# Problem Solving. Percentage Yield

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1 Skills Worksheet Problem Solving Percentage Yield Although we can write perfectly balanced equations to represent perfect reactions, the reactions themselves are often not perfect. A reaction does not always produce the quantity of products that the balanced equation seems to guarantee. This happens not because the equation is wrong but because reactions in the real world seldom produce perfect results. As an example of an imperfect reaction, look again at the equation that shows the industrial production of ammonia. N 2 (g) 3 (g) 2NH 3 (g) In the manufacture of ammonia, it is nearly impossible to produce 2 mol (34.08 g) of NH 3 from the simple reaction of 1 mol (28.02 g) of N 2 and 3 mol (6.06 g) of because some ammonia molecules begin breaking down into N 2 and molecules as soon as they are formed. There are several reasons that real-world reactions do not produce products at a yield of 100%. Some are simple mechanical reasons, such as: Reactants or products leak out, especially when they are gases. The reactants are not 100% pure. Some product is lost when it is purified. There are also many chemical reasons, including: The products decompose back into reactants (as with the ammonia process). The products react to form different substances. Some of the reactants react in ways other than the one shown in the equation. These are called side reactions. The reaction occurs very slowly. This is especially true of reactions involving organic substances. Chemists are very concerned with the yields of reactions because they must find ways to carry out reactions economically and on a large scale. If the yield of a reaction is too small, the products may not be competitive in the marketplace. If a reaction has only a 50% yield, it produces only 50% of the amount of product that it theoretically should. In this chapter, you will learn how to solve problems involving real-world reactions and percentage yield. Holt ChemFile: Problem-Solving Workbook 122 Percentage Yield

2 General Plan for Solving Percentage-Yield Problems 1 Mass of reactants Convert using the molar mass of the reactants. 2 Amount of reactants in mol Convert using the mole ratio of the limiting reactant to the product. 3 Theoretical amount of product in mol Convert using the molar mass of the product. 4 Theoretical mass of product 6 Percentage yield actual yield % yield 100 theoretical yield 5 Actual mass of product Holt ChemFile: Problem-Solving Workbook 123 Percentage Yield

3 Sample Problem 1 Dichlorine monoxide, Cl 2 O is sometimes used as a powerful chlorinating agent in research. It can be produced by passing chlorine gas over heated mercury(ii) oxide according to the following equation: HgO Cl 2 HgCl 2 Cl 2 O What is the percentage yield, if the quantity of reactants is sufficient to produce 0.86 g of Cl 2 O but only 0.71 g is obtained? Solution ANALYZE What is given in the problem? the balanced equation, the actual yield of Cl 2 O, and the theoretical yield of Cl 2 O What are you asked to find? the percentage yield of Cl 2 O Items Substance Mass available Molar mass Amount of reactant Coefficient in balanced equation Actual yield Theoretical yield (moles) Theoretical yield (grams) Data Cl 2 O NA* NA NA NA 0.71 g NA 0.86 g Percentage yield? * Although this table has many Not Applicable entries, you will need much of this information in other kinds of percentage-yield problems. PLAN What steps are needed to calculate the percentage yield of Cl 2 O? Compute the ratio of the actual yield to the theoretical yield, and multiply by 100 to convert to a percentage. Holt ChemFile: Problem-Solving Workbook 124 Percentage Yield

4 4 Theoretical mass of Cl 2 O in g actual yield % yield 100 theoretical yield 5 Actual mass of Cl 2 O in g 6 Percentage yield of Cl 2 O actual mass theoretical mass g Cl 2 O produced 100 percentage yield theoretical g Cl 2 O COMPUTE g Cl2O % yield g Cl O 2 EVALUATE Are the units correct? Yes; the ratio was converted to a percentage. Is the number of significant figures correct? Yes; the number of significant figures is correct because the data were given to two significant figures. Is the answer reasonable? Yes; 83% is about 5/6, which appears to be close to the ratio 0.71/0.86. Practice 1. Calculate the percentage yield in each of the following cases: a. theoretical yield is 50.0 g of product; actual yield is 41.9 g ans: 83.8% yield b. theoretical yield is 290 kg of product; actual yield is 270 kg ans: 93% yield Holt ChemFile: Problem-Solving Workbook 125 Percentage Yield

5 c. theoretical yield is kg of product; actual yield is kg ans: 69.1% yield d. theoretical yield is g of product; actual yield is g ans: 46% yield Holt ChemFile: Problem-Solving Workbook 126 Percentage Yield

6 Sample Problem 2 Acetylene, C 2, can be used as an industrial starting material for the production of many organic compounds. Sometimes, it is first brominated to form 1,1,2,2-tetrabromoethane,, which can then be reacted in many different ways to make other substances. The equation for the bromination of acetylene follows: acetylene 1,1,2,2-tetrabromoethane C 2 2Br2 CHBR 2 If 72.0 g of C 2 reacts with excess bromine and 729 g of the product is recovered, what is the percentage yield of the reaction? Solution ANALYZE What is given in the problem? What are you asked to find? the balanced equation, the mass of acetylene that reacts, and the mass of tetrabromoethane produced the percentage yield of tetrabromoethane Items Data Substance C 2 Mass available 72.0 g available NA Molar mass* g/mol g/mol Amount of reactant? NA Coefficient in balanced equation 1 1 Actual yield NA 729 g Theoretical yield (moles) NA? Theoretical yield (grams) NA? Percentage yield NA? * determined from the periodic table PLAN What steps are needed to calculate the theoretical yield of tetrabromoethane? Set up a stoichiometry calculation to find the amount of product that can be formed from the given amount of reactant. What steps are needed to calculate the percentage yield of tetrabromoethane? Compute the ratio of the actual yield to the theoretical yield, and multiply by 100 to convert to a percentage. Holt ChemFile: Problem-Solving Workbook 127 Percentage Yield

7 1 Mass of C 2 in g multiply by the inverse of the molar mass of C 2 2 Amount of C 2 in mol multiply by mole ratio: C 2 3 Theoretical amount of in mol multiply by the molar mass of 4 Theoretical mass of Percentage yield actual yield % yield 100 theoretical yield 5 Actual mass of COMPUTE 1 molar mass C 2 mole ratio molar mass given 1 mol C g C mol CHBr g CHBr g C 2 1 mol C 2 1 mol theoretical g actual grams theoretical grams g produced 100 percentage yield CHBr theoretical g g C 2 1 mol C 2 1 mol g g C 2 1 mol C 2 1 mol 956 g 729 g CHBr % yield 956 g EVALUATE Are the units correct? Yes; units canceled to give grams of. Also, the ratio was converted to a percentage. Is the number of significant figures correct? Yes; the number of significant figures is correct because the data were given to three significant figures. Is the answer reasonable? Yes; about 3 mol of acetylene were used and the theoretical yield is the mass of about 3 mol tetrabromoethane. Holt ChemFile: Problem-Solving Workbook 128 Percentage Yield

8 Practice 1. In the commercial production of the element arsenic, arsenic(iii) oxide is heated with carbon, which reduces the oxide to the metal according to the following equation: 2As 2 O 3 3C 3CO 2 4As a. If 8.87 g of As 2 O 3 is used in the reaction and 5.33 g of As is produced, what is the percentage yield? ans: 79.3% yield b. If 67 g of carbon is used up in a different reaction and 425 g of As is produced, calculate the percentage yield of this reaction. ans: 76% yield Holt ChemFile: Problem-Solving Workbook 129 Percentage Yield

9 Additional Problems 1. Ethyl acetate is a sweet-smelling solvent used in varnishes and fingernailpolish remover. It is produced industrially by heating acetic acid and ethanol together in the presence of sulfuric acid, which is added to speed up the reaction. The ethyl acetate is distilled off as it is formed. The equation for the process is as follows. acetic acid ethanol SO 4 ethyl acetate CH 3 COOH CH3 C OH CH 3 COOC CH 3 O Determine the percentage yield in the following cases: a g of ethyl acetate should be produced but only 43.9 g is recovered. b mol of ethyl acetate is produced but mol is expected. (Hint: Percentage yield can also be calculated by dividing the actual yield in moles by the theoretical yield in moles.) c mol of ethanol is reacted with excess acetic acid, but only 2.98 mol of ethyl acetate is produced. d. A mixture of 0.58 mol ethanol and 0.82 mol acetic acid is reacted and 0.46 mol ethyl acetate is produced. (Hint: What is the limiting reactant?) 2. Assume the following hypothetical reaction takes place. 2A 7B 4C 3D Calculate the percentage yield in each of the following cases: a. The reaction of mol of A produces mol of C. b. The reaction of 1.19 mol of A produces 1.41 mol of D. c. The reaction of 189 mol of B produces 39 mol of D. d. The reaction of 3500 mol of B produces 1700 mol of C. 3. Elemental phosphorus can be produced by heating calcium phosphate from rocks with silica sand (SiO 2 ) and carbon in the form of coke. The following reaction takes place. Ca 3 (PO 4 ) 2 3SiO 2 5C 3CaSiO 3 2P 5CO a. If 57 mol of Ca 3 (PO 4 ) 2 is used and 101 mol of CaSiO 3 is obtained, what is the percentage yield? b. Determine the percentage yield obtained if 1280 mol of carbon is consumed and 622 mol of CaSiO 3 is produced. c. The engineer in charge of this process expects a yield of 81.5%. If mol of Ca 3 (PO 4 ) 2 is used, how many moles of phosphorus will be produced? 4. Tungsten (W) can be produced from its oxide by reacting the oxide with hydrogen at a high temperature according to the following equation: WO 3 3 W 3 O a. What is the percentage yield if 56.9 g of WO 3 yields 41.4 g of tungsten? Holt ChemFile: Problem-Solving Workbook 130 Percentage Yield

10 b. How many moles of tungsten will be produced from 3.72 g of WO 3 if the yield is 92.0%? c. A chemist carries out this reaction and obtains 11.4 g of tungsten. If the percentage yield is 89.4%, what mass of WO 3 was used? 5. Carbon tetrachloride, CCl 4, is a solvent that was once used in large quantities in dry cleaning. Because it is a dense liquid that does not burn, it was also used in fire extinguishers. Unfortunately, its use was discontinued because it was found to be a carcinogen. It was manufactured by the following reaction: CS 2 3Cl 2 CCl 4 S 2 Cl 2 The reaction was economical because the byproduct disulfur dichloride, S 2 Cl 2, could be used by industry in the manufacture of rubber products and other materials. a. What is the percentage yield of CCl 4 if 719 kg is produced from the reaction of 410. kg of CS 2. b. If 67.5 g of Cl 2 are used in the reaction and 39.5 g of S 2 Cl 2 is produced, what is the percentage yield? c. If the percentage yield of the industrial process is 83.3%, how many kilograms of CS 2 should be reacted to obtain kg of CCl 4? How many kilograms of S 2 Cl 2 will be produced, assuming the same yield for that product? 6. Nitrogen dioxide, NO 2, can be converted to dinitrogen pentoxide, N 2 O 5, by reacting it with ozone, O 3. The reaction of NO 2 takes place according to the following equation: 2NO 2 (g) O 3 (g) N 2 O 5 (s or g) O 2 (g) a. Calculate the percentage yield for a reaction in which 0.38 g of NO 2 reacts and 0.36 g of N 2 O 5 is recovered. b. What mass of N 2 O 5 will result from the reaction of 6.0 mol of NO 2 if there is a 61.1% yield in the reaction? 7. In the past, hydrogen chloride, HCl, was made using the salt-cake method as shown in the following equation: 2NaCl(s) SO 4 (aq) Na 2 SO 4 (s) 2HCl(g) If 30.0 g of NaCl and mol of SO 4 are available, and 14.6 g of HCl is made, what is the percentage yield? 8. Cyanide compounds such as sodium cyanide, NaCN, are especially useful in gold refining because they will react with gold to form a stable compound that can then be separated and broken down to retrieve the gold. Ore containing only small quantities of gold can be used in this form of chemical mining. The equation for the reaction follows. 4Au 8NaCN 2 O O 2 4NaAu(CN) 2 4NaOH a. What percentage yield is obtained if 410 g of gold produces 540 g of NaAu(CN) 2? Holt ChemFile: Problem-Solving Workbook 131 Percentage Yield

11 b. Assuming a 79.6% yield in the conversion of gold to NaAu(CN) 2, what mass of gold would produce 1.00 kg of NaAu(CN) 2? c. Given the conditions in (b), what mass of gold ore that is 0.001% gold would be needed to produce 1.00 kg of NaAu(CN) 2? 9. Diiodine pentoxide is useful in devices such as respirators because it reacts with the dangerous gas carbon monoxide, CO, to produce relatively harmless CO 2 according to the following equation: I 2 O 5 5CO I 2 5CO 2 a. In testing a respirator, 2.00 g of carbon monoxide gas is passed through diiodine pentoxide. Upon analyzing the results, it is found that 3.17 g of I 2 was produced. Calculate the percentage yield of the reaction. b. Assuming that the yield in (a) resulted because some of the CO did not react, calculate the mass of CO that passed through. 10. Sodium hypochlorite, NaClO, the main ingredient in household bleach, is produced by bubbling chlorine gas through a strong lye (sodium hydroxide, NaOH) solution. The following equation shows the reaction that occurs. 2NaOH(aq) Cl 2 (g) NaCl(aq) NaClO(aq) O(l) a. What is the percentage yield of the reaction if 1.2 kg of Cl 2 reacts to form 0.90 kg of NaClO? b. If a plant operator wants to make 25 metric tons of NaClO per day at a yield of 91.8%, how many metric tons of chlorine gas must be on hand each day? c. What mass of NaCl is formed per mole of chlorine gas at a yield of 81.8%? d. At what rate in kg per hour must NaOH be replenished if the reaction produces 370 kg/h of NaClO at a yield of 79.5%? Assume that all of the NaOH reacts to produce this yield. 11. Magnesium burns in oxygen to form magnesium oxide. However, when magnesium burns in air, which is only about 1/5 oxygen, side reactions form other products, such as magnesium nitride, Mg 3 N 2. a. Write a balanced equation for the burning of magnesium in oxygen. b. If enough magnesium burns in air to produce 2.04 g of magnesium oxide but only 1.79 g is obtained, what is the percentage yield? c. Magnesium will react with pure nitrogen to form the nitride, Mg 3 N 2. Write a balanced equation for this reaction. d. If mol of Mg react with nitrogen and mol of Mg 3 N 2 is produced, what is the percentage yield of the reaction? Holt ChemFile: Problem-Solving Workbook 132 Percentage Yield

12 12. Some alcohols can be converted to organic acids by using sodium dichromate and sulfuric acid. The following equation shows the reaction of 1-propanol to propanoic acid. 3CH 3 C C OH 2Na 2 Cr 2 O 7 8 SO 4 3CH 3 C COOH 2Cr 2 (SO 4 ) 3 2Na 2 SO 4 11 O a. If 0.89 g of 1-propanol reacts and 0.88 g of propanoic acid is produced, what is the percentage yield? b. A chemist uses this reaction to obtain 1.50 mol of propanoic acid. The reaction consumes 136 g of propanol. Calculate the percentage yield. c. Some 1-propanol of uncertain purity is used in the reaction. If 116 g of Na 2 Cr 2 O 7 are consumed in the reaction and 28.1 g of propanoic acid are produced, what is the percentage yield? 13. Acrylonitrile, C 3 H 3 N(g), is an important ingredient in the production of various fibers and plastics. Acrylonitrile is produced from the following reaction: C 3 H 6 (g) NH 3 (g) O 2 (g) C 3 H 3 N(g) O(g) If 850. g of C 3 H 6 is mixed with 300. g of NH 3 and unlimited O 2, to produce 850. g of acrylonitrile, what is the percentage yield? You must first balance the equation. 14. Methanol, CH 3 OH, is frequently used in race cars as fuel. It is produced as the sole product of the combination of carbon monoxide gas and hydrogen gas. a. If 430. kg of hydrogen react, what mass of methanol could be produced? b. If kg of methanol are actually produced, what is the percentage yield? 15. The compound, C 6 H 16 N 2, is one of the starting materials in the production of nylon. It can be prepared from the following reaction involving adipic acid, C 6 H 10 O 4 : C 6 H 10 O 4 (l) 2NH 3 (g) 4 (g) C 6 H 16 N 2 (l) 4 O(l) What is the percentage yield if 750. g of adipic acid results in the production of 578 g of C 6 H 16 N 2? 16. Plants convert carbon dioxide to oxygen during photosynthesis according to the following equation: CO 2 O C 6 H 12 O 6 O 2 Balance this equation, and calculate how much oxygen would be produced if g of carbon dioxide reacts with a percentage yield of 63.4%. 17. Lime, CaO, is frequently added to streams and lakes which have been polluted by acid rain. The calcium oxide reacts with the water to form a base that can neutralize the acid as shown in the following reaction: CaO(s) O(l) Ca(OH) 2 (s) If mol of base are needed to neutralize the acid in a lake, and the above reaction has a percentage yield of 54.3%, what is the mass, in kilograms, of lime that must be added to the lake? Holt ChemFile: Problem-Solving Workbook 133 Percentage Yield

13 g CH 3 CHO; 29 g CH 3 C OH remains g HBr g SO a g Tb b. 2.4 g TbF 3 PERCENTAGE YIELD 1. a. 64.3% yield b. 58.0% yield c. 69.5% yield d. CH 3 C OH is limiting; 79% yield 2. a. 69.5% yield b. 79.0% yield c. 48% yield d. 85% yield 3. a. 59% yield b. 81.0% yield c mol P 4. a. 91.8% yield b mol W c g WO 3 5. a. 86.8% yield b. 92.2% yield c kg CS 2 ; kg S 2 Cl 2 6. a. 81% yield b g N 2 O % yield 8. a. 95% yield b g Au c kg ore 9. a. 87.5% yield b g CO 10. a. 71% yield b. 26 metric tons c g NaCl d. 500 kg per hour NaOH 11. a. 2Mg O 2 3 2MgO b. 87.7% yield c. 3Mg N 2 3 Mg 3 N 2 d. 56% yield 12. a. 80.% yield b. 66.2% yield c. 57.1% yield 13. 2C 3 H 6 (g) 2NH 3 (g) 3O 2 (g) 3 2C 3 H 3 N(g) 6 O(g) 91.0% yield 14. a. CO 2 3 CH 3 OH kg b. 91.5% yield % yield 16. 6CO 2 6 O 3 C 6 H 12 O 6 6O g O kg CaO Causes of Change THERMOCHEMISTRY kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol kj/mol 10. a. CH 4 (g) 2O 2 (g) 3 CO 2 (g) 2 O(g) C 3 H 8 (g) 5O 2 (g) 3 3CO 2 (g) 4 O(g) b. for methane: H kj/mol for propane: H 2043 kj/mol c. output methane kj/kg output propane kj/kg Methane yields more energy per mass kj/mol kj/mol kj/mol kj/mol kj/mol K 16. a kj/mol b. 36 kj/mol c kj/mol d. 496 kj/mol e kj/mol Gases GAS LAWS 1. a. 105 kpa b. 5.0 ml c kpa d dm 3 e atm f. 1.5 m m atm dm 3 5. a. 234 K b. 1.2 dm 3 c C d L e. 487 cm 3 f m 3 Holt Chemistry 327 Answer Key

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