Atomic Masses

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Atomic Masses the MOLE
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Counting Atoms

• Elemental Neon is a gas that can be found in the
  atmosphere.
• Dry air contains about 0.002 Ne
• Thats 500,000,000,000,000,000 atoms of neon
  every breath
• Scientists can deal with atoms quantitatively
  because they know some fundamental properties of
  the atoms of each element

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Counting Atoms

• Masses of atoms expressed in grams are extremely
  small.
• An atom of O-16 literally weighs
  0.0000000000000000000000266 g
• For most calcs in chemistry it is easier to use a
  relative atomic mass.
• for relative masses, an atom was arbitrarily
  chosen as the standard, by which all other
  masses are compared

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Counting Atoms

• The mass of all the other atoms are then
  expressed in relation to the standard
• C-12 atom acts as the standard
• A single C-12 atom was assigned a mass of
  12 atomic mass units (amu)
• 1 amu is exactly 1/12 of the mass of a C-12 atom
• Carbon has 12 nucleons therefore, the mass of a
  proton 1 amu

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Counting Atoms

• The masses of all other atoms are based on the
  mass of 1 amu
• Hydrogen has 1 proton therefore, it weighs 1
  amu
• Helium has 2 protons and 2 neutrons therefore, it
  weighs 4 amus
• Most elements occur naturally as a mixture of
  isotopes.
• For instance in the two isotopes of Chlorine
  (Cl-35 Cl-37)

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Counting Atoms

• 75 of all of the Cl atoms found in nature are
  the isotope Cl-35
• 25 of the all of the Cl atoms found in nature
  are the isotope Cl-37
• Cl-35 atoms are naturally more abundant than
  Cl-37
• Therefore, the average mass of Cl (taking into
  account isotopic abun-dance) should be closer to
  35 than to the median of 36.

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Counting Atoms

• Masses on the PT are weighted aver-ages of all of
  the naturally occurring isotopes of an element
• The average atomic mass on the PT is reflective
  of both the mass numbers of each isotope the
  abundance of each isotope

Heres how the masses were calculated on the
Periodic Table
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Counting Atoms

• Calculating average atomic masses

Naturally occurring copper consists of
69.17 Cu-63, which has a mass of 63 amu,
and 30.83 Cu-65, with a mass of 65 amu.

• The average atomic mass of Cu is calculated by
  multiplying the atomic mass of each isotope by
  its abundance and adding the results.

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Counting Atoms
(0.6917)(63 amu)
Cu-63
(0.3083)(65 amu)
Cu-65
63.6 amu

• The reported average atomic mass of naturally
  occurring Cu is 63.55 amu.

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Practice Time

• Gallium consists of two isotopes of masses 68.95
  amu and 70.95 amu with abundances of 60.16 and
  39.84, respectively. What is the average atomic
  mass of gallium?
• Naturally occurring element X exists in three
  isotopic forms X-28 (27.977 amu, 92.21
  abundance), X-29 (28.976 amu, 4.70 abundance),
  and X-30 (29.974 amu, 3.09 abundance). Calculate
  the atomic weight of X.

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Counting Atoms

• It is impractical to get caught up into working
  with 1 atom or 1 atoms mass.
• It makes more sense to work with a collection of
  atoms rather than individually

• Scientists were challenged to figure out a way to
  define a collection of particles
• And which could still be described in terms of a
  relative mass

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Counting Atoms

• The average C atom with an atomic mass of 12.0
  amus is 12 times heavier than the average H atom
• So 100 C atoms are 12 times heav-ier than 100 H
  atoms

• Logic says that any of C atoms would be 12
  times heavier than the same of H atoms
• This is true of any collection of atoms when
  compared relatively

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Counting Atoms

• If we assume we can relate the relative masses
  from the PT in the terms of grams
• With the literal masses of an atom (g) for each
  atom we use we seem to get the same number of
  atoms

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Counting Atoms
Hydrogen
Carbon
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Counting Atoms

• The number of atoms that are in the relative
  masses of elements identical in grams to the
  atomic masses on the PT is called Avogadros
  Number
• And is defined as a mole

• The mole becomes a counting unit much like the
  dozen.
• 1 dozen eggs 12 eggs
• 1 mole of eggs

602,000,000,000,000,000,000,000 eggs
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Counting Atoms

• The word mole was introduced by Wilhelm Oswald,
  who derived the term from the word moles meaning
  a heap or pile.
• We are just defining the pile as con-taining
  6.02x1023 items
• Because it is such a huge number of items we
  usually reserve the mole for atoms or molecules

1 mole is always 6.02 x 1023 items
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Counting Atoms

• The mole, whose abbreviation is mol, is the SI
  base unit for meas-uring amount of a pure
  substance.
• The mole is the chemists six-pack or dozen.
  Many objects in our everyday lives come in
  similar counting units.
• 1 ream 500 sheets of paper
• 1 pair of socks 2 socks
• 1 cube 24 cans

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REPRESENTATIVE PARTICLES MOLES REPRESENTATIVE PARTICLES MOLES REPRESENTATIVE PARTICLES MOLES REPRESENTATIVE PARTICLES MOLES

Atomic Nitrogen Atom N 6.02x1023
Nitrogen gas Molec. N2 6.02x1023
Water Molec. H2O 6.02x1023
Calcium ion Ion Ca2 6.02x1023
Calcium Fluoride Formula unit CaF2 6.02x1023
CHEMICAL
REP. PARTICLE
SUBTANCE
REPRESENTATIVE
FORMULA
PARTICLE
IN 1 MOL
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Counting Atoms

• We will learn in the near future that when a
  chemist reasons through a chemical reaction
  (recipe) they think in terms of X number of mols
  of this compound reacts with Y number of mols of
  this compound.
• So we need to know how to calculate the number of
  molecules or atoms are involved in that X number
  of mols

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Counting Atoms

• Using the mole in calculations 1

• How many moles of Magnesium
• is 1.25 x 1023 atoms of Magnesium?

• unit equality

• 1 mol Mg 6.02 x 1023 atoms Mg

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Counting Atoms

• The desired conversion is atoms? moles

1 mole Mg
1.25x1023 atoms Mg
6.02x1023atoms Mg
.208 mol Mg
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Practice Time

• To make sure adequate amounts of product AB is
  being made during a rxn you might need 3.33 mols
  of A reacting with 2.68 mols of B. How many
  atoms of A are reacting with how many atoms of B?
• If you burn sugar (C12H22O11) in pure oxygen you
  produce carbon dioxide and water as products. To
  burn 6.02x1023 molecules of sugar you also need
  7.22x1024 molecules of oxygen and you produce
  6.62x1024 molecules of water and 7.22x1024
  molecules of carbon dioxide. How many mols are
  reacted or produced for each component of the rxn?

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Counting Atoms

• Now suppose you want to determine how many atoms
  are in a mol of a compound or molecule
• To do this you must know how many atoms are
  involved in the molecule.
• To determine the number of atoms represented in a
  molecule requires knowing the chemical formula
• Eg, each molecule of Carbon Dioxide (CO2) is
  composed of 3 atoms

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Counting Atoms

• 1 mole of Carbon Dioxide contains Avogadros
  number of Carbon Dioxide molecules.
• Thus a mole of CO2 contains three times
  Avogadros of atoms

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Counting Atoms

• Using the mole in calculations 2

• How many atoms of Carbon are in 2.12 mols of
  Propane (C3H8)?

• unit equalities

• 1 mol C3H8 6.02x1023 molecules C3H8
• 1 molecule C3H8 3 atoms C

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The desired conversions are
Counting Atoms
moles ? molecules ? atoms
6.02x1023 molecules C3H8
3 atoms C
2.12 mols C3H8
1 molecule C3H8
1 mole C3H8
3.83x1024 atoms C
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Practice Time

• Back to burning sugar, 1 mol of sugar (C12H22O11)
  was burned with 12 mols of oxygen (O2) to produce
  11 mols of water (H2O) and 12 mols of Carbon
  dioxide (CO2). How many total atoms of oxygen
  are burned in the reaction (reactants), and how
  many total atoms of oxygen are produced in the
  reaction (products)?

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Counting Atoms

• We can also relate mass to the number of atoms
  and the mole.
• Relative atomic masses and the mol can be used to
  develop a method of measuring the amount of a
  sample.
• If we had a pile of C atoms that weighed 12 g and
  a pile of H atoms that weighed 1g
• each pile would contain the same number of atoms
  or 6.02x1023 atoms

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Counting Atoms

• The gram atomic masses of any 2 elements
  (since they are relative to C) must contain the
  same of atoms
• A pile of any atom that corresponds to its
  average atomic mass from the PT contains exactly
  6.02x1023 atoms of that element.
• And is equal to how much 1 mole of that sample
  would weigh in grams

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Counting Atoms

• What this allows us to do is to use the mass off
  of the periodic table to represent the mass of 1
  mole (or 6.02x1023 atoms) of that element
• 1 mol of C atoms weighs 12.01 g
• 1 mol of H atoms weighs 1.008 g
• 1 mol of W atoms weigh 183.8 g

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Counting Atoms

• This new version of mass from the periodic table
  is called the gram molar mass, or molar mass.
• Molar Mass mass of 1 mole of atoms/molecules/or
  formula units in grams
• abbreviated MM
• units grams/mol

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Counting Atoms

• We get the mass of 1 mole of any element off of
  the Periodic Table
• So how do we figure out the mass of a mole of a
  compound rather than just an element?
• To answer that question you must have the
  formula of the compound.

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Counting Atoms

• What is the mass of 1 mole of Sulfur Trioxide
  (SO3) A.K.A. Molar Mass?

• The formula of a compound tells you how many
  atoms of each element combine to make the
  representative particle of that compound.

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Counting Atoms

• You can calculate the mass of a mol-ecule of SO3
  by adding the MM of each of the atoms in the
  molecule
• The mass of 1 mole of S is 32.1g.
• The mass of 3 atoms of O is 3 times the MM of a
  single O atom, or (3)(15.99g) 47.97g
• So MM of 1 molecule of SO3 is 32.1g
  47.97g 80.1 g/mol

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Counting Atoms

• What is the MM of glucose (C6H12O6)?

(6CS)(12.011g/mol)
72.066g/mol
(12HS)(1.008 g/mol)
12.096g/mol
95.94g/mol
(6OS)(15.99 g/mol)
180.1g/mol
1 mole of C6H12O6 or 6.02x1023 molecules of the
compound it would weigh 180 grams
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Practice Time

• Determine the mass of 1 mole (Molar mass) of each
  of the following
• Zn
• Gd
• Zn(C2H3O2)2
• (NH4)3PO4
• C12H22O11

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Counting Atoms

• Using the mole in calculations

• How many grams are in 9.45 mol of
  Dinitrogen Trioxide (N2O3)

• The only connection to N2O3 and its mass is how
  much 1 mol of the compound weighs. But, using it
  as a comparison we can calculate the mass of 9.45
  mol.

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Counting Atoms

• Step 1 Determine the mass of 1 mol of N2O3

28.02g
(2Ns)(14.01g)
47.97g
(3Os)(15.99g)
75.99g

• If 1 mole of N2O3 weighs 75.99g than how much
  will 9.45 mols of N2O3 weigh?

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Counting Atoms

• Step 2 Convert the given moles to grams using
  the Molar mass equality.

75.99 g N2O3
9.45 mol N2O3
1 mol N2O3
718 g N2O3
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Counting Atoms

• Find the number of moles of 92.2g of Iron (III)
  Oxide (Fe2O3)

• The only connection to the mass of Fe2O3 and how
  that corresponds to mols is how that 1 mol of the
  compound weighs a certain of grams. Using that
  we can figure out how many moles weigh 92.2 g

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Counting Atoms

• Step 1 Determine the mass of 1 mol of Fe2O3

111.7g
(2Fes)(55.85g)
47.97g
(3Os)(15.99g)
159.67g

• If 1 mole of Fe2O3 weighs 157.67g than how many
  mols will weigh 92.2 g of Fe2O3?

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Counting Atoms

• Step 2 Convert the given mass to mols using the
  Molar mass equality

1 mol Fe2O3
92.2 g Fe2O3
159.67 g Fe2O3
.577mol Fe2O3
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Practice Time

• Vitamin C (C6H8O6), cannot be stored by the body
  and therefore, must be present in the diet. If
  an orange contains 70 mg of Vit C how many
  oranges are necessary to consume 2.5 mols of Vit
  C?
• Your supervisor _at_ Starbucks seems to enjoy
  messing with you. She says she needs you to
  bring her exactly (within reason) 1.33 mole of
  sugar (C12H22O11) for the Mint Mocha Chip
  Frappuccino blended coffee. How do you do that?

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Counting Atoms

• Another generality about the mole is that with
  matter in the gas phase we can develop another
  equality.
• Under the same conditions, equal volumes of gases
  contain equal numbers of particles.
• 1 mol of a gas will occupy the same volume as 1
  mol of any other gas under the same conditions.

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Molar Volume of a Gas

• 1 mole of any gas under the specific conditions
  of 0C and 1 atm (STP) will occupy a volume of
  22.4 L.

• 6.02x1023
• molecules of O2

• 6.02x1023
• molecules of CO2

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Counting Atoms

• What volume, in Liters, does 0.60 mol of SO2 gas
  occupy at STP?

• The only connection to the volume of any gas and
  how that corresponds to mols is that 1 mol of a
  gas occupies 22.4 Liters of space. Using that we
  can figure out the volume of 0.60 mols of a gas
  at STP.

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Counting Atoms

• Step 1 Use the equality 1 mol 22.4 L to do
  the conversion

22.4 L SO2
0.60 moles SO2
1 mole SO2
13 L SO2
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Practice Time

• The Snoopy balloon featured at the Macys
  Thanksgiving Day Parade has a volume of 15650
  ft3. How many moles of Helium are required to
  fill it up _at_ STP?

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Counting Atoms

• If you have a 35.67g piece of Chromium metal on
  your car, how many atoms of Chromium do you have?

• You are given mass and asked for number of
  particles
• Lets get some strategy

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Counting Atoms

• 1st convert given mass into moles
• To do this we use the molar mass (MM) of Cr which
  on the PT is 51.996g/mol
• Then we need to convert from mols to atoms using
  Avogadros number.

1 mole Cr
6.02x1023 atoms
35.67g Cr
51.996g Cr
1 mole Cr
4.130x1023 atoms of Cr
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Calculate the Missing Info
Formula Molar Mass Moles Mass Particles Gas Vol. _at_ STP
CH4 1.5 mol
H2SO4 79.0 g
CO 9.03x1023 molecules
Cu(NO3)2 93.8 g