# Chapter 11 “The Mathematics of Chemical Equations”

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Chapter 11 “The Mathematics of Chemical Equations”
What quantitative relationships exist between reactants & products?

Chapt. 11 OBJECTIVES Define “stoichiometry” & describe its importance.
Relate stoichiometry to balanced chemical equations. Identify & learn to solve different types of stoichiometry problems. Determine the “limiting reactant” (or “limiting reagent”) of a chemical reaction. Calculate the amount of product that forms when reactants are present in nonstoichiometric proportions. Determine ‘percent yield’ of a chemical reaction.

11-1 STOICHIOMETRY What is it?
The quantitative study of chemistry! Comes from the Greek: “stoichion” (element) & “metron” (measure). Includes what we studied in Chapter 10, plus the relationships between reactants & products in balanced chemical equations. Is stoichiometry important? YES! It is a vital part of ‘real-world’ manufacturing chemistry.

INTERPRETING BALANCED CHEMICAL EQUATIONS
Write the equation with correct formulas, and balance it. The coefficients relate to n molecules, or 2n, 7n, 100n, 2000n or even Avogadro’s number of molecules! The coefficients also relate to the moles of molecules! Summary: Coefficients in balanced chemical equations may be interpreted in terms of the relative number of particles involved in the reaction (atoms, molecules, ions, formula units) AND as the relative number of moles.

INTERPRETING BALANCED CHEMICAL EQUATIONS: Mole-Mole Problems
Convert from moles of one substance to moles of another in the balanced chemical equation. Makes use of molar ratios. Example: How many moles of HCl are needed to react with 5.70 moles of Zn by the reaction 2HCl + Zn  ZnCl2 + H2 5.70 mol Zn X (2 mol HCl)/(1 mol Zn) = 11.4 mol HCl Be careful with factor labels! How does a balanced chemical equation relate to the “Law of Conservation of Matter” ?

11-2 Solving Stoichiometry Problems
In Chapter 10 we learned how to use the mole to interconvert among numbers of particles, mass and volume for a given chemical formula. Now we will use these ideas in combination with balanced chemical equations to solve stoichiometry problems. The main types of problems are Mass-Mass Mass-Volume Volume-Volume

The Keys… …to solving Stoichiometry problems are… …the Molar Ratio,
…the Mole & Factor Labels!

Solving Stoichiometry Problems
QUANTITY OF “GIVEN” QUANTITY OF “UNKNOWN” CONVERT TO UNITS NEEDED CONVERT TO MOLES MOLES OF “GIVEN” MOLES OF “UNKNOWN” USE MOLAR RATIO (FROM BALANCED CHEMICAL EQUATION)

Solving Mass-Mass Problems
OF “GIVEN” MASS OF “UNKNOWN” CONVERT TO MASS (MOLAR MASS “UNKNOWN”) CONVERT TO MOLES (MOLAR MASS “GIVEN”) MOLES OF “GIVEN” MOLES OF “UNKNOWN” USE MOLAR RATIO (FROM BALANCED CHEMICAL EQUATION)

Solving Mass-Volume Problems
OF “GIVEN” VOLUME OF “UNKNOWN” GAS CONVERT TO VOLUME (GAS MOLAR VOLUME) CONVERT TO MOLES (MOLAR MASS “GIVEN”) MOLES OF “GIVEN” MOLES OF “UNKNOWN” USE MOLAR RATIO (FROM BALANCED CHEMICAL EQUATION)

EXAMPLE: Mass-Volume How many liters of O2 are needed to burn 424g of sulfur? (Assume STP conditions.) The equation: S + O2  SO2 424g S X (1 mol S/32.0g S) X (1 mol O2/1 mol S) X (22.4L O2/1 mol O2) = 297 L O2 Note that the labels cancel.

EXAMPLE: Mass-Mass Determine the mass of lithium hydroxide that will form in the reaction of g lithium nitride and water by the following equation: Li3N + 3H2O  3LiOH + NH3 Molar Mass of Li3N = 3 X (6.9) = 34.7 g/mol Molar Mass of LiOH = = 23.9 g/mol From the equation, 1 mol Li3N yields 3 mol LiOH. Therefore: 0.380g Li3N X (1 mol Li3N/34.7g Li3N) X (3 mol LiOH/1 mol Li3N) X (23.9g LiOH/1 mol LiOH) = 0.78 g LiOH Notice how the units cancel!

EXAMPLE: Volume-Volume
Determine the volumes of H2S and O2 needed to produce 14.2L of SO2 by the reaction 2 H2S + 3 O2  2 SO2 + 2 H2O. (Assume constant conditions or STP.) 14.2L SO2 X (2L H2S /2L SO2 ) = 14.2 L H2S 14.2L SO2 X (3L O2/2L SO2 ) = 21.3 L O2 Once more, notice how units cancel.

EXAMPLE: Other Types Many problems may be solved using the above general steps. Read the problem carefully to determine what is known (directly or by using molecular formulas), and then decide what factors are needed to find the unknown. Always write the complete labels and check that everything cancels except the correct units for the unknown. Do the math with a few keystrokes of the calculator. Estimate your answer and compare it to the final answer. Does your answer make sense?

11-3 Limiting Reactants & Percent Yield
Consider what is needed to make a ‘box lunch’ for each student in a class of 24 for a class trip. We’ll include a sandwich, a bag of chips, an apple, a box of juice, and a Twix®. What must we buy? (List everything!) Suppose, as we are packing the lunches, we find that one of the “helpers” got hungry and ate a package of chips. Now how many complete ‘box lunches’ can we make? Now, let’s further suppose that we find that three of the apples are bad! What does this do to the number of complete lunches we may prepare? What is limiting our ability to make 24 lunches? What will we have left? This is the concept behind “limiting reactants” (or “limiting reagents”) in a chemical reaction. One chemical runs out first, and this prevents the reaction from going to completion (100%). These are ‘nonstoichiometric’ conditions.

EXAMPLE 1: Identifying the Limiting Reactant
The quantities of products formed in a chemical reaction are always determined by the quantity of the limiting reactant. Solve the problem by determining the amount of product that would be formed by EACH REACTANT. (The one forming the least amount of product limits the reaction’s progress!) Example 1: Identify the limiting reactant when 3.6 mol of Al reacts with 5.0 mol Cl2 to produce AlCl3. Balanced Equation: 2Al + 3Cl2  2AlCl3 So 3.6 mol Al X (2 mol AlCl3/2 mol Al) = 3.6 mol AlCl3 formed Or 5.0 mol Cl2 X (2 mol AlCl3/3 mol Cl2) = 3.3 mol AlCl3 formed Chlorine gives the least amount of product, AlCl3, and so it is the limiting reactant.

EXAMPLE 2: Limiting Reactant Problems
Identify the limiting reagent (reactant) when 14.5 mol P reacts with 17.0 mol O2 to yield P4O10. Balanced Equation: 4P + 5O2  P4O10 So 14.5 mol P X (1 mol P4O10/4 mol P) = 3.62 mol P4O10 Or, 17.0 mol O2 (1 mol P4O10 /5 mol O2) = 3.40 mol P4O10 Oxygen gives the least amount of product, and so it is the limiting reactant (limiting reagent).

EXAMPLE 3: Limiting Reactant Problems
Identify the limiting reactant when 5.1g Li reacts with 1.5L fluorine gas (at STP) to form LiF. How many grams of LiF will result? Balanced equation: 2Li + F2  2LiF For Li: 5.1g Li X (1 mol Li/6.9g Li) X (2 mol LiF/2 mol Li) = 0.74 mol LiF For F2: 1.5L F2 X (1 mol F2/22.4L F2) X (2 mol LiF/1 mol F2) = 0.13 mol LiF Therefore fluorine is limiting, producing only 0.13 mol of LiF. 0.13 mol LiF X (25.9 g LiF/1 mol LiF) = 3.4 g LiF

EXAMPLE 4: Limiting Reactant Problems
If 4.1g Cr is heated with 9.3g chlorine gas, what mass of CrCl3 will result? Balanced equation: 2Cr + 3Cl2  2CrCl3 For Cr: 4.1g Cr X (1 mol Cr/52.0 g Cr) x (2 mol CrCl3/2 mol Cr) X (158.5g CrCl3/1 mol CrCl3) = 12g CrCl3 For Cl2: 9.3g Cl2 X (1 mol Cl2/71.0g Cl2) X (2 mol CrCl3/3 mol Cl2) X (158.5g CrCl3/1 mol CrCl3) = 14 g CrCl3 Cr limits the reaction to 12 g of product, CrCl3. See text page 366 – 370 for additional problems.

Why is ‘limiting reactant’ important?
Chemical reactions are run in industry every day to produce plastics, gasoline, building products, metals, electronic components, foods and hundreds of other chemicals. To run chemical plants effectively (\$\$\$\$\$) chemists and engineers try to control costs and the amounts of ‘reactants.’ Through careful studies and control of chemical reactions, they are able to maximize profits and minimize waste (pollution). Chemists and engineers measure the efficiency of reactions by measuring “percent yield.”

Calculating Percent Yield
A balanced chemical equation tells us the “expected” or “theoretical” yield. Most reactions do not ‘go to completion’ (100%) so the “actual” yield is generally lower than expected. Percent Yield = (Actual Yield)/(Expected Yield) X 100% Be sure to look at the stoichiometry of the balanced chemical reaction to calculate the expected yield! EXAMPLE: Determine the % yield of the reaction between 3.74g of Na and excess O2 if 5.34g Na2O2 is formed. (84.2%)

Did we meet the OBJECTIVES?
Define “stoichiometry” & describe its importance. Relate stoichiometry to balanced chemical equations. Identify & learn to solve different types of stoichiometry problems. Determine the “limiting reactant” of a chemical reaction. Calculate the amount of product that forms when reactants are present in nonstoichiometric proportions. Determine ‘percent yield’ of a chemical reaction.

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