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Chapter 10
Chemical Quantities
1
Measuring Matter
measure the amt of something by
• by count,
• by mass, and
• by volume.
2
Measuring Matter (1)
• Atoms, molecules and formula units are
extremely small.
• so many of them in even the smallest sample
that it’s impossible to actually count.
• Counting unit: mole.
3
Measuring Matter (2)
mole (mol)
• SI base unit used to measure the amt (# of
representative particles) of a sub.
• 1 mole of C =
# C atoms in exactly 12 g pure C-12 =
6.02 x 1023 atoms of C
4
Representative particles
Representative particles
atoms
Molecules
Substance
Elements, cpds
Covalent (molecular cpds)
Formula units
Ionic cpds
Ions, e-
Ionic cpds
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Measuring Matter (3)
1 mole of anything contains 6.02 x 1023 rep particles.
Avogadro’s #
atoms, molecules, formula units, e-, ions.
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What is a Mole? (1)
substance
Representative
particles
Chemical
formula
# of representative
particles in 1 mole
Atomic nitrogen atoms
N
6.02 x 1023 atoms
Nitrogen gas
molecules
N2
6.02 x 1023 molecules
Water
molecules
H2O
6.02 x 1023 molecules
Calcium ions
ions
Ca2+
6.02 x 1023 ions
Calcium
Fluoride
formula units
CaF2
6.02 x 1023
formula units
Sucrose
molecules
C12H22O12 6.02 x 1023 molecules
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Measuring Matter (4)
6.02 x 1023 -----Avogadro’s number (A)
602,000,000,000,000,000,000,000
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Question 1
Calculate the # of molecules in 15.7 mol CO2.
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Answer
9.45 x 1024 molecular CO2
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Convert moles to # of atoms
Propane is a gas used for cooking and heating. How
many atoms are in 2.12 mole of propane (C3H8).
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Measuring Matter (6)
The rep particle in
H2O is water
molecule.
12
Measuring Matter
The rep particle in
Cu is Cu atom.
13
Measuring Matter
The rep particle
in NaCl is NaCl
formula unit.
14
Converting Moles to Particles
Find how many particles of sucrose are in 3.50
moles of sucrose.
• 1 mole contains 6.02 x 1023 rep particles.
• write a conversion factor that relates rep
particles to moles of a sub.
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Converting Moles to Particles
• There are 2.11 x 1024 molecules of sucrose in
3.50 moles.
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Question 2
Calculate the # of moles in 9.22 x 1023 atom Fe.
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Answer
1.53 mol Fe
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Converting Particles to Moles
Zn is used as a corrosion-resistant coating on iron
and steel. It is also an essential trace element in
your diet. Calculate the # mol that contain 4.50
x 1024 atoms Zn.
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Converting Particles to Moles
• Multiply the # Zn atoms by the conversion
factor that is the inverse of Avogadro’s #.
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The Mass of a Mole
molar mass
• mass in g of 1 mole of any pure sub (an
element or a cpd)
• molar mass of any element = its atomic
mass
• has the units g/mol.
• molar mass of a cpd = sum of the # of g of
each element in one mole of the cpd
• has the units g/mol
21
Converting Mass to Moles
• A roll of Cu wire has a mass of 848 g.
• How many moles Cu are in the roll?
• Use the atomic mass Cu given on the PT to
apply a conversion factor to the mass given.
22
Converting Moles to Mass
Calculate the mass of 0.625 moles of Ca.
• Use the molar mass Ca to apply a
conversion factor to the # moles given.
• According to the PT,
the atomic mass Ca is
40.078 amu.
• So the molar mass Ca
is 40.078 g.
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Converting Moles to Mass
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Question 3
Calculate the mass of 6.89 mol Sb.
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Answer
839g Sb
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Question 4
A chemist needs 0.0700 mol Se for a rxn. What
mass Se should the chemist use?
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Answer
5.53g Se
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Converting Mass to # of Particles
Calculate the # atoms in 4.77 g Pb.
• To find the # of atoms in the sample, you
must first determine how many moles are
in 4.77 g Pb.
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Converting Mass to # of Particles
According to data from the
PT, the molar mass of Pb is
207.2 g/mol. Apply a
conversion factor to convert
mass to moles.
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Converting Mass to # of Particles
Now use a 2nd conversion factor to convert moles
to # particles.
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Converting Mass to # of Particles
Convert from # particles to mass
# moles = # particles divided by Avogadro’s #
Mass = # moles multiplied by molar mass
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Moles of Cpds
• 1 mole is Avogadro’s # (6.02 x 1023) of
particles of a sub.
• If the sub is a molecular cpd (e.g. ammonia
(NH3), a mole is 6.02 x 1023 molecules of NH3.
• If the sub is an ionic cpd (e.g. baking soda-NaHCO3), a mole is 6.02 x 1023 formula
units of NaHCO3
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Moles of Cpds
1 mole of a cpd contains as many moles of each
element as are indicated by the subscripts in
the formula for the cpd.
• e.g. 1 mole NH3 consists of 1 mole N atoms
and 3 moles H atoms.
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Molar Mass of a Cpd
• The molar mass of a cpd is the mass of 1 mole
of the rep particles of the cpd.
• Because each rep particle is composed of 2 or
more atoms, the molar mass of the cpd is found
by adding the molar masses of all of the atoms
in the rep particle.
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Molar Mass of a Cpd
molar mass NH3 = mass 1 mole N atoms + the
mass 3 moles H atoms.
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Molar Mass of a Cpd
Molar mass NH3 = molar mass N +
3 (molar mass H)
Molar mass NH3 = 14 g + 3(1g) = 17 g/mol
You can use the molar mass of a cpd to
convert between mass and moles
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Converting Mass of a Cpd to Moles
molar mass H2O = 2(molar mass H) + molar mass O
• The molar mass H2O as a conversion factor to
determine moles H2O.
• Notice that 1.000 kg is converted to
1.000 x 103 g for the calculn.
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Converting Mass of a Cpd to Moles
39
Molar Volume (1)
Molar volume
 Volume of a mole of gas
STP
 std temp (0°C or 273 K) and pressure
(1 atm pressure or 101.3kPa)
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Molar Volume (2)
At STP, 1 mol of any gas occupies a vol of
22.4 L
At STP, volume of any gas is 22.4L
At STP, density of a gas
= molar mass divided by molar volume
= molar mass (g) divided by 22.4 L
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Molar Volume (2)
What is the vol of 3.20 x 10-3 mol CO2 at STP?
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Molar Volume (3)
What is the vol of 3.70 mol N2 at STP?
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Molar Volume (4)
At STP, what volume do 1.25 mol He occupy?
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Molar Volume (5)
At STP, what vol. do 0.335 mol C2H6 occupy?
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Question 5
Calculate the # of moles in 17.2 g of benzene (C6H6).
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Answer
0.220 mol C6H6
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CST example 1
How many moles of CH4 are contained in 96.0 g
of CH4?
A
B
C
D
3.00 moles
6.00 moles
12.0 moles
16.0 moles
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CST example 2
How many moles of C-12 are contained in
exactly 6 g of C-12?
A 0.5 moles
B 2.0 moles
C 3.01 x 1023 moles
D 6.02 x 1023 moles
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CST example 3
How many atoms are contained in 97.6 g of
platinum (Pt)?
A
B
C
D
5.16 x 1030
3.01 x 1023
1.20 x 1024
1.10 x 1028
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CST example 4
How many atoms are in a chromium sample with
a mass of 13 g?
A 1.5 x 1023
B 3.3 x 1023
C 1.9 x 1026
D 2.4 x 1024
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CST example 5
When methane (CH4) gas is burned in the presence of oxygen,
the following chemical rxn occurs.
CH4 + 2O2 → CO2 + 2H2O
If 1 mole of methane reacts with 2 moles of oxygen, then
A 6.02x1023 molecules of CO2 and 6.02x1023 molecules
of H2O are produced.
B 1.2x1024 molecules of CO2 and 1.2x 1024 molecules
of H2O are produced.
C 6.02x1023 molecules of CO2 and 1.2x1024 molecules of
H2O are produced.
D 1.2x1024 molecules of CO2 and 6.02x1023 molecules of
H2O are produced.
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CST problem 6
How many moles of chlorine gas are contained in 9.02
x 1023 molecules?
A
B
C
D
1.5 moles
2.0 moles
6.02 moles
9.03 moles
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The Mass of a Mole of an Element
The atomic mass of an element
• expressed in g is the mass of a mole of the
element.
 The mass of a mole of an element is its
molar mass.
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The Mass of a Mole of an Element
One molar mass of C, S, Hg, and Fe are shown.
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The Mass of a Mole of an Element
56
The Mass of a Mole of a Cpd
The Mass of a Mole of a Cpd
How is the mass of a mole of a cpd calculated?
57
The Mass of a Mole of a Cpd
To calculate the molar mass of a cpd, find the #
of g of each element in 1 mole of the cpd. Then
add the masses of the elements in the cpd.
58
The Mass of a Mole of a Cpd
Substitute the unit g for a.m.u. Thus 1 mol of
SO3 has a mass of 80.1 g.
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Quiz
2. A mole of hydrogen gas, H2(g), contains
6.02 x 1023
• molecules.
• atoms.
• amu.
• grams.
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Quiz
3. The atomic mass of fluorine is 19.0 amu, so
the molar mass is
• 19.0 amu.
• 19.0 g.
• 6.02 x 1023 amu.
• 6.02 x 1023 g.
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Quiz
4. Calculate the molar mass of ammonium nitrate.
• 45.02 g
• 80.05 g
• 60.06 g
• 48.05 g
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Converting Moles to Particles
Find the # of rep particles in a # of moles just as
you found the # of roses in 3.5 dz.
• the rep particle is a molecule,
• so the # of molecules of sucrose is obtained
by multiplying 3.50 moles of sucrose by the
conv. factor, Avogadro’s #.
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Converting Particles to Moles
Find out how many moles are represented by a
certain # of rep particles
• Use the inverse of Avogadro’s # as a
conversion. factor.
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Mass of a Mole
atomic masses can be found on the PT, but the values
shown are not integers.
• e.g. 12.011 amu for C, 1.008 amu for H,
and 4.003 amu for He.
• These differences occur because the recorded
values are weighted averages of the masses
of all the naturally occurring isotopes of
each element.
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