# 1.4.1 Calculate theoretical yields from chemical equations.

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1.4.1 Calculate theoretical yields from chemical equations.
IB Topic 1: Quantitative Chemistry 1.4: Mass Relationships in Chemical Reactions 1.4.1 Calculate theoretical yields from chemical equations. 1.4.2 Determine the limiting reactant and the reactant in excess when quantities of reacting substances are given. 1.4.3 Solve problems involving theoretical, experimental and percentage yield.

Review: Identify the mole ratio of any two species in a chemical reaction.
How do you calculate the quantity of reactants and products in chemical reactions? Use the chemical equation to predict ratio of reactants and products N2 + 3H2  2NH3 1 molecule N2 reacts with 3 molecules H2 producing 2 molecules NH3 1 mole N2 reacts with 3 moles H2 producing 2 moles NH3 The balanced equations gives us the ratio in particles or moles (not mass) of the chemicals involved in the reaction. The ratio of N2 to NH3 is 1:2 The ratio of NH3 to H2 is 2:3 The ratio of H2 to N2 is 3:1

Review: Identify the mole ratio of any two species in a chemical reaction.
Consider the reaction: 2C8H O2  16CO2 + 18H2O What is the ratio of O2 to CO2? 25:16 What is the ratio of H2O to C8H18? 18:2 What is the ratio of CO2 to H2O? What is the ratio of O2 to C8H18? Remember these ratios are in particles or moles. We will be using moles.

1.4.1 Calculate theoretical yields from chemical equations.
Theoretical Yield is the amount of product that would result if all the limiting reagent reacted. In essence, theoretical yield is what you calculate We use a process called stoichiometry: It is the calculation of quantities in chemical reactions.

1.4.1 Calculate theoretical yields from chemical equations.
How many moles of sodium chloride will be produced if you react 2.6 moles of chlorine gas with an excess (more than you need) of sodium metal? 2 Na + Cl2  2 NaCl 2.6 moles Cl2 2 mol NaCl 1 mol Cl2 = 5.2 moles NaCl

1.4.1 Calculate theoretical yields from chemical equations.
Most of the time in chemistry, the amounts are given in grams instead of moles We still go through moles and use the mole ratio, but now we also use molar mass to get to grams Example: How many grams of chlorine are required to react completely with 5.00 moles of sodium to produce sodium chloride? 2 Na + Cl2  2 NaCl 5.00 moles Na 1 mol Cl g Cl2 2 mol Na 1 mol Cl2 = 177g Cl2

1.4.1 Calculate theoretical yields from chemical equations.
Calculate the mass in grams of Iodine required to react completely with 0.50 moles of aluminum. 2 Al + 3 I2  2 AlI3 0.50 moles Al 3 moles I g I2 2 moles Al 1 mole I2 = g I2

1.4.1 Calculate theoretical yields from chemical equations.
We can also start with mass and convert to moles of product or another reactant We use molar mass and the mole ratio to get to moles of the compound of interest Calculate the number of moles of ethane (C2H6) needed to produce 10.0 g of water 2 C2H6 + 7 O2  4 CO2 + 6 H20 10.0 g H2O 1 mol H2O 2 mol C2H6 18.0 g H2O 6 mol H20 = mol C2H6

1.4.1 Calculate theoretical yields from chemical equations.
Calculate how many moles of oxygen are required to make 10.0 g of aluminum oxide 4 Al + 3 O2  2 Al2O3 10.0g Al2O mol Al2O mol O2 101.96g Al2O mol Al2O3 = mol O2

1.4.1 Calculate theoretical yields from chemical equations.
Most often we are given a starting mass and want to find out the mass of a product we will get (called theoretical yield) or how much of another reactant we need to completely react with it (no leftover ingredients!) Now we must go from grams to moles, mole ratio, and back to grams of compound we are interested in

1.4.1 Calculate theoretical yields from chemical equations.
Ex. Calculate how many grams of ammonia are produced when you react 2.00g of nitrogen with excess hydrogen. N2 + 3 H2  2 NH3 2.00g N mol N mol NH g NH3 28.02g N2 1 mol N mol NH3 = 2.4 g NH3

1.4.1 Calculate theoretical yields from chemical equations.
How many grams of calcium nitride are produced when 2.00 g of calcium reacts with an excess of nitrogen? 3 Ca + N2  Ca3N2 2.00g Ca 1 mol Ca 1 mol Ca3N g Ca3N2 40.08g Ca 3 mol Ca mol Ca3N2 = 2.47 g Ca3N2

1.4.1 Calculate theoretical yields from chemical equations.
How much oxygen does it take to burn grams of octane?

1.4.1 Calculate theoretical yields from chemical equations.
How much oxygen does it take to burn grams of octane? Write the balanced chemical equation: 2C8H O2  16CO2 + 18H2O

1.4.1 Calculate theoretical yields from chemical equations.
How much oxygen does it take to burn grams of octane? 2C8H O2  16CO2 + 18H2O Mass of O2 required: mol (32.00 g/mol) = g O2

1.4.1 Calculate theoretical yields from chemical equations.
In a spectacular reaction called the thermite reaction, iron(III) oxide reacts with aluminum producing iron and aluminum oxide. How many grams of iron will be produced from 43.7 grams of aluminum?

1.4.1 Calculate theoretical yields from chemical equations.
In a spectacular reaction called the thermite reaction, iron(III) oxide reacts with aluminum producing iron and aluminum oxide. How many grams of iron will be produced from 43.7 grams of aluminum? Write the balanced chemical equation: Fe2O3 + 2Al  2Fe + Al2O3

1.4.1 Calculate theoretical yields from chemical equations.
In a spectacular reaction called the thermite reaction, iron(III) oxide reacts with aluminum producing iron and aluminum oxide. How many grams of iron will be produced from 43.7 grams of aluminum? Write the balanced chemical equation: Fe2O3 + 2Al  2Fe + Al2O3 Mass of Fe produced: 43.7 grams Al x 1 mole Al/ Al x 2Fe/2Al x 55.8 g/ 1mol) = g Fe

1 cup butter 1/2 cup white sugar 1 cup packed brown sugar 1 teaspoon vanilla extract 2 eggs 2 1/2 cups all-purpose flour 1 teaspoon baking soda 1 teaspoon salt 2 cups semisweet chocolate chips Makes 3 dozen If we had the specified amount of all ingredients listed, could we make 4 dozen cookies? What if we had 6 eggs and twice as much of everything else, could we make 9 dozen cookies? What if we only had one egg, could we make 3 dozen cookies?

1.4.2 Determine the limiting reactant and the reactant in excess when quantities of reacting substances are given. Limiting Reactants You are given amounts for two reactants and one reactant will run out first. This is called the limiting reactant. The reactant that is left over is called the excess reactant. For example: A strip of zinc metal weighing 2.00 g is placed in a solution containing 2.50 g of silver nitrate causing the following reaction to occur: Zn + 2AgNO3  2Ag + Zn(NO3)2 How many grams of Ag will be produced? AgNO3 is the limiting reactant because it will produce the least amount of Ag. Zn is the reactant in excess. There will be Zn left over after the reaction

Limiting Reactant Most of the time in chemistry we have more of one reactant than we need to completely use up other reactant. That reactant is said to be in excess (there is too much). The other reactant limits how much product we get. Once it runs out, the reaction s. This is called the limiting reactant.

Method for determining the L.R.
1) Pick A Product 2) Try ALL the reactants 3) The lowest answer will be the correct answer 4) The reactant that gives the lowest answer will be the limiting reactant

Limiting Reactant 10.0g of aluminum reacts with 35.0 grams of chlorine gas to produce aluminum chloride. Which reactant is limiting, which is in excess, and how much product is produced? 2 Al + 3 Cl2  2 AlCl3 Start with Al: Now Cl2: 10.0 g Al 1 mol Al mol AlCl g AlCl3 27.0 g Al mol Al mol AlCl3 = 49.4g AlCl3 35.0g Cl mol Cl mol AlCl g AlCl3 71.0 g Cl mol Cl mol AlCl3 = 43.9g AlCl3

LR Example Continued We get 49.4g of aluminum chloride from the given amount of aluminum, but only 43.9g of aluminum chloride from the given amount of chlorine. Therefore, chlorine is the limiting reactant. Once the 35.0g of chlorine is used up, the reaction comes to a complete

Limiting Reactant Practice
15.0 g of potassium reacts with 15.0 g of iodine. Calculate which reactant is limiting and how much product is made.

Limiting Reactant Practice
2 K + I2  2 KI Potassium: Iodine: Iodine is the limiting reactant and we get 19.6 g of potassium iodide 15.0g K 1 mol K mol KI g KI 39.1g K mol K mol KI = 63.7g KI 15.0 g I mol I mol KI g KI 254 g I mol I mol KI = 19.6 g KI

Finding the Amount of Excess
By calculating the amount of the excess reactant needed to completely react with the limiting reactant, we can subtract that amount from the given amount to find the amount of excess. Can we find the amount of excess potassium in the previous problem?

Finding Excess Practice
15.0 g of potassium reacts with 15.0 g of iodine. 2 K + I2  2 KI We found that Iodine is the limiting reactant, and 19.6 g of potassium iodide are produced. 15.0 g I mol I mol K g K 254 g I mol I mol K = 4.62 g K USED! 15.0 g K – 4.62 g K = g K EXCESS Given amount of excess reactant Amount of excess reactant actually used Note that we started with the limiting reactant! Once you determine the LR, you should only start with it!

Limiting Reactant: Recap
You can recognize a limiting reactant problem because there is MORE THAN ONE GIVEN AMOUNT. Convert ALL of the reactants to the SAME product (pick any product you choose.) The lowest answer is the correct answer. The reactant that gave you the lowest answer is the LIMITING REACTANT. The other reactant(s) are in EXCESS. To find the amount of excess, subtract the amount used from the given amount. If you have to find more than one product, be sure to start with the limiting reactant. You don’t have to determine which is the LR over and over again!

Putting it all together
At high temperatures, sulfur combines with iron to form the brown-black iron (II) sulfide: Fe (s) + S (l)  FeS (s) In one experiment, 7.62 g of Fe are allowed to react with 8.67 g of S. What is the limiting reagent, and what is the reactant in excess? How much of the excess reactant is left over? Calculate the mass of FeS formed.

Fe is the limiting reagent S is in excess ??? g of S is left over 12.2 g FeS formed

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
The theoretical yield from a chemical reaction is the yield calculated by assuming the reaction goes to completion. In practice we often do not obtain as much product from a reaction mixture as theoretically possible due to a number of factors: Many reactions do not go to completion Some reactants may undergo two or more reactions simultaneously forming undesired products Not all of the desired product can be separated from the rest of the products The amount of a specified pure product actually obtained from a given reaction is the experimental or actual yield. Percentage yield indicates how much of a desired product is obtained from a reaction Percentage yield = experimental yield of a product x 100% theoretical yield of a product

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
Consider the reaction: P O2  P4O10 If 272 g of phosphorus reacts, the percentage yield of tetraphosphorus decoxide is 89.5%. What mass of P4O10 is obtained? Theoretical amt: 272 g/1 x 1mole/124.0 g x 1mol P4O10/ 1mole P4 x 284 g/ 1mol =622.9 g Experimental amt: 623 g x .895 = 558 g

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
Consider the reaction: P4O H2O  4H3PO4 If 558 g of P4O10 reacts, the experimental yield of H3PO4 is 746 g. What is the percentage yield of H3PO4? Theoretical amt: 558 g/1 x 1 mol/284 g x 4 mol H3PO4 / 1 mol P4O10 x 98.0 g / 1 mol = X X= 770. g H3PO4 Percentage yield: 746 g x 100% = 96.9% 770 g

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
Consider the reaction: Fe2O CO  2Fe + 3CO2 When 84.8 g iron(III) oxide reacts with an excess of carbon monoxide, 54.3 g of iron is produced. What is the percentage yield of this reaction?

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
Consider the reaction: Fe2O CO  2Fe + 3CO2 When 84.8 g iron(III) oxide reacts with an excess of carbon monoxide, 54.3 g of iron is produced. What is the percentage yield of this reaction? Theoretical amt: 84.8 g/1 x 1 mol/159.2 g x 2 mol Fe / 1 mole Fe2O3 x 55.8 g/ 1mol Fe2O3 = X X = g Fe Percentage yield: 54.3 g x 100% = 91.4% 59.4 g

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
If 50.0 g silicon dioxide is heated with an excess of carbon, the percentage yield of silicon carbide 76.0%. What mass of silicon carbide will actually be produced? SiO C  SiC + 2CO

1.4.3 Solve problems involving theoretical, experimental and percentage yield.
If 50.0 g silicon dioxide is heated with an excess of carbon, the percentage yield of silicon carbide 76.0%. What mass of silicon carbide will actually be produced? SiO C  SiC + 2CO Theoretical amt: 50.0 g/ 1 x 1 mol/60.1 g x 1mol SiC/1mol SiO2 x 40.1 g/ 1mol =X X = g SiC Experimental yield: 33.4 g x .760% = 25.4 g SiC