The Mathematics of Chemical Equations Stoichiometry The Mathematics of Chemical Equations

9.1: Balanced Chemical Equations 1. Provides qualitative and quantitative information. 2. Supports the Law of Conservation of Mass 3. 2H2 + O2 → 2H2O The above equation is interpreted in terms of particles as follows: A. 2 molecules of H2 react with 1 molecule of O2 to produce 2 molecules of water. The ratio of H2 to O2 to H2O is 2:1:2. OR

2H2 + O2 → 2H2O B. 20 molecules of H2 react with 10 molecules of O2 to produce 20 molecules of water. Again, the ratio of H2 to O2 to H2O is 2:1:2.

2H2 + O2 → 2H2O C. The original equation can then be interpreted as follows: 2 moles of H2 react with 1 mole of O2 to produce 2 moles of water. The ratio of H2 to O2 to H2O is 2:1:2.

D. It is more convenient to interpret the coefficients as the number of moles, because we measure amounts of substances by grams in the laboratory. We can convert between grams and moles in solving problems involving chemical reactions. 4. Stoichiometry: The study of the mathematical (quantitative) relationships that exist in a formula and in a chemical reaction. 5. The word Stoichiometry comes from the Greek word “stoicheion” meaning element, and “metron”, meaning measure.

6. Importance: The safe, economical and reproducible manufacture of chemicals (or food) and the safe administration of pharmaceuticals. 7. Proof: The Law of conservation of mass is shown by the balanced equation, or by adding up all the masses of reactants and products to determine if they are equal. (also works with number of atoms)

8. Mole-Mole Problems require 3 steps to determine the molar ratio: Stoichiometryville Map A. Write Equation (reactants → products) B. Balance the equation to determine the molar ratio C. Mole to Mole ratio used to convert units

Welcome to Stoichiometryville Mass Mass Given Substance Substance to be determined Molar Mass Molar Mass Particles Moles Particles Mole Ratio Moles 6.02 x 1023 6.02 x 1023 22.4 L 22.4 L Volume Volume

Ex #1) Ammonium nitrate decomposes into dinitrogen monoxide and water Ex #1) Ammonium nitrate decomposes into dinitrogen monoxide and water. How many moles of N2O are produced from 2.25 moles of reactants? Equation: NH4NO3  N2O + 2 H2O Ratio: 1 : 1 : 2 2.25 mol NH4NO3

Equation: 2 HCl + Zn  ZnCl2 + H2 Ratio: 2 : 1 : 1 : 1 Ex #2) Hydrochloric acid reacts with zinc in a single replacement reaction, how many moles of HCl are needed to react with 2.3 moles of Zn? ? mol 2.3 mol Equation: 2 HCl + Zn  ZnCl2 + H2 Ratio: 2 : 1 : 1 : 1

Stoichiometry Problems: 1. A balanced equation represents a chemical reaction that conforms to the Law of Conservation of Mass 2. Subscripts can NEVER be changed to balance a chemical equation. 3. The total atoms/mass of the reactants is the same as the total atoms/mass of the products. 4. Coefficients in a balanced equation relate moles of substances in the reaction. 5. Coefficients are used in constructing the molar ratio for a stoichiometric problem. 6. Grams of the known must first be converted to moles, then use the molar ratio to relate the 2 substances, finally convert the moles of the unknown to grams.

7. Mass-Mass Problems: 4Al + 3O2 → 2Al2O3 C6H12O6 + 6O2 → 6CO2 + 6H2O Ex#1)What mass of aluminum oxide can be prepared by the reaction of 67.5 g of Al and oxygen? 67.5 g ?g 4Al + 3O2 → 2Al2O3 Ex#2)Glucose is used as an energy source by the human body. Calculate the number of grams of oxygen needed to oxidize (burn) 12.5 g of glucose. Write the balanced combustion reaction. 12.5 g ?g C6H12O6 + 6O2 → 6CO2 + 6H2O

Ex #3) During WWII, Germany used a method called the Haber Process to produce ammonia for explosives. Today a similar process is used to make fertilizers. If excess of nitrogen is reacted with 1.71 mol of hydrogen, how many grams of ammonia, NH3 is produced? N2 + 3 H2 → 2 NH3 1.71 mol ? g Ex #4) iron will react with oxygen gas to produce iron (III) oxide. How many grams of iron (III) oxide will be produced if 0.18 mol of iron reacts? 4Fe + 3O2 → 2Fe2O3 .18 mol ?g

8. Mass-Volume Problems: Airbags contain a powder called sodium azide (NaN3). When exposed to a spark the sodium azide quickly decomposes into sodium and nitrogen gas. If an uninflated airbag contains 125 g of NaN3, what volume in liters of nitrogen gas will be produced at STP? 2 NaN3 + 2 Na → 3 N2 125 g ? L 9. Volume-Volume Problems: What volume in liters of hydrogen gas is needed to react completely with 15.5 L of nitrogen gas to produce ammonia gas (NH3) at STP? 3 H2 + N2 → 2 NH3 ? L 15.5 L

Ex) If a recipe for 1 cake is: and your kitchen contains: 5. The limiting reactant is the starting substance that becomes used up first when a chemical reaction occurs. It controls how much or how little product can be formed. Ex) If a recipe for 1 cake is: and your kitchen contains: 2 cups flour 7 cups flour 2 eggs 2 dozen eggs 1 cup sugar 9 cups sugar 1½Tbls. baking powder 10 Tbls. baking pwdr 1 cup water unlimited water ⅓ cup oil 3⅓ cups oil How many cakes can you make given the ingredients present in your kitchen? 3 What ingredient is the limiting reactant? flour How many eggs are left over after making the cakes? 18

What is the most NO you can make? ______ 6. 4 NH3 + 5 O2 → 4 NO + 6 H2O 3.50g ? g 3.25g What is the most NO you can make? ______ Which reactant is the limiting reactant? ________ 2.63 g oxygen

Reactants → Products