Atomic Masses & the MOLE� - PowerPoint

							Atomic Masses & the MOLE…
• Neon is a gas that can be found in
  the atmosphere.
  – Dry air contains about 0.002% Ne
  – That’s 500,000,000,000,000,000
    atoms of neon every breath
• Scientists can deal with atoms quant-
  itatively because they know some
  fundamental properties of the atoms
  of each element
• Masses of atoms expressed in grams
  are extremely small.
  – An atom of Oxygen -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
I. Atomic Mass
A. Relative Mass is when you
  measure the mass of all
  atoms based on the
  measurement of one
  particular atom.
1.C-12 atom acts as the standard to
  compare all other atoms
2. 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
3. The masses of all other atoms are
 based on the mass of 1 amu
  – H has 1 proton= 1 amu
  – He has 2 protons and nuetrons= 4
    amus
A proton weighs
  1.007276 amu
A neutron weighs
  1.008665 amu
II. Average Atomic Mass

 A. Most elements exist in nature as
  isotopes
   • 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
1.Average atomic mass is the mass on
  the PT and is the average of all of the
  naturally occurring isotopes of an
  element
Example:
We have 25 marbles that each
 weigh 2 g and 75 marbles that
 weigh one gram. What is the
 average atomic mass for these
 marbles?
2. Calculating average atomic masses:

 a. Cu
 69.17% Cu-63 has a mass of 63 amu,
 30.83% Cu-65 has a mass of 65 amu.

 • It’s calculated by multiplying the atomic
   mass of each isotope by its abundance
   and adding the results.
Cu-63        (0.6917)(63 amu)
Cu-65      + (0.3083)(65 amu)

              63.6 amu
• The reported average atomic mass of
  naturally occurring Cu is 63.55 amu.
Your Turn:
b. Practice #1.
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?
•
c. Practice #2.
   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),
    X-30 (29.974 amu, 3.09% abundance)

. Calculate the atomic weight of X.
•
B. Relating Mass to the number of
Atoms
 • It is impractical to get caught up into
   working with 1 atom’s mass because
   usually you working with a large
   number of atoms.
• 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
1. The average C atom with an atomic
  mass of 12.0 amus is 12 times
  heavier than the average H atom
  a.So 100 C atoms are 12 times
    heavier than 100 H atoms
  b. any # of C atoms would be 12
 times heavier than the same # of H
 atom
• 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

            1 atom      
15.999g
        2.6561*10 g       6.0235 *10 atoms
                     23 
                                       23

                        
Counting Atoms

             1 atom      
        
1.00797g                   6.0231*1023 atoms
                      24 
         1.6735*10 g 


             1 atom     
         1.9941*1023 g   6.0235*10 atoms
12.0115g                
                                      23

                        
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 Avogadro’s 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 =
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
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 chemist’s 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
 REPRESENTATIVE PARTICLES & MOLES



 Atomic
 Nitrogen
              Atom       N     6.02x1023
 Nitrogen
    gas
              Molec.     N2    6.02x1023
  Water       Molec.    H 2O   6.02x1023
Calcium ion    Ion      Ca2+   6.02x1023
 Calcium      Formula
 Fluoride       unit    CaF2   6.02x1023
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
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
Counting Atoms
The desired conversion is:
atoms moles

                        1 mole Mg
1.25x1023 atoms Mg
                     6.02x1023atoms Mg

               = .208 mol Mg
Your Turn:
• 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?
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
Counting Atoms
• 1 mole of Carbon Dioxide contains
  Avogadro’s number of Carbon
  Dioxide molecules.
  – Thus a mole of CO2 contains three
    times Avogadro’s # of atoms
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
Counting Atoms
The desired conversions are:
    moles  molecules  atoms

         6.02x1023
2.12   molecules C3H8   3 atoms C
mols
C3H8    1 mole C3H8     1 molecule
                           C3H8
                =3.83x1024 atoms C
Your Turn:
• 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)?
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
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
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
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
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.
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.
  Formula    Model    Formula    Model
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
Counting Atoms
What is the MM of glucose (C6H12O6)?

 (6C’S)(12.011g/mol) = 72.066g/mol
(12H’S)(1.008 g/mol) = 12.096g/mol
  (6O’S)(15.99 g/mol) = 95.94g/mol
                       180.1g/mol
          1 mole of C6H12O6 or
6.02x1023 molecules of the compound –
      it would weigh 180 grams
Practice Time:
• Determine the mass of 1 mole (Molar
  mass) of each of the following:
  –   Zn
  –   Gd
  –   Zn(C2H3O2)2
  –   (NH4)3PO4
  –   C12H22O11
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.
Counting Atoms
Step 1: Determine the mass of 1 mol
        of N2O3

       (2N’s)(14.01g) = 28.02g
       (3O’s)(15.99g) = 47.97g
                            75.99g

  If 1 mole of N2O3 weighs 75.99g than how
      much will 9.45 mols of N2O3 weigh?
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
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
Counting Atoms
Step 1: Determine the mass of 1 mol of
        Fe2O3

       (2Fe’s)(55.85g) = 111.7g
        (3O’s)(15.99g) = 47.97g
                          159.67g

If 1 mole of Fe2O3 weighs 157.67g than how
   many mols will weigh 92.2 g of Fe2O3?
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
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?
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.
Molar Volume of a Gas

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

                 6.02x1023        6.02x1023
               molecules of O2 molecules of CO2
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.
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
Practice Time:
• The Snoopy balloon featured at the
  Macy’s Thanksgiving Day Parade has a
  volume of 15650 ft3. How many moles of
  Helium are required to fill it up @ STP?
Counting Atoms
 If you have a 35.67g piece of Chro-
 mium metal on your car, how many
  atoms of Chromium do you have?
• You are given mass and asked for
  number of particles
• Let’s get some strategy
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 Avogadro’s number.
          1 mole Cr 6.02x1023 atoms
35.67g Cr
          51.996g Cr   1 mole Cr
           =   4.130x10 23 atoms   of Cr
Calculate the Missing Info…
           Molar                                Gas Vol.
 Formula           Moles   Mass     Particles
           Mass                                 @ STP
                   1.5
  CH4
                   mol
 H2SO4                     79.0 g
                                    9.03x1023
  CO                                molecules

Cu(NO3)2                   93.8 g