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Chapter 10 Quantity Relationships in Chemical Reactions

Chapter 10 Quantity Relationships in Chemical Reactions. Conversion Factors from Equations. The coefficients in a chemical equation give us the conversion factors to convert from the number of moles of one substance, to the number of moles of other substance in a reaction.

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Chapter 10 Quantity Relationships in Chemical Reactions

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  1. Chapter 10Quantity Relationshipsin Chemical Reactions

  2. Conversion Factors from Equations The coefficients in a chemical equation give us the conversion factors to convert from the number of moles of one substance, to the number of moles of other substance in a reaction. 4 NH3(g) + 5 O2 (g)  4 NO(g) + 6 H2O (g)

  3. Conversion Factors from Equations Example: How many moles of water are formed by the reaction of 3.20 moles of ammonia NH3 with oxygen. Step 1: Write and balance the chemical equation:

  4. Conversion Factors from Equations 4 NH3(g) + 5 O2 (g)  4 NO(g) + 6 H2O (g) Step2 Find what is given : 3.20 mol NH3 Step 3 Find what is to be found: ? mol H2O Step 4 Find the path : mol NH3 mol H2O Step 5 : Find the right conversion factor

  5. Conversion Factors from Equations 4 NH3(g) + 5 O2 (g)  4 NO(g) + 6 H2O (g) Step 6 Set up the calculation: 3.20 mol NH3 x (6 mol H2O / 4 mol NH3) = 4.80 mol H2O Note that 6 and 4 are exact numbers; they do not affect the significant figures in the final answer.

  6. Conversion Factors from Equations Example 2 How many moles of oxygen are required to burn 2.40 moles of ethane, C2H6? Step 1: Write the chemical equation 2 C2H6(g) + 7 O2 (g)  4 CO2(g) + 6 H2O (l) • conversion conversion factor  • Number of moles C2H6 number of moles O2: 7 mol O2/ 2 mol C2H6 • Number of moles C2H6 number of moles H2O : 6 mol H2O / 2 mol C2H6 • Number of moles C2H6 number of moles CO2 : 4 mol CO2 / 2 mol C2H6 • Number of moles O2 number of moles CO2 : 4 mol CO2/ 7 mol O2 • Number of moles O2 number of moles H2O : 6 mol H2O / 7 mol O2 • Number of moles CO2 number of moles H2O 6 mol H2O / 4 mol CO2:

  7. Conversion Factors from Equations 2 C2H6(g) + 7 O2 (g)  4 CO2(g) + 6 H2O (l) Step2 Find what is given : 2.40 mol C2H6 Step 3 Find what is to be found: ? mol O2 Step 4 Find the path : mol C2H6 mol O2 Step 5 : Find the right conversion factor 7 mol O2/ 2 mol C2H6

  8. Conversion Factors from Equations 2 C2H6(g) + 7 O2 (g)  4 CO2(g) + 6 H2O (l) Step 6 Set up the calculation: 2.40 mol C2H6 x (7 mol O2/ 2 mol C2H6) = 8.40 mol O2 Note that 7 and 2 are exact numbers; they do not affect the significant figures in the final answer.

  9. Conversion Factors from Equations Example 3 Ammonia is formed from its elements. How many moles of hydrogen are needed to produce 4.20 moles NH3. Chemical equation : N2 + 3 H2 2 NH3

  10. Conversion Factors from Equations N2 + 3 H2 2 NH3 Given 4.20 moles NH3 Wanted mol H2 Path 4.20 moles NH3 mol H2 Factor 3 mol H2/ 2 moles NH3 Calculation 4.20 moles NH3 x (3 mol H2/ 2 moles NH3) = 6.30 mol NH3

  11. Mass–Mass Stoichiometry How to Solve a Stoichiometry Problem: The Stoichiometry Path Step 1: Change the mass of the given species to moles. Step 2: Change the moles of the given species to the moles of the wanted species. Step 3: Change the moles of the wanted species to mass.

  12. Mass–Mass Stoichiometry Mass-to-Mass Stoichiometry Path Mass of Moles of Moles of Mass of Given Given Wanted Wanted Molar Mass Equation Molar Mass coefficients Mass Given × × ×

  13. Mass–Mass Stoichiometry Example 1 Calculate the number of grams of carbon dioxide produced by burning 66.0 g of heptanes C7 H16 (l) Step 1 Chemical reaction : C7H16(l) + 11 O2 (g)  7 CO2(g) + 8 H2O (l) Step2 Find what is given : 66.0 g C7H16 Step 3 Find what is to be found: ? g of CO2

  14. Mass–Mass Stoichiometry C7H16(l) + 11 O2 (g)  7 CO2(g) + 8 H2O (l) Step 4 Find the path : g of C7H16 mol C7H16 mol CO2 g of CO2 Step 5 : Find the right conversion factors g of C7H16 mol C7H16 : 1 mol C2H6/ 100.20 g C7H16 mol C7H16  mol CO2 7 mol CO2/ 1 mol C7H16 mol CO2  g of CO2 44.01 g CO2/ 1 mol CO2

  15. Mass–Mass Stoichiometry C7H16(l) + 11 O2 (g)  7 CO2(g) + 8 H2O (l) Step 6 Set up the calculation:  66.0 g C7H16 x (1 mol C7H16/ 100.20 g C7H16) x (7 mol CO2/ 1 mol C7H16) x (44.01 g CO2/ 1mol CO2) = 203 g of CO2

  16. Percent Yield The actual yield of a chemical reaction is usually less than the ideal yield predicted by a stoichiometry calculation because: • reactants may be impure • the reaction may not go to completion • other reactions may occur Actual yield is experimentally determined.

  17. Percent Yield Percent yield expresses the ratio of actual yield to ideal yield: % yield = × 100%

  18. Percent Yield Example Calculate the theoretical yield of carbon dioxide and the percent yield when burning of 66.0 grams of C7 H16 produced 181 grams of CO2 . C7H16(l) + 11 O2 (g)  7 CO2(g) + 8 H2O (l) Theoretical yield of CO2 66.0 g x ( 1mol C7H16/ 100.20 g C7H16) x ( 7 mol CO2 / 1 mol. C7H16) x ( 44.01 CO2 / 1 mol. CO2 ) = = 203 g CO2 Percent yield = ( 181g/203g) x 100 = 89.2 %

  19. Percent Yield Example: Consider the reaction of hydrogen and nitrogen that forms ammonia with a 92.2% yield. What quantity of ammonia will be produced by reacting 125 g of hydrogen with excess nitrogen? Solution: Use 92.2% yield as a PER expression: 3 H2 + N2 2 NH3 125 g H2 × × × × = 649 g NH3

  20. Limiting Reactants Three atoms of carbon react with two molecules of oxygen: C(g) + O2(g) CO2(g)

  21. Limiting Reactants The reaction will stop when two molecules of oxygen are used up. Two carbon dioxide molecules will form; One carbon atom will remain unreacted: C + O2 CO2 Start 3 2 0 Used (+) or Produced (–) – 2 – 2 + 2 Finish 1 0 2

  22. Limiting Reactants Limiting Reactant The reactant that is completely used up. (Oxygen) Excess Reactant The reactant initially present in excess. (some will remain unreacted) (Carbon)

  23. Limiting Reactants • The reactant that is completely used up by the reaction, is called the limiting reactant. Other reactants have some excess which will remain unreacted. • There are two approaches to solving limiting reactant problems: the comparison of moles method and the smaller amount method.

  24. Limiting Reactants: Compare Moles Comparison-of-Moles Method How to Solve a Limiting Reactant Problem: • Convert the number of grams of each reactant to moles. • Identify the limiting reactant by comparing the theoretical mole ratio of reactants to the actual mole ratio. • Calculate the number of moles of each species that reacts or is produced using the limiting reactant number of moles. • Calculate the number of moles of each species that remains after the reaction. • Change the number of moles of each species to grams.

  25. Limiting Reactants: Compare Moles Example Calculate the mass of antimony(III) iodide that can be produced by the reaction of 129 g antimony, Sb (Z=51), and 381 g iodine. Also find the number of grams of the element that will be left. 2 Sb + 3 I2  2 SbI3 Calculate the number of moles: Moles of Sb = 129 g Sb x (1 mol Sb/ 121.8 g Sb) = 1.06 mol Sb Moles of I2 = 381 g I2 x (1 mol I2 / 253.8 g I2 ) = 1.50 mol I2

  26. Limiting Reactants: Compare Moles 2 Sb + 3 I2  2 SbI3 Theoretical mole ratio: mol of I2 / mol of Sb = 3 mol of I2 / 2 mol of Sb = 1.5 mol of I2 / 1 mol of Sb Actual mole ratio: mol of I2 / mol of Sb = 1.5 mol of I2 / 1.06 mol of Sb =1.42 mol of I2 / 1 mol of Sb Actual mole ratio of iodine over antimony is smaller than theoretical mole ratio, so iodine is the limiting reactant and antimony is in excess.

  27. Limiting Reactants: Compare Moles 2 Sb + 3 I2  2 SbI3 The number of mole Sbused = 1.50 mol of I2 x ( 2 mol of Sb/ 3 mol of I2 ) = 1.00 mol of Sb mol of Sb in excess = (1.06 - 1.00) mol of Sb = 0.06 mol of Sb mass of Sb in excess = 0.06 mol of Sb x (121.8 g Sb/mol Sb) = 7 g Sb

  28. Limiting Reactants: Compare Moles 2 Sb + 3 I2  2 SbI3 The number of mole SbI3 produced = 1.50 mol of I2 x ( 2 mol of SbI3 / 3 mol of I2 ) = 1.00 mol of SbI3 mass of SbI3 produced = 1.00 mol of SbI3 x (502.5 g SbI3 /mol SbI3) = 502.5 g SbI3

  29. Limiting Reactants: Smaller Amount How to Solve a Limiting Reactant Problem by Smaller Amount Method • Calculate the amount of product that can be formed by the initial amount of each reactant. • The reactant that yields the smaller amount of product is the limiting reactant. • The smaller amount of product is the amount that will be formed when all of the limiting reactant is used up. • Calculate the amount of excess reactant that is used by the total amount of limiting reactant. • Subtract from the amount of excess reactant present initially the amount that is used by all of the limiting reactant. The difference is the amount of excess reactant that is left.

  30. Limiting Reactants: Smaller Amount Example Calculate the mass of antimony(III) iodide that can be produced by the reaction of 129 g antimony, Sb (Z=51), and 381 g iodine. Also find the number of grams of the element that will be left. 2 Sb + 3 I2  2 SbI3 Solution: Step 1 is to calculate the amount of product that can be formed by the initial amount of each reactant.

  31. Limiting Reactants: Smaller Amount 2 Sb + 3 I2  2 SbI3 First, assume that antimony is the limiting reactant. Grams of SbI3 produced = 0.129g Sb x(1 mol Sb/121.8 gSb) x (2mol SbI3/2mol Sb) x (502.5 g SbI3 /molSbI3) = = 532 g SbI3

  32. Limiting Reactants: Smaller Amount 2 Sb + 3 I2  2 SbI3 Second, assume that iodine is the limiting reactant. grams of SbCl3 produced = 381g I2 x ( mol I2 / 253.8 g I2 ) x (2mol SbI3/3mol I2) x (502.5 g SbI3 / mol SbI3) = • = 503 g SbI3 • The reactant iodine, which yields the smaller amount (503 g) of SbI3 , is the limiting reactant. • The amount of antimony(III) iodide produced is 503 g.

  33. Limiting Reactants: Smaller Amount 2 Sb + 3 I2  2 SbI3 The amount of antimony required is calculated as follows Grams of antimony required = 381 g I2 x (1 mol I2 /253.8 g I2 ) x (2 mol Sb/ 3 mol I2) x (121.8 g Sb/mol Sb) = 122 g Sb • The amount of antimony in excess = 129 g (initial) – 122g (used) = 7 g Sb (left)

  34. Energy Energy The ability to do work or transfer heat. SI (derived) energy unit: Joule Joule (J): The amount of energy exerted when a force of one newton (force required to cause a mass of 1 kg to accelerate at a rate of 1 m/s2) is applied over a displacement of one meter: 1 joule = 1 newton × 1 meter 1 J = 1 kg • m2/sec2

  35. Energy Non-SI metric energy unit: Calorie calorie (historical definition): Amount of energy required to raise the temperature of 1 g of water by 1°C. calorie (modern definition) 1 cal 4.184 J A food Calorie (Cal) is a thermochemical kilocalorie. In scientific writing it is capitalized; in everyday writing, interpret the context. 1 kcal = 4.184 kJ

  36. Thermochemical Equations Enthalpy H = E + PV Where E is the internal energy of the system, P is the pressure of the system, and V is the volume of the system. P, V, E, H which depend only on the present state of the system, and do not depend on the system’s past or future, are called state functions. ∆H is the enthalpy of reaction. ∆ means “change in”: It is determined by subtracting the initial quantity from the final quantity

  37. Thermochemical Equations Enthalpy of Reaction, ∆H It can be demonstrated that for a reaction studied at constant pressure the heat of reaction is a measure of the change in enthalpy1 for the system. Heat of reaction = H(products) - H (reactants ) = Δ H When a system gives off heat (reaction is exothermic) enthalpy of the system goes down and Δ H has a negative value. When a reaction absorbs heat (reaction is endothermic) enthalpy increases and Δ H is positive. .

  38. Thermochemical Equations There are two ways to write a thermochemical Equation Method 1 The ΔH of the reaction is written to the right of the equation 2 C2H6 (g) + 7O2 (g)  4CO2 (g)+ 6H2O (g) ΔH = -2855 kJ Method 2 Energy is included in the thermochemical equation as if it were a reactant or product. 2 C2H6 (g) + 7O2 (g)  4CO2 (g)+ 6H2O (g) + 2855 kJ

  39. Thermochemical Stoichiometry Since there is a proportional relationship between moles of different substances and heat of reaction, conversion factors can be written between kilojoules and moles of any substance. These factors are used in solving thermochemicalstoichiometry problems.

  40. Thermochemical Stoichiometry Example : How many kilojoules of heat are released when 73.0 g C2H6 (g) burn Equation : 2 C2H6 (g) + 7O2 (g)  4CO2 (g)+ 6H2O (l) + 3119 kJ

  41. Thermochemical Stoichiometry 2 C2H6 (g) + 7O2 (g)  4CO2 (g)+ 6H2O (l) + 3119 kJ Given 73.0 g C2H6 (g)  Wanted : kJ Path g C2H6 (g)  mol C2H6 (g)  kJ Factors (1 mol C2H6 / 30.07 g C2H6 ) (3119 kJ/ 2 mol C2H6 (g))

  42. Thermochemical Stoichiometry 2 C2H6 (g) + 7O2 (g)  4CO2 (g)+ 6H2O (l) + 3119 kJ Solve the problem: 73.0 g C2H6 (g) x (1 mol C2H6 / 30.07 g C2H6) x (3119 kJ/ 2 mol C2H6 (l) ) = = 3.79 x 103 kJ

  43. ThermochemicalStoichiometry Example: When propane, C3H8(g), is burned to form gaseous carbon dioxide and liquid water, 2.22 × 103 kJ of heat is released for every mole of propane burned. What quantity of heat is released when 1.00 × 102 g of propane is burned? Solution: First, write and balance the thermochemical equation to determine the stoichiometric relationships. C3H8 (g) + 5 O2(g)3 CO2(g) + 4 H2O (l) ∆H = –2.22x103kJ

  44. Thermochemical Stoichiometry C3H8 (g) + 5 O2 (g)3 CO2 (g) + 4 H2O (l) ∆H = –2.22 × 103 kJ GIVEN: 1.00 × 102 g C3H8 1 mol C3H8/44.09 g C3H8 PATH: g C3H8 mol C3H8 2.22 × 103 kJ/1 mol C3H8 kJ 1.00 × 102 g C3H8 × × = 5.04 × 103 kJ

  45. HOMEWORK Homework: 1, 7, 23, 35, 45, 47, 67.

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