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					Chemical Composition

      Chapter 8
         Counting by Weighing
• When dealing with objects of different
  size/shape, one needs to consider the
  “average mass” of each type of object

Remember average atomic mass from last unit?

We calculated it in grams…
            Atomic Mass Unit
• Since grams, kilograms, etc are too large of a
  unit when dealing with atoms, we use the
  atomic mass unit (amu) as our unit of choice

• 1 amu = 1.66 x 10-24 g
         Average Atomic Mass
• On the periodic table, the average atomic
  mass for an individual atom is the same
  number that we used last unit, just with units
  of amu instead of grams

• Example:
  the average atomic mass for a carbon is 12.01
  amu (check your periodic table)
     Calculating Mass Using amu
• Calculate the mass of a sample that contains
  23 nitrogen atoms.

                    14.01 amu
     23 N atoms x ------------------ = 322.2 amu
                       N atom
     Calculating Number of Atoms
               from Mass
• Calculate the number of oxygen atoms in a
  sample that has a mass of 288 amu.

                 1 O atom
   288 amu x -------------------- = 18 O atoms
                16.00 amu
              Counting Units
• You’re already familiar with counting units:

  – Dozen = 12 of something
  – Gross = 144 of something
  – Pair = 2 of something

• Well, now we have a new one…
                 The Mole
• A mole contains 6.022 x 1023 of something

• 6.022 x 1023 is called Avogadro’s number

• Example: A mole of eggs is equal to 6.022 x
  1023 eggs (that’s A LOT of eggs!!)
                Molar Mass
• The molar mass of a substance is the mass (in
  grams) of one mole of the substance

• The molar mass of an element is the same as
  the mass given on the periodic table

• Example, the molar mass of sodium (Na) is
  22.99 g (this is the mass of one mole, or 6.022
  x 1023 atoms of sodium)
                Calculating Moles and
                  Number of Atoms
• Calculate both the number of moles in a sample
  of chromium (Cr) containing 5.00 x 1020 atoms
  and the mass of the sample.
                             1 mol
5.00 x 1020 atoms x ------------------------- = 8.30 x 10-4 mol
                    6.022 x 1023 atoms

                       52.00 grams Cr
8.30 x 10-4 mol x --------------------------- = 0.0432 grams Cr
                        1 mol
     Molar Mass of Compounds
• You can find the molar mass of a compound by
  adding the individual molar masses of the
  constituent elements.

• Example: the molar mass of NaCl is equal to
  the molar masses of Na + Cl (22.99 g + 35.45 g)
  = 58.44 g/mol
         Calculate Molar Mass
• Calculate the molar mass for sodium sulfate,
  Na2SO4 .

(2 x 22.99 g) + (1 x 32.07 g) + (4 x 16.00 g)

  molar mass = 142.05 g Na2SO4
             Formula Weight
• You may sometimes see the term “formula
  weight” instead of molar mass for ionic

• We will use the term molar mass for all
     Calculating Mass from Moles
• What is the mass of 4.32 moles of HCl.

First, calculate the molar mass of HCl.
     1.008 + 35.45 = 36.458 g/mol

Then, calculate the mass.
                  36.458 g
4.32 moles x ----------------------- = 157 grams HCl
                    1 mol
      Calculating Moles from Mass
• How many moles are in 56.2 grams of KBr?

First, calculate the molar mass of KBr.
   39.10 + 79.90 = 119 g/mol

Then calculate how many moles are in 56.2 grams.
                1 mol
56.2 grams x ------------------- = 0.472 mol
                 119 g
     Calculating Number of Molecules
• How many atoms of silver (Ag) are in a 5.60 gram sample?

First, find the molar mass of silver.  107.9 g/mol

Then, find the number of moles in the sample.

                  1 mol
5.60 grams x -------------------- = 0.0519 mol
                  107.9 g

Then find the number of atoms.

                6.022 x 1023 atoms
0.0519 mol x ------------------------------- = 3.13 x 1022 atoms
                    1 mol
       Calculating Mass Percent
• Mass percent can be calculated by dividing
  the mass of one element in 1 mole of the
  compound by the mass of 1 mole of the

• You need to use the subscripts to find the
  moles and mass of each element in the
 Calculating Mass Percent (cont’d)
• Example: Calculate the mass percent of
  carbon in ethanol (C2H5OH).

Mass of C = 2 mol x 12.01 g/mol = 24.02 g
Mass of H = 6 mol x 1.008 g/mol = 6.048 g
Mass of O = 1 mol x 16.00 g/mol = 16.00 g
       Mass of 1 mol of C2H5OH = 46.07 g
                                      (molar mass)
Mass percent of C = (24.02 g / 46.07 g) x 100%
                   = 52.14%
       Calculating Mass Percent
• Penicillin, like many of the molecules
  produced by living systems, is a large molecule
  containing many atoms. One type of
  penicillin, penicillin F, has the formula
  C14H20N2SO4. Compute the mass percent of
  EACH element in this compound.
      Remember from last unit?
• Empirical formula is the simplest formula –
  expresses smallest whole-number ratios of
  atoms present
• Molecular formula gives the actual
  composition of the molecules that are present

• Example: C2H2 would be molecular, CH would
  be empirical
  Determining Empirical Formulas
Find the empirical formulas for each of the
  following molecular formulas:

• C6H6
• C12H4Cl4O2
• C6H16N2
  Determining Empirical Formulas
Find the empirical formulas for each of the
  following molecular formulas:

• C6H6                CH
• C12H4Cl4O2          C6H2Cl2O
• C6H16N2             C3H8N
    Calculating Empirical Formulas
• Obtain the mass of each element present (in grams)
• Determine the number of moles of each type of atom present
• Divide the number of moles of each element by the smallest
  number of moles to convert the smallest number to 1. If all
  numbers obtained are integers (whole numbers), these are
  the subscripts in the empirical formula. If not continue on to
  step 4.
• Multiply the numbers you derived in step 3 by the smallest
  integer that will convert all of them to whole numbers. This
  set of whole numbers represents the subscripts in the
  empirical formula.
   Calculating Empirical Formulas
When a 0.3546-g sample of vanadium metal is heated
  in air, it reacts with oxygen to achieve a final mass
  of 0.6330g. Calculate the empirical formula of this
  vanadium oxide.
Step 1: Calculate the mass of oxygen that reacted.
Step 2: Use the atomic masses (50.94 for V and 16.00
  for O) to calculate the number of moles of each.
Step 3: divide both numbers by the smaller number
Step 4: multiply both numbers by the smallest integer
  to get both as whole numbers.
  Calculating Empirical Formulas
Example – will be done on board…
  Calculating Molecular Formulas
• You will be given the empirical formula and
  the molar mass
• Remember, the molecular formula is some
  multiple of the empirical formula
  – (empirical formula)n
• Divide molar mass by empirical formula mass
  to find “n”
• Multiply the empirical formula by “n” to find
  the molecular formula
 Calculating Molecular Formulas
Example – will be done on board…
A white powder is analyzed and found to have
  an empirical formula of P2O5. The compound
  has a molar mass of 283.88 g. What is the
  compound’s molecular formula?

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