1 Calculations From Chemical Equations Chapter 9 Hein and Arena Version 1.1

2 Chapter Outline 9.1 A Short ReviewA Short Review 9.2 Introduction to Stoichiometry: The Mole-Ratio MethodIntroduction to Stoichiometry: The Mole-Ratio Method 9.3 Mole-Mole CalculationsMole-Mole Calculations 9.4 Mole-Mass CalculationsMole-Mass Calculations 9.5 Mass-Mass CalculationsMass-Mass Calculations 9.6 Limiting-Reactant and Yield CalculationsLimiting-Reactant and Yield Calculations

3 The molar mass of an element is its atomic mass in grams. It contains x atoms (Avogadro’s number) of the element. The molar mass of an element or compound is the sum of the atomic masses of all its atoms.

4 Avogadro’s Number of Particles x Particles Molar Mass 1 MOLE

5 1 mole = x molecules1 mole = x atoms1 mole = x ions

6 2 2 Al + Fe 2 O 3  Fe + Al 2 O 3  For calculations of mole-mass-volume relationships. –The chemical equation must be balanced. 2 mol 1 mol The equation is balanced. –The coefficient in front of a formula represents the number of moles of the reactant or product.

7 Introduction to Stoichiometry: The Mole-Ratio Method

8 Stoichiometry: The area of chemistry that deals with the quantitative relationships between reactants and products. Mole Ratio: a ratio between the moles of any two substances involved in a chemical reaction. –The coefficients used in mole ratio expressions are derived from the coefficients used in the balanced equation.

9 N 2 + 3H 2  2NH 3 1 mol2 mol3 mol

10 1 mol2 mol3 mol N 2 + 3H 2  2NH 3

11 The mole ratio is used to convert the number of moles of one substance to the corresponding number of moles of another substance in a stoichiometry problem. The mole ratio is used in the solution of every type of stoichiometry problem.

12 The Mole Ratio Method 1.Convert the quantity of starting substance to moles (if it is not already moles) 2.Convert the moles of starting substance to moles of desired substance. 3.Convert the moles of desired substance to the units specified in the problem.

13 Identify the starting substance from the data given in the problem statement. Convert the quantity of the starting substance to moles, if it is not already in moles. Step 1 Determine the number of moles of starting substance.

14 How many moles of NaCl are present in grams of NaCl? The molar mass of NaCl = g.

15 How many moles of NaCl are present in grams of NaCl? The molar mass of NaCl = g.

16 The number of moles of each substance in the balanced equation is indicated by the coefficient in front of each substance. Use these coefficients to set up the mole ratio. Step 2 Determine the mole ratio of the desired substance to the starting substance.

17 Step 2 Determine the mole ratio of the desired substance to the starting substance. Multiply the number of moles of starting substance (from Step 1) by the mole ratio to obtain the number of moles of desired substance.

18 In the following reaction how many moles of PbCl 2 are formed if moles of NaCl react? 2NaCl(aq) + Pb(NO 3 ) 2 (aq)  PbCl 2 (s) + 2NaNO 3 (aq)

19 Step 3. Calculate the desired substance in the units specified in the problem. If the answer is to be in moles, the calculation is complete If units other than moles are wanted, multiply the moles of the desired substance (from Step 2) by the appropriate factor to convert moles to the units required.

20 Step 3. Calculate the desired substance in the units specified in the problem.

21 Step 3. Calculate the desired substance in the units specified in the problem.

22 Step 3. Calculate the desired substance in the units specified in the problem.

23 Mole-Mole Calculations

24 Phosphoric Acid Phosphoric acid (H 3 PO 4 ) is one of the most widely produced industrial chemicals in the world. Most of the world’s phosphoric acid is produced by the wet process which involves the reaction of phosphate rock, Ca 5 (PO 4 ) 3 F, with sulfuric acid (H 2 SO 4 ). Ca 5 (PO 4 ) 3 F(s) + 5H 2 SO 4  3H 3 PO 4 + HF + 5CaSO 4

25 Mole Ratio Calculate the number of moles of phosphoric acid (H 3 PO 4 ) formed by the reaction of 10 moles of sulfuric acid (H 2 SO 4 ). Ca 5 (PO 4 ) 3 F + 5H 2 SO 4  3H 3 PO 4 + HF + 5CaSO 4 Step 1 Moles starting substance: 10.0 mol H 2 SO 4 Step 2 The conversion needed is moles H 2 SO 4  moles H 3 PO 4 1 mol5 mol3 mol1 mol5 mol

26 Step 2 The conversion needed is moles Ca 5 (PO 4 ) 3 F  moles H 2 SO 4 Calculate the number of moles of sulfuric acid (H 2 SO 4 ) that react when 10 moles of Ca 5 (PO 4 ) 3 react. Ca 5 (PO 4 ) 3 F + 5H 2 SO 4  3H 3 PO 4 + HF + 5CaSO 4 Mole Ratio Step 1 The starting substance is 10.0 mol Ca 5 (PO 4 ) 3 F 1 mol5 mol3 mol1 mol5 mol

27 Mole-Mass Calculations

28 1.The object of this type of problem is to calculate the mass of one substance that reacts with or is produced from a given number of moles of another substance in a chemical reaction. 2.If the mass of the starting substance is given, we need to convert it to moles.

29 3.We use the mole ratio to convert moles of starting substance to moles of desired substance. 4.We can then change moles of desired substance to mass of desired substance if called for by the problem.

30 Mole Ratio Calculate the number of moles of H 2 SO 4 necessary to yield 784 g of H 3 PO 4. Ca 5 (PO 4 ) 3 F+ 5H 2 SO 4  3H 3 PO 4 + HF + 5CaSO 4 Method 1 Step by Step Step 1 The starting substance is 784 grams of H 3 PO 4. Step 2 Convert grams of H 3 PO 4 to moles of H 3 PO 4. Step 3 Convert moles of H 3 PO 4 to moles of H 2 SO 4 by the mole-ratio method.

31 Mole Ratio Calculate the number of moles of H 2 SO 4 necessary to yield 784 g of H 3 PO 4 Ca 5 (PO 4 ) 3 F+ 5H 2 SO 4  3H 3 PO 4 + HF + 5CaSO 4 Method 2 Continuous grams H 3 PO 4  moles H 3 PO 4  moles H 2 SO 4 The conversion needed is

32 Method 1 Step by Step Step 1 The starting substance is 12.0 moles of NH 3 Step 2 Calculate moles of H 2 by the mole-ratio method. Step 3 Convert moles of H 2 to grams of H 2. Calculate the number of grams of H 2 required to form 12.0 moles of NH 3. N 2 + 3H 2  2NH 3 Mole Ratio

33 Mole Ratio moles NH 3  moles H 2  grams H 2 Calculate the number of grams of H 2 required to form 12.0 moles of NH 3. N 2 + 3H 2  2NH 3 Method 2 Continuous The conversion needed is

34 Mass-Mass Calculations

35 Solving mass-mass stoichiometry problems requires all the steps of the mole-ratio method. 1.The mass of starting substance is converted to moles. 2.The mole ratio is then used to determine moles of desired substance. 3.The moles of desired substance are converted to mass of desired substance.

36 Calculate the number of grams of NH 3 formed by the reaction of 112 grams of H 2. N 2 + 3H 2  2NH 3 Method 1 Step by Step Step 1 The starting substance is 112 grams of H 2. Convert 112 g of H 2 to moles. grams  moles Step 2 Calculate the moles of NH 3 by the mole ratio method.

37 Calculate the number of grams of NH 3 formed by the reaction of 112 grams of H 2. N 2 + 3H 2  2NH 3 Method 1 Step by Step Step 3 Convert moles NH 3 to grams NH 3. moles  grams

38 Calculate the number of grams of NH 3 formed by the reaction of 112 grams of H 2. N 2 + 3H 2  2NH 3 grams H 2  moles H 2  moles NH 3  grams NH 3 Method 2 Continuous

39 Limiting-Reactant and Yield Calculations

40 It is called the limiting reactant because the amount of it present is insufficient to react with the amounts of other reactants that are present. The limiting reactant limits the amount of product that can be formed. The limiting reactant is one of the reactants in a chemical reaction. Limiting Reactant

41 How many bicycles can be assembled from the parts shown? From eight wheels four bikes can be constructed. From four frames four bikes can be constructed. From three pedal assemblies three bikes can be constructed. The limiting part is the number of pedal assemblies. 9.2

42 H 2 + Cl 2  2HCl  + 7 molecules H 2 can form 14 molecules HCl 4 molecules Cl 2 can form 8 molecules HCl 3 molecules of H 2 remain H 2 is in excess Cl 2 is the limiting reactant 9.3

43 1.Calculate the amount of product (moles or grams, as needed) formed from each reactant. 2.Determine which reactant is limiting. (The reactant that gives the least amount of product is the limiting reactant; the other reactant is in excess. 3.Calculate the amount of the other reactant required to react with the limiting reactant, then subtract this amount from the starting quantity of the reactant. This gives the amount of the that substance that remains unreacted. Steps Used to Determine the Limiting Reactant

44 How many moles of HCl can be produced by reacting 4.0 mol H 2 and 3.5 mol Cl 2 ? Which compound is the limiting reactant? Step 1 Calculate the moles of HCl that can form from each reactant. H 2 + Cl 2 → 2HCl Step 2 Determine the limiting reactant. The limiting reactant is Cl 2 because it produces less HCl than H 2.

45 How many moles of silver bromide (AgBr) can be formed when solutions containing 50.0 g of MgBr 2 and g of AgNO 3 are mixed together? How many grams of the excess reactant remain unreacted? Step 1 Calculate the grams of AgBr that can form from each reactant. MgBr 2 (aq) + 2AgNO 3 (aq) → 2AgBr(s) + Mg(NO 3 ) 2 (aq) The conversion needed is g reactant → mol reactant → mol AgBr → g AgBr

46 How many moles of silver bromide (AgBr) can be formed when solutions containing 50.0 g of MgBr 2 and g of AgNO 3 are mixed together? How many grams of the excess reactant remain unreacted? Step 2 Determine the limiting reactant. MgBr 2 (aq) + 2AgNO 3 (aq) → 2AgBr(s) + Mg(NO 3 ) 2 (aq) The limiting reactant is MgBr 2 because it forms less Ag Br.

47 How many grams of the excess reactant (AgNO 3 ) remain unreacted? Step 3 Calculate the grams of unreacted AgNO 3. First calculate the number of grams of AgNO 3 that will react with 50 g of MgBr 2. MgBr 2 (aq) + 2AgNO 3 (aq) → 2AgBr(s) + Mg(NO 3 ) 2 (aq) The conversion needed is g MgBr 2 → mol MgBr 2 → mol AgNO 3 → g AgNO 3 The amount of MgBr 2 that remains is g AgNO g AgNO 3 =7.7 g AgNO 3

48 The quantities of products calculated from equations represent the maximum yield (100%) of product according to the reaction represented by the equation. Reaction Yield

49 Many reactions fail to give a 100% yield of product. This occurs because of side reactions and the fact that many reactions are reversible.

50 The theoretical yield of a reaction is the calculated amount of product that can be obtained from a given amount of reactant. The actual yield is the amount of product finally obtained from a given amount of reactant.

51 The percent yield of a reaction is the ratio of the actual yield to the theoretical yield multiplied by 100.

52 Silver bromide was prepared by reacting g of magnesium bromide and an adequate amount of silver nitrate. Calculate the percent yield if g of silver bromide was obtained from the reaction: MgBr 2 (aq) + 2AgNO 3 (aq) → 2AgBr(s) + Mg(NO 3 ) 2 (aq) Step 1 Determine the theoretical yield by calculating the grams of AgBr that can be formed. The conversion needed is g MgBr 2 → mol MgBr 2 → mol AgBr → g AgBr

53 Silver bromide was prepared by reacting g of magnesium bromide and an adequate amount of silver nitrate. Calculate the percent yield if g of silver bromide was obtained from the reaction: MgBr 2 (aq) + 2AgNO 3 (aq) → 2AgBr(s) + Mg(NO 3 ) 2 (aq) Step 2 Calculate the percent yield. must have same units

54 Key Concepts 9.1 A Short ReviewA Short Review 9.2 Introduction to Stoichiometry: The Mole-Ratio MethodIntroduction to Stoichiometry: The Mole-Ratio Method 9.3 Mole-Mole CalculationsMole-Mole Calculations 9.4 Mole-Mass CalculationsMole-Mass Calculations 9.5 Mass-Mass CalculationsMass-Mass Calculations 9.6 Limiting-Reactant and Yield CalculationsLimiting-Reactant and Yield Calculations