Transcript The Mole

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Chapter 10
Chemical
Composition
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Counting by Weighing
• Atoms are too small and there are too many
to count individually.
• Compare to M&M’s in a candy store.
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Atomic Mass: Counting Atoms
by Weighing
Because atoms are so small we can’t use the
conventional units of grams and kilograms.
Mass of a single carbon atom:
1.99 x 10-23 g
1 atomic mass unit = 1.66 x 10-24g
AMU
• Precisely,1/12 the mass of an atom of carbon12. The carbon-12 (C-12) atom has six protons
and six neutrons in its nucleus.
• In imprecise terms, one AMU is the average of
the proton rest mass and the neutron rest mass.
This is approximately 1.67377 x 10 -27 kilogram
(kg), or 1.67377 x 10 -24 gram (g). The mass of
an atom in AMU is roughly equal to the sum of
the number of protons and neutrons in the
nucleus.
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Atomic Mass: Counting
Atoms by Weighing
Elements occur in nature as mixtures of isotopes
Carbon =
98.89% 12C
1.11% 13C
<0.01% 14C
Carbon’s average atomic mass = 12.01 amu
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The Mole
In the lab we will be measuring in grams not
amu’s.
You can consider them to be equivalent.
26.98 g Al = 26.98 amu Al
? g Cu = 63.66 amu Cu
63.66 g
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The Mole
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6.022 X 10
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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
Avagadro
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
Figure 8.1: All of these examples of
pure elements contain the same number
(a mole) of atoms: 6.022x1023 atoms.
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Hmco Photo File
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.
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Figure 8.2: One-mole samples of iron (nails),
iodine crystals, liquid mercury, and powdered sulfur.
Hmco Photo File
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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Learning Check
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!
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, ionics are compounds 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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Molar Mass
• The Mass of 1 mole (in grams)
• Equal to the numerical value of the average
atomic mass (get from 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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A 1-mol sample of graphite
(a form of carbon) weighs 12.01 g.
Hmco Photo File
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Calculations with Molar Mass
molar mass
Grams
1 mol
mass (g)
Moles
mass (g)
1 mol
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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!
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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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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Molar Mass of Molecules and
Compounds
Mass(g) of 1 mol = sum of the atomic masses
1 mole of CaCl2
1 mole Ca x 40.1 g/mol
+ 2 moles Cl x 35.5 g/mol
111.1 g/mol CaCl2
1 mole of N2O4 = 92.0 g/mol
Learning Check!
A. Molar Mass of K2O = ? Grams/mole
94.2 g/mol K2O
B. Molar Mass of antacid Al(OH)3 = ?
Grams/mole
78.02 g/mol Al(OH)3
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Learning Check
Prozac, C17H18F3NO, is a widely used
antidepressant that inhibits the uptake of
serotonin by the brain. Find its molar
mass.
STOICHIOMETRY
- the study of the
quantitative
aspects of
chemical
reactions.
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Learning Check!
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)
• 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
Calculating Formula Mass
Calculate the formula mass of magnesium carbonate, MgCO3.
24.31 g + 12.01 g + 3(16.00 g) =
84.32 g
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Calculating Percentage Composition
Calculate the percentage composition of magnesium carbonate,
MgCO3.
From previous slide:
24.31 g + 12.01 g + 3(16.00 g) = 84.32 g
 24.31 
Mg  
  100  28.83%
 84.32 
 12.01 
C 
  100  14.24%
 84.32 
 48.00 
O
  100  56.93%
 84.32 
100.00
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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
Formulas
Empirical formula: the lowest whole number ratio of
atoms in a compound.
Molecular formula: the true number of atoms of each
element in the formula of a compound.
 molecular formula = (empirical formula)n
[n = integer]
 molecular formula = C6H6 = (CH)6
 empirical formula = CH
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Formulas (continued)
Formulas for ionic compounds are ALWAYS
empirical (lowest whole number ratio).
Examples:
NaCl
MgCl2
Al2(SO4)3
K2CO3
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Formulas (continued)
Formulas for molecular compounds MIGHT be
empirical (lowest whole number ratio).
Molecular:
H2O
C6H12O6
C12H22O11
Empirical:
H2O
CH2O
C12H22O11
Empirical Formula Determination
1. Base calculation on 100 grams of compound.
2. Determine moles of each element in 100 grams of
compound.
3. Divide each value of moles by the smallest of the values.
4. Multiply each number by an integer to obtain all whole
numbers.
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Empirical Formula Determination
Adipic acid contains 49.32% C, 43.84% O, and 6.85% H by
mass. What is the empirical formula of adipic acid?
 49.32 g C 1 mol C   4.107 mol C
12.01 g C 
 6.85 g H 1 mol H   6.78 mol H
1.01 g H 
 43.84 g O 1 mol O   2.74 mol O
16.00 g O 
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Empirical Formula Determination
(part 2)
Divide each value of moles by the smallest of the values.
Carbon:
Hydrogen:
4.107 mol C
 1.50
2.74 mol O
6.78 mol H
 2.47
2.74 mol O
2.74 mol O
Oxygen:
 1.00
2.74 mol O
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Empirical Formula Determination
(part 3)
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Multiply each number by an integer to obtain all whole
numbers.
Carbon: 1.50
x 2
Hydrogen: 2.50
x 2
3
Empirical formula:
5
Oxygen: 1.00
x 2
2
C3H5O2
Finding the Molecular Formula
The empirical formula for adipic acid is C3H5O2. The
molecular mass of adipic acid is 146 g/mol. What is
the molecular formula of adipic acid?
1. Find the formula mass of C3H5O2
3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g
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Finding the Molecular Formula
The empirical formula for adipic acid is C3H5O2. The
molecular mass of adipic acid is 146 g/mol. What is
the molecular formula of adipic acid?
2. Divide the molecular mass by the mass given
by the emipirical formula.
3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g
146
2
73
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Finding the Molecular Formula
The empirical formula for adipic acid is C3H5O2. The
molecular mass of adipic acid is 146 g/mol. What is
the molecular formula of adipic acid?
3. Multiply the empirical formula by this number to
get the molecular formula.
3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g
146
2
73
(C3H5O2) x 2 =
C6H10O4
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Chemical Formulas of Compounds
(HONORS only)
• 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
(HONORS only)
• Empirical Formula
The formula of a compound that
expresses the smallest whole number
ratio of the atoms present.
Ionic formula are always empirical formula
• Molecular Formula
The formula that states the actual
number of each kind of atom found in one
molecule of the compound.
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To obtain an Empirical Formula
(HONORS only)
1. Determine the mass in grams of each
element present, 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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require mole ratios so convert grams to moles
moles of N = 2.34g of N = 0.167 moles of N
14.01 g/mole
moles of O = 5.34 g = 0.334 moles of O
16.00 g/mole
N 0.167 O 0.334  NO 2
Formula: N O
0.167
0.334
0.167
0.167
(HONORS only)
Calculation of the Molecular Formula
(HONORS only)
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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Empirical Formula from % Composition
(HONORS only)
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?
Consider a sample size of 100 grams
This will contain 28.60 grams of B and
10.60 grams H
Determine the number of moles of each
Determine the simplest whole number ratio
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