Formula Writing• Atom Accounting

• Mass of atoms and formulas

• Empirical Formula

• Molecular Formula

• Moles

• Avogadro’s number

• Percent composition

• Equation balancing

Atoms in a Formula

• Each atom contained is listed by it’s symbol– Na, K, Mn, O, S, ….

• Subscripts give atom quantities in formula– NaOH (no need for “1” if only one atom)– N2, O2, H2 (diatomic molecules have 2 atoms)

• Empirical formula gives only atom ratios– C2H6O represents Ethyl Alcohol– 3 elements and 9 atoms in the formula

• Structural formulas provide behavior clues– C2H5OH is also Ethyl Alcohol (“alcohol” group is -OH)– CH3OH is Methyl Alcohol (same –OH group)

Mass of Molecules

• Molecule mass is sum of element masses– C2H6O represents Ethyl Alcohol (empirical)

• Carbon: 2 atoms * 12.01 amu = 24.02• Hydrogen: 6 atoms * 1.008 amu = 6.048• Oxygen: 1 atom * 16.00 amu = 16.00

– Formula or Molecule mass is Sig-Fig sum• Round down result to least precise input• 2 Sig-Fig after decimal in this case• 24.02 + 6.05+16.00 = 46.07 amu (grams/mole)

Carbon Dioxide

Formula Unit or Empirical Formula

• Formula Unit is a ratio– Lowest whole number ratio of atoms– Smallest representative unit of a substance– Lowest reduced ratio of ions in a compound– It’s a ratio, may (or may not) be real material

• Example is mass of formula unit– Formula Unit of Sodium Chloride = NaCl

• Na=22.99 amu, Cl=35.45 amu, NaCl=58.44 amu• 1 mole (6.02*10^23 atoms) of NaCl is 58.44 grams

Origin of Moles

• Periodic chart fundamentally based on particles– Proton counting defines element number– Proton + Neutron counting defines element mass– How to assign laboratory weights to elements?

• Could define a reference number of atoms– Use 10^10 or other arbitrary number?– How to count the atoms ?– Requires more conversions, calculations

• We define formula mass = total AMU in grams– Simplifies calculations via periodic chart– Links periodic chart to arbitrary mass unit

• 1 kilogram = 1000 cm^3 water = 1 liter water

Origin of Moles

• Mole comes from MOLEcular weight– Reference laboratory mass (grams) set equal

to the atomic mass number (pure number).– This is arbitrary (grams are based on water)

• We could have used pounds, grains, or stones

– Weights of elements in grams will be proportional to the atomic mass numbers

– The weight in grams equal to the molecular mass is defined as the MOLE

– Most precise definition has mole equal to number of atoms in 12 grams of Carbon-12

Avogadro’s Number• Gram is an arbitrary value

– Originally based on 1 cubic centimeter of water, 1 liter=1kilogram

– Meter based on ¼ circumference of earth

• AMU is dimensionless, a counting method– Protons = Z, the atomic number– Mass = A = Z + n, including neutrons

• Atomic mass is an isotope average– Not a whole number, a weighted average of all natural isotopes

• 1 “mole” defined as material equal to formula weight– How many atoms is that ?

• 6.022 x 10^23 atoms/molecules per mole– A consequence of the other definitions– Can be demonstrated experimentally

• Oil on water 1 molecule thick (Chem 1A book example)• Electrical generation of hydrogen, our future experiment

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

Mole Relationships

• 1 Mole defined as– Element’s atomic mass # expressed in grams

• The “natural” weighted average of all isotopes

– Formula weight of atoms in a molecule• Sum of atomic masses for elements involved

– 6.022 x 10^23 atoms or molecules• Avogadro’s number is the SAME for all Moles

– 22.4 liters of gas (at STP) • Gasses are compressible, liquids & solids are not• “STP” ≡ Standard Temp (0oC) & Pressure (1 Atm)

Mole relationships

Mass• Formula mass or molecular mass

– Sum of atomic masses in the formula– CH4 (methane)

• Carbon has mass of 12.01 (1 atom in formula)• Hydrogen has mass of 1.008 (4 atoms in formula)• 12.01 + (4*1.008) = 16.033 grams/mole

– Convenient to set up a M W spreadsheet• Do molecular weights only ONCE• Simple adaptations are easy• Refer to the chart visually and electronically• << operating spreadsheet example on Jaguar>>

Percent Composition• Formula does NOT give weight % directly

– Some atoms are heavier than others– Hydrogen = 1 Oxygen = 16

• For H2O, Hydrogen not 2/3 (67%) molecule mass

– Uranium = 238, Fluorine = 19• For UF6, Fluorine is not 6/7 (86%) of the total mass

• Formulas must be converted to mass– For water

• H=2*1.008 = 2.016, O = 16.00, H2O = 18.02 gm/mol• Hydrogen therefore 2/18 or 11.1% of water’s mass

– For UF6

• U = 238.0 , F = 6*19.00, so UF6 = 352.0 gm/mole• Fluorine is (6*19)/((6*19)+238) = 114/352 = 32.4% of mass

Mass % example

• C2H6O Ethyl Alcohol (empirical)• Carbon: 2 atoms * 12.01 amu = 24.02• Hydrogen: 6 atoms * 1.008 amu = 6.048• Oxygen: 1 atom * 16.00 amu = 16.00• Total = 24.02 + 6.05+16.00 = 46.07 grams/mole

• Mass percentages readily determined• Carbon is 24.02 / 46.07 = 52.14% of total mass• Hydrogen is 6.05 / 46.07 = 13.13% of total mass• Oxygen is 16.00 / 46.07 = 34.73% of total mass• Total = 100%

Empirical Formulas

• Empirical Formulas based only on atom ratios– Does NOT provide chemical structure– Empirical Formula “CH” is simply a ratio, NOT material

• Could be C2H2 (Ethylene)• Could be C6H6 (Benzene)• Any material with Carbon:Hydrogen ratio 1:1 fits the model

• What use is an empirical formula?– Some analysis tools give only atomic percentages

• X-ray florescence (light emission characteristic of elements)– Some methods provide mass ratios

• Burning fuels yield measurable grams of H2O and CO2

– Grams of products yield moles, moles provide atomic ratios

– Establishes ratio of atoms in formula• Additional step to turn empirical into molecular formula

Iron into Iron Oxide … or rust

Empirical Formula(reverse of finding % mass)

• Typical “real-world” problem– Starting materials and end result are known– What is formula of the resulting material?

• Rusting of Iron (text example)– Pure Iron 1.62 gram, after rusting = 2.31 gram

• Oxygen must be difference 2.31-1.62 = 0.69 gram• Moles of Iron = 1.62/55.85 = 0.029 mol• Moles of Oxygen = 0.69/18.00 = 0.043 mol• Mole Ratio Oxy / Iron =0.043 / 0.029 = 1.5

– Atomic ratios must be whole numbers– Multiply by 2 to clear fractions 2 mole Fe + 3 mole Oxy

• Can also divide by lowest mole amount– 0.029 / 0.029 = 1 unit Iron, 0.043/0.029 = 1.5 units Oxy– Resulting whole number multiples are 2 and 3

– Empirical formula becomes Fe2O3

Elemental Analysis

• A means to determine empirical formulas– Observed grams of each product material– Convert grams to moles of elements

• Grams / (gram/mole) = moles of CO2, H2O, etc.

• Moles of products moles of constituent atoms

– Do “conservation of mass” reality check• Is everything accounted for?• Grams of elements add up to observed products?

– Missing grams may mean missing element(s)

Elemental Analysis

• Note the moles of all elements– Will NOT be integers, just values– Find lowest common denominator– Divide ALL elemental moles by common denominator

• Result will often be simple multiples• If results are integer values, you’re done!

– The empirical formula is those integers beneath the element

– If results contain non-integers, 1 more step required• Trial multiplication using integers which clear the fractions• Final result WILL be integer values to use in formulas.

Route to Empirical Formula

Burning is typical Empirical method

• Fuel is unknown hydrocarbon

• Burning in air yields known products– Carbon Dioxide and Water– Grams of each used to calculate moles– Moles yield amounts of carbon and hydrogen– Empirical formula gives ratio of C and H– More data required to determine real material

• C4H9 multiple possibilities (e.g. Octane = C8H18)

• Apparatus to determine percentages of carbon and hydrogen in a compound.

• Copper oxide helps to oxidize traces of carbon and carbon monoxide to carbon dioxide, and to oxidize hydrogen to water.

Molecular Formulas

• Deduce molecular formula from empirical formula– Most common situation– Homework problems

• Need to know quantities involved– Assume we know molecular mass of starting material

• Molecular mass / empirical mass = small number ratio• Small number ratio * empirical formula = molecular formula

– Benzene example • Molecular Mass =78, determined by other means• Empirical formula mass = 13 (based on C:H ratio of 1:1)• Ratio is 78/13=6, therefore Molecular Formula is C6H6

Empirical Molecular Formula

• A typical “real-world” situation– Initial analysis gives empirical result

• Only the ratios are known

– Calculate mass of empirical formula• For CH, 12.01 + 1.008 = 13.02

– Compare to molecular weight by other means• If 26.04 then empirical is ½, and material is C2H2

• If 78.11 then empirical is 1/6 and material is C6H6

Summary, Empirical vs Molecular

• Formulas– Empirical Formula is only a ratio of atoms

• whole numbers• Benzene lowest order ratio would be CH • Empirical often not very useful alone

– Molecular Formula = correct ratios and quantity• Benzene would be C6H6

• Molecular formula accurately reflects composition

Isotopes• Not all element atoms weigh the same

– Some have more neutrons than others• Uranium-235 (chain reaction fission) is element 92• Uranium-238 (no chain reaction) also element 92• Difference is 3 neutrons, different mass isotopes• isotope chart on Jaguar

• Natural elements include all the isotopes– Mass in nature is the AVERAGE weight

• Might include tens of isotopes• Weighted average relies on relative quantities• Same average value everywhere on earth (we believe)

– One atom of element must be single isotope

Diatomic• Diatomic Molecules

– 7 elements exist as diatomic, or paired atoms• Formation of “double atom” molecules via covalent bond• H2, N2, O2, F2, Cl2, Br2, I2

• Each atom shares outer electrons, so both have 8– Bonding can include 1, 2, or 3 pairs of electrons

• Diatomic elements have twice the mass– Oxygen molecule is O2, from two atoms of Oxygen– Weight of O2 is twice that of Oxygen on chart

• 32 grams per mole of O2 not 16• Volumes of diatomic same as mono-atomic, • 22.4 liter/mole for atomic and diatomic

– Diatomic nature only applies to elements• Oxygen bonds one at a time inside molecules

Mass Nomenclature Details• Atomic Mass

– What an atom weighs on atomic scale• Sum of protons, electrons, electrons

– Single atom must be a particular isotope• NOT the average 35.45 AMU for all chlorine

– C12 atomic mass = 12.0 / 6.02*10^23

• Gram atomic Mass– Mass of one mole of atoms (not molecules)– Monatomic (not diatomic pairs)– Isotopic average atomic weight in grams – 35.45 gm/mole average for Chlorine isotopes

Mass Nomenclature• Molecule Mass (molecular mass)

– What a molecule weighs on molecular scale– Sum of individual isotopic masses in molecule– Exact answer means knowing the isotopes

• Na23+Cl35=NaCl58 or 58 grams per mole• (58 g/mole) / (6.02*10^23 molec/mole) = 9.63E-23 g/molecule

• Molar Mass, or Gram Molar Mass– What a mole of a material weighs in grams

• Involves 6.02*10^23 atoms or molecules

– Utilizes average isotope mass of elements• What’s on the periodic chart, for everyday calculations

Now to the Experiment

• Types of reactions• Balancing a reaction• Reaction drivers

– Activity Series• More active element replaces less active (pg 249)

– Gas evolution• Removes product from solution, prevents reversal

– Precipitate• Removes product from solution, prevents reversal

– Water formation• Water not very ionic, Acid + Base = water

Types of reactions

• Single Replacement – More active element replaces less active

• Zn + CuSO4 Cu + ZnSO4

• Zn + H2SO4 ZnSO4 + H2(g)

• Double Replacement– Swap partners to make gas, precip., water

• HCl + NaOH NaCl + HOH

• AgNO3 + NaCl AgCl(s) + NaNO3

More Reaction Types

• Formation from elements– 2H2 + O2 2H2O

– Fe + Cl2 FeCl2

• Decomposition– NaN3 2Na + 3N2 (Auto Air Bag, McMurry p 353)

– 2NI3 N2 + 3I2

• Water Formation– Acid + Base = water, H+ + OH- = H2O

Now to the Reactions

• Balancing a reaction– Conservation of Mass

• No added or missing materials• Same number of element atoms on each side

– Conservation of charge (applies to ions)• Same number and sign of charge on each side

– Usual pecking order• Balance Cations (Na, Fe) or Carbon first• Hydrogen balance (next to last if other cations)• Oxygen balance last, to fit water or oxides formed• Multiply to get rid of diatomic gas fractions (O2)

Rusting Iron example

• Fe (iron) + O2 Fe2O3 (rust) - unbalanced– 2 Fe on right requires 2 Fe on left

• 2Fe + O2 Fe2O3 - still unbalanced

– 3 oxygen on right requires 3 on left• 2Fe + 3/2 O2 Fe2O3 - balance OK but fractions

– Clear fraction by multiplying by denominator• 4Fe + 3 O2 2Fe2O3 - Balanced, no fractions

– Double check number of atoms both sides• You’re done

Burning methane example

• CH4 + O2 CO2 + H2O - unbalanced– carbon on = carbon on right, carbon OK– 4 hydrogen on left requires 4 on right

• CH4 + O2 CO2 + 2H2O – unbalanced

– Total of 4 oxygen on right, requires 4 on left• CH4 + 2O2 CO2 + 2H2O – balanced !

– Double check, same # atoms both sides?– You’re done

Samples from exercise

• Now we will do a few examples on board

• Students choose one from each page

• Work it out, then class review