12.E: Stoichiometry Applications (Exercises)

The following questions are related to the material covered in this chapter. For additional discussion on each topic, also check the links included in each heading.

5.1: Stoichiometry

1. Think back to the pound cake recipe. What possible conversion factors can you construct relating the components of the recipe?
2. Think back to the pancake recipe. What possible conversion factors can you construct relating the components of the recipe?
3. What are all the conversion factors that can be constructed from the balanced chemical reaction: \[\ce{2H2(g) + O2(g) → 2H2O(ℓ)}?\]
4. What are all the conversion factors that can be constructed from the balanced chemical reaction N₂(g) + 3H₂(g) → 2NH₃(g)?
5. Given the chemical equation : Na(s) + H₂O(ℓ) → NaOH(aq) + H₂(g)
   1. Balance the equation.
   2. How many molecules of H₂ are produced when 332 atoms of Na react?
6. Given the chemical equation: S(s) + O₂(g) → SO₃(g)
   1. Balance the equation.
   2. How many molecules of O₂ are needed when 38 atoms of S react?
7. For the balanced chemical equation:

6H⁺(aq) + 2MnO₄⁻(aq) + 5H₂O₂(ℓ) → 2Mn²⁺(aq) + 5O₂(g) + 8H₂O(ℓ)

how many molecules of H₂O are produced when 75 molecules of H₂O₂ react?

8. For the balanced chemical reaction 2C₆H₆(ℓ) + 15O₂(g) → 12CO₂(g) + 6H₂O(ℓ)

   how many molecules of CO₂ are produced when 56 molecules of C₆H₆ react?

9. Given the balanced chemical equation Fe₂O₃(s) + 3SO₃(g) → Fe₂(SO₄)₃

   how many molecules of Fe₂(SO₄)₃ are produced if 321 atoms of S are reacted?

10. For the balanced chemical equation CuO(s) + H₂S(g) → CuS + H₂O(ℓ)

    how many molecules of CuS are formed if 9,044 atoms of H react?

11. For the balanced chemical equation Fe₂O₃(s) + 3SO₃(g) → Fe₂(SO₄)₃

    suppose we need to make 145,000 molecules of Fe₂(SO₄)₃. How many molecules of SO₃ do we need?

12. One way to make sulfur hexafluoride is to react thioformaldehyde, CH₂S, with elemental fluorine:

CH₂S + 6F₂ → CF₄ + 2HF + SF₆

If 45,750 molecules of SF₆ are needed, how many molecules of F₂ are required?

13. Construct the three independent conversion factors possible for these two reactions:
    1. 2H₂ + O₂ → 2H₂O
    2. H₂ + O₂ → H₂O₂

Why are the ratios between H₂ and O₂ different?

The conversion factors are different because the stoichiometries of the balanced chemical reactions are different.

14. Construct the three independent conversion factors possible for these two reactions:
    1. 2Na + Cl₂ → 2NaCl
    2. 4Na + 2Cl₂ → 4NaCl

What similarities, if any, exist in the conversion factors from these two reactions?

Answers

1. \[\frac{1\, pound\, butter}{1\, pound\, flour}\] or \[\frac{1\, pound\, sugar}{1\, pound\, eggs}\] are two conversion factors that can be constructed from the pound cake recipe. Other conversion factors are also possible.1 pound butter1 pound flour
2.  

3. 2 molecules H21 molecule O2" role="presentation" style="position:relative;" tabindex="0">\[\frac{2\, molecules\, H_{2}}{1\, molecule\, O_{2}}\] , \[\frac{1\, molecule\, O_{2}}{2\, molecules\, H_{2}O}\] , \[\frac{2\, molecules\, H_{2}}{2\, molecules\, H_{2}O}\] and their reciprocals are the conversion factors that can be constructed. 2 molecules H21 molecule O2" role="presentation" style="position:relative;" tabindex="0">2 molecules H21 molecule O2

4.  
5. 1. 2Na(s) + 2H₂O(ℓ) → 2NaOH(aq) + H₂(g)
   2. 166 molecules
6.  
7. 120 molecules
8.  
9. 107 molecules
10.  
11. 435,000 molecules
12.  
13. 1. \[\frac{2\, molecules\, H_{2}}{1\, molecule\, O_{2}}\ , \frac{1\, molecule\, O_{2}}{2\, molecules\, H_{2}O}\ , \frac{2\, molecules\, H_{2}}{2\, molecules\, H_{2}O}\]
    2. \[\frac{1\, molecules\, H_{2}}{1\, molecule\, O_{2}}\ , \frac{1\, molecule\, O_{2}}{2\, molecules\, H_{2}O_{2}}\ , \frac{1\, molecule\, H_{2}}{1\, molecule\, H_{2}O_{2}}\]

5.4: Mole-Mass and Mass-Mass Calculations

1. What mass of CO₂ is produced by the combustion of 1.00 mol of CH₄?CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(ℓ)
2. What mass of H₂O is produced by the combustion of 1.00 mol of CH₄? CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(ℓ)
3. What mass of HgO is required to produce 0.692 mol of O₂? 2HgO(s) → 2Hg(ℓ) + O₂(g)
4. What mass of NaHCO₃ is needed to produce 2.659 mol of CO₂? 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(ℓ) + CO₂(g)
5. How many moles of Al can be produced from 10.87 g of Ag? Al(NO₃) ₃(s) + 3Ag → Al + 3AgNO₃
6. How many moles of HCl can be produced from 0.226 g of SOCl₂? SOCl₂(ℓ) + H₂O(ℓ) → SO₂(g) + 2HCl(g)
7. How many moles of O₂ are needed to prepare 1.00 g of Ca(NO₃)₂? Ca(s) + N₂(g) + 3O₂(g) → Ca(NO₃) ₂(s)
8. How many moles of C₂H₅OH are needed to generate 106.7 g of H₂O? C₂H₅OH(ℓ) + 3O₂(g) → 2CO₂(g) + 3H₂O(ℓ)
9. What mass of O₂ can be generated by the decomposition of 100.0 g of NaClO₃? 2NaClO₃ → 2NaCl(s) + 3O₂(g)
10. What mass of Li₂O is needed to react with 1,060 g of CO₂? Li₂O(aq) + CO₂(g) → Li₂CO₃(aq)
11. What mass of Fe₂O₃ must be reacted to generate 324 g of Al₂O₃? Fe₂O₃(s) + 2Al(s) → 2Fe(s) + Al₂O₃(s)
12. What mass of Fe is generated when 100.0 g of Al are reacted? Fe₂O₃(s) + 2Al(s) → 2Fe(s) + Al₂O₃(s)
13. What mass of MnO₂ is produced when 445 g of H₂O are reacted? H₂O(ℓ) + 2MnO₄⁻(aq) + Br⁻(aq) → BrO₃⁻(aq) + 2MnO₂(s) + 2OH⁻(aq)
14. What mass of PbSO₄ is produced when 29.6 g of H₂SO₄ are reacted? Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(ℓ)
15. If 83.9 g of ZnO are formed, what mass of Mn₂O₃ is formed with it? Zn(s) + 2MnO₂(s) → ZnO(s) + Mn₂O₃(s)
16. If 14.7 g of NO₂ are reacted, what mass of H₂O is reacted with it? 3NO₂(g) + H₂O(ℓ) → 2HNO₃(aq) + NO(g)
17. If 88.4 g of CH₂S are reacted, what mass of HF is produced? CH₂S + 6F₂ → CF₄ + 2HF + SF₆

18. If 100.0 g of Cl₂ are needed, what mass of NaOCl must be reacted?

NaOCl + HCl → NaOH + Cl₂

Answers

1. 44.0 g
2.  

3. 3.00 × 10² g

4.  

5. 0.0336 mol

6.  

7. 0.0183 mol

8.  

9. 45.1 g

10.  

11. 507 g

12.  

13. 4.30 × 10³ g

14.  

15. 163 g

16.  

17. 76.7 g

5.5: Yields

1. What is the difference between the theoretical yield and the actual yield?
2. What is the difference between the actual yield and the percent yield?
3. A worker isolates 2.675 g of SiF₄ after reacting 2.339 g of SiO₂ with HF. What are the theoretical yield and the actual yield? SiO₂(s) + 4HF(g) → SiF₄(g) + 2H₂O(ℓ)
4. A worker synthesizes aspirin, C₉H₈O₄, according to this chemical equation. If 12.66 g of C₇H₆O₃ are reacted and 12.03 g of aspirin are isolated, what are the theoretical yield and the actual yield? C₇H₆O₃ + C₄H₆O₃ → C₉H₈O₄ + HC₂H₃O₂
5. A chemist decomposes 1.006 g of NaHCO₃ and obtains 0.0334 g of Na₂CO₃. What are the theoretical yield and the actual yield? 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(ℓ) + CO₂(g)
6. A chemist combusts a 3.009 g sample of C₅H₁₂ and obtains 3.774 g of H₂O. What are the theoretical yield and the actual yield? C₅H₁₂(ℓ) + 8O₂(g) → 5CO₂ + 6H₂O(ℓ)
7. What is the percent yield in Exercise 3?
8. What is the percent yield in Exercise 4?
9. What is the percent yield in Exercise 5?

10. What is the percent yield in Exercise 6?

Answers

1. Theoretical yield is what you expect stoichiometrically from a chemical reaction; actual yield is what you actually get from a chemical reaction.
2.  

3. theoretical yield = 4.052 g; actual yield = 2.675 g

4.  

5. theoretical yield = 0.635 g; actual yield = 0.0334 g

6.  

7. 66.02%

8.  

9. 5.26%

5.6: Limiting Reagents

1. The box below shows a group of nitrogen and hydrogen molecules that will react to produce ammonia, NH₃. What is the limiting reagent?

2. The box below shows a group of hydrogen and oxygen molecules that will react to produce water, H₂O. What is the limiting reagent?

3. Given the statement “20.0 g of methane is burned in excess oxygen,” is it obvious which reactant is the limiting reagent?
4. Given the statement “the metal is heated in the presence of excess hydrogen,” is it obvious which substance is the limiting reagent despite not specifying any quantity of reactant?
5. Acetylene (C₂H₂) is formed by reacting 7.08 g of C and 4.92 g of H₂. 2C(s) + H₂(g) → C₂H₂(g)

   What is the limiting reagent? How much of the other reactant is in excess?

6. Ethane (C₂H₆) is formed by reacting 7.08 g of C and 4.92 g of H₂. 2C(s) + 3H₂(g) → C₂H₆(g)

   What is the limiting reagent? How much of the other reactant is in excess?

7. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactant is in excess?

\[\underset{35.6\, g}{P_{4}O_{6}(s)}+6\underset{4.77\, g}{H_{2}O(l)}\rightarrow 4H_{3}PO_{4}\]

8. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactant is in excess?

\[\underset{377\, g}{3NO_{2}(g)}+\underset{244\, g}{H_{2}O(l)}\rightarrow 2HNO_{3}(aq)+NO(g)\]

9. To form the precipitate PbCl₂, 2.88 g of NaCl and 7.21 g of Pb(NO₃)₂ are mixed in solution. How much precipitate is formed? How much of which reactant is in excess?

10. In a neutralization reaction, 18.06 g of KOH are reacted with 13.43 g of HNO₃. What mass of H₂O is produced, and what mass of which reactant is in excess?

Answers

1. Nitrogen is the limiting reagent.
2.  

3. Yes; methane is the limiting reagent.

4.  

5. C is the limiting reagent; 4.33 g of H₂ are left over.

6.  

7. H₂O is the limiting reagent; 25.9 g of P₄O₆ are left over.

8.  

9. 6.06 g of PbCl₂ are formed; 0.33 g of NaCl is left over.

   7 Energy and Chemical Processes

   1. Sulfur dioxide (SO₂) is a pollutant gas that is one cause of acid rain. It is oxidized in the atmosphere to sulfur trioxide (SO₃), which then combines with water to make sulfuric acid (H₂SO₄).

   • Write the balanced reaction for the oxidation of SO₂ to make SO₃. (The other reactant is diatomic oxygen.)

   • When 1 mol of SO₂ reacts to make SO₃, 23.6 kcal of energy are given off. If 100 lb (1 lb = 454 g) of SO₂ were converted to SO₃, what would be the total energy change?

   2. Ammonia (NH₃) is made by the direct combination of H₂ and N₂ gases according to this reaction:

   N₂(g) + 3H₂(g) → 2NH₃(g) + 22.0 kcal

   • Is this reaction endothermic or exothermic?
   • What is the overall energy change if 1,500 g of N₂ are reacted to make ammonia?

   3. A 5.69 g sample of iron metal was heated in boiling water to 99.8°C. Then it was dropped into a beaker containing 100.0 g of H₂O at 22.6°C. Assuming that the water gained all the heat lost by the iron, what is the final temperature of the H₂O and Fe?

   4. A 5.69 g sample of copper metal was heated in boiling water to 99.8°C. Then it was dropped into a beaker containing 100.0 g of H₂O at 22.6°C. Assuming that the water gained all the heat lost by the copper, what is the final temperature of the H₂O and Cu?

   5. When 1 g of steam condenses, 540 cal of energy is released. How many grams of ice can be melted with 540 cal?

   6. When 1 g of water freezes, 79.9 cal of energy is released. How many grams of water can be boiled with 79.9 cal?

   7. The change in energy is +65.3 kJ for each mole of calcium hydroxide [Ca(OH)₂] according to the following reaction:

   Ca(OH)₂(s) → CaO(s) + H₂O(g)

   8. How many grams of Ca(OH)₂ could be reacted if 575 kJ of energy were available?

   9. The thermite reaction gives off so much energy that the elemental iron formed as a product is typically produced in the liquid state:

   2Al(s) + Fe₂O₃(s) → Al₂O₃(s) + 2Fe(ℓ) + 204 kcal

   How much heat will be given off if 250 g of Fe are to be produced?

   10. A normal adult male requires 2,500 kcal per day to maintain his metabolism.

   • Nutritionists recommend that no more than 30% of the calories in a person’s diet come from fat. At 9 kcal/g, what is the maximum mass of fat an adult male should consume daily?
   • At 4 kcal/g each, how many grams of protein and carbohydrates should an adult male consume daily?

   11. A normal adult male requires 2,500 kcal per day to maintain his metabolism.

   • At 9 kcal/g, what mass of fat would provide that many kilocalories if the diet was composed of nothing but fats?
   • At 4 kcal/g each, what mass of protein and/or carbohydrates is needed to provide that many kilocalories?

   12. The volume of the world’s oceans is approximately 1.34 × 10²⁴ cm³.

   • How much energy would be needed to increase the temperature of the world’s oceans by 1°C? Assume that the heat capacity of the oceans is the same as pure water.
   • If Earth receives 6.0 × 10²² J of energy per day from the sun, how many days would it take to warm the oceans by 1°C, assuming all the energy went into warming the water?

   13. Does a substance that has a small specific heat require a small or large amount of energy to change temperature? Explain.

   14. Some biology textbooks represent the conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate ions as follows:

   ATP → ADP + phosphate + energy

   What is wrong with this reaction?

   15. Assuming that energy changes are additive, how much energy is required to change 15.0 g of ice at −15°C to 15.0 g of steam at 115°C? (Hint: you will have five processes to consider.)

   Answers

   1. 2SO₂ + O₂ → 2SO₃
   2. 16,700 kcal

   2.

   exothermic 1177 kcal

   about 23.1°C

   4. about 23.0°C

   5. 6.76 g

   6. 0.148 g

   652 g

   8. 457 kcal

   1. 83.3 g
   2. 438 g

   10.

   a. 278 g

   b. 625 g

   11.

   1.34 × 10²⁴ cal 93 days

   12. A substance with smaller specific heat requires less energy per unit of mass to raise its temperature,

   13. A reactant is missing: H₂O is missing.

   14. Total energy = 11,019 cal

5.7: Additional Exercises

1. How many molecules of O₂ will react with 6.022 × 10²³ molecules of H₂ to make water? The reaction is 2H₂(g) + O₂(g) → 2H₂O(ℓ).
2. How many molecules of H₂ will react with 6.022 × 10²³ molecules of N₂ to make ammonia? The reaction is N₂(g) + 3H₂(g) → 2NH₃(g).
3. How many moles are present in 6.411 kg of CO₂? How many molecules is this?
4. How many moles are present in 2.998 mg of SCl₄? How many molecules is this?
5. What is the mass in milligrams of 7.22 × 10²⁰ molecules of CO₂?
6. What is the mass in kilograms of 3.408 × 10²⁵ molecules of SiS₂?
7. What is the mass in grams of 1 molecule of H₂O?
8. What is the mass in grams of 1 atom of Al?
9. What is the volume of 3.44 mol of Ga if the density of Ga is 6.08 g/mL?
10. What is the volume of 0.662 mol of He if the density of He is 0.1785 g/L?
11. For the chemical reaction 2C₄H₁₀(g) + 13O₂(g) → 8CO₂(g) + 10H₂O(ℓ)

    assume that 13.4 g of C₄H₁₀ reacts completely to products. The density of CO₂ is 1.96 g/L. What volume in liters of CO₂ is produced?

12. For the chemical reaction 2GaCl₃(s) + 3H₂(g) → 2Ga(ℓ) + 6HCl(g)

    if 223 g of GaCl₃ reacts completely to products and the density of Ga is 6.08 g/mL, what volume in milliliters of Ga is produced?

13. Calculate the mass of each product when 100.0 g of CuCl react according to the reaction 2CuCl(aq) → CuCl₂(aq) + Cu(s)

    What do you notice about the sum of the masses of the products? What concept is being illustrated here?

14. Calculate the mass of each product when 500.0 g of SnCl₂ react according to the reaction 2SnCl₂(aq) → SnCl₄(aq) + Sn(s)

    What do you notice about the sum of the masses of the products? What concept is being illustrated here?

15. What mass of CO₂ is produced from the combustion of 1 gal of gasoline? The chemical formula of gasoline can be approximated as C₈H₁₈. Assume that there are 2,801 g of gasoline per gallon.
16. What mass of H₂O is produced from the combustion of 1 gal of gasoline? The chemical formula of gasoline can be approximated as C₈H₁₈. Assume that there are 2,801 g of gasoline per gallon.
17. A chemical reaction has a theoretical yield of 19.98 g and a percent yield of 88.40%. What is the actual yield?
18. A chemical reaction has an actual yield of 19.98 g and a percent yield of 88.40%. What is the theoretical yield?

19. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactants are in excess?

\[\underset{35.0\, g}{P_{4}}+\underset{12.7\, g}{3NaOH}+\underset{9.33\, g}{3H_{2}O}\rightarrow 2Na_{2}HPO_{4}+PH_{3}\]

20. Given the initial amounts listed, what is the limiting reagent, and how much of the other reactants are in excess?

\[\underset{46.3\, g}{2NaCrO_{2}}+\underset{88.2\, g}{3NaBrO_{4}}+\underset{32.5\, g}{2NaOH}\rightarrow 3NaBrO_{3}+2Na_{2}CrO_{4}+H_{2}O\]

21. Verify that it does not matter which product you use to predict the limiting reagent by using both products in this combustion reaction to determine the limiting reagent and the amount of the reactant in excess. Initial amounts of each reactant are given.

\[\underset{26.3\, g}{C_{3}H_{8}}+\underset{21.8\, g}{5O_{2}}\rightarrow 3CO_{2}(g)+4H_{2}O(l)\]

22. Just in case you suspect Exercise 21 is rigged, do it for another chemical reaction and verify that it does not matter which product you use to predict the limiting reagent by using both products in this combustion reaction to determine the limiting reagent and the amount of the reactant in excess. Initial amounts of each reactant are given.

\[\underset{35.0\, g}{2P_{4}}+\underset{12.7\, g}{6NaOH}+\underset{9.33\, g}{6H_{2}O}\rightarrow 3Na_{2}HPO_{4}+5PH_{3}\]

Answers

1. 1.2044 × 10²⁴ molecules
2.  

3. 145.7 mol; 8.77 × 10²⁵ molecules

4.  

5. 52.8 mg

6.  

7. 2.99 × 10⁻²³ g

8.  

9. 39.4 mL

10.  

11. 20.7 L

12.  

13. 67.91 g of CuCl₂; 32.09 g of Cu. The two masses add to 100.0 g, the initial amount of starting material, demonstrating the law of conservation of matter.

14.  

15. 8,632 g

16.  

17. 17.66 g

18.  

19. The limiting reagent is NaOH; 21.9 g of P₄ and 3.61 g of H₂O are left over.

20.  

21. Both products predict that O₂ is the limiting reagent; 20.3 g of C₃H₈ are left over.