# Mathematical Relationships with Chemical Equations…Stoichiometry

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Mathematical Relationships with Chemical Equations…Stoichiometry
The Mole II Mathematical Relationships with Chemical Equations…Stoichiometry

Suppose… You have to make a number of BLTs (bacon, lettuce, tomato sandwiches). Each sandwich requires 2 slices of bread, 4 slices of bacon, 2 slices of tomato, 1 leaf of lettuce, and 1 tbsp of mayonnaise. How many sandwiches can you make with 24 slices of bacon? 14 pieces of bread? 7 slices of tomato?

1 molecule C3H8 + 5 molecules O2
Information Contained in a Balanced Equation Viewed in Terms of Reactants C3H8(g) + 5O2(g) Products 3CO2(g) + 4H2O(g) molecules 3 molecules CO2 + 4 molecules H2O 1 molecule C3H8 + 5 molecules O2 amount (mol) 1 mol C3H8 + 5 mol O2 3 mol CO2 + 4 mol H2O 44.09 amu C3H amu O2 mass (amu) amu CO amu H2O mass (g) 44.09 g C3H g O2 g CO g H2O total mass (g) g

Stoichiometry The relation between the quantities of substances that take part in a chemical reaction or form a compound “"Stoichiometry" is derived from the Greek words στοιχείον (stoikheion, meaning element) and μέτρον (metron, meaning measure.” (http://en.wikipedia.org/wiki/Stoichiometry)

Info in a Chemical Equation
2C8H18(l) + 25O2 (g)  16CO2 (g) + 18H2O (g) 2 mol C8H18 = 25 mol O2 = 16 mol CO2 = 18 mol H2O So…

Summary of the mass-mole-number relationships in a chemical reaction.
MASS(g) of compound A MASS(g) of compound B MM (g/mol) of compound A MM (g/mol) of compound B AMOUNT(mol) of compound A molar ratio from balanced equation AMOUNT(mol) of compound B Avogadro’s number (molecules/mol) Avogadro’s number (molecules/mol) MOLECULES (or formula units) of compound A MOLECULES (or formula units) of compound B

Questions to Ask When Solving a Problem
Are grams mentioned? If yes you will need to use a molar mass conversion. Are you comparing two different substances? If yes you will need a conversion using the coefficients in an equation. Are particles (atoms or molecules) involved? If yes you will need a conversion with Avogadro’s number. You may need any number of these conversions depending on the problem.

Calculating Amounts of Reactants and Products
PROBLEM: In a lifetime, the average American uses 1750 lb(794 g) of copper in coins, plumbing, and wiring. Copper is obtained from sulfide ores, such as chalcocite, or copper(I) sulfide, by a multistep process. After an initial grinding, the first step is to “roast” the ore (heat it strongly with oxygen gas) to form powdered copper(I) oxide and gaseous sulfur dioxide. How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide? (b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted? (c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide?

Calculating Amounts of Reactants and Products
SOLUTION: 2Cu2S(s) + 3O2(g) Cu2O(s) + 2SO2(g) (a) How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide? 3mol O2 2mol Cu2S 10.0mol Cu2S (a) = 15.0mol O2 (b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted? 10.0mol Cu2S 2mol SO2 2mol Cu2S 64.07g SO2 1 mol SO2 (b) = 641g SO2 (c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide? 2.86kg Cu2O 103g Cu2O 1kg Cu2O 1 mol Cu2O 143.10g Cu2O (c) 3mol O2 2mol Cu2O 32.00g O2 1 mol O2 1 kg O2 103g O2 = 0.959kg O2

Now suppose… You have to make BLTs (bacon, lettuce, tomato sandwiches). Each sandwich requires 2 slices of bread, 4 slices of bacon, 2 slices of tomato, 1 leaf of lettuce, and 1 tbsp of mayonnaise. How many sandwiches can you make with 24 slices of bacon and 14 pieces of bread?

Limiting Reactants In most chemical changes you do not have the exact amounts of all reactants. In this case, one reactant will run out first. This reactant will limit the amount of product and so is called the limiting reactant or limiting reagent. The reactant(s) left over is called the excess reactant.

Calculating Amounts of Reactant and Product in a Limiting-Reactant Problem
A fuel mixture used in the early days of rocketry is composed of two liquids, hydrazine (N2H4) and dinitrogen tetraoxide(N2O4), which ignite on contact to form nitrogen gas and water vapor. How many grams of nitrogen gas form when 1.00x102 g of N2H4 and 2.00x102 g of N2O4 are mixed?

Calculating Amounts of Reactant and Product in a Limiting-Reactant Problem
SOLUTION: 2 N2H4(l) + N2O4(l) N2(g) H2O(l) 3 4 1 mol N2H4 32.05g N2H4 1.00x102g N2H4 3 mol N2 2mol N2H4 = 4.68mol N2 2.00x102g N2O4 1 mol N2O4 92.02g N2O4 3 mol N2 1mol N2O4 = 6.51mol N2 N2H4 is the limiting reactant because it produces less product, N2, than does N2O4. 1 mol N2 28.02g N2 4.68mol N2 = 131g N2

Excess Reactant How much reactant was left in the previous problem?
6.51 mol N2 possible but only 4.68 mol made = 1.83 mol N2 not made

How many grams of aluminum carbonate are formed when 20
How many grams of aluminum carbonate are formed when 20.0 grams of sodium carbonate react with 25.0 grams of aluminum nitrate? How much of which reactant is left over?

Percent Yield Reactions do not always go to completion for many reasons. Percent yield is an expression of how much of the expected product actually formed. The theoretical amount generally comes from the stoichiometry of the reaction.

Calculating Percent Yield
PROBLEM: Silicon carbide (SiC) is an important ceramic material that is made by allowing sand (silicon dioxide, SiO2) to react with powdered carbon at high temperature. Carbon monoxide is also formed. When g of sand is processed, 51.4 g of SiC is recovered. What is the percent yield of SiC from this process? SOLUTION: SiO2(s) + 3C(s) SiC(s) + 2CO(g) 100.0 g SiO2 1 mol SiO2 60.09 g SiO2 = mol SiO2 mol SiO2 = mol SiC = 1.664 51.4 g 66.73 g 1.664 mol SiC 40.10 g SiC 1 mol SiC x 100 =77.0% = g

Calculating Amounts of Reactants and Products for a Reaction in Solution
PROBLEM: Specialized cells in the stomach release HCl to aid digestion. If they release too much, the excess can be neutralized with antacids. A common antacid contains magnesium hydroxide, which reacts with the acid to form water and magnesium chloride solution. As a government chemist testing commercial antacids, you use 0.10M HCl to simulate the acid concentration in the stomach. How many liters of “stomach acid” react with a tablet containing 0.10g of magnesium hydroxide?

Calculating Amounts of Reactants and Products for a Reaction in Solution
Mg(OH)2(s) + 2HCl(aq) MgCl2(aq) + 2H2O(l) 1 mol Mg(OH)2 58.33g Mg(OH)2 2 mol HCl 1 mol Mg(OH)2 0.10g Mg(OH)2 = 3.4x10-3 mol HCl 1L 0.10mol HCl 3.4x10-3 mol HCl = 3.4x10-2 L HCl