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4. Stoichiometry
1. Stoichiometric Equations
2. Limiting Reagent Problems
3. Percent Yield
4. Limiting Reagent Problems
5. Concentrations of Solutes
6. Chemical Analysis
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4.1 Stoichiometry
“Chemical Arithmetic”
Objective: Determine Quantitative
Relationships Between Reactants and
Products
Two “Ways” to Quantify Matter
1. Count
2. Measure
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Stoichiometry
•Chemical Equations Relate the Numbers of Various
Species to Each Other (Counted Quantities)
•We Observe Measurable Quantities Like Mass
and Volume
Measured
Quantity
Reactants
Counted
Quantity
Reactants
Counted
Quantity
Products
Measured
Quantity
Products
•We Need to be Able to Connect the Two
Chemical
EquationMass, Volume,
Pressure, Temperature)
Mass, Volume,
Pressure, Temperature)
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3 Basic Steps
Measured
Quantity
Reactants
Counted
Quantity
Reactants
Counted
Quantity
Products
Measured
Quantity
Products1.
1. Mass to Mole Conversion: Determine # of Moles of all
Species Present (Start with Mass – something you can measure)
2.
2. Mole to Mole Conversion: Use Stoichiometric Ratios to
Relate Various Species to Each Other
3.
3. Mole to Mass Conversion: Multiple Moles Product by Molar
Mass (End with Mass P – something you can measure)
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Combustion of Ethanol
Consider the combustion of 16.0 g ethanol
What kind of questions
can we ask?
C2H5OH
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Combustion of Ethanol
Consider the combustion of 16.0 g ethanol
C2H5OH + 3O2 2CO2 + 3H2O
4. Quantity of Water Produced (moles or mass)
2. Quantity of Oxygen Consumed (moles or mass) .
3. Quantity of CO2 Produced (moles or mass)
(5. Quantity of Energy Produced or Consumed)
1. Quantity of Ethanol Consumed in Moles
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Quantity of Ethanol Consumed
in Moles
C2H5OH + 3O2 2CO2 + 3H2O
2 52 5
2 5
(16.0 )( )46.02
0.348
mol C H OHg C H OH
g
mol C H OH
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Quantity of Oxygen Consumed
in Moles or Grams
C2H5OH + 3O2 2CO2 + 3H2O
2 5 22 5 2
2 5
3(16.0 )( )( ) 1.04
46.02
mol C H OH mol Og C H OH mol O
g mol C H OH
2 5 22 5
2 5 2
2
3 32.0(16.0 )( )( )( )
46.02
33.4
mol C H OH mol O gg C H OH
g mol C H OH mol O
g O
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Quantity of Carbon Dioxide Produced
in Moles or Grams
C2H5OH + 3O2 2CO2 + 3H2O
2 5 22 5 2
2 5
2(16.0 )( )( ) 0.695
46.02
mol C H OH mol COg C H OH mol CO
g mol C H OH
2 5 22 5
2 5 2
2
2 44.01(16.0 )( )( )( )
46.02
30.6
mol C H OH mol CO gg C H OH
g mol C H OH mol CO
g CO
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Quantity of Water Produced
in Moles or Grams
C2H5OH + 3O2 2CO2 + 3H2O
2 5 22 5 2
2 5
3(16.0 )( )( ) 1.04
46.02
mol C H OH mol H Og C H OH mol H O
g mol C H OH
2 5 22 5
2 5 2
2
3 18.015(16.0 )( )( )( )
46.02
18.8
mol C H OH mol H O gg C H OH
g mol C H OH mol H O
g H O
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4.2 Limiting Reagent Problems
•Stoichiometric Proportions: Reactants mixed in
Ratios Given by Stoichiometric Coefficients.
Everything is Completely Consumed
•Nonstoichiometric Proportions: Reactants are
Mixed in Ratios Different than Stoichiometric
Coefficients. One species is Completely
Consumed (Limiting Reagent) While Another
is not Completely Consumed (Excess Reagent)
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Theoretical Yield
The Maximum Amount of Product Which
Could be Produced by the Complete
Consumption of the Limiting Reagent
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Silver Tarnishes in the Presence of Hydrogen
Sulfide and Oxygen due to the Reaction:
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
How many grams of Silver Sulfide Would be
Formed from 2.4g Ag, 0.48g H2S & 0.16g O2?
2.4g Ag
0.48g H2S
0.16g O2(1mol O2/32g)
(1mol Ag/107.9g)
(1mol H2S/34g)
(2mol Ag2S/mol O2)=
(2mol Ag2S/4mol Ag)=
(2mol Ag2S/2mol H2S)=
Oxygen is the Limiting Reagent
0.011mol Ag2S
0.014mol Ag2S
0.010mol Ag2S
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Mass Silver Sulfide Produced:
(0.010mol Ag2S) (247.9Ag2S/mol)=2.5g Ag2S
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
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How Do We Quickly Identify Limiting
Reactants in Stoichiometric Problems?
1. Determine Moles for Each Reactant
2.Divide Each by It’s Stoichiometric
Coefficient.
3. Limiting Reagent Has Smallest Value
(Reactants are in Stoichiometric Proportions if
all Values are Equal)
(Now Answer the Question)
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A Closer Look at the Last Problem
2.4g Ag(1mol Ag/107.9g) (2mol Ag2S/4mol Ag)= 0.011mol Ag2S
0.48g H2S(1mol H2S/34g) (2mol Ag2S/2mol H2S)=0.014mol Ag2S
0.16g O2 (1mol O2/32g) (2mol Ag2S/mol O2) =0.010mol Ag2S
2.4g Ag(1mol Ag/107.9g) (1/4mol Ag) (2mol Ag2S )= 0.011mol Ag2S
0.48g H2S(1mol H2S/34g) (1/2mol H2S) (2mol Ag2S )= 0.014mol Ag2S
0.16g O2 (1mol O2/32g) (1/mol O2) (2mol Ag2S ) = 0.010mol Ag2S
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
Determine Moles
Each Species
Divide by
Coefficient
Note: Next Step Multiples
all by the Same Value
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A Closer Look at Short Cut Method
2.4g Ag(1mol Ag/107.9g) /4mol Ag)= 0.00556
0.48g H2S(1mol H2S/34g) /2mol H2S)=0.00706
0.16g O2 (1mol O2/32g) /mol O2) =0.005
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
Possible Questions;
1. Theoretical Mass Yield Ag2S
2. Theoretical Mass Yield H2O
3. Excess Ag
4. Excess H2S
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Theoretical Mass Yield Ag2S
0.16g O2 (mol O2/32g)(2molAg2S /mol O2)(247.9g/molAg2S )= 2.5g
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
or
[0.005](2molAg2S )(247.9g/molAg2S)= 2.5g
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Theoretical Mass Yield H2O
0.16g O2 (mol O2/32g)(2molH2S /mol O2)(18g/molH2O )=0.18g
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
or
[0.005](2molH2O )(18g/mol H2O)= 0.18g
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Excess Mass of Ag
Mass Ag Left Over = Initial Mass -Mass Consumed
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
2.4g- 0.16gO2 (mol O2/32g)(4molAg /molO2)(107.9g/molAg ) = 0.2g
or
2.4- [0.005](4 molAg )(107.9g/mol Ag) = 0.2g
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Excess Mass of H2S
Mass H2S Left Over = Initial Mass -Mass Consumed
4Ag + 2H2S + O2 ----> 2Ag2S + 2H2O
0.48g- 0.16gO2 (mol O2/32g)(2molH2S /molO2)(34g/molH2S) = 0.24g
or
0.48 - [0.005](2 molH2S)(34g/mol H2S) = 0.24g
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How Much Oxygen is Left Over?
None:
It is the limiting reagent
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Class Problem
Phosphoric Acid can be synthesized from
phosphorus, oxygen and water according
to the following reactions:
4P + 5O2 -----> P4O10
P4O10 + 6H2O ---> 4H3PO4
Starting with 20.0g P, 30.0g O2 and 15.0 g
H2O, how many grams of Phosphoric
acid can be Produced?
P&O
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Combining Equations gives:
eq1. 4P + 5O2 -----> P4O10
eq2 P4O10 + 6H2O ---> 4H3PO4
eq3 4P + 5O2 + 6H2O -----> 4H3PO4
(Note, the P4O10 could be considered as a
reaction intermediate)
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4P + 5O2 + 6H2O -----> 4H3PO4
20gP(mol P/31g)(1/4 molP) = 0.1613
30gO2(molO2/32g)(1/ 5mol O2) = 0.1875
15gH2O(molH2O/18g)(1/6mol H2O) = 0.1389
0.1389(4molH3PO4)(98g H3PO4/mol)
= 54.5g H3PO4
(15gH2O)(molH2O/18g)(4molH3PO4/6mol H2O) (98g H3PO4/mol)
= 54.5g H3PO4
OR
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4.3 Percent Yields
Often Times the Actual Yield of a
Chemical Reaction is Less Than That
Predicted by the Complete Consumption
of the Limiting Reagent
Percent Yield = Actual Yield (100)
Theoretical Yield
Note: Theoretical Yield Is Based on the Complete
Consumption of the Limiting Reagent
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Why Would the Actual Yield Be
Less Than the Theoretical Yield?
1. Equilibrium State (where Reactants exist together
with Products)
2. Existence of Intermediates (two step process like
formation of Phosphoric Acid)
3. Kinetic Factors (the reaction is slow, maybe not all of
the reactants have “diffused” together).
4. Alternative Chemical Reactions (there may be more
than one possible product produced).
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Determine Percent Yield if 2.3g of
Silver Sulfide form when 2.4g Ag,
0.28g H2S & 0.16g O2 react.
From Previous Problem,
the Theoretical Yield is
2.5g Ag2S
%Yield (Ag2S) = (2.3g/2.5g)100
= 92%
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Class Problem
If, 20.0g P, 30.0g O2 and 15.0 g H2O;
Yields 50.3 g H3PO4, what is the
Percent Yield?
Note in Previous Problem the Theoretical Yield
was determined to be 54.5 g phosphoric acid.
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Class Problem:
(50.3g H3PO4/ 54.5g H3PO4)(100)
= 92.3% Yield H3PO4
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4.4 Chemical Equations &
Chemical Analysis
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Acidum Formicum – Formic AcidWhat is the empirical formula
of Formic Acid?
Obtained through the distillation of Formica rufa
Formic acid contains H, O and C,
combustion of 2.4527 g of formic acid
yields 0.9606g water
and 2.3482g of carbon dioxide.
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Empirical Formula of Formic Acid
from Combustion Data
Sample (CxHyOn)
furnace H2O absorber
CO2
absorber
excessoxygen
2.4527g
formic acid0.9606g 2.3482g
mH = .9606g(2gH/18gH2O ) = .1067g H
mC = 2.3482g(12gC/44gCO2 ) = .6404g C
mO = 2.4527g - .1067g - .6404g = 1.7056gO
Step 1: Determine Mass of each element
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Step 2: Determine Mole of Each Element1
0.1067 0.10671.008
10.6404 0.0533
12.01
11.7056 0.1066
16.00
molmoles H gH mol H
g
molmoles C gC mol C
g
molmoles O gO mol O
g
Step 3: Divide by Smallest Number
1: 0.1067 2
0.0533
1: 0.0533 1
0.0533
1: 0.1066 2
0.0533
H
C
O
CH2O2
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4.5 Concentration of a Solute
1. Mass Concentration: mass solute m
vol solution VTypical Units: g/L
2. Mole Concentration: moles solute n
Mvol solution V
(Molarity) Typical Units: M=mol/L
Conventions
m = mass
n = moles
M = molarity
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Molarity
moles soluteM molarity
Liter solution
Why is Molarity so Important in Solution
Stoichiometric Calculations?
Because solutes are typically reactants and we can measure
the solution volume, this gives us the moles solute. ie., we
can “Count moles solute” by measuring the volume of a
solution of known Molarity
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Calculate the Molarity of a Solution if 2.00 g NaCl
is diluted to 250.0 ml with water.
1(2.00 )( )( ) .137
58.45 .250
mol NaClg NaCl M
g L
What mass of NaOH(s) would you need to
make 500. mL of .70M NaOH?
.70 40.500 ( )( ) 14
mol NaOH g NaOHL g
L mol
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How do You Make 500.0 ml of .1560M
CuSO4?
1. Calculate amount of Copper(II) Sulfate you
will need.
4 40.1560 159.60.5000 ( )( ) 12.45
mol CuSO g CuSOL g
L mol
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2. Weight the Copper(II) Sulfate
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3. Quantitatively Transfer to 500 ml
Volumetric Flask
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Concentration of Ions
The concentration of ions are related to the salt
via it’s formula
Al2(SO4)3 2 Al+3 + 3 SO4-2
What are the ion concentrations for a
1M Al2(SO4) solution?
2M in Al+3 and 3M in SO4-2
(5M in Total Ion Concentration)
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Dilution Problems
Many Reagents Come as Stock Solutions
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Adding Solvent Does Not Change The Moles
of Solute
Moles Before
Dilution
Moles After
Dilution=
MiVi = MfVf
nM n MV
V
ninitial = nfinal
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How would we make 100. mL of
4.0 M Sulfuric Acid from Stock
16 M Sulfuric Acid?
1. Determine Amount of 16 M
Sulfuric Acid needed.
4.0( ) ( )100 25
16
f
i f
i
M MV V mL mL
M M
MiVi = MfVf
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2. Accurately Measure 25mL
with Volumetric Pipet (TD)
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3. Transfer to 100ml Volumetric Flask
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4. Dilute to Volume
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pH Scale
pH = -log[H3O+]
pX = -log[X]
[H+] = 10-pH = 1
10pH
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pH & Significant Figures
What is pH if [H+] = 3.50x10-6?
5.456
Exact # tells
position of
decimal
Shows # of significant
figures
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pH of Strong Acids & Bases
Consider 100% Dissociation
What is the pH of a 0.00836M HCl
solution?
pH=-log(0.00836)=2.078
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pH of Strong Acids & Bases
What is the hydronium ion
concentration for a solution with
a pH of 4.041?
[H3O+]=10-pH = 10-4.041= 9.099x10-5
= 9.10x10-5
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Solution Reaction Stoichiometry
2. Write Balanced Net Ionic Eq.
3. Calculate Moles of Each Reactant
4. Determine Limiting Reagent
5. Calculate Moles of Other Reactants
and Products as Desired
6. Convert Results to Desired Units (Moles,
Molarity, Mass…)
1. Identify species present and possible rxns.
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Solution Stoichiometry Problem
Consider mixing 30.0mL of 0.750M
sodium chromate with 40.0 mL of 0.500 M
aluminum chloride.
1. Predict the mass and identity of
any precipitate formed.
2. Predict the concentrations of any
ions remaining in solution.
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1. Write Balanced Eq.
3Na2CrO4(aq) + 2AlCl3(aq) 6NaCl + Al2(CrO4)3
2. Use Solubility Rules to Predict
States of Products
3Na2CrO4(aq) + 2AlCl3(aq) 6NaCl(aq) + Al2(CrO4)3(s)
3. Write Net Ionic Equation
3CrO4-2 + 2Al+3
Al2(CrO4)(s)
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3. Identify Initial Moles of all
Species
2 4
2 4
.750 20.0300 0.0450
mol Na CrO mol Nal mol Na
l mol Na CrO
222 4 4
4
2 4
.7500.0300 0.0225
mol Na CrO mol CrOl mol CrO
l mol Na CrO
333
3
.50.0400 0.0200
mol AlCl mol All mol Al
l mol AlCl
Na+:
CrO4-2:
Al+3:
Cl-: 3
3
.5 30.0400 0.0600
mol AlCl mol Cll mol Cl
l mol AlCl
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4. Determine Precipitate Based
on Complete Consumption of
Limiting Reagent
3CrO4-2 + 2Al+3
Al2(CrO4)(s)
2 4 2 42 3 34 2 42 3
4
401.960.0225 3.01
3
mol Al CrO g Al CrOmol CrO g Al CrO
mol CrO mol
2 4 2 43 3 32 43 3
401.960.0200 4.02
2
mol Al CrO g Al CrOmol Al g Al CrO
mol Al mol
3.01g Al2(CrO4)3
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5. Determine Concentration of
Excess Reagent
molesInitial - molesConsumed
volTotal
33 2
4 2
4
20.0200 0.0225
30.0714
0.0400 0.0300
mol Almol Al mol CrO
mol CrOM
l l
0.714M Al+3
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6. Determine Concentration of
Spectator Ions
Na+: 0.0450 mol Na+
0.0700 L= 0.643M
Cl-: 0.0600 mol Cl-
0.0700 L0.857M=
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Acid-Base Titrations
Analytical Technique to Determine the Quantity
of an Unknown Acid or Base by Neutralizing
With an Acid or Base of Known Concentration.
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Titration Procedures
1. Add Acid to
Erlenmeyer Flask,
then add indicator
2. Add Base with
Buret
3. Quit When
Indicator Turns
pink
ab-tit
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What is the concentration of an unknown Sulfuric
Acid solution if it takes 35mL of .40 M NaOH to
neutralize 50.0 mL of the acid?
2NaOH + H2SO4 ---> Na2SO4 + 2H2O
4242 14.0)
05.0
1)(
2
1)(
4.(035. SOHM
LNaOHmol
SOHmol
L
NaOHmolNaOHL
-Note, we are using the initial volume of the acid as
we want to know it’s initial strength