Transcript Unit E Chemical Quantities

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Unit E: The Mole
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6.02 X 10
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Learning Objectives
• Identify Avogadro’s Number
• Distinguish between counting numbers and
mass/volume numbers
• Calculate the number of particles in a mole
• Calculate the number of moles in a quantity
STOICHIOMETRY
- the study of the
quantitative
aspects of
chemical
reactions.
- Stoich =
element
- Metry = study
of (think:
geometry)
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Avogadro's Number (the
Mole)
• A counting unit
• Similar to a dozen, except instead of 12,
it’s 602 billion trillion
602,000,000,000,000,000,000,000
• 6.02 X 1023 (in scientific notation)
• This number is named in honor of
Amedeo _________ (1776 – 1856), who
studied quantities of gases and
discovered that no matter what the gas
was, there were the same number of
molecules present in a given volume
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Just How Big is a Mole?
• Enough soft drink cans to cover the
surface of the earth to a depth of
over 200 miles.
• If you had Avogadro's number of
unpopped popcorn kernels, and
spread them across the United
States of America, the country would
be covered in popcorn to a depth of
over 9 miles.
• If we were able to count atoms at the
rate of 10 million per second, it
would take about 2 billion years to
count the atoms in one mole.
• In other words: a LOT.
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Everybody Has Avogadro’s
Number!
But Where Did it Come From?
• It was NOT just picked!
It was MEASURED.
• One of the better
methods of measuring
this number was the
Millikan Oil Drop
Experiment
• Since then we have
found even better ways
of measuring using xray technology
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Try it yourself…
Suppose we invented a new collection unit
called a rapp. One rapp contains 8 objects.
1. How many paper clips in 1 rapp?
a) 1
b) 4
c) 8
2. How many oranges in 2.0 rapp?
a) 4
b) 8
c) 16
3. How many rapps contain 40 gummy bears?
a) 5
b) 10
c) 20
The Mole
• 1 dozen cookies = 12 cookies
• 1 mole of cookies = 6.02 X 1023 cookies
• 1 dozen cars = 12 cars
• 1 mole of cars = 6.02 X 1023 cars
• 1 dozen Al atoms = 12 Al atoms
• 1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same,
but the MASS is very different! (a mole of
cars will probably weigh more than a mole of
cookies!)
Mole is abbreviated mol (gee, that’s a lot
quicker to write, huh?)
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A Mole of Particles
Contains 6.02 x 1023 particles
1 mole C
= 6.02 x 1023 C atoms
1 mole H2O
= 6.02 x 1023 H2O molecules
1 mole NaCl
= 6.02 x 1023 NaCl “molecules
(technically, ionic compounds are ratios not
molecules so they are called formula units)
6.02 x 1023 Na+ ions and
6.02 x 1023 Cl– ions
Avogadro’s Number as
Conversion Factor
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6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Note that a particle could be an atom OR a molecule!
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Learning Check
1. Number of atoms in 0.500 mole of Al
a) 500 Al atoms
b) 6.02 x 1023 Al atoms
c) 3.01 x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) 1.0 mole S atoms
b) 3.0 mole S atoms
c) 1.1 x 1048 mole S atoms
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Part 2: Molar Mass
• Describe what molar mass is
• Distinguish between gram molecular mass
and gram formula mass
• Find the molar mass of elements and
compounds
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Molar Mass
• The mass (in grams) of 6.02 x 1023 particles (1
mole) of a substance
• Equal to the average atomic mass (mass
number) on the periodic table
1 mole of C atoms
=
12.0 g
1 mole of Mg atoms
=
24.3 g
1 mole of Cu atoms
=
63.5 g
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The Unit
• We express molar mass using
the unit g/mol(grams per mole)
• Similar to density (g/mL)
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Formula/Atomic/Molecular Mass
• Gram atomic mass (gam) is the mass of 1
mole of atoms
• Gram Molecular Mass (gmm) is the mass
of 1 mole of molecules (covalent only!)
• Gram Formula Mass (gfm) is the mass of
1 mole of ionic compounds
These are all examples of the same thing:
molar mass!
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Other Names Related to Molar Mass
• Molecular Mass/Molecular Weight: If you have a single
molecule, mass is measured in amu’s instead of grams.
But, the molecular mass/weight is the same numerical value
as 1 mole of molecules. Only the units are different. (This is
the beauty of Avogadro’s Number!)
• Formula Mass/Formula Weight: Same goes for
compounds. But again, the numerical value is the same.
Only the units are different.
• THE POINT: You may hear all of these terms
which mean the SAME NUMBER… just different units
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Learning Check!
Find the molar mass
(usually we round to the tenths place)
A. 1 mole of Br atoms =
B. 1 mole of Sn atoms =
79.9 g/mole
118.7 g/mole
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Molar Mass of Molecules and
Compounds
Mass in grams of 1 mole equal numerically to
the sum of the atomic masses
1 mole of CaCl2
= 111.1 g/mol
1 mole Ca x 40.1 g/mol
+ 2 moles Cl x 35.5 g/mol
1 mole of N2O4
= 111.1 g/mol CaCl2
= 92.0 g/mol
Learning Check!
A. Molar Mass of K2O = ? Grams/mole
94. 2 g/mol
B. Molar Mass of antacid Al(OH)3 = ?
Grams/mole
78.0 g/mol
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Challenge
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar
mass.
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Calculations with Molar Mass
molar mass
Grams
Moles
• Moles to Grams/Grams to Moles
• Particles to Grams/Grams to Particles
• Volume
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Converting Moles and Grams
Aluminum is often used for the structure
of light-weight bicycle frames. How
many grams of Al are in 3.00 moles of
Al?
3.00 moles Al
? g Al
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1. Molar mass of Al
1 mole Al = 27.0 g Al
2. Conversion factors for Al
27.0g Al
1 mol Al
or
1 mol Al
27.0 g Al
3. Setup 3.00 moles Al
Answer
x
27.0 g Al
1 mole Al
= 81.0 g Al
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Learning Check!
After leaving his bike out all night, Mr.
Pinson collected a 36g sample of Iron
(II) Oxide from his wheel. How many
moles of rust were formed?
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Challenge!
The artificial sweetener aspartame
(Nutra-Sweet) formula C14H18N2O5 is
used to sweeten diet foods, coffee and
soft drinks. How many moles of
aspartame are present in 225 g of
aspartame?
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Atoms/Molecules and Grams
• Since 6.02 X 1023 particles = 1
mole
AND
1 mole = molar mass
(grams)….
• You can convert
atoms/molecules to moles
and then moles to grams!
(Two step process)
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…But!!
• You can’t go directly from atoms to
grams!!!! You MUST go thru MOLES.
• That’s like asking 2 dozen cookies
weigh how many ounces if 1 cookie
weighs 4 oz? You have to convert to
dozen first!
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Calculations
molar mass
Grams
Avogadro’s number
Moles
particles
Everything must go through
Moles!!!
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Atoms/Molecules and Grams
How many atoms of Cu are
present in 35.4 g of Cu?
35.4 g Cu
1 mol Cu
63.5 g Cu
6.02 X 1023 atoms Cu
1 mol Cu
= 3.4 X 1023 atoms Cu
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Learning Check!
How many atoms of K are present in
78.4 g of K?
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Learning Check!
What is the mass (in grams) of 1.20 X
1024 molecules of glucose (C6H12O6)?
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Learning Check!
How many atoms of O are present in
78.1 g of oxygen?
78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O
32.0 g O2 1 mol O2
1 molecule O2
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Volume of a Mole
• Through experimentation, scientists have
discovered that 1 mole of any gas will
occupy the same volume: 22.4 L
• They will still have different molar masses,
however, and so their densities will be
different
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Example
• How much space will 2.5 moles of N2 gas
occupy?
2.5 moles x 22.4 L = 56 L
mole
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Example 2
• How many moles are in 34.5 L of methane
gas?
34.5 L x 1 mole =
22.4 L
1.54 Moles CH3
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Try it yourself
1.
2.
3.
4.
1.34 moles ozone = ? L
13 L of mustard gas = ? Moles
230 L of Helium gas = ? Moles
5.6 moles Nitrogen gas = ? L
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Percent Composition
What is the percent carbon in C5H8NO4 (the
glutamic acid used to make MSG
monosodium glutamate), a compound used
to flavor foods and tenderize meats?
a) 8.22 %C
b) 24.3 %C
c) 41.1 %C
Chemical Formulas of Compounds
• Formulas give the relative numbers of atoms or
moles of each element in a formula unit - always a
whole number ratio (the law of definite
proportions).
NO2
2 atoms of O for every 1 atom of N
1 mole of NO2 : 2 moles of O atoms to every 1
mole of N atoms
• If we know or can determine the relative number
of moles of each element in a compound, we can
determine a formula for the compound.
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Types of Formulas
• Empirical
• Molecular (true)
Empirical Formula
• The formula of a compound
that expresses the smallest
whole number ratio of the
atoms present.
• Ionic formula are always
empirical formulas
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Molecular Formula (true
formula)
• The formula that states the
actual number of each kind of
atom found in one molecule
of the compound.
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Examples
Empirical
Formula
CH
CH2O
NaCl
CH4N
Molecular
Formula
C2H2
C6H12O6
NaCl
C2H8N2
To obtain an Empirical Formula
1. Convert % to grams, if necessary
2. Calculate the number of moles of each
element.
3. Divide each by the smallest number of
moles to obtain the simplest whole
number ratio.
4. If whole numbers are not obtained* in
step 3), multiply through by the smallest
number that will give all whole numbers
* Be
careful! Do not round off numbers prematurely
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A sample of a brown gas, a major air
pollutant, is found to contain 2.34 g N
and 5.34g O. Determine a formula for
this substance.
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1. Convert 2.34g N x 1 mole N = 0.167
grams to
14g
mol
moles
5.34g O x 1 mole O = 0.333 mol
16g
A sample of a brown gas, a major air
pollutant, is found to contain 2.34 g N
and 5.34g O. Determine a formula for
this substance.
2. Divide
by
smallest
mol
number
0.167 mol N ___________
0.333 mol O
___________
0.167
0.167
= About 1
= About 2
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A sample of a brown gas, a major air
pollutant, is found to contain 2.34 g N
and 5.34g O. Determine a formula for
this substance.
3. Assign
1 mole N for every 2
ratio
moles O =
numbers
NO2
to formula
Note: This is an empirical formula, NOT a
molecular formula! The compound is not
necessarily Nitrogen Dioxide!
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Empirical Formula Song
1.
2.
3.
4.
% to Grams
Grams to Moles
Divide by the Smallest
Multiply to Whole!
Empirical Formula from % Composition
A substance has the following composition by
mass: 60.80 % Na ; 28.60 % B ; 10.60 % H
What is the empirical formula of the substance?
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Consider a sample size of 100 grams
This will contain 60.8g of Na, 28.60 grams
of B and 10.60 grams H
Note: Because % Composition is a constant,
you could use ANY sample size to find
empirical formula…but 100g is the easiest
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1. Convert grams to moles
60.8g Na x 1 mole Na = 2.65 mol
23g
28.60g B x 1 mole B = 2.65 mol
10.8g
10.60g H x 1 mole H = 10.6 mol
1g
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2. Divide by smallest mole
2.65 mol Na __________
2.65 mol B 10.60
mol H
__________
__________
2.65
2.65
2.65
=1
=1
Ratio = 1:1:4
=4
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3. Assign ratio to elements in
formula
1:1:4 = NaBH4
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Practice: Empirical Formula
1.
2.
3.
4.
94.1% O, 5.9% H OH
79.8% C, 20.2% H CH3
67.6% Hg, 10.8% S, 21.6% O HgSO4
27.59% C, 1.15% H, 16.09% N, 55.17% O
C2HNO3
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Multiply to Whole
• You cannot round anything more than .1
• 1.3 = 1.3, NOT 1!
• To convert to whole numbers, multiply the
whole problem by 2, 3, or 4
• 1.5 x 2 = 3
1.25 x 4 = 5
• 1.3 x 3 = 3.999 (4)
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Example w/ Multiply to Whole
A sample contains 70% iron, 30% oxygen.
What is its empirical formula?
1. % to grams
70% = 70g Fe
30% = 30g O
1.25
2. Grams to moles 70g x 1mole = ____
=1
55.8g 1.25
3. Divide by the
30g x 1 mole = 1.875
____ = 1.5
Smallest
16g
1.25
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4. Multiply to Whole
( FeO1.5 )
2
= Fe2O3
Calculation of the Molecular Formula
A compound has an empirical formula
of NO2. The colourless liquid, used in
rocket engines has a molar mass of
92.0 g/mole. What is the molecular
formula of this substance?
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1. Find molar mass of Empirical
Formula (efm)
Element
N
O
# of
Atoms
1
2
Mass per
Atom
14
16
Total
Mass
14
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= 46g
2. Divide molar mass of
compound by empirical formula
mass
92g = 2
46g
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3. Multiply the answer by the
formula subscripts
• NO2 x 2 = N2O4
=The compound is
Dinitrogen Tetroxide
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Practice: Molecular Formula
1. Ethylene glycol (CH3O), used in
antifreeze, with a molar mass of 62g/mol
C2H6O2
2. P-dichlorobenzene (C3H2Cl), makes up
mothballs with molar mass of 147g/mol
C6H4Cl2