Problem Solving. Percentage Composition

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1 Skills Worksheet Problem Solving Percentage Composition Suppose you are working in an industrial laboratory. Your supervisor gives you a bottle containing a white crystalline compound and asks you to determine its identity. Several unlabeled drums of this substance have been discovered in a warehouse, and no one knows what it is. You take it into the laboratory and carry out an analysis, which shows that the compound is composed of the elements sodium, carbon, and oxygen. Immediately, you think of the compound sodium carbonate, Na 2, a very common substance found in most laboratories and used in many industrial processes. Before you report your conclusion to your boss, you decide to check a reference book to see if there are any other compounds that contain only the elements sodium, carbon, and oxygen. You discover that there is another compound, sodium oxalate, which has the formula Na 2 C 2 O 4. When you read about this compound, you find that it is highly poisonous and can cause serious illness and even death. Mistaking sodium carbonate for sodium oxalate could have very serious consequences. What can you do to determine the identity of your sample? Is it the common industrial substance or the dangerous poison? Fortunately, you can determine not only which elements are in the compound, but also how much of each element is present. As you have learned, every compound has a definite composition. Every water molecule is made up of two hydrogen atoms and one oxygen atom, no matter where the water came from. A formula unit of sodium chloride is composed of one sodium atom and one chlorine atom, no matter whether the salt came from a mine or was obtained by evaporating sea water. Likewise, sodium carbonate always has two sodium atoms, one carbon atom, and three oxygen atoms per formula unit, giving it the formula Na 2 ; and a formula unit of sodium oxalate always contains two sodium atoms, two carbon atoms, and four oxygen atoms, giving it the formula Na 2 C 2 O 4. Because each atom has a definite mass, each compound will have a distinct composition by mass. This composition is usually expressed as the percentage composition of the compound the percentage by mass of each element in a compound. To identify a compound, you can compare the percentage composition obtained by laboratory analysis with a calculated percentage composition of each possible compound. Holt ChemFile: Problem-Solving Workbook 7 Percentage Composition

2 General Plan for Determining Percentage Composition of a Compound 1 Molar mass of element Convert using the formula of the compound. 2 Mass of element per mole of compound Convert by multiplying by the inverse of the molar mass of the compound. Then convert to a percentage by multiplying by Mass of element in a sample of compound Convert by expressing percentage as a fraction and then multiplying by the mass of the sample. Percentage element in the compound Repeat 1, 2, and for each remaining element in the compound. 4 Percentage composition of the compound Holt ChemFile: Problem-Solving Workbook 74 Percentage Composition

3 Sample Problem 1 Determine the percentage composition of sodium carbonate, Na 2. Solution ANALYZE What is given in the problem? What are you asked to find? the formula of sodium carbonate the percentage of each element in sodium carbonate (the percentage composition) Items Data Formula of sodium carbonate Na 2 Molar mass of each element* Na g/mol C g/mol O g/mol Molar mass of sodium carbonate g/mol Percentage composition of sodium carbonate?% * determined from the periodic table PLAN What step is needed to determine the mass of each element per mole of compound? Multiply the molar mass of each element by the ratio of the number of moles of that element in a mole of the compound (the subscript of that element in the compound s formula). What steps are needed to determine the portion of each element as a percentage of the mass of the compound? Multiply the mass of each element by the inverse of the molar mass of the compound, and then multiply by 100 to convert to a percentage. Step 1 1 Molar mass of Na multiply by the subscript of Na in Na 2 2 Mass Na per mole Na 2 molar mass Na g Na 1 mol Na ratio of mol Na per mol Na 2 from formula 2 mol Na g Na 1 mol Na2 1 mol Na 2 Holt ChemFile: Problem-Solving Workbook 75 Percentage Composition

4 Step 2 2 Mass Na per mole Na 2 multiply by the inverse of the molar mass of Na 2 and multiply by 100 Percentage Na in Na 2 from Step 1 g Na 1 molar mass Na 2 1 mol Na percentage Na in Na2 1 mol Na g Na2 Now you can combine Step 1 and Step 2 into one calculation. combining Steps 1 and g Na 2 mol Na 1 mol Na 2 CO 100 percentage Na in Na 2 1 mol Na 1 mol Na g Na 2 Finally, determine the percentage of carbon and oxygen in Na 2 by repeating the calculation above with each of those elements. Percentage of each element in Na 2 repeat Steps 1 and 2 for each remaining element 4 Percentage composition COMPUTE percentage sodium g Na 1 mol Na percentage carbon g C 1 mol C percentage oxygen g O 1 mol O 2 mol Na 1 mol Na 2 CO % Na 1 mol Na g Na 2 1 mol C 1 mol Na 2 CO % C 1 mol Na g Na 2 mol O 1 mol Na 2 CO % O 1 mol Na g Na 2 Element sodium carbon oxygen EVALUATE Are the units correct? Yes; the composition is given in percentages. Percentage 4.8% Na 11.% C 45.29% O Holt ChemFile: Problem-Solving Workbook 76 Percentage Composition

5 Is the number of significant figures correct? Yes; four significant figures is correct because the molar masses have four significant figures. Is the answer reasonable? Yes; the percentages add up to 100 percent. Practice 1. Determine the percentage composition of each of the following compounds: a. sodium oxalate, Na 2 C 2 O 4 ans: 4.1% Na, 17.9% C, 47.76% O b. ethanol, C 2 H 5 OH ans: 52.1% C, 1.15% H, 4.72% O c. aluminum oxide, Al 2 O ans: 52.92% Al, 47.08% O d. potassium sulfate, K 2 SO 4 ans: 44.87% K, 18.40% S, 6.72% O 2. Suppose that your laboratory analysis of the white powder discussed at the beginning of this chapter showed 42.59% Na, 12.02% C, and 44.99% oxygen. Would you report that the compound is sodium oxalate or sodium carbonate (use the results of Practice Problem 1 and Sample Problem 1)? ans: sodium carbonate Holt ChemFile: Problem-Solving Workbook 77 Percentage Composition

6 Sample Problem 2 Calculate the mass of zinc in a 0.00 g sample of zinc nitrate, Zn(NO. Solution ANALYZE What is given in the problem? What are you asked to find? the mass in grams of zinc nitrate the mass in grams of zinc in the sample Items Mass of zinc nitrate Data 0.00 g Formula of zinc nitrate Zn(NO Molar mass of zinc nitrate g/mol Mass of zinc in the sample? g PLAN What steps are needed to determine the mass of Zn in a given mass of Zn(NO? The percentage of Zn in Zn(NO can be calculated and used to find the mass of Zn in the sample. 1 Molar mass of Zn multiply by the mole ratio of Zn to Zn(NO 2 Mass Zn per mole Zn(NO multiply by the inverse of the molar mass of Zn(NO, then multiply by Mass Zn in g in sample express percentage as a fraction and multiply by the mass of the sample Percentage Zn in Zn(NO molar mass Zn ratio of mol Zn per mol Zn(NO from formula 65.9 g Zn 1 mol Zn 1 mol 100 percentage Zn 1 mol Zn 1 mol Zn(NO g Zn(NO percentage Zn expressed as a fraction 1 molar mass Zn(NO g Zn given g Zn(NO g Zn in sample 100 g Zn(NO COMPUTE 65.9 g Zn 1 mol Zn 1 mol Zn(NO ) % Zn 1 mol Zn 1 mol Zn(NO g Zn(NO Holt ChemFile: Problem-Solving Workbook 78 Percentage Composition

7 Note that mass percentage is the same as grams per 100 g, so 4.52% Zn in Zn(NO is the same as 4.52 g Zn in 100 g Zn(NO g Zn 0.00 g Zn(NO 10.6 g Zn 100 g Zn(NO EVALUATE Are the units correct? Yes; units cancel to give the correct units, grams of zinc. Is the number of significant figures correct? Yes; four significant figures is correct because the data given have four significant figures. Is the answer reasonable? Yes; the molar mass of zinc is about one third of the molar mass of Zn(NO, and 10.6 g Zn is about one third of 0.00 g of Zn(NO. Practice 1. Calculate the mass of the given element in each of the following compounds: a. bromine in 50.0 g potassium bromide, KBr ans:.6 g Br b. chromium in 1.00 kg sodium dichromate, Na 2 Cr 2 O 7 ans: 97 g Cr c. nitrogen in 85.0 mg of the amino acid lysine, C 6 H 14 N 2 O 2 ans: 16. mg N d. cobalt in 2.84 g cobalt(ii) acetate, Co(C 2 H O 2 ans: g Co Holt ChemFile: Problem-Solving Workbook 79 Percentage Composition

8 HYDRATES Many compounds, especially ionic compounds, are produced and purified by crystallizing them from water solutions. When this happens, some compounds incorporate water molecules into their crystal structure. These crystalline compounds are called hydrates because they include water molecules. The number of water molecules per formula unit is specific for each type of crystal. When you have to measure a certain quantity of the compound, it is important to know how much the water molecules contribute to the mass. You may have seen blue crystals of copper(ii) sulfate in the laboratory. When this compound is crystallized from water solution, the crystals include five water molecules for each formula unit of CuSO 4. The true name of the substance is copper(ii) sulfate pentahydrate, and its formula is written correctly as CuSO 4 5H 2 O. Notice that the five water molecules are written separately. They are preceded by a dot, which means they are attached to the copper sulfate molecule. On a molar basis, a mole of CuSO 4 5H 2 O contains 5 mol of water per mole of CuSO 4 5H 2 O. The water molecules contribute to the total mass of CuSO 4 5H 2 O. When you determine the percentage water in a hydrate, the water molecules are treated separately, as if they were another element. Sample Problem Determine the percentage water in copper(ii) sulfate pentahydrate, CuSO 4 5H 2 O. Solution ANALYZE What is given in the problem? What are you asked to find? the formula of copper(ii) sulfate pentahydrate the percentage water in the hydrate Items Data Formula of copper(ii) sulfate pentahydrate Molar mass of H 2 O Molar mass of copper(ii) sulfate pentahydrate* CuSO 4 5H 2 O g/mol g/mol Percentage H 2 O in CuSO 4 5H 2 O?% * molar mass of CuSO 4 mass of 5 mol H 2 O Holt ChemFile: Problem-Solving Workbook 80 Percentage Composition

9 PLAN What steps are needed to determine the percentage of water in CuSO 4 5H 2 O? Find the mass of water per mole of hydrate, multiply by the inverse molar mass of the hydrate, and multiply that by 100 to convert to a percentage g H 2 O 1 mol H 2 O COMPUTE g H 2 O 1 mol H 2 O 1 Molar mass of H 2 O multiply by the mole ratio of H 2 O to CuSO 4 5H 2 O molar mass H 2 O ratio of moles H 2 O per mole CuSO 4 5H 2O from formula 5 mol H 2 O 1 mol CuSO 4 5H 2 O 5 mol H 2 O 1 mol CuSO 4 5H 2 O 2 Mass H 2 O per mole CuSO 4 5H 2 O Percentage H 2 O in CuSO 4 5H 2 O 1 mol CuSO g CuSO 4 5H O 2 5H O 2 1 mol CuSO 4 5H 2 O g CuSO 4 5H 2 O % H 2 O EVALUATE Are the units correct? Yes; the percentage of water in copper(ii) sulfate pentahydrate was needed. Is the number of significant figures correct? Yes; four significant figures is correct because molar masses were given to at least four significant figures. Is the answer reasonable? Yes; five water molecules have a mass of about 90 g, and 90 g is a little more than 1/ of 250 g; the calculated percentage is a little more than 1/. 1 molar mass CuSO 4 5H 2 O multiply by the inverse of the molar mass of CuSO 4 5H 2O; then multiply by percentage H 2 O Holt ChemFile: Problem-Solving Workbook 81 Percentage Composition

10 Practice 1. Calculate the percentage of water in each of the following hydrates: a. sodium carbonate decahydrate, Na 2 10H 2 O ans: 62.97% H 2 O in Na 2 10H 2 O b. nickel(ii) iodide hexahydrate, NiI 2 6H 2 O ans: 25.71% H 2 O in NiI 2 6H 2 O c. ammonium hexacyanoferrate(iii) trihydrate (commonly called ammonium ferricyanide), (NH 4 Fe(CN) 6 H 2 O ans: % H 2 O in (NH 4 Fe(CN) 6 H 2 O d. aluminum bromide hexahydrate ans: 28.85% H 2 O in AlBr 6H 2 O Holt ChemFile: Problem-Solving Workbook 82 Percentage Composition

11 Additional Problems 1. Write formulas for the following compounds and determine the percentage composition of each: a. nitric acid b. ammonia c. mercury(ii) sulfate d. antimony(v) fluoride 2. Calculate the percentage composition of the following compounds: a. lithium bromide, LiBr b. anthracene, C 14 H 10 c. ammonium nitrate, NH 4 NO d. nitrous acid, HNO 2 e. silver sulfide, Ag 2 S f. iron(ii) thiocyanate, Fe(SCN g. lithium acetate h. nickel(ii) formate. Calculate the percentage of the given element in each of the following compounds: a. nitrogen in urea, NH 2 CONH 2 b. sulfur in sulfuryl chloride, SO 2 Cl 2 c. thallium in thallium(iii) oxide, Tl 2 O d. oxygen in potassium chlorate, KClO e. bromine in calcium bromide, CaBr 2 f. tin in tin(iv) oxide, SnO 2 4. Calculate the mass of the given element in each of the following quantities: a. oxygen in 4.00 g of manganese dioxide, MnO 2 b. aluminum in 50.0 metric tons of aluminum oxide, Al 2 O c. silver in 25 g silver cyanide, AgCN d. gold in g of gold(iii) selenide, Au 2 Se e. selenium in 68 g sodium selenite, Na 2 SeO f. chlorine in g of 1,1-dichloropropane, CHCl 2 CH 2 CH 5. Calculate the percentage of water in each of the following hydrates: a. strontium chloride hexahydrate, SrCl 2 6H 2 O b. zinc sulfate heptahydrate, ZnSO 4 7H 2 O c. calcium fluorophosphate dihydrate, CaFPO 2H 2 O d. beryllium nitrate trihydrate, Be(NO H 2 O Holt ChemFile: Problem-Solving Workbook 8 Percentage Composition

12 6. Calculate the percentage of the given element in each of the following hydrates. You must first determine the formulas of the hydrates. a. nickel in nickel(ii) acetate tetrahydrate b. chromium in sodium chromate tetrahydrate c. cerium in cerium(iv) sulfate tetrahydrate 7. Cinnabar is a mineral that is mined in order to produce mercury. Cinnabar is mercury(ii) sulfide, HgS. What mass of mercury can be obtained from 50.0 kg of cinnabar? 8. The minerals malachite, Cu 2 (OH, and chalcopyrite, CuFeS 2, can be mined to obtain copper metal. How much copper could be obtained from kg of each? Which of the two has the greater copper content? 9. Calculate the percentage of the given element in each of the following hydrates: a. vanadium in vanadium oxysulfate dihydrate, VOSO 4 2H 2 O b. tin in potassium stannate trihydrate, K 2 SnO H 2 O c. chlorine in calcium chlorate dihydrate, CaClO 2H 2 O 10. Heating copper sulfate pentahydrate will evaporate the water from the crystals, leaving anhydrous copper sulfate, a white powder. Anhydrous means without water. What mass of anhydrous CuSO 4 would be produced by heating g of CuSO 4 5H 2 O? 11. Silver metal may be precipitated from a solution of silver nitrate by placing a copper strip into the solution. What mass of AgNO would you dissolve in water in order to get 1.00 g of silver? 12. A sample of Ag 2 S has a mass of 62.4 g. What mass of each element could be obtained by decomposing this sample? 1. A quantity of epsom salts, magnesium sulfate heptahydrate, MgSO 4 7H 2 O, is heated until all the water is driven off. The sample loses 11.8 g in the process. What was the mass of the original sample? 14. The process of manufacturing sulfuric acid begins with the burning of sulfur. What mass of sulfur would have to be burned in order to produce 1.00 kg of H 2 SO 4? Assume that all of the sulfur ends up in the sulfuric acid. Holt ChemFile: Problem-Solving Workbook 84 Percentage Composition

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