Stoichiometry& S’mores
• All about quantity
– Relative amounts of reactants & products
– Percent composition and yields
• Reactions must be balanced
– Total input equals total output
• Formulas represent atomic rations
– ratios usually involve small whole numbers
• Usually one or more materials in excess
– More air than burning wood
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Stoichiometry
• The quantitative aspect of chemistry
– How much of each material is involved
• Materials react on atomic ratio basis
– Can’t use grams directly, different mass atoms
– The “mole” is defined as same # of atoms
– Moles behave like atoms, but can be weighed
– Moles are simply a mathematical convenience
3
Quantitative Relationships
in Chemical Reactions
• Coefficients in a reaction = quantity
• Reactions occur in Mole multiples
– Moles are key reaction quantities
– Mass to moles of reactants
– Reaction product back to mass if need be
• Percent Yield
– Actual / theoretical = yield
• Limiting Reactants
– One reactant (almost) always in surplus
4
Stoichiometry
• Stoichiometry rests upon the law of conservation
of mass, and the law of definite proportions.
• chemical reactions combine in definite (usually
simple) ratios of chemicals.
• chemical (non-nuclear) reactions can neither
create nor destroy matter
• The amount of each element must be the same
throughout the overall reaction. For example, the
amount of element X on reactant side must
equal the amount of X on the product side.
5
Reaction occurs in atomic ratios
6
Why the “Mole”?
• Reactions occur in atom ratios
– We cannot count atoms, need an alternative
• We can weigh a large number of atoms
– How many to use, how to make it convenient?
• Mole defined: “grams = atomic mass #”
– Every element has a different atomic mass
• Sum of protons and neutrons, average value
– All elements moles will have 6.02*1023 atoms
– This is “Avogadro’s Number”
– Value is a result of how we defined the gram
• Now we have the equivalent of weighing atoms
– Mole is simply a mathematical convenience
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How much is 1 mole of Gold?
Atomic number 79 (protons), mass 197 (protons+neutrons)
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Mole relationships
10
Simple Ratio Reaction
11
Mass Balance Requirement
• Stoichiometry is used to balance chemical
equations. For example, the two diatomic
gases, hydrogen and oxygen, can combine
to form liquid water, as described by the
following equation
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Equation must be balanced
13
Balancing the Hydrogens
14
Balancing the oxygens
15
Calculation procedure
16
17
Stoichiometry Conversions
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• Stoichiometry is used not only to balance chemical
equations but also is used in conversions — i.e.
converting from grams to moles, or from grams to
milliliters. For example, if there were 2.00 g of NaCl, to
find the number of moles, one would do the following
• From periodic chart, Na=23.00 grams/mole, Cl=35.44
grams/mole, so sum is 23.00+35.44=58.44 gram/mole
19
Sequence of events
• Convert mass to moles (or molecules)
– Cannot balance an equation with grams
– Atoms weigh different amounts
• Balance equation of reactants + products
– Mass Balance + Charge Balance
– Ratio multipliers refer to moles or molecules
• Convert moles back to mass
– Answers often desired in grams
– We weigh in grams, calculate in moles
20
Thermite reaction Demonstration
mixing two powders and igniting them liberates liquid iron
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Thermite Application, welding a railroad
22
Reactions amounts & mole ratios
• Stoichiometry is used to find the right
amount of reactants to use in a chemical
reaction. An example is thermite reaction,
To completely react with 85.0 grams of iron (III) oxide,
28.7 grams of aluminum are needed.
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Simplified Thermite calculation
• GIVEN items
– Reaction is Fe2O3 + 2 Al  Fe + 2 Al2O3
– 160 grams of Fe2O3 available
• Need to go through Mole conversion
– iron oxide = (2*55.85)+(3*16) = 159.7 g/mol
– 160 gram / 159.7 gram/mole = 1.00 mole iron oxide
• Reaction requires 2 moles Al per Fe2O3
– Iron Oxide = 1.00 moles, so Al is 2.00 mole
• Convert answer in moles back to grams
– Al at 2.00 mole * 27 gm/mole = 54 grams Aluminum
• Mix 160 grams iron oxide with 54 grams Aluminum
– Light the fuse and get out of the way!
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Yield
• Lots of common usages
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–
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–
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Crop Yield
Investment return
Failure point in strength of materials
Energy of nuclear reaction (kilotons TNT)
Traffic sign
• Chemistry usage definition
– Theoretical Yield (quantity)
• Output amount predicted by chemical reaction
– Practical or Actual yield (percentage)
• What you really got versus theoretical amount
• Due to various loss mechanisms
– Competing reactions, not 100% is desired product
– Incomplete reactions
– Errors, technical problems, accidents ….
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Yield Calculations
• Example is Salt & Sand mixture
– Start with 6 grams of mixture
• Unknown ratio of salt and sand from Santa Cruz Beach
• Sample was 5 grams, but some got spilled on floor
– End result after separation (example only)
• Separated Salt was 0.2 grams, after drying
• Separated Sand was 3.8 grams, after drying
• Total recovery was 0.2 + 3.8 = 4 grams
– Percentage of each constituent recovered
• 0.2 / 4 = 0.05 = 5% Salt
• 3.8 / 4 = 0.95 = 95% Sand
• Recovery percentages should add to 100%
– Yield is recovery (output) versus input
• 4 grams-out / 5 grams-in = 4 / 5 = 80 % yield
• Loss is (5-4)/5 = 1 / 5 = 20%
26
Percent into Mass
• Exam example
–
–
–
–
–
–
Bauxite = Al2O3 is source for aluminum
Aluminum molar mass is 27 gm/mol
Aluminum oxide molar mass is 102 gram/mol
% aluminum in the oxide is 27*2/102 = 53%
Every 100 grams oxide contains 53 gm Al
Assume Bauxite ore is 70% pure
• with 30% “junk” by weight …
• 100 kilograms dirty ore * 70%  70 kg pure Bauxite
– If we need 100kg of pure Bauxite from 70% ore …
• Need MORE than the pure stuff, since “dirt” included in ore
• Actual need 100kg/70% = 100kg/0.70 = 143 kg of dirty ore
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Limiting Reactants
• Nature rarely provides 100% balance
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–
–
–
Oxygen in air exceeds animal and fuel needs
Almost always an excess of all but 1 reactant
One which runs out first = “Limiting” reactant
Even with perfect balance of reactants
• Reaction may not end in timely fashion (or ever)
– A social analogy
• Last single boy finding last single girl on our planet
– Earth has 6.9 billion people = 6.9*109
– Assume 50% are girls, 50% boys = 3.45*109 girls or boys
» Pairs form until last 2 remaining singles are left
» Last couple’s chance of meeting = 1/(3.45E9)2
» Similar to rolling dice, probability ≈ 1/10E18
» 1 Mole=6*10E23, over 1 million more than social example
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Limiting Reactant
29
Usually one material is consumed completely, others are
unreacted “left overs”, note that green material is gone after
reaction, red remains with products blue and purple
30
Hindenberg Disaster
Hydrogen + Oxygen (21% of atmosphere)  water
Which ingredient was in excess?
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Limiting Reactant Calculations Overview
• Grams input
– Mass of starting materials (e.g. 100gm H2)
• Grams to Atoms (mole) conversion
– Calculate moles of products reactant
– 100gmH2 / 2.016gm per mol = 49.6 mole
• Apply stoichiometry formula and ratios
– Same numbers of atoms (moles) on both sides
– Minimum product defines limiting reactant
• Convert product & leftover moles to grams
– 6.25 moles H2O * 18 gm/mol = 113 gm water
32
Stoichiometry Details
• Equal weight of different mass molecules
– 100 grams Hydrogen + 100 grams Oxygen
• 100 gm H2 / 2.016 gm/mol = 49.60 moles Hydrogen
• 100 gm O2 / 32.00 gm/mol = 3.125 moles Oxygen
– Moles behave like atoms, 2H2 + O2  2H2O
• We need 2 moles H2 for every mole O2
– In this example product limited to 6.250 moles
• Hydrogen is in excess, consumed only 6.250 moles
• Excess hydrogen 49.60 – 6.25 = 43.35 moles H2
– Back to “real world” of grams we can weigh
•
•
•
•
Product = 6.25 mole * 18.03 gm/mol = 112.7 gm H2O
Excess = 43.35 mole * 2.016 gm/mol = 87.3 gm H2
Was mass conserved (input = output)? … yes
Input 100+100=200gm, Output 112.7+87.3=200 gm
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Limiting Social Reactants?
Boys+Girls couples, similar to S’mores experiment today
Social issues have similarities to chemistry
• 50/50 male/female ratio is not exact
• Subject to societal influence
Darwinism in reverse?
• Chinese practice of favoring boy babies
– Results in no wives for many boys
• Wars eliminate mostly men
– Results in no husbands for many girls
• Which sex is today’s limiting reactant ?
– Depends on where you look
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People as “Excess Reactants”, in 2010
Country
Population
Males
Females
Excess
M/F %
World
China
India
Saudi Arabia
United Arab Emirates
Pakistan
Nigeria
Bangladesh
Iran (Islamic Republic of)
Afghanistan
Ireland
Norway
Viet Nam
Thailand
Italy
Poland
6,895,889,018
1,341,335,152
1,224,614,327
27,448,086
7,511,690
173,593,383
158,423,182
148,692,131
73,973,630
31,411,743
4,469,900
4,883,111
87,848,445
69,122,234
60,550,848
38,276,660
3,477,829,638
696,340,752
632,546,781
15,196,132
5,223,594
88,236,978
80,201,003
75,308,800
37,541,222
16,251,571
2,236,442
2,442,819
43,417,900
33,972,348
29,615,920
18,466,775
3,418,059,380
644,994,400
592,067,546
12,251,954
2,288,096
85,356,405
78,222,179
73,383,331
36,432,408
15,160,172
2,233,458
2,440,292
44,430,545
35,149,886
30,934,928
19,809,885
59,770,258
51,346,352
40,479,235
2,944,178
2,935,498
2,880,573
1,978,824
1,925,469
1,108,814
1,091,399
2,984
2,527
-1,012,645
-1,177,538
-1,319,008
-1,343,110
102
108
107
124
228
103
103
103
103
107
100
100
98
97
96
93
Mexico
Germany
113,423,047
82,302,465
55,933,041
40,340,771
57,490,006
41,961,694
-1,556,965
-1,620,923
97
96
France
Brazil
Japan
Ukraine
United States of America
Russian Federation
62,787,427
194,946,470
126,535,920
45,448,329
310,383,948
142,958,164
30,548,615
95,937,239
61,654,165
20,913,685
153,139,563
66,134,540
32,238,812
99,009,231
64,881,755
24,534,644
157,244,385
76,823,624
-1,690,197
-3,071,992
-3,227,590
-3,620,959
-4,104,822
-10,689,084
95
97
95
85
97
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Today’s experiment
• Practical work with Stoichiometry
– Key to quantitative measurements
– Report due next week, with review sheet (1 page)
• S’mores analogy
– Use everyday edibles as “elements”
• C=Chocolate, G=graham cracker, M=marshmallow
– Combine elements into a “compound”
• S’mores is the compound (a sandwich)
• 2G + C + M  G2CM (or CG2M, CMG2, MG2C)
– Determine reaction limitations
• When some materials used up, reaction stops
• Calculate leftovers
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Stoichiometry and S’mores
• A practical hands-on experiment
– Mouth size atoms and molecules
– Simple ratios of ingredients
– Limiting reactants (what we run out of first)
– Excess reactants (what’s left over)
– A very visual demonstration of stoichiometry
37
What’s a S’more ?
Girl Scout camping-out creation from 1927
2 Graham Crackers + 1 Chocolate + 1 Marshmallow
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Why S’mores?
• A hands-on demonstration of atomic ratios
– Will create a “molecule” using edible “atoms”
• G = Graham Cracker “atom”
• C = Chocolate bar “atom”
• M = Marshmallow “atom”
– How do these “atoms” combine?
• 2G + 1C + 1M  G2CM (or CG2M, MCG2)
• Similar to 2H + O  H2O
– Coefficients could be atoms, moles of atoms
• The ratio is the important variable in experiment
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Balancing Equations
• Same atoms before & after rearrangement
– Mass not created or destroyed in reactions
– Need to find correct multipliers (coefficients)
– Reactants and products must be realistic
• Experiment is about combining elements
– magnesium atoms + oxygen atoms
– Mg + O2  MgO (unbalanced)
– 2Mg + O2  2MgO (balanced, mass conserved)
• S’mores
– 2 graham cracker + 1 chocolate + 1 Marshmallow
– 2G + C + M  G2CM
• G2 since 2 “atoms” of Graham Cracker in S’mores “molecule”
• Just like H2 in H2O for water
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Traditional Campfire Method
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Place chocolate bar on graham cracker
Heat up the marshmallow over open fire
Put hot marshmallow over chocolate
Put another cracker on top
Squeeze together, insides melt together
Eat it (Yum!)
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Laboratory Method
• Start with fixed amounts of “elements”
• Weigh each component
– Can weigh more than 1, take an average
• Assemble S’mores “compound”
– Weigh the compound
– Demonstrates conservation of mass,
• Mass of atoms in = mass of molecule out (in = out)
– Demonstrates Dalton’s law of simple multiples
• Have some fun
– Bunsen Burner is our “campfire”
– Does heating change the “compound” ?
42
Campfire Cuisine
Toasted marshmallow melts the chocolate
Graham crackers top & bottom form a sandwich,
makes it easier to handle the hot materials
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Proper S’mores construction
2 Graham Crackers + 1 chocolate +1 marshmallow
Sizes in illustration below are about right
Ignore the score marks on chocolate bar
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Consistency Helps
• Graham Crackers
– Come in scored large sheets
– We’ll use SMALLEST portion of sheet
– Typically 1/4 of whole cracker (scored to break)
• Chocolate
– Chocolate bars come in various sizes
– Chocolate size should approximates the cracker
• The WHOLE chocolate bar
– Should not be much smaller or greatly overhanging cracker
• Marshmallow will be one size
– One per S’more, these are flattened for our purpose
• Being consistent helps calculations
– Results will be comparable to other students
– Simpler overall class experience
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S’mores Math
• We will consider the available materials
– Given # of Crackers, chocolate, Marshmallows
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1 gross of anything = 144 units (a dozen dozen)
How many “atoms” in the given mass
How do these atoms combine, balanced equations
how much product (# of molecules) can be made?
What is left over, the excess reagent
– Given mass of ingredients
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36 pounds of each ingredient
Convert “moles” of materials to atoms
Create S’mores compounds
What is limiting reagent?
Calculate excess materials
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FIRST THING: fix page 1
• S’more should have following recipe
• TWO graham crackers, one on each side
– Not one as listed on first page
– Can’t have a 1-sided sandwich!
– Sticky fingers with two hot marshmallows
• ONE chocolate bar per sandwich
– Should fit the cracker fairly closely
• ONE marshmallow per sandwich
– not two as on the data sheet
– S’more = 2 cracker + 1 Choc. + 1 MM
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Page 2, question 4
answers based on page 1 assumptions
• Given 1 gross (144 units) of each element
– 144 units crackers = 9.0 lbs
• 144/9 = 16 crackers per pound
• 9/144 = 0.0625 pounds per cracker
– 144 units chocolate = 36.0 lbs
• 144/36 = 4 chocolate bars per pound
• 36/144 = 0.25 pounds per chocolate bar
– 144 units marshmallow = 3.0 lb
• 144/3 = 48 marshmallows per pound
• 3/144 = 0.0208 pounds per marshmallow
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Page 3 question 5
assumption is changed from 144 units to 36 pounds
must use prior data for pounds per unit to get quantities
• Assumption = 36 pounds of each element
– 36 lbs crackers * 16 cracker/lb = 576 crackers
• 144 units / 9 lbs = 16 crackers per pound
• But it takes 2 crackers, so 576/2 = 288 max S’mores
– 36 lbs choc * 4 choc./lb = 144 chocolate bars
• 144 units / 36 lb = 4 choc. Bars per pound
• This becomes limiting reactant (fewest S’mores)
– 36 lbs marshmallow * 48 MM/lb = 1728 MM
• 144 units / 3 lb = 48 marshmallows per pound
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Your S’mores assembly
• Given amounts are page 5 line item 6
– 1 Hershey chocolate bar
– 6 Marshmallows
– 5 Graham Crackers
• Used for
– Questions 1-5 on page 6
– Questions 1-6 on page 7
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Page 8 question 3
• C2H2 + 2 H2  C2H6
– 30.3gm / 26.04molarmass = 1.16 mole C2H2
• Molar mass = (2*12.01)+(2*1.088) = 26.04gm/mol
– 4.14gm/2.016 molarmass = 2.05 mole H2
– 2.05moleH2 * (1/2) = 1.025 moleC2H2
• This is less than available, so H2 is limiting reactant
– 1.025moleC2H6 * 30.1molarmass = 30.9g C2H6
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Page 8 question 6
• One rexn product not mentioned is water
– 4 NH3 + 3 O2  2 N2 + 6 H2O
– 24.5gm/17.0molarmass = 1.44 moles NH3
– 30.8gm/32.0molarmass = 0.963 moles O2
• 0.963moleO2 * (4/3) = 1.28 mole NH3 required
• We have 1.44 mole NH3 , so O2 is limiting reactant
– 0.963moleO2 * (2/3) = 0.641moles N2 product
• 0.641moleN2 * 28.0 gm/mol = 18.0 grams N2
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Experiment
• Lets learn some stoichiometry
• And have a little fun …
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Baby Steps vs OneBigCalc
• Baby steps more intuitive
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Get one item at a time right (e.g. gramsmoles)
Balance formulas/equations while in “mole mode”
Put dimensions in every step
Convert result to desired (e.g. molesgrams)
Apply yield issues
• OneBigCalc simpler but may be harder to follow
– Page 280 of text has 5 “daisy-chained” terms
– Simpler to break into a few pieces (show demo)
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People as “Excess Reactants”
Country
Population
Males
Females
Excess
M/F %
World
6,895,889,018
3,477,829,638
3,418,059,380
59,770,258
102
5,223,594
787,836
1,633,272
1,633,725
384,264
696,340,752
632,546,781
3,182,231
14,407,367
2,236,442
7,244,774
153,139,563
29,615,920
11,380,424
18,466,775
261,028
4,739,632
189,652
66,134,540
618,151
2,288,096
473,999
1,103,460
1,148,710
341,676
644,994,400
592,067,546
3,004,996
13,993,650
2,233,458
7,219,965
157,244,385
30,934,928
12,010,341
19,809,885
282,628
5,244,013
216,162
76,823,624
722,989
2,935,498
313,837
529,812
485,015
42,588
51,346,352
40,479,235
177,235
413,717
2,984
24,809
-4,104,822
-1,319,008
-629,917
-1,343,110
-21,600
-504,381
-26,510
-10,689,084
-104,838
228
166
148
142
112
108
107
106
103
100
100
97
96
95
93
92
90
88
86
57
85
United Arab Emirates
7,511,690
Bahrain
1,261,835
Kuwait
2,736,732
Oman
2,782,435
Bhutan
725,940
China
1,341,335,152
India
1,224,614,327
Jordan
6,187,227
Malaysia
28,401,017
Ireland
4,469,900
Ecuador
14,464,739
United States of America 310,383,948
Italy
60,550,848
Mozambique
23,390,765
Poland
38,276,660
China, Macao SAR
543,656
Hungary
9,983,645
Martinique
405,814
Russian Federation
142,958,164
Estonia
1,341,140