# LECTURE Nine CHM 151 ©slg TOPICS: 1. Calculating from Balanced Equation: “Stoichiometry” 2. Limiting Reagent, % Yield.

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LECTURE Nine CHM 151 ©slg TOPICS: 1. Calculating from Balanced Equation: “Stoichiometry” 2. Limiting Reagent, % Yield

Stoichiometry: Introduction Let us balance one more equation, using techniques introduced in last lecture: Fe 2 O 3(s) + HCl (aq) ---> H 2 O + FeCl 3(aq) a) Fe 2 O 3(s) + HCl (aq) ---> H 2 O + 2FeCl 3(aq) b) Fe 2 O 3(s) + 6HCl (aq) ---> H 2 O + 2FeCl 3(aq) c) Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq)

Now let us go one step further and determine the quantitative relationships a BALANCED equation implies, utilizing the below: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) On the most basic level, the equation counts number of “molecules” or ionic “formula units”of each species are needed in order for this reaction to occur: 1 “formula unit” Fe 2 O 3 + 6 molecules HCl---> 3 molecules H 2 O + 2 “formula units” FeCl 3

But, we know we can’t reach into a box and pull out molecules: we have to weigh out a specific mass of the molecules and then figure out how many we have because they are too tiny to count. To count by weighing, we use the mole, knowing that 1 MOLE of molecules = 6.022 X 10 23 molecules and we can work with our equation in terms of moles...

The relationship: 1 “formula unit” Fe 2 O 3 + 6 molecules HCl---> 3 molecules H 2 O + 2 “formula units” FeCl 3 BECOMES: 1 mole Fe 2 O 3 + 6 moles HCl---> 3 moles H 2 O + 2 moles FeCl 3 and...

When we talk moles, we can talk mass in grams by calculating the molar masses of the compounds involved: Fe 2 O 3 : 2 Fe= 2X 55.85 = 111.70 3O = 3X 16.00 = 48.00 159.70 g/mol Fe 2 O 3 HCl: 1H = 1.01 1Cl = 35.45 36.46 g/mol HCl

FeCl 3 : 1 Fe = 1 X 55.847 = 55.85 3 Cl = 3 X 35.45 = 106.35 162.20 g/mol FeCl 3 H 2 O: 2H = 2X1.01 = 2.02 1O = 1X 16.00 = 16.00 18.02 g/mol H 2 O

1 mole Fe 2 O 3 = 1 mol X 159.70 g/mol Fe 2 O 3 = 159.70 g 6 moles HCl = 6 mol X 36.46 g/mol HCl = 218.76 g 3 moles H 2 O = 3 mol X 18.02 g/mol H 2 O = 54.06 g 2 moles FeCl 3 = 2 mol X 162.20 g/mol FeCl 3 = 324.40 g Equivalent: 1 mol Fe 2 O 3 + 6 mol HCl---> 3 mol H 2 O + 2 mol FeCl 3 159.70 g Fe 2 O 3 + 218.76 g HCl ---> 54.06 g H 2 O + 324.40 g FeCl 3

159.70 g Fe 2 O 3 + 218.76 g HCl ---> 54.06 g H 2 O + 324.40 g FeCl 3 Note how the Law Of Conservation of Matter has been upheld: 159.70 g + 218.76 g ---> 54.06 g + 324.40 g 378.46 g total mass reactants -----> 378.46 g total mass products

Let us now apply our new knowledge to problem solving situations: In all cases, we will use the equation we have developed: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol If we start with 25.00 g of Fe 2 O 3, how many moles and how many g of HCl are required for the reaction, and how many g of FeCl 3 and moles of water will we theoretically obtain?

To solve, copy balanced equation, and insert under each reactant and product the molar mass and any question or information given in the problem: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 25.00g ?g, mol ?moles ?g We can now proceed to solve each question:

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 25.00g ?g, mol Question #1: 25.00 g Fe 2 O 3 = ? mol HCl Relationships: 159.70 g Fe 2 O 3 = 1 mol Fe 2 O 3 1 mol Fe 2 O 3 = 6 mol HCl

PATHWAY: g Fe 2 O 3 ---> mol Fe 2 O 3 ---> mol HCl Conversion factor: M Conversion factor: balanced equation

Conversion factor: M Conversion factor: M Conversion factor: balanced equation Question #2: 25.00 g Fe 2 O 3 = ? g HCl

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 25.00g ?g, mol ?moles ?g answer:.9393 mol, 34.25 g To finish: Question #3: 25.00 g Fe 2 O 3 = ? mol H 2 O Question #4: 25.00 g Fe 2 O 3 = ? g FeCl 3

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq Question #3: 25.00 g Fe 2 O 3 = ? mol H 2 O Question #4: 25.00 g Fe 2 O 3 = ? g FeCl 3

To prove we did everything in a correct fashion, let’s see if it all adds up: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 25.00g ?g, mol ?moles ?g answer:.9393 mol,.4696 mol 34.25 g ---> 8.462 g 50.78 g 25.00 + 34.25 = 59.25 g reactants 8.462 + 50.78 = 59.245 g products

GROUP WORK: How many g of Fe 2 O 3 are required to make 75.00 g of FeCl 3 ? Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol ? g 75.00 g PATHWAY: g FeCl 3 --->mol FeCl 3 ---> mol Fe 2 O 3 ---> g Fe 2 O 3

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 162.20 g/mol Answer: 36.92 g Fe 2 O 3 required

Next, let’s consider problems we’ll call “LIMITING REAGENT PROBLEMS” In this type of problem, amounts OF BOTH reactants will be given to you, and you’ll be asked to calculate how much of one or more products can be formed. In most cases, one given value will be in excess, to insure that all of the other reagent is used up.

We can call the the reactant present in excessive amount “the excess reagent” and we can call the reactant we expect to get used up “the limiting reagent” because it limits the amount of product which we can form..... Never try to guess from amounts given which reactant is which; you should always calculate to determine the nature of both given reactants. There are several ways this can be accomplished; I will present the method I am most comfortable with:

Let’s use the same equation we have been considering today: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 35.00 g 100.0 g ? g Now, suppose you were given 100.0 g HCl and 35.00 g Fe 2 O 3. How many g of FeCl 3 will you theoretically obtain? Amounts of both: Limiting Reagent problem

My method of choice: Calculate g of product from each reactant. The reactant which gives you the larger amount of product is the excess reagent. The amount of product calculated from this reagent answer is incorrect, too much... The reactant that gives you the smaller amount of product is the limiting reagent. (The calculation from the limiting reagent gives is the correct answer!).....

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 35.00 g 100.0 g ? g The question becomes: 35.00 g Fe 2 O 3 = ? g FeCl 3 100.0 g HCl = ? g FeCl 3 which answer is correct? GROUP WORK: CALCULATE BOTH, DECIDE!

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 35.00 g 100.0 g ? g 35.00 g Fe 2 O 3 = ? g FeCl 3

100.0 g HCl = ? g FeCl 3 Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 35.00 g 100.0 g ? g

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 35.00 g 100.0 g ? g 35.00 g Fe 2 O 3 = ? g FeCl 3 = 71.10 g FeCl 3 Limiting Reagent Correct 100.0 g HCl = ? g FeCl 3 = 148.3 g FeCl 3 TOO MUCH!

Theoretical, Actual and Percent Yield So far we have considered how much product we could theoretically obtain from a given reaction by calculating from a balanced equation. We have been working with the following equation, so let’s finish up the topic with it: Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol

“theoretical yield” is the amount of any product you calculate from your balanced equation, using the limiting reagent when amounts of all reactants are given. “actual yield” is the amount of product you actually obtain from a given experiment using the reaction described in the balanced equation; this amount is rarely as large as the theoretical yield. Percent yield = actual yield X 100% theoretical yield

Let’s recall the last problem we did: If 35.00 g Fe 2 O 3 were reacted with 100.0 g HCl, how many g of FeCl 3 would theoretically be obtained? We calculated the amount of product from both reactants, and decided that 71.10 g of FeCl 3 would be the “expected” amount of product, based on the limiting reagent and balanced equation. (See next slide)

Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol ? g, theoretical 35.00 g 100.0 g ans: 71.10 g Too much

Now suppose you ran the reaction in the laboratory and discovered that you could only isolate 65.88 g of FeCl 3. The next question asked would be, “what is your percent yield for this experiment?” Fe 2 O 3(s) + 6HCl (aq) ---> 3H 2 O + 2FeCl 3(aq) 159.70 g/mol 36.46 g/mol 18.02 g/mol 162.20 g/mol 71.10 g theoretical 35.00 g 100.0 g 65.88 g actual % Yield = ?

Percent yield = actual yield X 100 theoretical yield % Yield = 65.88 g obtained or “actual” X 100 71.10 g calculated or “theoretical” = 92.66 % End, Lecture 9

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