The Mole

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The Mole
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Not the type of mole we are talking about
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Measuring Matter

• You often measure the amount of something by one
  of three different methods
• Count
• Mass
• Volume

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ConversionsTry the practice problems on page
289!!!

• 12 apples 1 dozen apples Count
• 12 apples
• 1dozen apples
• 1 dozen apples .20 bushel Volume
• 1 dozen apples
• .20 bushel
• 1 dozen apples 2.0 kg Mass
• 1 dozen apples
• 2.0 kg

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The Mole
Q how long would it take to spend a mole of 1
coins if they were being spent at a rate of 1
billion per second?
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Mollionaire

• Q how long would it take to spend a mole of 1
  coins if they were being spent at a rate of 1
  billion per second?
• A 6.02 x 1023 / 1 000 000 000
• 6.02 x 1014 payments 6.02 x 1014 seconds
• 6.02 x 1014 seconds / 60 1.003 x 1013 minutes
• 1.003 x 1013 minutes / 60 1.672 x 1011 hours
• 1.672 x 1011 hours / 24 6.968 x 109 days
• 6.968 x 109 days / 365.25 1.908 x 107 years
• A It would take 19 million years

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What is a Mole?

• Just as 12 eggs is a dozen ( a specific number
  of particles), a mole is 6.02 x 10 23 particles.
• This number of representative particles is called
  Avogadros number.
• Thats Avogadro, not
• Avocado!!!!

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What is meant by representative
particles? Representative particles are whatever
you are talking about atoms, molecules, or
formula units (ions). The representative particle
of most elements is the atom. Seven elements
exist as diatomic molecules, and, as such, its
representative particle is the molecule. The
seven H2, N2, O2, F2, Cl2, Br2, I2.
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• OK, so now we know that a mole is 6.02 x1023
  representative particles. So how many atoms are
  in one mole of an compound, or how many moles are
  in 6.02 x 1023 atoms?
• Example
• How many moles are in 6.02 x 1023 atoms of
  silver?
• Solution
• Determine the conversion factor.
• 1 mole 6.02 x 1023 representative particles

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6.02 x 1023 Ag atoms x
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To find the number of atoms in a mole of a
compound, you must determine the number of atoms
in a representative formula of that
compound. Example How many oxygen atoms
are in a mole of CO2?
1 mole CO2 x
12.04 x 1023 atoms O2 or, 1.204 x 1024 atoms
O2.
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Converting Number of Particles to Moles

• Look on Page 290 and 291
• Try the practice problems!!!!

How many representative Particles are in one
mole??
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When discussing the mole, using atoms leads to
very large numbers. An easier way to discuss
moles is to work with grams of atoms instead. The
gram atomic mass (gam) is the atomic mass of an
element expressed in grams. For carbon, the gam
is 12.0 g. For atomic hydrogen, the gam is 1.0
g. What is the gam for iron and mercury? (55.85 g
200.6 g) How many atoms are contained in the
gram atomic mass of an element? The gam contains
one mole of atoms (6.02 x 1023 atoms) of that
element.
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Thus, if 12.0 g of carbon is the gam of carbon,
12.0 g is 1 mol of carbon, and has 6.02 x 1023
atoms. What is the mass of a mole of a
compound? To answer this you must know the
formula of the compound. The formula tells you
the number of atoms of each element in a
representative particle of that compound. You
calculate the mass of a mole of a compound by
adding together the atomic masses of the atoms
making up the compound. This is called gram
molecular mass (gmm) Example What is the
molecular mass of SO3?
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Molar mass

• The mass of one mole is called molar mass
• E.g. 1 mol Li 6.94 g Li
• This is expressed as 6.94 g/mol
• What are the following molar masses?
• S SO2
• Cu3(BO3)2

32.06 g/mol
64.06 g/mol
308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6
Cu x 3 63.55 x 3 190.65 B x 2 10.81 x
2 21.62 O x 6 16.00 x 6
96.00 308.27
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Molar mass

• The mass of one mole is called molar mass
• E.g. 1 mol Li 6.94 g Li
• This is expressed as 6.94 g/mol
• What are the following molar masses?
• S SO2
• Cu3(BO3)2

32.06 g/mol
64.06 g/mol
308.27 g/mol
Calculate molar masses (to 2 decimal places)
CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6
110.98 g/mol (Ca x 1, Cl x 2) 96.11 g/mol (N x
2, H x 8, C x 1, O x 3) 32.00 g/mol (O x
2) 811.54 g/mol (Pb x 3, P x 2, O x 8) 180.18
g/mol (C x 6, H x 12, O x 6)
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Example How many grams are in 7.20 mol of
N2O3? N2 28.0 g O3 48.0 g 1 mole N2O3
76.0 g
7.20 mol N2O3
547.2 g N2O3
5.47 x 102 g N2O3
You Try It! 1. How many grams in .720 mol Be? 2.
How many moles in 2.40 g N2?
6.48 g
0.086 mol
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Easy peasy!!
Now lets see if the fog has lifted.
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Example

• If I have 2.00 moles of C13H18O2, how many moles
  of each atom would I have?

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Formula Mass

• mass of a molecule, ion, or formula unit
• sum of mass of all atoms in the chemical formula
• in amu
• Ex H2O
• 18.01528 amu
• formula mass molecular mass for molecular
  compound

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Example

• Find formula mass of potassium chlorate.
• KClO3
• 1(39.0983) 1(35.4527) 3(15.9994)
• 122.549 amu

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Molar Masses

• mass of one mole of pure substance
• numerically equal to formula mass
• units g/mol
• Find molar mass of barium nitrate.
• Ba(NO3)2
• 1(137.327) 2(14.00674) 6(15.9994)
• 261.337 g/mol

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Molar Mass in Conversions

• can be used as a conversion factor
• between grams and moles
• What is the mass in grams of 2.50 mol of oxygen
  gas?

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Example

• Ibuprofen, C13H18O2, is the active ingredient in
  many pain relievers.
• Find molar mass
• (13 x 12.011) (18 x 1.00794) (2 x 15.9994)
• 206.29 g/mol

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Example

• If the tablets in a bottle contain a total of 33
  g of ibuprofen, how many moles are in one bottle?
• How many molecules of ibuprofen are in the
  bottle?

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Example

• What is the number of moles of carbon in that
  bottle?
• What is the total mass in grams of carbon in the
  bottle?

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The Amount of A Mole of Gas
We have seen that one-mole amounts of liquids or
solids have different volumes than other solids
or liquids. What about the volume of gas? Moles
of gases have very predictable volumes. Changing
temperature or pressure of a gas can vary the
volume. That is why the volume of a gas is
measured at a standard temperature and pressure
(STP). Standard temperature is 0C. Standard
pressure is 101.2 kPa or 1 atmosphere (atm) At
STP, 1 mol of any gas occupies a volume of 22.4
L.
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22.4 L is known as the molar volume of a gas
which means it contains 6.02 x 1023
representative particles of that gas.
Example Determine the volume, in liters, of
0.600 mol of SO2 gas at STP.
0.600 mol SO2
13.4 L SO2
Assuming STP, how many moles are in 67.2 L SO2?
67.2 L SO2
3 mol SO2
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Review 1. What volume, in liters, will 0.680
mol of a certain gas occupy? 2. How
many moles is 1.33 x 104 mL of O2 at STP?
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Mass/Density of a Gas
Would 22.4 L of one gas also have the same mass
as 22.4 L of another gas at STP? Probably not. A
mole of one gas have a mass equal to its gfm.
Different gases usually have different
gfms. Measuring the volume of a gas is preferred
to measuring mass. Knowing the volume can also
help find the density of the gas. Density is
found by dividing the mass of a gas by its
volume. Because volume can change with a change
in temperature, density is measured at STP.
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Density (at STP)
Example What is the density of oxygen gas at
STP? (in grams per liter.)
1.43 g/L
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Percent Composition
To keep your lawn healthy, wealthy, and wise you
need to use fertilizer. You cant just use any
ol fertilizer. You need to use one that has the
right mixture of elements or compounds depending
on what you need to do. You need to know the
relative amount of each nutrient. This is the
same in the laboratory. When you make a new
compound, you need to determine its formula by
finding the relative amounts of elements in the
compound. The relative amounts are expressed as
the percent composition, the percent by mass of
each element in a compound.
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There are as many percent values as there are
elements in the compound. The percentages must
add up to 100.
mass of element X
x 100
Example An 8.20-g piece of magnesium combines
with a 5.40-g sample of oxygen completely to
form a compound. What is the percent composition
of this compound?
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1. Find mass of compound. 13.60 g mass of
compound (8.20 g 5.40 g) 2. Find of each
element
Mg
60.3
O

39.7
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Once you determine the percent composition of a
compound you can determine the number of grams of
an element in a specific amount of compound.
Example Calculate the mass of carbon in 82.0 g
of propane, C3H8. 1. Determine composition of
C3H8.
C3H8 44.0 g
C
H
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2. Use conversion factor based on percent by
mass of carbon in ethane. a. 81.8 C
means that for every 100 g C3H8, 81.8 g will
be C.
82 g C3H8
67.1 g C
Check to see if 67.1/82 81.8
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Problems Calculate the amount of hydrogen
in a. 350 g C2H6. b. 20.2 g NaHSO4 c. 124 g
Ca(C2H3O2) 2 d. 378 g HCN e. 100 g H2O
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Empirical Formulas
Once you make a new compound in the laboratory,
you can determine the percent composition
information. Once you know the percent
composition, you can determine the empirical
formula of the compound. The empirical formula
gives the lowest whole number ratio of the atoms
of the elements in a compound. CO2 is an
empirical formula because it is the lowest
whole-number ratio. N2H4 (an explosive) has an
empirical formula of NH2.
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What is the empirical formula of a compound that
is 25.9 N and 74.1 O? 1. Remember
composition means that in 100 g of that
compound each equals that many grams. 2.
Change g to moles
25.9 g N x
1.85 mol N
74.1 g O x
4.63 mol O
N1.85O4.63 mole ratio Not empirical formula
because needs to be whole-numbers.
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3. Divide both molar values by smallest value
to give you a 1 for element with smallest
value.
1 mol N
2.50 mol O
Is N1O2.5 correct? No, not a whole number. Just
multiply both values by a number to make a whole
number. 1 x 2 2 mol N 2.50 x 2 5 mol O Now
you have whole numbers. empirical formula N2O5
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If grams are already given to you, just convert
to moles. Example Analysis of a compound
indicates it contains 2.08 g K, 1.40 g Cr, and
1.74 g O. Find its empirical formula.
2.08 g K x
.053 mol K
1.40 g Cr x
.027 mol Cr
1.74 g O x
.109 mol O
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Then divide by smallest mole number to get mole
ratio. Multiply if you need to.
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Molecular Formula
Determining the empirical formula does not always
tell you the actual molecular formula. An example
is methanol and glucose. CH2O methanol
(empirical and molecular) C6H12O6 glucose
(molecular) Same empirical different molecular
formula. Well, then, how do you know if you have
empirical or molecular? You need to know the
molar mass of the compound.
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The molecular formula is some multiple of the
empirical formula based on their masses.
(simplest formula)x molecular formula, where
x whole-number multiple
(simplest-formula mass)x molecular-formula mass
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Example The simplest formula of a compound
containing phosphorus and oxygen was found to
be P2O5. The molar mass of this compound is
283.889 g/mol. What is the molecular formula of
this compound? (simplest-formula mass)x
molecular-formula mass
1.999
(P2O5)2 molecular formula
P4O10