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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 in fireplace

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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 practical convenience

• 1 mole of gas is 22.4 liters• 1 mole of solid simply the atomic weight in grams

– 1 mole of carbon is 12 grams, iron is 55.8 grams, etc.

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Los Alamos National Laboratory's Periodic Table

Group**

Period 1 IA 1A

18

VIIIA 8A

1 1 H

1.008

2

IIA 2A

13

IIIA 3A

14

IVA 4A

15

VA 5A

16

VIA 6A

17

VIIA 7A

2 He 4.003

2 3

Li 6.941

4 Be 9.012

5 B

10.81

6 C

12.01

7 N

14.01

8 O

16.00

9 F

19.00

10 Ne 20.18

8 9 10

3 11

Na 22.99

12 Mg 24.31

3

IIIB 3B

4

IVB 4B

5

VB 5B

6

VIB 6B

7

VIIB 7B

------- VIII -------

------- 8 -------

11

IB 1B

12

IIB 2B

13 Al 26.98

14 Si

28.09

15 P

30.97

16 S

32.07

17 Cl

35.45

18 Ar 39.95

4 19 K

39.10

20 Ca 40.08

21 Sc 44.96

22 Ti

47.88

23 V

50.94

24 Cr 52.00

25 Mn 54.94

26 Fe 55.85

27 Co 58.47

28 Ni 58.69

29 Cu 63.55

30 Zn 65.39

31 Ga 69.72

32 Ge 72.59

33 As 74.92

34 Se 78.96

35 Br 79.90

36 Kr 83.80

5 37

Rb 85.47

38 Sr

87.62

39 Y

88.91

40 Zr

91.22

41 Nb 92.91

42 Mo 95.94

43 Tc (98)

44 Ru 101.1

45 Rh 102.9

46 Pd 106.4

47 Ag 107.9

48 Cd 112.4

49 In

114.8

50 Sn 118.7

51 Sb 121.8

52 Te 127.6

53 I

126.9

54 Xe 131.3

6 55

Cs 132.9

56 Ba 137.3

57 La* 138.9

72 Hf 178.5

73 Ta 180.9

74 W

183.9

75 Re 186.2

76 Os 190.2

77 Ir

190.2

78 Pt

195.1

79 Au 197.0

80 Hg 200.5

81 Tl

204.4

82 Pb 207.2

83 Bi

209.0

84 Po (210)

85 At (210)

86 Rn (222)

7 87 Fr

(223)

88 Ra (226)

89 Ac~ (227)

104 Rf (257)

105 Db (260)

106 Sg (263)

107 Bh (262)

108 Hs (265)

109 Mt (266)

110 ---

()

111 ---

()

112 ---

()

114 ---

()

116 ---

()

118 ---

()

Lanthanide Series*

58 Ce 140.1

59 Pr

140.9

60 Nd 144.2

61 Pm (147)

62 Sm 150.4

63 Eu 152.0

64 Gd 157.3

65 Tb 158.9

66 Dy 162.5

67 Ho 164.9

68 Er

167.3

69 Tm 168.9

70 Yb 173.0

71 Lu 175.0

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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.

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Reaction occurs in atomic ratiosMass of hydrogen and oxygen atoms very different, reactions depend on ratios of atoms, not their mass

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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

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Simple Ratio Reaction

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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

Equation must be balancedsame number of atoms on both sides

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Balancing the Hydrogenjone molecule of H2 contains 2 hydrogen atoms

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Balancing the oxygenone molecule of oxygen (O2) contains two atoms of oxygen

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Calculation procedure

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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

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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

Thermite reaction Demonstrationmixing two powders and igniting them liberates liquid iron

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Thermite Application, welding a railroad

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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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Steps in Thermite calculation• GIVEN items

– Reaction is Fe2O3 + 2 Al Fe + 2 Al2O3

– 85 grams of Fe2O3 available

• Need to go through Mole conversion– iron oxide = (2*55.85)+(3*16) = 159.7 g/mol– 85 gram / 159.7 gram/mole = 0.5322 mole iron oxide

• Reaction requires 2 moles Al per Fe2O3

– Iron Oxide = 0.532 moles, so Al is 1.064 mole

• Convert answer in moles back to grams– Al at 1.064 mole * 27 gm/mole = 28.74 grams Aluminum

• Mix 85 grams iron oxide with 29 grams Aluminum– Light the fuse and get out of the way!

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Yield• Lots of common usages

– 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 (experiment 20)

– 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%

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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

– 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

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

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Hindenberg DisasterHydrogen + 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 & O2)

• Grams to Atoms (mole) conversion– Calculate moles of products reactant

– 100gm H2 / 2.016 gm per mol = 49.6 mole

– 100gm O2 / 32.00 gm per mol = 3.13 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

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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

People as “Excess Reactants”, in 2010rankings arranged by excess numbers of males or females per country

Country Population Males Females Excess M/F %World 6,895,889,018 3,477,829,638 3,418,059,380 59,770,258 102China 1,341,335,152 696,340,752 644,994,400 51,346,352 108India 1,224,614,327 632,546,781 592,067,546 40,479,235 107

Saudi Arabia 27,448,086 15,196,132 12,251,954 2,944,178 124United Arab Emirates 7,511,690 5,223,594 2,288,096 2,935,498 228

Pakistan 173,593,383 88,236,978 85,356,405 2,880,573 103Nigeria 158,423,182 80,201,003 78,222,179 1,978,824 103

Bangladesh 148,692,131 75,308,800 73,383,331 1,925,469 103Iran (Islamic Republic of) 73,973,630 37,541,222 36,432,408 1,108,814 103

Afghanistan 31,411,743 16,251,571 15,160,172 1,091,399 107Ireland 4,469,900 2,236,442 2,233,458 2,984 100Norway 4,883,111 2,442,819 2,440,292 2,527 100

Viet Nam 87,848,445 43,417,900 44,430,545 -1,012,645 98Thailand 69,122,234 33,972,348 35,149,886 -1,177,538 97

Italy 60,550,848 29,615,920 30,934,928 -1,319,008 96Poland 38,276,660 18,466,775 19,809,885 -1,343,110 93

Mexico 113,423,047 55,933,041 57,490,006 -1,556,965 97

Germany 82,302,465 40,340,771 41,961,694 -1,620,923 96

France 62,787,427 30,548,615 32,238,812 -1,690,197 95Brazil 194,946,470 95,937,239 99,009,231 -3,071,992 97Japan 126,535,920 61,654,165 64,881,755 -3,227,590 95

Ukraine 45,448,329 20,913,685 24,534,644 -3,620,959 85United States of America 310,383,948 153,139,563 157,244,385 -4,104,822 97

Russian Federation 142,958,164 66,134,540 76,823,624 -10,689,084 86

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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

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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

• 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” ?

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Campfire CuisineToasted 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 rightIgnore 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• 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• 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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Basic S’mores-ology

• S’more should have following recipe

• TWO graham crackers, one on each side– Can’t have a 1-sided sandwich!

• ONE chocolate bar per sandwich– Should fit the cracker fairly closely

• ONE marshmallow per sandwich– New ones are sized for our purpose

• S’more = 2 cracker + 1 Choc. + 1 MM

Critical Thinking question 2answers based on data provided

• 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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Critical Thinking question 3assumption 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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Exercises, 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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Exercises, 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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Being Careful …

• This is a laboratory … not a restaurant– We don’t often eat an experiment, need extra steps– Need to avoid any risk of food contamination

• Safety precautions required1. Clean the bench top surface to be used with damp

paper towels to remove any residues.2. Food must not contact bench tops, set out food

items on paper towels … keep everything clean!3. Weighing food requires a paper towel on scale, then

use “tare” to ignore the towel’s weight4. If you choose to toast marshmallows, use a wooden

coffee stir-stick, NOT lab forceps

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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

– Get one item at a time right (e.g. gramsmoles)– Balance formulas/equations while in “mole mode”– Put dimensions in every step– Convert result to desired (e.g. molesgrams)– 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)

People as “Excess Reactants”

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Country Population Males Females Excess M/F %World 6,895,889,018 3,477,829,638 3,418,059,380 59,770,258 102

United Arab Emirates 7,511,690 5,223,594 2,288,096 2,935,498 228Bahrain 1,261,835 787,836 473,999 313,837 166Kuwait 2,736,732 1,633,272 1,103,460 529,812 148Oman 2,782,435 1,633,725 1,148,710 485,015 142Bhutan 725,940 384,264 341,676 42,588 112China 1,341,335,152 696,340,752 644,994,400 51,346,352 108India 1,224,614,327 632,546,781 592,067,546 40,479,235 107

Jordan 6,187,227 3,182,231 3,004,996 177,235 106Malaysia 28,401,017 14,407,367 13,993,650 413,717 103Ireland 4,469,900 2,236,442 2,233,458 2,984 100

Ecuador 14,464,739 7,244,774 7,219,965 24,809 100United States of America 310,383,948 153,139,563 157,244,385 -4,104,822 97

Italy 60,550,848 29,615,920 30,934,928 -1,319,008 96Mozambique 23,390,765 11,380,424 12,010,341 -629,917 95

Poland 38,276,660 18,466,775 19,809,885 -1,343,110 93China, Macao SAR 543,656 261,028 282,628 -21,600 92

Hungary 9,983,645 4,739,632 5,244,013 -504,381 90Martinique 405,814 189,652 216,162 -26,510 88

Russian Federation 142,958,164 66,134,540 76,823,624 -10,689,084 86Estonia 1,341,140 618,151 722,989 -104,838 85

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Quantitative Relationshipsin Chemical Reactions

• Coefficients in a reaction = quantity• Reactions occur in Mole (atomic) multiples

– Moles are key reaction quantities• Stepwise reaction

– Convert Mass to moles of reactants– Balance the reaction (mole ratios)– Reaction product back to mass if needed

• Percent Yield– Actual / theoretical = yield

• Limiting Reactants– One reactant (almost) always in surplus