Stoichiometry Sample Problems PDF

## Sample Problem Set **Name:** **Class:** **Date:** ### Stoichiometry So far in your chemistry course, you have learned that chemists count quantities of elements and compounds in terms of moles and that they relate moles of a substance to mass by using the molar mass. In addition, you have le...

## Sample Problem Set **Name:** **Class:** **Date:** ### Stoichiometry So far in your chemistry course, you have learned that chemists count quantities of elements and compounds in terms of moles and that they relate moles of a substance to mass by using the molar mass. In addition, you have learned to write chemical equations so that they represent the rearrangements of atoms that take place during chemical reactions, and you have learned to balance these equations. In this chapter you will be able to put these separate skills together to accomplish one of the most important tasks of chemistry - using chemical equations to make predictions about the quantities of substances that react or are given off as products and relating those quantities to one another. This process of relating quantities of reactants and products in a chemical reaction to one another is called stoichiometry. **First, look at an analogy.** Suppose you need to make several sandwiches to take on a picnic with friends. You decide to make turkey-and-cheese sandwiches using the following "equation": - 2 bread slices + 2 turkey slices + 1 lettuce leaf + 1 cheese slice → 1 turkey-and-cheese sandwich This equation shows that you need these ingredients in a ratio of 2:2:1:1, respectively. You can use this equation to predict that you would need 30 turkey slices to make 15 sandwiches or 6 cheese slices to go with 12 turkey slices. Zinc reacts with oxygen according to the following balanced chemical equation: - 2Zn + O2 → 2ZnO Like the sandwich recipe, this equation can be viewed as a "recipe" for zinc oxide. It tells you that reacting two zinc atoms with a molecule of oxygen will produce two formula units of zinc oxide. Can you predict how many zinc oxide units could be formed from 500 zinc atoms? Could you determine how many moles of oxygen molecules it would take to react with 4 mol of zinc atoms? What if you had 22 g of zinc and wanted to know how many grams of ZnO could be made from it? Keep in mind that the chemical equation relates amounts, not masses, of products and reactants. The problems in this chapter will show you how to solve problems of this kind. ### **Sample Problem Set continued** ### **General Plan for Solving Stoichiometry Problems** 1. **Mass of substance A** * Convert using the molar mass of A. 2. **Amount in mol of substance A** * Convert using the mole ratio, given in the balanced chemical equation. 3. **Amount in mol of substance B** * Convert using the molar mass of B. 4. **Mass of substance B** ### **Sample Problem Set continued** ### **Sample Problem 1** Ammonia is made industrially by reacting nitrogen and hydrogen under pressure, at high temperature, and in the presence of a catalyst. The equation is N2(g) + 3H2(g) → 2NH3(g). If 4.0 mol of H2 react, how many moles of NH3 will be produced? **Solution** **ANALYZE** * What is given in the problem? The balanced equation, and the amount of H2 in moles * What are you asked to find? The amount of NH3 produced in moles Organization of data is extremely important in dealing with stoichiometry problems. You will find that it is most helpful to make data tables such as the following one. | Items | Substance | Data | |:-------------------|:----------|:-------| | Substance | H2 | 3 | | Coefficient in balanced equation | NH3 | 2 | | Molar mass | NA | NA | | Amount | 4.0 mol | ? mol | | Mass of substance | NA | NA | *NA means not applicable to the problem* **PLAN** What steps are needed to calculate the amount of NH3 that can be produced from 4.0 mol H2? * Multiply by the mole ratio of NH3 to H2 determined from the coefficients of the balanced equation. ``` Amount of H2 in mol (given) * mole ratio (2 mol NH3 / 3 mol H2) = Amount of NH3 in mol ``` **COMPUTE** ``` 4.0 mol H2 * 2 mol NH3 / 3 mol H2 = 2.7 mol NH3 ``` **EVALUATE** * Are the units correct? * Yes; the answer has the correct units of moles NH3. * Is the number of significant figures correct? * Yes; two significant figures is correct because data were given to two significant figures. * Is the answer reasonable? * Yes; the answer is 2/3 of 4.0. **Practice** 1. How many moles of sodium will react with water to produce 4.0 mol of hydrogen in the following reaction? * 2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g) * ans: 8.0 mol Na 2. How many moles of lithium chloride will be formed by the reaction of chlorine with 0.046 mol of lithium bromide in the following reaction? * 2LiBr(aq) + Cl2(g) → 2LiCl(aq) + Br2(l) * ans: 0.046 mol LiCl 3. Aluminum will react with sulfuric acid in the following reaction. * 2Al(s) + 3H2SO4(l) → Al2(SO4)3(aq) + 3H2(g) * a. How many moles of H2SO4 will react with 18 mol Al? * ans: 27 mol H2SO4 * b. How many moles of each product will be produced? * ans: 27 mol H2, 9 mol Al2(SO4)3 4. Propane burns in excess oxygen according to the following reaction. * C3H8 + 5O2 → 3CO2 + 4H2O * a. How many moles each of CO2 and H2O are formed from 3.85 mol of propane? * ans: 11.6 mol CO2, 15.4 mol H2O * b. If 0.647 mol of oxygen is used in the burning of propane, how many moles each of CO2 and H2O are produced? How many moles of C3H8 are consumed? * ans: 0.388 mol CO2, 0.518 mol H2O, 0.129 mol C3H8 ### **Sample Problem Set continued** ### **Sample Problem 2** Potassium chlorate is sometimes decomposed in the laboratory to generate oxygen. The reaction is 2KCIO3(S) →2KCI(s) + 3O2(g). What mass of KCIO3 do you need to produce 0.50 mol O2? **Solution** **ANALYZE** * What is given in the problem? The amount of oxygen in moles * What are you asked to find? The mass of potassium chlorate | Items | Substance | Data | |:--------------------| :--------- |:------| | Substance | KClO3 | 2 | | Coefficient in balanced equation | O2 | 3 | | Molar mass | 122.55 g/mol | NA | | Amount | ? mol | 0.50 mol | | Mass | ? g | NA | *determined from the periodic table* **PLAN** What steps are needed to calculate the mass of KClO3 needed to produce 0.50 mol O2? * Use the mole ratio to convert amount of O2 to the amount of KClO3. Then convert amount of KCIO3 to mass of KCIO3. ``` Amount of O2 in mol * mole ratio (2 mol KCIO3 / 3 mol O2) * molar mass of KCIO3 = Mass of KCIO3 in g ``` **COMPUTE** ``` 0.50 mol O2 * 2 mol KCIO3 / 3 mol O2 * 122.55 g KCIO3 / 1 mol KCIO3 = 41 g KCIO3 ``` **EVALUATE** * Are the units correct? * Yes; units canceled to give grams of KClO3. * Is the number of significant figures correct? * Yes; two significant figures is correct. * Is the answer reasonable? * Yes; 41 g is about 1/3 of the molar mass of KClO3, and 0.5 × 2/3 = 1/3. **Practice** 1. Phosphorus burns in air to produce a phosphorus oxide in the following reaction: * 4P(s) + 5O2(g) → P4O10(S) * a. What mass of phosphorus will be needed to produce 3.25 mol of P4O10? * ans: 403 g P * b. If 0.489 mol of phosphorus burns, what mass of oxygen is used? What mass of P4O10 is produced? * ans: 19.6 g O2, 15.4 g P2O4 2. Hydrogen peroxide breaks down, releasing oxygen, in the following reaction: * 2H2O2(aq) → 2H2O(l) + O2(g) * a. What mass of oxygen is produced when 1.840 mol of H2O2 decomposes? * ans: 29.44 g O2 * b. What mass of water is produced when 5.0 mol O2 is produced by this reaction? * ans: 180 g H2O ### **Sample Problem Set continued** ### **Sample Problem 3** How many moles of aluminum will be produced from 30.0 kg Al2O3 in the following reaction? * 2Al2O3 → 4Al + 3O2 **Solution** **ANALYZE** * What is given in the problem? The mass of aluminum oxide * What are you asked to find? The amount of aluminum produced | Items | Substance | Data | |:------|:----------|:--------| | Substance | Al2O3 | 2 | | Coefficient in balanced equation | Al | 4 | | Molar mass | 101.96 g/mol | NA | | Amount | ? mol | ? mol | | Mass | 30.0 kg | NA | **PLAN** What steps are needed to calculate the amount of Al produced from 30.0 kg of Al2O3? * The molar mass of Al2O3 can be used to convert to moles Al2O3. The mole ratio of Al:Al2O3 from the coefficients in the equation will convert to moles Al from moles Al2O3. ``` Mass of Al2O3 in kg * 1000 g/kg * inverse of the molar mass of Al2O2 * mole ratio (4 mol Al / 2 mol Al2O3) = Amount of Al in mol ``` **COMPUTE** ``` 30.0 kg Al2O3 * 1000 g/kg * 1 mol Al2O3 / 101.96 g Al2O3 * 4 mol Al / 2 mol Al2O3 = 588 mol Al ``` **EVALUATE** * Are the units correct? * Yes; units canceled to give moles of Al. * Is the number of significant figures correct? * Yes; three significant figures is correct. * Is the answer reasonable? * Yes; the molar mass of Al2O3 is about 100, so 30 kg of Al2O3 is about 300 mol. The mole ratio of Al:Al2O3 is 2:1, so the answer should be about 600 mol Al. **Practice** 1. Sodium carbonate reacts with nitric acid according to the following equation. * Na2CO3(s) + 2HNO3 → 2NaNO3 + CO2 + H2O * a. How many moles of Na2CO3 are required to produce 100.0 g of NaNO3? * ans: 0.5882 mol Na2CO3 * b. If 7.50 g of Na2CO3 reacts, how many moles of CO2 are produced? * ans: 0.0708 mol CO2 2. Hydrogen is generated by passing hot steam over iron, which oxidizes to form Fe3O4, in the following equation. * 3Fe(s) + 4H2O(g) → 4H2(g) + Fe3O4(s) * a. If 625 g of Fe3O4 is produced in the reaction, how many moles of hydrogen are produced at the same time? * ans: 10.8 mol H2 * b. How many moles of iron would be needed to generate 27 g of hydrogen? * ans: 10. mol Fe ### **Sample Problem Set continued** ### **Sample Problem 4** Methane burns in air by the following reaction: * CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) What mass of water is produced by burning 500. g of methane? **Solution** **ANALYZE** * What is given in the problem? The mass of methane in grams * What are you asked to find? The mass of water produced | Items | Substance | Data | |:------|:----------|:---------| | Substance | CH4 | 1 | | Coefficient in balanced equation | H2O | 2 | | Molar mass | 16.05 g/mol | 18.02 g/mol | | Amount | ? mol | ? mol | | Mass | 500. g | ? g | **PLAN** What steps are needed to calculate the mass of H2O produced from the burning of 500. g of CH4? * Convert grams of CH4 to moles CH4 by using the molar mass of CH4. Use the mole ratio from the balanced equation to determine moles H2O from moles CH4. Use the molar mass of H2O to calculate grams H2O. ``` Mass of CH4 in g * inverse of the molar mass of CH4 * mole ratio (2 mol H2O / 1 mol CH4) * molar mass of H2O = Mass of H2O in g ``` **COMPUTE** ``` 500. g CH4 * 1 mol CH4 / 16.05 g CH4 * 2 mol H2O / 1 mol CH4 * 18.02 g H2O / 1 mol H2O = 1.12×10³ g H2O ``` **EVALUATE** * Are the units correct? * Yes; mass of H2O was required, and units canceled to give grams H2O. * Is the number of significant figures correct? * Yes; three significant figures is correct because the mass of CH4 was given to three significant figures. * Is the answer reasonable? * Yes; CH4 and H2O have similar molar masses, and twice as many moles of H2O are produced as moles CH4 burned. So, you would expect to get a little more than 1000 g of H2O. **Practice** 1. Calculate the mass of silver bromide produced from 22.5 g of silver nitrate in the following reaction: * 2AgNO3(aq) + MgBr2(aq)→ 2AgBr(s) + Mg(NO3)2(aq) * ans: 24.9 g AgBr 2. What mass of acetylene, C2H2, will be produced from the reaction of 90. g of calcium carbide, CaC2, with water in the following reaction? * CaC2(s) + 2H2O(l) → C2H2(g) + Ca(OH)2(s) * ans: 37 g C2H2 3. Chlorine gas can be produced in the laboratory by adding concentrated hydrochloric acid to manganese(IV) oxide in the following reaction: * MnO2(s) + 4HCl(aq) → MnCl2(aq) + 2H2O(l) + Cl2(g) * a. Calculate the mass of MnO2 needed to produce 25.0 g of Cl2. * ans: 30.7 g MnO2 * b. What mass of MnCl2 is produced when 0.091 g of Cl2 is generated? * ans: 0.16 g MnCl2