass of one water molecule is g SUMMARY Calculating Mass, Amounts in Moles, and Number of Entities 1 n represents the amount in moles, m the mass measured, M the molar mass, N the number of entities, and N A Avogadro s constant (Table 1) m 2 n M 3 m nm 4 N nn A Table 1: Stoichiometry, Symbols and Units Symbol Quantity Unit n amount in moles mol m mass mg, g, kg M molar mass g/mol N number of entities atoms, ions, formula units, molecules N A Avogadro s constant, Quantities in Chemical Formulas 175
6 Try This Activity Counting Atoms, Molecules, and Other Entities Using the materials and equipment supplied, calculate and measure the quantities described in each of the steps below Write an explanation of your calculations Materials: balance, graduated cylinder, beaker, disposable cups, copper pennies, iron nails, granulated sugar, table salt, chalk, water Determine the mass of a drop of water by measuring the mass of 50 drops of water Place a single drop of water on the lab bench and record the time it takes for it to completely evaporate Calculate how many molecules of water evaporate per second Calculate the number of copper atoms in a penny and use that number to calculate the value of each atom of copper in the penny Measure into a graduated cylinder half a mole of sucrose molecules (C 12 ) Record the reading on the graduated cylinder Measure into a graduated cylinder the quantity of sugar that contains two moles of carbon atoms Record the reading on the graduated cylinder Measure the mass of a piece of chalk Use the piece of chalk to write your full name on the chalkboard Measure the mass of the chalk again Calculate the number of atoms that were needed to write your name (assume chalk is made entirely of calcium carbonate) Dissolve 300 g of table salt (assume NaCl (s) ) in 200 ml of water Calculate the number of sodium ions in the salt solution Calculate the number of iron atoms in the iron nail Calculate the number of years to span a mole of seconds Answers 9 (a) 1802 g/mol (b) 4401 g/mol (c) 5844 g/mol (d) g/mol (e) g/mol 10 (a) 2921 mol (b) 856 mol (c) 0907 mol (d) mol (e) 245 mol 11 (a) 719 g (b) 896 g (c) 103 g (d) kg (e) g 12 (a) molecules (b) molecules Practice 9 Calculate the molar mass of each of the following substances: (a) H 2 O (l) (water) (b) CO 2(g) (respiration product) (c) NaCl (s) (pickling salt, sodium chloride) (d) C 12 (table sugar, sucrose) (e) (NH 4 ) 2 Cr 2 O 7(s) (ammonium dichromate) 10 Calculate the amount of pure substance present (in moles) in each of the following samples of pure substances: (a) a 1000kg bag of table sugar (b) a 500g box of pickling salt (c) 400 g of propane, C 3 H 8(g), in a campstove cylinder (d) 325 mg of acetylsalicylic acid (Aspirin), HC 9 H 7 O 4(s), in a headacherelief tablet (e) 150 g of 2propanol (rubbing alcohol), CH 3 CH 2 OHCH 3(l), from a pharmacy 11 Calculate the mass of each of the following substances: (a) 422 mol of ammonia in a windowcleaning solution (b) 0224 mol of sodium hydroxide in a draincleaning solution (c) 573 mmol of water vapour produced by a laboratory burner (d) 944 kmol of potassium permanganate fungicide (e) 077 mol of ammonium sulfate fertilizer 12 Calculate the number of entities in each of the following samples: (a) 15 mol of solid carbon dioxide, in dry ice (b) 15 g of ammonia gas, in household cleaners 176 Chapter 4
7 44 (c) 15 g of hydrogen chloride gas, in hydrochloric acid (d) 15 g of sodium chloride, in table salt 13 Calculate the mass, in grams, of the characteristic entity in each of the following samples: (a) carbon dioxide from respiration (b) glucose from photosynthesis (c) oxygen from photosynthesis 14 How many water molecules are in a 1000 L bottle of water? (Recall the density of water is 100 g/ml) Answers 12 (c) molecules (d) formula units 13 (a) g (b) g (c) g molecules Section 44 Questions 1 (a) Calculate the number of oxygen molecules in 15 mol of oxygen gas, O 2(g) (b) Calculate the number of atoms in 15 mol of O 2(g) 2 A daily vitamin tablet contains 90 mg of vitamin C The chemical name for vitamin C is ascorbic acid, H 2 C 6 H 6 O 6 How many molecules of vitamin C are you taking each day if you take a daily vitamin tablet? 3 A thyroid condition called goitre can be treated by increasing iodine in the diet Iodized salt contains calcium iodate, Ca(IO 3 ) 2(s), which is added to table salt (a) How many atoms of iodine are in mol of calcium iodate? (b) What is the mass of calcium iodate that contains that many atoms of iodine? 4 A recipe for a sweetandsour sauce calls for 500 g water 200 g sugar (C 12 ) 25 g vinegar (assume acetic acid), HC 2 H 3 O 2(l) 15 g citric acid (C 6 H 8 O 7(s) ) 5 g salt (NaCl (s) ) Convert the recipe into amounts in moles 5 If necessary, use density as a conversion factor to answer the following questions (The density of elements can be referenced on the periodic table) (a) If the density of pure ethanol is 0789 g/ml, how many ethanol molecules are there in a 17mL sample of ethanol, the approximate quantity of ethanol in a bottle of beer? (b) How many nickel atoms are there in 072 cm 3 of a nickel sample, the approximate volume of a Canadian quarter? (c) How many water molecules are there in a 100mL sample of pure water? Applying Inquiry Skills 6 Silver ions in waste solutions can be recovered by immersing copper metal in the solution (Figure 4) The solid copper loses mass as copper goes into solution as ions Crystals of silver are deposited on the copper metal Design an experiment to determine the ratio of the amount in moles of copper ions dissolved to (continued) Figure 4 When copper metal is placed in a solution of silver ions, a single displacement reaction occurs Copper ions go into solution and silver crystals are formed Quantities in Chemical Formulas 177
8 the amount in moles of silver atoms formed Describe the procedure, materials, and equipment used, safety procedures, and explain the calculations needed Making Connections 7 Suppose that there is a prestigious award given by the Academy of Science each year to the most significant scientific concept Write a paper nominating the mole concept for this award, citing the mole s role and importance in the application of chemical reactions in society, industry, and the environment 45 Percentage Composition Figure 1 This experimental car burns hydrogen as a fuel, producing water vapour as an exhaust The dish collects solar energy, which is used to dissociate water into hydrogen and oxygen Using molar mass values from a periodic table, we can calculate the mass of reactants and products in chemical reactions if we already know the chemical formulas However, when a new substance is produced, we first need to determine its chemical formula To do this, we need to determine the chemical composition of the compound, that is, what elements it is made of and the quantities of each element In this section, we will experimentally determine the composition by mass of a substance and then convert the mass amounts to percentages, to give us the percentage composition We can then use atomic mass and molar mass to determine the correct chemical formula Before we begin, we will practise the mathematical steps in the calculation of percentage composition from mass measurements of reactants and products Let s consider 20 g of red jelly beans mixed with 30 g of green jelly beans What is the percentage composition of the mixture, by mass? The percentage of red jelly beans by mass would be 20 g of the total 50 g, which is 20 g/50 g 100%, or 40% Similarly, the percentage of green jelly beans would be 30 g of the total 50 g, which is 60% Now let s look at the percentage composition of water Water is formed when hydrogen is allowed to react with oxygen, a reaction that gives off large amounts of energy (Figure 1) The results of an experiment revealed that 25 g of hydrogen, when completely reacted, produced 225 g of water What is the percentage composition of water by mass? Since 25 g of hydrogen combined with an amount of oxygen to produce 225 g of water, we can calculate the mass of oxygen by subtraction: m H 25 g m H2 O 225 g m O (225 25) g 200 g mh % H m 100% H 2 O 25 g % H 100% 111% 2 25 g Similarly, % O g 100% 22 5 g % O 889% 178 Chapter 4
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