Calculations Involving the Mole

Transcription

1 Calculations Involving the Mole 22 When making chocolate chip cookies, it is me convenient to add a particular mass of chocolate chips to the mix than a particular number of chocolate chips (Figure 1) You have learned that the number of small objects in a collection can be calculated if you know the mass of one a small number of the objects and the mass of the collection F example, if you want to make 10 cookies with approximately 10 chocolate chips per cookie, you should add at least 100 chocolate chips to the mix Instead of counting out 100 chocolate chips, you could calculate the mass that contains 100 chocolate chips If the mass of one chocolate chip is 01 g, how many grams of chocolate chips must be added to the cookie mix? Recall that the symbol m represents mass In this example, the key value is 100 chocolate chips, the conversion fact equation is 1 chocolate chip 01 g, and the required value is the mass of chocolate chips, m chocolate chips m chocolate chips 100 chocolate chips m chocolate chips 10 g 01 g 1 chocolate chip You would need to add 10 g of chocolate chips to the mix Calculations Involving Atoms When chemists need a certain amount of a chemical, they cannot count out the atoms, ions, molecules, fmula units Instead, they calculate the mass of the chemical that contains the required amount, just as you would calculate the mass of chocolate chips you need to make cookies Then, using a precise balance, they measure out the calculated mass of the chemical The next three Sample Problems show the relationships among mass, molar mass, and amount when dealing with elements Figure 1 It is me convenient to determine the number of chocolate chips by mass than by counting SAMPLE problem 1 Calculating Mass from Amount in Moles Calculate the mass, in grams, of 200 mol of calcium atoms n Ca 200 mol Ca (key value) Infmation f a conversion fact equation is not given in this problem You can use the molar mass of the element, however, to produce the necessary equation Look up the molar mass of calcium in the periodic table M Ca 4008 g/mol Ca 1 mol Ca 4008 g Ca (conversion fact equation) The required value is the mass of calcium atoms, m Ca (Remember that the symbol m is used to represent mass) NEL Quantities in Chemistry 93

2 Step 3: List Possible Conversion Facts The possible conversion facts are 1 mol Ca 4008 g Ca 4008 g Ca 1 mol Ca Remember that the units in the denominat of the conversion fact must be the same as the units of the key value required value key value conversion fact 4008 g Ca m Ca 200 mol Ca 1 mol Ca m Ca 802 g Ca The mass of 200 mol of calcium is 802 g Calculate the mass of 0200 mol of nitrogen atoms n N 0200 mol N M N 1401 g/mol N 1 mol N 1401 g N 1401 g N m N 0200 mol N 1 mol N m N 280 g N The mass of 0200 mol of nitrogen atoms is 280 g Answers g 2 80 g 1 Calculate the mass of 160 mol of aluminum atoms 2 Calculate the mass of 025 mol of sulfur atoms SAMPLE problem 2 Calculating Amount in Moles from Mass What amount of gold is in a 2758-g nugget of pure gold (Figure 2)? You can use the molar mass of an element to calculate the amount of atoms, in moles, in a sample of known mass Figure 2 Gold is a precious metal that can be mixed with other metals, such as nickel and platinum, to create jewellery m Au 2758 g Au (key value) M Au g/mol Au (value from periodic table) g Au (conversion fact equation) 94 Unit 2 NEL

3 Section 22 The required value is the amount of gold, n Au Step 3: List Possible Conversion Facts The possible conversion facts are g Au g Au required value key value conversion fact n Au 2758 g Au g Au n Au 140 mol Au There is 140 mol of gold in a 2758-g nugget of pure gold What amount of helium is in a balloon that contains 160 g of helium gas (Figure 3)? m He 160 g He M He 400 g/mol He 1 mol He 400 g He 1 mol He n He 160 g He 400 g He n He 0400 mol He Figure 3 Helium is less dense than air and will cause this balloon to float There is 0400 mol of helium in a balloon that contains 160 g of helium gas 3 What amount of iron is in a 330-g iron nail? 4 What amount of silver is in a silver coin that contains 236 g of pure silver? 5 What amount of copper is in a bracelet that contains 765 g of pure copper? Answers mol Fe mol Ag mol Cu So far, you have learned to calculate the mass of an element when the amount is known; the amount (in moles) of an element when the mass is known You can also calculate the number of atoms in an element when the mass is known; the mass of an element when the number of atoms is known NEL Quantities in Chemistry 95

4 In Sample Problem 3, the element (gold) is the same as the element in Sample Problem 2, and it has the same mass, so you can compare the two solutions SAMPLE problem 3 Calculating the Number of Atoms from Mass How many atoms of gold are in a 2758-g nugget of pure gold? You can divide this problem into two parts to solve it In the first part, the molar mass of the element is used to calculate the amount of gold in the nugget, as in Sample Problem 2 In the second part, the amount of gold is used to calculate the number of gold atoms in the nugget Part 1: Calculate Amount of Gold m Au 2758 g Au (key value) M Au g/mol Au g Au (conversion fact equation) The required value f this part of the solution is the amount of gold atoms, n Au Step 3: List Possible Conversion Facts The possible conversion facts are g Au g Au required value key value conversion fact n Au 2758 g Au n Au 140 mol Au g Au Part 2: Calculate Number of Gold Atoms The amount of gold that was calculated in Part 1 is the key value f Part 2 n Au 140 mol Au (key value) The conversion fact equation f this part is obtained from the fact that one mole of atoms contains Avogadro s number of atoms atoms Au (conversion fact equation) The required value is the number of atoms of gold, N Au (Remember that N represents the number of entities) 96 Unit 2 NEL

5 Section 22 Step 3: List Possible Conversion Facts The possible conversion facts are atoms Au n Au 140 mol Au 23 atoms Au n Au atoms Au There are atoms of gold in a 2758-g nugget of pure gold Parts 1 and 2 can be combined into a single-line calculation by substituting the key value given in the problem and the conversion facts from Parts 1 and 2 Notice that conversion fact 1 (from Part 1) converts the mass of gold into the amount of gold Conversion fact 2 (from Part 2) converts the amount of gold into the number of gold atoms required value key value conversion fact 1 conversion fact 2 N Au 2758 g Au atoms Au g Au N Au atoms Au There are atoms of gold in a 2758-g nugget of pure gold atoms Au How many atoms of sulfur are in a 2300-g sample of pure sulfur (Figure 4)? Part 1: Calculate Amount of Sulfur m S 2300 g S M S 3206 g/mol S 1 mol S 3206 g S n S 2300 g S n S 717 mol S 1 mol S 3206 g S Part 2: Calculate Number of Sulfur Atoms N S 717 mol S 23 atoms S 1 mol S N S atoms S Figure 4 Sulfur is a component of black gunpowder, and it is used to improve the strength of natural rubber There are atoms of sulfur in a 2300-g sample of sulfur Alternative single-line solution: N S 2300 g S 1 mol S 3206 g S N S atoms S There are atoms of sulfur in a 2300-g sample of sulfur atoms S 1 mol S NEL Quantities in Chemistry 97

6 Answers C atoms Ne atoms Hg atoms 6 How many atoms of carbon are in a 330-g diamond (pure carbon)? 7 How many atoms of neon are in a neon sign that contains 680 g of neon? 8 How many atoms of mercury are in the bulb of a thermometer, if the mercury has a mass of 782 g? molecular element a molecule that contains two me atoms of one type of element compound a molecule that contains two me atoms of different elements, is a combination of oppositely charged ions The Molar Mass of Molecular Elements and Compounds Molecular elements contain two me atoms of one element only Hydrogen, H 2(g), fluine, F 2(g), ozone, (g), and sulfur, S 8(s), are examples of molecular elements Compounds are molecules that contain two me atoms of different elements, they are combinations of oppositely charged ions represented by fmula units Water, H 2 O (l), carbon dioxide, CO 2(g), and ammonia, NH 3(g), are examples of molecular compounds Sodium chlide, NaCl (s), is an example of an ionic compound The molar mass of a molecule is equal to the sum of the molar masses of all the atoms in the molecule The molar mass of an ionic compound is equal to the sum of the molar masses of all the ions in the fmula unit of the ionic compound F example, the molar mass of hydrogen chlide, HCl (g),is equal to the sum of the molar mass of hydrogen and the molar mass of chline The following Sample Problem shows how to calculate the molar mass of a compound SAMPLE problem 4 Calculating the Molar Mass of a Compound Calculate the molar mass of water In 1 mol of water, there are 2 mol of hydrogen atoms and 1 mol of oxygen atoms Add together the molar masses of these atoms to obtain the molar mass of the compound Notice that you have to multiply the molar mass of hydrogen by 2 because there are two hydrogen atoms in every water molecule M H2 O 2(M H ) 1(M O ) 2(101 g/mol) 1(1600 g/mol) 202 g/mol 1600 g/mol M H2 O 1802 g/mol The molar mass of water is 1802 g/mol Calculate the molar mass of sodium hydrogen carbonate (baking soda), NaHC(s) 98 Unit 2 NEL

7 Section 22 M NaHCO3 1(M Na ) 1(M H ) 1(M C ) 3(M O ) 1(2299 g/mol) 1(101 g/mol) 1(1201 g/mol) 3(1600 g/mol) 2299 g/mol 101 g/mol 1201 g/mol 4800 g/mol M NaHCO g/mol The molar mass of sodium hydrogen carbonate is 8401 g/mol 9 Calculate the molar mass of octane (a component of gasoline), C 8 H 18(l) 10 Calculate the molar mass of acetylsalicylic acid (Aspirin), C 9 O 4(s) 11 Calculate the molar mass of calcium sulfate (gypsum), CaSO 4(s) Answers g/mol g/mol g/mol Calculations Involving Molecules and Compounds Earlier in this section, you learned how to perfm various calculations involving elements The following Sample Problems show how the same principles can be applied to molecules and ionic compounds SAMPLE problem 5 Calculating Mass from Amount in Moles Sodium fluide is added to toothpaste and tap water to help prevent tooth decay Calculate the mass of 200 mol of sodium fluide, NaF (s) n NaF 200 mol NaF (key value) Calculate the molar mass of the compound, M NaF, to determine the conversion fact equation M NaF 1(2299 g/mol) 1(1900 g/mol) M NaF 4199 g/mol NaF 1 mol NaF 4199 g NaF (conversion fact equation) The required value is the mass of sodium fluide, m NaF Step 3: List Possible Conversion Facts The possible conversion facts are 1 mol NaF 4199 g NaF 4199 g NaF 1 mol NaF NEL Quantities in Chemistry 99

8 required value key value conversion fact 4199 g NaF m NaF 200 mol NaF 1 mol NaF m NaF 840 g NaF The mass of 200 mol of sodium fluide is 840 g Calculate the mass of 117 mol of ozone, (g) n O3 117 mol M O3 3(1600 g/mol) M O g/mol 1 mol 4800 g m O3 117 mol m O3 562 g 4800 g 1 mol O3 The mass of 117 mol of ozone is 562 g Answers g g 12 Calculate the mass of 0900 mol of ammonia, NH 3(g) 13 Calculate the mass of 360 mol of freon-12, CCl 2 F 2(g) SAMPLE problem 6 Calculating Amount in Moles from Mass Iron(III) oxide, Fe 2 (s), is me commonly known as rust (Figure 5) What amount of iron(iii) oxide is in a 772-g sample? Figure 5 Cars have steel frames and bodies that rust when exposed to water and oxygen 100 Unit 2 NEL

9 Section 22 m Fe2 O 772 g Fe 3 2 (key value) M Fe2 O 2(5585 g/mol) 3(1600 g/mol) 3 M Fe2 O 1597 g/mol Fe g Fe 2 (conversion fact equation) The required value is the amount of iron(iii) oxide, n Fe2 Step 3: List Possible Conversion Facts The possible conversion facts are 1597 g Fe g Fe 2 1 mol Fe2 required value key value conversion fact n Fe2 772 g Fe 2 n Fe mol Fe g Fe2 There is 0483 mol of iron(iii) oxide in a 772-g sample What amount of propane, C 3 (g), is in a tank that is filled with 500 kg of propane? m C3 500 kg C 3 m C g C 3 M C3 H 3(1201 g/mol) 8(101 g/mol) 8 M C3 H 4411 g/mol C mol C g C 3 n C g C 3 n C3 113 mol C g C 3 1 kg C3 1 mol C g C3 There is 113 mol of propane in a tank with 500 kg of propane in it Alternative single-line solution: n C3 500 kg C g C 3 1 kg C3 1 mol C g C3 n C3 113 mol C 3 There is 113 mol of propane in a tank with 500 kg of propane in it NEL Quantities in Chemistry 101

10 Answers mol mol 14 What amount of magnesium hydroxide, Mg(OH) 2(s), is in 2040 g of magnesium hydroxide? 15 What amount of sucrose (table sugar), C 12 H 22 O 11(s), is in a bag that contains 100 kg of sucrose? You can also calculate the number of entities (molecules fmula units) in a sample of known mass using the fact-label method Notice that singleline solutions are used in the following Sample Problem and SAMPLE problem 7 Calculating the Number of Entities from Mass How many fmula units of the ionic compound iron(iii) oxide, Fe 2 (s), are in 772 g of iron(iii) oxide? m Fe2 O 772 g Fe 3 2 (key value) M Fe2 O 2(5585 g/mol) 3(1600 g/mol) 3 M Fe2 O 1597 g/mol Fe 3 2 The following two conversion fact equations will be used: conversion fact equation 1: 1597 g/mol Fe 2 (from M Fe2 O ) 3 conversion fact equation 2: fmula units Fe 2 (from mole definition) The required value is the number of iron(iii) oxide fmula units, N Fe2 Step 3: List Possible Conversion Facts The possible conversion facts from conversion fact equation 1 are O 1597 g Fe 2 O g Fe2 1 mol Fe2 The possible conversion facts from conversion fact equation 2 are fmula units Fe fmula units Fe 2 Remember to select conversion facts such that the units in the denominat of conversion fact 1 match the units of the key value, and the units in the denominat of conversion fact 2 match the units in the numerat of conversion fact Unit 2 NEL

11 Section 22 required value key value conversion fact 1 conversion fact 2 N Fe2 772 g Fe g Fe2 N Fe fmula units Fe 2 There are fmula units of iron(iii) oxide in a 772-g sample fmula units Fe 2 Calcium hydroxide, Ca(OH) 2(s), is an ionic compound that is used to make slaked lime, a substance that is used as a top-coat on the walls of many homes How many fmula units of calcium hydroxide are in a sample of slaked lime that contains 2500 g of calcium hydroxide? m Ca(OH) g Ca(OH) 2 M Ca(OH)2 1(4008 g/mol) 2(1600 g/mol) 2(101 g/mol) M Ca(OH)2 741 g/mol Ca(OH) 2 N Ca(OH) g Ca(OH) 2 1 mol Ca(OH) g Ca(OH) fmula units Ca(OH) 2 1 mol Ca(OH) 2 N Ca(OH) fmula units Ca(OH) 2 There are fmula units of calcium hydroxide in a sample that contains 2500 g of calcium hydroxide 16 How many molecules of water are in a bottle that contains 2500 g of water? 17 How many fmula units of cobalt(iii) dichromate, Co 2 (Cr 2 O 7 ) 3(s), are in a 330-kg sample? Answers molecules fmula units Calculating the Number of Atoms from the Mass of Molecules Calculating the number of atoms in a sample of molecules can be tricky If the sample contains a molecular element, then the atoms are all the same If the sample contains a compound, however, then there are different atoms to consider The following Sample Problem involves a molecular element, and the involves a compound Note the differences in the two calculations NEL Quantities in Chemistry 103

12 SAMPLE problem 8 Calculating the Number of Atoms Sand is composed of silicon dioxide, SiO 2(s) How many atoms of oxygen are in a bag of pure sand, which contains 100 kg of silicon dioxide? m SiO2 100 kg SiO 2 (key value) M SiO2 1(2809 g/mol) 2(1600 g/mol) M SiO g/mol SiO 2 The following conversion fact equations will be used in the solution: 1kg 1000 g (metric equality) 1 mol SiO g SiO 2 (from M SiO2 ) 1 mol SiO units SiO 2 (from mole definition) 2 atoms O 1 unit SiO 2 (since there are two oxygen atoms per unit of silicon dioxide) The required value is the number of oxygen atoms, N O Step 3: List Possible Conversion Facts See the conversion fact equations in step 1 and the cresponding conversion facts in step 4 There are four conversion facts in this solution N O key value conversion fact 1 conversion fact 2 conversion fact 3 conversion fact g SiO 1 mol SiO units SiO 2 atoms O 100 kg SiO kg SiO g SiO2 1 mol SiO 2 1 unit SiO2 N O atoms O There are atoms of oxygen in a bag that contains 100 kg of pure sand One fm of solid sulfur is composed of S 8(s) molecules How many atoms of sulfur are in an 180-g chunk of solid sulfur? m S8 180 g S 8 M S8 8(3206 g/mol) M S g/mol S 8 1 mol S g S 8 1 mol S molecules S 8 atoms S N S 180 g S g S8 1 mol S8 1 molecule S8 N S atoms S There are atoms of sulfur in an 180-g chunk of solid sulfur 104 Unit 2 NEL

13 Section How many atoms of fluine are in 44 g of fluine gas? 19 How many atoms of nitrogen are in 126 kg of nitrogen gas? 20 How many atoms of hydrogen are in 295 g of ethene, C 2 H 4(g)? 21 How many atoms of oxygen are in 0170 mg of strontium hydroxide, Sr(OH) 2(s)? Answers F atoms N atoms H atoms O atoms SUMMARY Steps in the Fact-Label Method Step 3: List Possible Conversion Facts Use the following solution equation: required value key value conversion fact conversion fact Note: Use as many conversion facts as required TRY THIS activity Counting Atoms, Molecules, and Other Entities Use the following materials to measure and/ calculate the quantity described in each step below Write an explanation of each calculation Materials: balance, graduated cylinder, beaker, disposable cups, copper pennies, iron nails, granulated sugar, table salt, chalk, water 1 Determine the mass of a drop of water by measuring the mass of 50 drops of water 2 Place a single drop of water on the lab bench, and recd the time the drop takes to evapate completely Calculate how many molecules of water evapate per second 3 Calculate the number of copper atoms in a penny Use the number of copper atoms to calculate the monetary value of each atom of copper in the penny Assume that the penny contains pure copper only 4 Measure half a mole of sucrose molecules, C 12 H 22 O 11(s), into a graduated cylinder 5 Measure the quantity of sugar that contains two moles of carbon atoms into a graduated cylinder Recd the reading on the graduated cylinder 6 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 you used to write your name (Assume that chalk is made entirely of calcium carbonate) 7 Dissolve 300 g of table salt (assume NaCl (s) ) in 200 ml of water Calculate the number of sodium ions in the salt solution 8 Calculate the number of iron atoms in an iron nail 9 Calculate the number of years in one mole of seconds NEL Quantities in Chemistry 105

14 Section 22 Questions 1 Magnesium hydroxide, Mg(OH) 2(s), is a key ingredient in some antacid tablets What is the molar mass of magnesium hydroxide? 2 Ozone, (g), is a molecule that protects you from dangerous solar radiation What is the molar mass of ozone in the upper atmosphere? 3 If the molar mass of a substance is 672 g/mol, what is the mass of 80 mol of the substance? 4 Calculate the mass of a mole of sucrose, C 12 H 22 O 11(s) 5 (a) How many atoms of aluminum are in 01 mol of aluminum? (b) How many fmula units of magnesium chlide, MgCl 2(s), are in 35 mol of magnesium chlide? 6 Calculate the amount of entities in each of the following samples of pure substances: (a) 500 kg of table sugar (sucrose), C 12 H 22 O 11(s) (b) 250 g of naphthalene moth balls, C 10 (s) (c) 350 g of propane, C 3 (g), in a camp stove cylinder (d) 275 mg of acetylsalicylic acid (Aspirin), C 9 O 4(s), in a headache relief tablet (e) 240 g of 2-propanol (rubbing alcohol), C 3 O (l) 7 Calculate the mass, in grams, of each of the following substances: (a) 267 mol of ammonia in a window-cleaning solution (b) 0965 mol of sodium hydroxide, NaOH (s), in a drain-cleaning solution (c) 197 mol of water vapour produced by a Bunsen burner (d) 385 mol of potassium permanganate (a fungicide), KMnO 4(s) (e) 047 mol of ammonium sulfate (a fertilizer), (NH 4 ) 2 SO 4(s) 8 Calculate the number of molecules in each of the following samples: (a) 25 mol of solid carbon dioxide in dry ice (b) 25 g of ammonia gas in household cleaning solutions (c) 25 g of hydrogen chlide in hydrochlic acid 9 Calculate the mass, in grams, of 010 mol of each of the following substances: (a) carbon dioxide (b) glucose, C 6 H 12 O 6(s) (c) oxygen gas 10 Calculate the number of oxygen molecules in 27 mol of oxygen gas 11 A daily vitamin tablet contains 90 mg of vitamin C The chemical name f vitamin C is ascbic acid, C 6 O 6(s) If you take one vitamin tablet each day, how many molecules of vitamin C are you taking? 12 A recipe f a sweet and sour sauce calls f the following ingredients: 450 g water 100 g sugar, C 12 H 22 O 11(s) 30 g vinegar (containing 24 g acetic acid, HC 2 H 3 O 2(aq) ) 2 g salt, NaCl (s) Convert the recipe into amounts (in moles) F vinegar, use 24 g of acetic acid Applying Inquiry Skills 13 Silver ions in a solution of silver salts can be recovered by immersing copper metal in the solution (Figure 6) Crystals of pure silver are deposited on the copper metal Design an experiment to determine the number of moles of silver atoms that fm Describe the procedure, materials, and safety procedures Explain the required calculations Making Connections 14 The Academy of Science is giving a prestigious award to the most significant scientific concept Write a brief paper, nominating the mole f this award Cite the role and imptance of the mole in the application of chemical reactions in society, industry, and the environment Figure 6 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 fmed 106 Unit 2 NEL