The Mole and Molar Masses

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The Mole and Molar Masses

• Notes Chapter 10
• Chemistry I

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10-1 Chemical MeasurementsHow you measure how
much?

• You can measure mass,
• or volume,
• or you can count pieces.
• In chemistry we measure mass in grams.
• Volume in liters.
• Pieces in ????

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Units for Quantity?

• Similar to 1 Dozen 12
• Atoms, molecules, formula units, ions are
  exceedingly small.
• Typical means of counting large quantities are
  not adequate
• Need a new unit of measure.

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Counting by Weighing and Avogadros Number

• How would you estimate the number of nails in a
  box?
• Empty box weighs 213 g
• Box plus nails 1340 g
• Weight of one nail 0.450 g
• Mass of nails 1340 g 213 g 1127 g
• Number of nails (1127 g of nails) 1 nail
  2504.4 nails
• 0.450 g of nails
• 2.50 X 103 nails

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MOLES

• Defined as the number of carbon atoms in exactly
  12 grams of carbon-12.
• 1 mole is 6.02 x 1023 particles or pieces.
• The pieces can be atoms, molecules, or formula
  units.
• Treat it like a very large dozen
• 6.02 x 1023 is called Avogadro's number

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Representative Particles

• The smallest pieces of a substance
• For a dozen eggs it is the egg
• For a molecular compound it is a molecule
• For an ionic compound it is the formula unit.
• For an element it is an atom

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A mole of something

• A mole refers to Avogadros number of
  representative particles of a substance,
• 1 mol Mg 6.02 x 1023 atoms of magnesium
• 1 mol of C6H12O6 6.02 x 1023 molecules of
  glucose
• 1 mol of NaCl 6.02 x 1023 formula units of
  sodium chloride

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Measuring Moles

• Remember relative atomic mass?
• The AMU was one twelfth the mass of a carbon-12
  atom.
• Since the mole is the number of atoms in 12 grams
  of carbon-12
• The decimal number on the periodic table is also
  the mass of 1 mole of those atoms in grams.
• 1 gram mole carbon 12.01 grams carbon
• or
• 1 mole carbon 12.01 grams carbon

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Gram Atomic Mass

• The mass of 1 mole of an element in grams
  (instead of AMUs).
• Gram atomic masses
• Carbon 12.011 grams
• Oxygen 15.999 grams
• Hydrogen 1.0079 grams
• Etc.
• We can count things by weighing them

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The gram atomic masses (GAM)of any two elements
must contain the same number of atoms!

• The GAM of carbon contains the same number of
  atoms as the GAM of Oxygen or the GAM of Sulfur,
  etc.
• Some of carbon atoms will always be 12 times
  more massive than the same of hydrogen atoms

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How many atoms are contained in a gram atomic
mass of an element?

• One GAM of carbon has 12.011 grams
• One GAM of carbon has . . . 1 mole of atoms!

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The gram atomic mass is the mass of one mole of
atoms of any element

• The gram atomic mass of magnesium is 24.305
  grams.
• One mole of magnesium atoms has a mass of 24.305
  grams.
• 1 mol Mg 6.02 x 1023 atoms 24.305 grams

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Practice Determine the mass of 1 mol of the
following atoms

• Sodium
• Selenium
• Lead

• 23.0 g
• 79.0 g
• 207.2 g

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Gram Molecular Mass (GMM)

• For molecular (covalently bonded) compounds
• Determine the chemical formula
• Find the GAM of each atom in formula
• Add up all of the GAMs to find the GMM.

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EXAMPLE What is the mass of one mole of Sulfur
Dioxide?

• The chemical formula for sulfur dioxide is SO2
  
• The GAM of sulfur is 32.06 g
• The GAM of oxygen is 15.999 g
• The gram molecular mass of SO2 is
  32.0615.99915.999 64.058 grams

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PRACTICE What is the mass of one mole of
dinotrogen pentoxide molecules?

• Chemical formula N2O5
• The GAM of nitrogen is 14.007 g
• The GAM of oxygen is 15.999 g
• The GMM of N2O5 is
• 2(14.007) 5(15.999) 108.009 grams

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What about ionic compounds?

• It is inappropriate to calculate the gram
  molecular mass of an ionic compound.
• In this case, we do the same kind of calculation,
  but we call it the gram formula mass.
• The gram formula mass (GFM) is the mass of one
  mole of an ionic compound.

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PRACTICE What is the mass of a mole of calcium
Iodide?

• Chemical formula CaI2
• The GAM of calcium is 40.08 g
• The GAM of iodine is 126.90 g
• The GFM of CaI2 is
• 1(40.08) 2(126.90) 293.88 grams

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gam, gmm, gfm also known ssMOLAR MASSES

• GAM the mass of a mole of atoms also called
  atomic weight
• GMM the mass of a mole of molecules also called
  molecular weight
• GFM the mass of a mole of formula units also
  called formula weight

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Examples

• Calculate the molar mass of the following and
  tell me what type it is.
• Na2S
• N2O4
• C
• Ca(NO3)2
• C6H12O6
• (NH4)3PO4

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10-2 Mole ConversionsUsing Molar Mass

• Finding moles of compounds
• Counting pieces by weighing

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Molar Mass

• The number of grams of atoms, ions, or molecules.
• We can make conversion factors from these.
• To change grams of a compound to moles of a
  compound.

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Now you have a new set of conversion factors!!

• Grams A x (1 mole A) moles of A
• MM of A
• Moles B x (MM of B) grams of B
• moles B

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For example

• How many moles is 5.69 g of NaOH?
• Need to change grams to moles
• For NaOH
• 1 mole Na 22.99 g
• 1 mole O 16.00 g
• 1 mole H 1.01 g
• 1 mole NaOH 40.00 g

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Examples

• What is the mass of 3.5 moles of CO2

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EXAMPLE What is the mass of 3.5 moles of carbon
dioxide?

• Chemical formula CO2
• The GAM of carbon is 12.011 g
• The GAM of oxygen is 15.999 g
• The GMM of CO2 is
• 1(12.011) 2(15.999) 44.009 grams/mol
• 3.5 mol CO2 x (44.009 grams CO2)
• 1 mol CO2
• 154.0315 grams CO2
• 154.032 grams CO2 (with proper sig figs)

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Moles can also be used to find volumes of gases
at standard temperature and pressure

• 1 mole of gas at STP occupies 22.4 liters (dm3)
• Find the volume of 5 moles of oxygen at STP
• ? dm3 5.00 moles O2 X 22.4 dm3 / 1mole 112
  dm3
• Find the volume of 14 grams of Nitrogen at STP
• ?dm3 14 g N2 X 1mole N2 / 28g X 22.4 dm3 /
  1mole 11.2 dm3

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Try This

• How many grams is 9.87 moles of H2O?
• How many liters of gas?
• How many molecules?
• How many total atoms?

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All the things we can change

• Change moles to grams
• Moles to atoms
• Moles to formula units
• Moles to molecules
• Moles to liters
• Molecules to atoms
• Formula units to atoms
• Formula units to ions
• Grams to moles, liters, or particles

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10-3 Determining Empirical Formula Percent
Composition

• Like all percents
• Part x 100
• whole
• Find the mass of each component
• Divide by the total mass.

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Example

• 29.0 g of Ag reacts with 4.30 g of S to form a
  compound. Find the composition of the
  compound.
• 29.0 g of Ag
• 4.30 g of S
• 33.30 g Total
• 29.0 g Ag x 100 87.087 Ag
• 33.30 g
• 4.30 g S x 100 12.912 S
• 33.30 g

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Getting it From the Formula

• Find the composition for CHCl3 (chloroform)
• First calculate the gram formula mass
• (1 x 12.011g) (1 x 1.0079 g) (3 x 35.453 g)
  119.377 g
• Second ? find the by mass for each element
• 12.011 g x 100 10.061 C
• 119.377 g
• 1.0079 g x 100 .84429 H
• 119.377 g
• 3 x 35.453 g x 100 89.094 Cl3
• 119.377 g

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Getting it from the formula

• If we know the formula, assume you have 1 mole.
• Now you know the pieces and the whole.

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Empirical Formula

• From percentage to formula

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The Empirical Formula

• The lowest whole number ratio of elements in a
  compound.
• The molecular formula is the actual ratio of
  elements in a compound.
• The two can be the same.
• HO empirical formula
• H2O2 molecular formula
• H2O both

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Calculating Empirical

• Find the lowest whole number ratio
• C6H12O6
• CH4N
• It is not just the ratio of atoms, it is also the
  ratio of moles of atoms.
• In1 mole of CO2 there is 1 mole carbon and 2
  moles of oxygen.
• In one molecule of CO2 there is 1 atom of C and
  2 atoms of O.

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Calculating Empirical

• Means we can get ratio from percent composition.
• Assume you have 100 g
• The percentages become grams
• Can turn grams to moles
• Find lowest whole number ratio by dividing by the
  smallest.

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Example

• What is the empirical formula for

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Example

• Calculate the empirical formula of a compound
  composed of 38.67 C, 16.22 H, and 45.11 N.
• Assume 100 g so
• 38.67 g C x 1 mol C 3.220 mole C
• 12.01 g C
• 16.22 g H x 1 mol H 16.09 mole
  H
• 1.01 g H
• 45.11 g N x 1 mol N 3.219 mole N
• 14.01 g N

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Example

• The ratio is 3.220 mol C 1 mol C
• 3.219 mol N 1 mol N
• The ratio is 16.09 mol H 5 mol H
• 3.219 mol N 1 mol N
• C1H5N1
• Divide all the moles by the smallest number of
  moles to get the ratio of moles (these are the
  subscripts)

DO THE PRACTICE PROBLEMS!
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Molecular Formula From Empirical

• If you know the molecular mass of a compound and
  its empirical formula you can calculate the
  molecular formula. Divide the molecular mass by
  the mass of the empirical formula this gives a
  multiplier for the subscripts.
• Example The empirical formula of a compound is
  CH3 but its molar mass is 90 g/mol, what is the
  molecular formula?
• CH3 is 15 g/mol The compound is 90g/mol
• So the compound has 6 x1 6 atoms of
  carbon
• and 6 x 3 18 atoms of hydrogen
• so the molecular
  formula is C6H18