# Problem Solving. Mole Concept

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1 Skills Worksheet Problem Solving Mole Concept Suppose you want to carry out a reaction that requires combining one atom of iron with one atom of sulfur. How much iron should you use? How much sulfur? When you look around the lab, there is no device that can count numbers of atoms. Besides, the merest speck (0.001 g) of iron contains over a billion billion atoms. The same is true of sulfur. Fortunately, you do have a way to relate mass and numbers of atoms. One iron atom has a mass of amu, and g of iron contains atoms of iron. Likewise, g of sulfur contains atoms of sulfur. Knowing this, you can measure out g of iron and g of sulfur and be pretty certain that you have the same number of atoms of each. The number is called Avogadro s number. For most purposes it is rounded off to Because this is an awkward number to write over and over again, chemists refer to it as a mole (abbreviated mol) objects is called a mole, just as you call 12 objects a dozen. Look again at how these quantities are related g of iron iron atoms 1 mol of iron g of sulfur sulfur atoms 1 mol of sulfur 1 Mass of substance General Plan for Converting Mass, Amount, and Numbers of Particles Convert using the molar mass of the substance. 2 3 Amount of Number of atoms, substance Use Avogadro's molecules, or formula in moles number for conversion. units of substance Holt ChemFile: Problem-Solving Workbook 48 Mole Concept

2 PROBLEMS INVOLVING ATOMS AND ELEMENTS Sample Problem 1 A chemist has a jar containing g of iron filings. How many moles of iron does the jar contain? Solution ANALYZE What is given in the problem? What are you asked to find? mass of iron in grams amount of iron in moles Items Mass of iron Molar mass of iron* Amount of iron Data g g/mol? mol * determined from the periodic table PLAN What step is needed to convert from grams of Fe to number of moles of Fe? The molar mass of iron can be used to convert mass of iron to amount of iron in moles. 1 Mass of Fe in g multiply by the inverse molar mass of Fe 2 Amount of Fe in mol 1 molar mass Fe given 1 mol Fe g Fe mol Fe g Fe COMPUTE g Fe 1 mol Fe mol Fe g Fe EVALUATE Are the units correct? Yes; the answer has the correct units of moles of Fe. Holt ChemFile: Problem-Solving Workbook 49 Mole Concept

3 Is the number of significant figures correct? Yes; the number of significant figures is correct because there are four significant figures in the given value of g Fe. Is the answer reasonable? Yes; g Fe is about seven times the molar mass. Therefore, the sample contains about 7 mol. 1. Calculate the number of moles in each of the following masses: a g of aluminum ans: 2.38 mol Al b g of silicon ans: 1.00 mol Si c g of sulfur ans: mol S d g of zinc ans: mol Zn Holt ChemFile: Problem-Solving Workbook 50 Mole Concept

4 Sample Problem 2 A student needs mol of zinc for a reaction. What mass of zinc in grams should the student obtain? Solution ANALYZE What is given in the problem? What are you asked to find? amount of zinc needed in moles mass of zinc in grams Items Amount of zinc Molar mass of zinc Mass of zinc Data mol g/mol? g PLAN What step is needed to convert from moles of Zn to grams of Zn? The molar mass of zinc can be used to convert amount of zinc to mass of zinc. 2 Amount of Zn in mol multiply by the molar mass of Zn 1 Mass of Zn in mol molar mass Zn given g Zn mol Zn g Zn 1 mol Zn COMPUTE mol Zn g Zn 1 mol Zn 23.9 g Zn EVALUATE Are the units correct? Yes; the answer has the correct units of grams of Zn. Is the number of significant figures correct? Yes; the number of significant figures is correct because there are three significant figures in the given value of mol Zn. Is the answer reasonable? Yes; mol is about 1/3 mol g is about 1/3 the molar mass of Zn. Holt ChemFile: Problem-Solving Workbook 51 Mole Concept

5 1. Calculate the mass of each of the following amounts: a mol sodium ans: 28.0 g Na b mol copper ans: 921 g Cu c mol mercury ans: 55.2 g Hg d mol magnesium ans: Mg Holt ChemFile: Problem-Solving Workbook 52 Mole Concept

6 Sample Problem 3 How many moles of lithium are there in lithium atoms? Solution ANALYZE What is given in the problem? What are you asked to find? number of lithium atoms amount of lithium in moles Items Number of lithium atoms Avogadro s number the number of atoms per mole Amount of lithium Data atoms atoms/mol? mol PLAN What step is needed to convert from number of atoms of Li to moles of Li? Avogadro s number is the number of atoms per mole of lithium and can be used to calculate the number of moles from the number of atoms. 3 Number of Li atoms multiply by the inverse of Avogadro's number 2 Amount of Li in mol 1 Avogadro's number given 1 mol Li atoms Li mol Li atoms Li COMPUTE mol Li 1024 atoms Li mol Li atoms Li EVALUATE Are the units correct? Yes; the answer has the correct units of moles of Li. Is the number of significant figures correct? Yes; four significant figures is correct. Is the answer reasonable? Yes; is approximately twice Avogadro s number. Therefore, it is reasonable that this number of atoms would equal about 2 mol. Holt ChemFile: Problem-Solving Workbook 53 Mole Concept

7 1. Calculate the amount in moles in each of the following quantities: a atoms of rubidium ans: mol Rb b atoms of krypton ans: mol Kr c atoms of lead ans: mol Pb d atoms of vanadium ans: mol V Holt ChemFile: Problem-Solving Workbook 54 Mole Concept

8 CONVERTING THE AMOUNT OF AN ELEMENT IN MOLES TO THE NUMBER OF ATOMS In Sample Problem 3, you were asked to determine the number of moles in atoms of lithium. Had you been given the amount in moles and asked to calculate the number of atoms, you would have simply multiplied by Avogadro s number. Steps 2 and 3 of the plan for solving Sample Problem 3 would have been reversed. 1. Calculate the number of atoms in each of the following amounts: a mol bismuth ans: atoms Bi b. 2.5 mol manganese ans: atoms Mg c mol helium ans: atoms He d mol strontium ans: atoms Sr Holt ChemFile: Problem-Solving Workbook 55 Mole Concept

9 Sample Problem 4 How many boron atoms are there in 2.00 g of boron? Solution ANALYZE What is given in the problem? What are you asked to find? mass of boron in grams number of boron atoms Items Mass of boron Molar mass of boron Avogadro s number the number of boron atoms per mole of boron Number of boron atoms Data 2.00 g g/mol atoms/mol? atoms PLAN What steps are needed to convert from grams of B to number of atoms of B? First, you must convert the mass of boron to moles of boron by using the molar mass of boron. Then you can use Avogadro s number to convert amount in moles to number of atoms of boron. 1 Mass of B in g multiply by the inverse of the molar mass of boron 2 Amount of B in mol 3 Number of B atoms multiply by Avogadro's number 1 molar mass B Avogadro's number given 1 mol B atoms B g B atoms B g B 1 mol B COMPUTE 1 mol B 2.00 g B atoms B g B 1023 atoms B 1 mol B EVALUATE Are the units correct? Yes; the answer has the correct units of atoms of boron. Is the number of significant figures correct? Yes; the mass of boron was given to three significant figures. Holt ChemFile: Problem-Solving Workbook 56 Mole Concept

10 Is the answer reasonable? Yes; 2 g of boron is about 1/5 of the molar mass of boron. Therefore, 2.00 g boron will contain about 1/5 of an Avogadro s constant of atoms. 1. Calculate the number of atoms in each of the following masses: a g of aluminum ans: atoms Al b g of lanthanum ans: atoms La c g of gallium ans: atoms Ga d g beryllium ans: atoms Be Holt ChemFile: Problem-Solving Workbook 57 Mole Concept

11 CONVERTING NUMBER OF ATOMS OF AN ELEMENT TO MASS Sample Problem 4 uses the progression of steps to convert from the mass of an element to the number of atoms. In order to calculate the mass from a given number of atoms, these steps will be reversed. The number of moles in the sample will be calculated. Then this value will be converted to the mass in grams. 1. Calculate the mass of the following numbers of atoms: a atoms of tantalum ans: g Ta b atoms of cobalt ans: g Co c atoms of argon ans: g Ar d atoms of helium ans: 79.7 g He Holt ChemFile: Problem-Solving Workbook 58 Mole Concept

12 PROBLEMS INVOLVING MOLECULES, FORMULA UNITS, AND IONS How many water molecules are there in g of water? What is the mass of 15.7 mol of nitrogen gas? Both of these substances consist of molecules, not single atoms. Look back at the diagram of the General Plan for Converting Mass, Amount, and Numbers of Particles. You can see that the same conversion methods can be used with molecular compounds and elements, such as CO 2, H 2 O, H 2 SO 4, and O 2. For example, 1 mol of water contains H 2 O molecules. The mass of a molecule of water is the sum of the masses of two hydrogen atoms and one oxygen atom, and is equal to amu. Therefore, 1 mol of water has a mass of g. In the same way, you can relate amount, mass, and number of formula units for ionic compounds, such as NaCl, CaBr 2, and Al 2 (SO 4 ) 3. Sample Problem 5 How many moles of carbon dioxide are in 66.0 g of dry ice, which is solid CO 2? Solution ANALYZE What is given in the problem? What are you asked to find? mass of carbon dioxide amount of carbon dioxide Items Data Mass of CO g Molar mass of CO g/mol Amount of CO 2? mol PLAN What step is needed to convert from grams of CO 2 to moles of CO 2? The molar mass of CO 2 can be used to convert mass of CO 2 to moles of CO 2. 1 Mass of CO 2 in g multiply by the inverse of the molar mass of CO 2 2 Amount of CO 2 in mol 1 molar mass CO 2 given 1 mol CO 2 mol CO 2 g CO g CO2 COMPUTE 1 mol CO g CO g CO mol CO 2 Holt ChemFile: Problem-Solving Workbook 59 Mole Concept

13 EVALUATE Are the units correct? Yes; the answer has the correct units of moles CO 2. Is the number of significant figures correct? Yes; the number of significant figures is correct because the mass of CO 2 was given to three significant figures. Is the answer reasonable? Yes; 66 g is about 3/2 the value of the molar mass of CO 2. It is reasonable that the sample contains 3/2 (1.5) mol. 1. Calculate the number of moles in each of the following masses: a g of boron tribromide, BBr 3 ans: mol BBr 3 b g of sodium fluoride, NaF ans: mol NaF c g of methanol, CH 3 OH ans: 23.4 mol CH 3 OH d g of calcium chlorate, Ca(ClO 3 ) 2 ans: mol Ca(ClO 3 ) 2 Holt ChemFile: Problem-Solving Workbook 60 Mole Concept

14 CONVERTING MOLES OF A COMPOUND TO MASS Perhaps you have noticed that Sample Problems 1 and 5 are very much alike. In each case, you multiplied the mass by the inverse of the molar mass to calculate the number of moles. The only difference in the two problems is that iron is an element and CO 2 is a compound containing a carbon atom and two oxygen atoms. In Sample Problem 2, you determined the mass of mol of zinc. Suppose that you are now asked to determine the mass of mol of the molecular compound ammonia, NH 3. You can follow the same plan as you did in Sample Problem 2, but this time use the molar mass of ammonia. 1. Determine the mass of each of the following amounts: a mol of NH 3 ans: g NH 3 b mol of glucose, C 6 H 12 O 6 ans: 21.6 g C 6 H 12 O 6 c mol barium chloride, BaCl 2 ans: g or 1.45 kg BaCl 2 d mol of propane, C 3 H 8 ans: 0.2 g C 3 H 8 Holt ChemFile: Problem-Solving Workbook 61 Mole Concept

15 Sample Problem 6 Determine the number of molecules in mol of hexane, C 6 H 14. Solution ANALYZE What is given in the problem? What are you asked to find? amount of hexane in moles number of molecules of hexane Items Amount of hexane Avogadro s number the number of molecules per mole of hexane Molecules of hexane Data mol molecules/mol? molecules PLAN What step is needed to convert from moles of C 6 H 14 to number of molecules of C 6 H 14? Avogadro s number is the number of molecules per mole of hexane and can be used to calculate the number of molecules from number of moles. 2 Amount of C 6 H 14 in mol multiply by Avogadro's number 3 Number of C 6 H 14 molecules COMPUTE given mol C 6 H 14 Avogadro's number mol C 6 H molecules C 6 H 14 molecules C 1 mol C 6 H 6 H molecules C 6 H 14 1 mol C 6 H molecules C 6 H 14 EVALUATE Are the units correct? Yes; the answer has the correct units of molecules of C 6 H 14. Is the number of significant figures correct? Yes; three significant figures is correct. Is the answer reasonable? Yes; multiplying Avogadro s number by 0.05 would yield a product that is a factor of 10 less with a value of Holt ChemFile: Problem-Solving Workbook 62 Mole Concept

16 1. Calculate the number of molecules in each of the following amounts: a mol of methane, CH 4 ans: molecules CH 4 b mol of nitrogen gas, N 2 ans: molecules N 2 c mol of phosphorus trichloride, PCl 3 ans: molecules PCl 3 d mol of vitamin C, ascorbic acid, C 6 H 8 O 6 ans: molecules C 6 H 8 O 6 Holt ChemFile: Problem-Solving Workbook 63 Mole Concept

17 USING FORMULA UNITS OF IONIC COMPOUNDS Ionic compounds do not exist as molecules. A crystal of sodium chloride, for example, consists of Na ions and Cl ions in a 1:1 ratio. Chemists refer to a combination of one Na ion and one Cl ion as one formula unit of NaCl. A mole of an ionic compound consists of formula units. The mass of one formula unit is called the formula mass. This mass is used in the same way atomic mass or molecular mass is used in calculations. 1. Calculate the number of formula units in the following amounts: a mol of potassium bromide, KBr ans: formula units KBr b mol of magnesium chloride, MgCl 2 ans: formula units MgCl 2 c mol of sodium carbonate, Na 2 CO 3 ans: formula units Na 2 CO 3 d mol of lead(ii) nitrate, Pb(NO 3 ) 2 ans: formula units Pb(NO 3 ) 2 Holt ChemFile: Problem-Solving Workbook 64 Mole Concept

18 CONVERTING NUMBER OF MOLECULES OR FORMULA UNITS TO AMOUNT IN MOLES In Sample Problem 3, you determined the amount in moles of the element lithium. Suppose that you are asked to determine the amount in moles of copper(ii) hydroxide in formula units of Cu(OH) 2. You can follow the same plan as you did in Sample Problem Calculate the amount in moles of the following numbers of molecules or formula units: a formula units of Cu(OH) 2 ans: mol Cu(OH) 2 b molecules of H 2 S ans: mol H 2 S c formula units of nickel(ii) sulfate, NiSO 4 ans: mol NiSO 4 d molecules of hydrogen peroxide, H 2 O 2 ans: mol H 2 O 2 Holt ChemFile: Problem-Solving Workbook 65 Mole Concept

19 Sample Problem 7 What is the mass of a sample consisting of formula units of MgSO 4? Solution ANALYZE What is given in the problem? What are you asked to find? number of magnesium sulfate formula units mass of magnesium sulfate in grams Items Number of formula units of magnesium sulfate Avogadro s number the number of formula units of magnesium sulfate per mole Molar mass of magnesium sulfate Mass of magnesium sulfate Data formula units formula units/mol g/mol? g PLAN What steps are needed to convert from formula units of MgSO 4 to grams of MgSO 4? First, you must convert the number of formula units of MgSO 4 to amount of MgSO 4 by using Avogadro s number. Then you can use the molar mass of MgSO 4 to convert amount in moles to mass of MgSO 4. 3 Number of MgSO 4 formula units 1 Mass of MgSO 4 in g multiply by the inverse of Avogadro's number 2 Amount of MgSO 4 in mol multiply by the molar mass of MgSO 4 1 Avogadro's number given 1 mol MgSO formula units MgSO formula units MgSO 4 molar mass MgSO g MgSO 4 g MgSO 1 mol 4 MgSO4 Holt ChemFile: Problem-Solving Workbook 66 Mole Concept

20 COMPUTE 1 mol MgSO formula units MgSO formula units MgSO 4 EVALUATE Are the units correct? Yes; the answer has the correct units of grams of MgSO 4. Is the number of significant figures correct? Yes; the number of significant figures is correct because data were given to three significant figures. Is the answer reasonable? Yes; 2 g of MgSO 4 is about 1/60 of the molar mass of MgSO 4. Therefore, 2.00 g MgSO 4 will contain about 1/60 of an Avogadro s number of formula units g MgSO 4 1 mol MgSO 4 1. Calculate the mass of each of the following quantities: a molecules of hydrogen, H 2 ans: 8.08 g H g MgSO 4 b formula units of aluminum hydroxide, Al(OH) 3 ans: g Al(OH) 3 c molecules of bromine pentafluoride, BrF 5 ans: 24.0 g BrF 5 d formula units of sodium oxalate, Na 2 C 2 O 4 ans: 26.7 g Na 2 C 2 O 4 Holt ChemFile: Problem-Solving Workbook 67 Mole Concept

21 CONVERTING MOLECULES OR FORMULA UNITS OF A COMPOUND TO MASS In Sample Problem 4, you converted a given mass of boron to the number of boron atoms present in the sample. You can now apply the same method to convert mass of an ionic or molecular compound to numbers of molecules or formula units. 1. Calculate the number of molecules or formula units in each of the following masses: a g of sodium sulfide, Na 2 S ans: formula units Na 2 S b g of nickel(ii) nitrate, Ni(NO 3 ) 2 ans: formula units Ni(NO 3 ) 2 c. 260 mg of acrylonitrile, CH 2 CHCN ans: molecules CH 2 CHCN Holt ChemFile: Problem-Solving Workbook 68 Mole Concept

22 Additional Problems 1. Calculate the number of moles in each of the following masses: a g of palladium b g of iron c kg of tantalum d g of antimony e kg of barium f g of molybdenum 2. Calculate the mass in grams of each of the following amounts: a mol of chromium b. 550 mol of aluminum c mol of neon d. 7 mol of titanium e mol of xenon f mol of lithium 3. Calculate the number of atoms in each of the following amounts: a mol of germanium b mol of copper c mol of tin d mol of carbon e mol of zirconium f mol of potassium 4. Calculate the number of moles in each of the following quantities: a atoms of cobalt b atoms of tungsten c atoms of silver d atoms of plutonium e atoms of radon f. 8 trillion atoms of cerium 5. Calculate the number of atoms in each of the following masses: a g of gold b. 812 g of molybdenum c mg of americium d kg of neon e mg of bismuth f. 37 g of uranium Holt ChemFile: Problem-Solving Workbook 69 Mole Concept

23 6. Calculate the mass of each of the following: a atoms of rubidium b Avogadro s numbers of manganese atoms c atoms of tellurium d Avogadro s numbers of rhodium atoms e atoms of radium f atoms of hafnium 7. Calculate the number of moles in each of the following masses: a g of acetic acid, CH 3 COOH b g of lead(ii) nitrate, Pb(NO 3 ) 2 c kg of iron(iii) oxide, Fe 2 O 3 d mg of ethylamine, C 2 H 5 NH 2 e g of stearic acid, C 17 H 35 COOH f kg of ammonium sulfate, (NH 4 ) 2 SO 4 8. Calculate the mass of each of the following amounts: a mol of selenium oxybromide, SeOBr 2 b. 488 mol of calcium carbonate, CaCO 3 c mol of retinoic acid, C 20 H 28 O 2 d mol of nicotine, C 10 H 14 N 2 e mol of strontium nitrate, Sr(NO 3 ) 2 f mol of uranium hexafluoride, UF 6 9. Calculate the number of molecules or formula units in each of the following amounts: a mol of tungsten(vi) oxide, WO 3 b mol of strontium nitrate, Sr(NO 3 ) 2 c mol of toluene, C 6 H 5 CH 3 d mol of -tocopherol (vitamin E), C 29 H 50 O 2 e mol of hydrazine, N 2 H 4 f mol of nitrobenzene C 6 H 5 NO Calculate the number of molecules or formula units in each of the following masses: a. 285 g of iron(iii) phosphate, FePO 4 b g of C 5 H 5 N c. 85 mg of 2-methyl-1-propanol, (CH 3 ) 2 CHCH 2 OH d g of mercury(ii) acetate, Hg(C 2 H 3 O 2 ) 2 e g of lithium carbonate, Li 2 CO 3 Holt ChemFile: Problem-Solving Workbook 70 Mole Concept

24 11. Calculate the mass of each of the following quantities: a molecules of fluorine, F 2 b formula units of beryllium sulfate, BeSO 4 c molecules of chloroform, CHCl 3 d. 31 billion formula units of chromium(iii) formate, Cr(CHO 2 ) 3 e molecules of nitric acid, HNO 3 f molecules of freon 114, C 2 Cl 2 F Precious metals are commonly measured in troy ounces. A troy ounce is equivalent to 31.1 g. How many moles are in a troy ounce of gold? How many moles are in a troy ounce of platinum? of silver? 13. A chemist needs 22.0 g of phenol, C 6 H 5 OH, for an experiment. How many moles of phenol is this? 14. A student needs mol of iodine crystals, I 2, for an experiment. What mass of iodine crystals should the student obtain? 15. The weight of a diamond is given in carats. One carat is equivalent to 200. mg. A pure diamond is made up entirely of carbon atoms. How many carbon atoms make up a 1.00 carat diamond? g of calcium chloride, CaCl 2, is dissolved in kg of water. a. How many moles of CaCl 2 are in solution? How many moles of water are present? b. Assume that the ionic compound, CaCl 2, separates completely into Ca 2 and Cl ions when it dissolves in water. How many moles of each ion are present in the solution? 17. How many moles are in each of the following masses? a g (1.000 pound) of sucrose (table sugar), C 12 H 22 O 11 b pound of table salt, NaCl 18. When the ionic compound NH 4 Cl dissolves in water, it breaks into one ammonium ion, NH 4, and one chloride ion, Cl. If you dissolved 10.7 g of NH 4 Cl in water, how many moles of ions would be in solution? 19. What is the total amount in moles of atoms in a jar that contains atoms of chromium, atoms of nickel, and atoms of copper? 20. The density of liquid water is g/ml at 25 C. a. Calculate the mass of ml (about a cupful) of water. b. How many moles of water are in ml of water? Hint: Use the result of (a). c. Calculate the volume that would be occupied by mol of water at 25 C. d. What mass of water is mol of water? Holt ChemFile: Problem-Solving Workbook 71 Mole Concept

25 21. An Avogadro s number (1 mol) of sugar molecules has a mass of 342 g, but an Avogadro s number (1 mol) of water molecules has a mass of only 18 g. Explain why there is such a difference between the mass of 1 mol of sugar and the mass of 1 mol of water. 22. Calculate the mass of aluminum that would have the same number of atoms as 6.35 g of cadmium. 23. A chemist weighs a steel cylinder of compressed oxygen, O 2, and finds that it has a mass of g. After some of the oxygen is used in an experiment, the cylinder has a mass of g. How many moles of oxygen gas are used in the experiment? 24. Suppose that you could decompose mol of Ag 2 S into its elements. a. How many moles of silver would you have? How many moles of sulfur would you have? b. How many moles of Ag 2 S are there in 38.8 g of Ag 2 S? How many moles of silver and sulfur would be produced from this amount of Ag 2 S? c. Calculate the masses of silver and sulfur produced in (b). Holt ChemFile: Problem-Solving Workbook 72 Mole Concept

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