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The Mole Concept
Richard Parsons, (RichardP)
CK12 Editor

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AUTHORS
Richard Parsons, (RichardP)
CK12 Editor
EDITORS
Shonna Robinson, (ShonnaR)

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Complete terms can be found at http://www
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ck12
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The Mole Concept

C HAPTER

1

The Mole Concept

C HAPTER O UTLINE
1
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2

The Mole

1
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4

Empirical and Molecular Formulas

1

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Determining Formula and Molar Masses

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1
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Vocabulary
formula mass the sum of the atomic masses of the atoms in a formula
molecular mass the mass of a molecule found by adding the atomic masses of the atoms comprising the molecule

Introduction
When atoms of one element chemically combine with atoms of another element, a compound is formed
...
The formula of a compound contains chemical symbols that tell us
what elements are in the compound
...
For
example, the formula MgCl2 tells us that this compound is composed of the elements magnesium and chlorine, which
combine in the ratio of two atoms of chlorine for each atom of magnesium
...


Formula Mass
The periodic table tells us the relative masses of all the elements
...
In this way, we can compare the relative
masses of any two atoms in the table
...
The formula mass of a compound is the sum of all the atomic
masses in the formula
...
This formula tells us that water is composed of
hydrogen and oxygen and has a ratio of two hydrogen atoms for each oxygen atom
...

Example:
What is the formula mass of H2 O?
Solution:
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Element Atomic Mass Number of Atoms
per Formula
H
1
...
0 daltons
1

Chapter 1
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0 daltons
16
...
0 daltons

The formula mass of H2 O = 18
...

Example:
What is the formula mass of Ca(NO3 )2 ?
Solution:
Element Atomic Mass Number of Atoms
per Formula
Ca
40
...
0 daltons
2
O
16
...
0 daltons
28
...
0 daltons
164
...
0 daltons
...
For example,
the atomic mass of an oxygen atom is 16 daltons, the atomic mass of a fluorine atom is 19 daltons, and the formula
mass of a water molecule is 18 daltons
...


Terminology
Since ionic compounds do not form individual molecules, the term formula mass is the only proper term to describe
this relative mass
...
While it is important to understand this distinction, no professional
chemists have had their degrees in chemistry recalled when they referred to the “molecular mass” of NaCl due to a
slip of the tongue
...

• Not all substances exist as molecules, so the term molecular mass is not used for all substances
...


Further Reading / Supplemental Links
This website has lessons, worksheets, and quizzes on various high school chemistry topics
...

• http://www
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org/gcurran/sho/sho/lessons/lesson56
...
1
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ck12
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Calculate the formula mass for each of the following
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b
...

d
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f
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h
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On average, how many times heavier are bromine atoms than neon atoms?
3
...
If 25
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50 grams of oxygen, what is the atomic mass of M?

4

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Chapter 1
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2 The Mole

Lesson Objectives
The student will:
• express the value of Avogadro’s number and explain its relevance to moles
...

• use the molar mass to convert to grams given the number of moles of a substance, and vice versa
...
02 × 1023
molar mass the mass in grams of one mole of a substance
mole an Avogadro’s number of objects; 1
...
0 grams and contains
6
...
For these reasons, we often deal with groups of small objects and even have names for these groups
...
We frequently buy objects in groups of twelve, like doughnuts
or pencils
...

A group of 144 objects is called a gross
...
Atoms and molecules are
too small to see, let alone to count or measure
...

This video introduces the concept of the mole (3b, 3c): http://www
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com/watch?v=AsqEkF7hcII (9:44)
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The Mole

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Avogadro’s Number
In chemistry, it is nearly impossible to deal with a single atom or molecule
...
Since molecules are extremely small, you might suspect that the number
of particles in this group is going to be very large
...
02 × 1023
particles, and the name of this group is the mole (abbreviated as mol)
...
02 × 1023 is called Avogadro’s
number and is symbolized as the capital letter N
...
One mole of any object contains an Avogadro’s number,
or 6
...

The number of objects in a mole was not chosen arbitrarily
...
02 × 1023 was chosen
...
Chemists realized that they obtained
equal numbers of particles when they used one atomic or molecular mass in grams of the substances
...
If they measured out one atomic mass in grams of both substances (in other words, 12 grams
of carbon and 32 grams of sulfur), they would have the same number of atoms of each element
...
This logic is the same
as knowing that if a basketball has twice the mass of a soccer ball, then 100 lbs of basketballs and 50 lbs of soccer
balls both contain the same number of balls
...
One grammolecular mass of any substance had the same number of particles in it
...

That number turned out to be 6
...
This number of particles continued to be called a gram-molecular
mass for many years, but eventually the name was changed to the mole
...
00 mole of carbon-12 atoms has a mass of 12
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02 × 1023 atoms
...
00 mole of water has a mass of 18
...
02×1023 molecules
...
02 × 1023 particles
...
02 × 1023 particles of a substance is now called the molar mass (mass of 1
...


Converting Molecules to Moles and Vice Versa
We now know that because the mass of a single molecule of H2 SO4 is 98 daltons, the mass of an Avogadro’s number
of H2 SO4 molecules is 98 grams
...
02 × 1023 molecules
...
02 × 1023 molecules into 98 grams,
we will get the mass of a single H2 SO4 molecule in grams
...
6 × 10−22 grams/molecule – tiny, indeed
...

Example:
How many moles are present in 1, 000, 000, 000 (1 billion or 1 × 109 ) molecules of water?

Solution:

moles = (1, 000, 000, 000 molecules) ·

1 mole
6
...
7 × 10−15 moles

You should note that this amount of water is too small for even our most delicate balances to determine the mass
...

Example:
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Chapter 1
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00100 mole?
Solution:

molecules = (0
...
02×1023 molecules
1 mole

= 6
...


Converting Grams to Moles and Vice Versa
We can also convert back and forth between grams of substance and moles
...
To convert the grams of a substance into moles, we divide by the molar mass
...

Example:
How many moles are present in 108 grams of water?
Solution:

grams
moles = molar mass =

108 grams
18
...
00 moles

Example:
What is the mass of 7
...
50 moles) · (56
...
grams

This video tells a story to help students remember the easy way to perform mole conversions (3d): http://www
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com/watch?v=Kg-zaG0ckVg (2:52)
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Lesson Summary
• There are 6
...
00 mole
...
02 × 1023 is called Avogadro’s number
...

• The number of moles in a given mass of substance can be found by dividing the mass by the formula mass
expressed in grams/mole
...
org website allows users to view streaming videos of the Annenberg series of chemistry videos
...
The website has a video that
7

1
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The Mole

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apply to this lesson called “The Mole
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org/resources/series61
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Lesson 9-1 is on the
mole
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fordhamprep
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htm
The website below reviews how to calculate the molar mass of chemical compounds
...
brinkster
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html

Review Questions
1
...

a
...

c
...


60
...
73 grams of NH4 Cl
5
...
0 grams of PbO2

2
...

a
...

c
...


0
...
437 moles of NaOH
0
...
00 moles of ZnCl2

3
...
0
...
6
...
0
...
How many moles are present in the following quantities?
a
...
00 × 1020 molecules of H2 O
b
...
00 × 1025 molecules of H2
c
...
How many molecules, atoms, or formula units are present in the following masses?
a
...
00 gram of Na2 CO3
b
...
00 grams of helium
c
...
grams of H2 O
6
...

a
...
00 × 1023 molecules of H2
b
...
00 × 1024 formula units of AlPO4
c
...
00 × 1022 formula units of NaOH

7
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If you determined that the volume of a silver bar is 100
...
5 g/mL
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ck12
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The Mole Concept

1
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• calculate the percent composition by mass given the formula or name of a compound
...
The ore is removed from the mine and partially purified by
washing away dirt and other materials not chemically bound to the metal of interest
...
The
value of the original ore is very dependent on how much pure metal can eventually be separated from it
...
The ore can be evaluated before it is mined or smelted
to determine what percent of the ore can eventually become pure metal
...


Percent Composition from Masses
Compounds are made up of two or more elements
...
Water, for example, is always 11% hydrogen and 89% oxygen
by mass
...

Percentage composition can be determined experimentally
...
The mass of each element is measured and then divided by the total mass of the original
compound
...
The fraction can then be
multiplied by 100% to convert it into a percent
...
0 grams of ammonia, NH3 , yields 41
...
00 grams of
hydrogen upon decomposition
...
3
...
ck12
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0
50
...
00
50
...
0 grams of Ca(OH)2 in the lab produces 13
...
8 grams of oxygen,
and 0
...
What is the percent composition of calcium hydroxide?
Solution:

13
...
0

% calcium =

10
...
0

% oxygen =

grams
grams · (100%) = 54
...
2%

0
...
0

% hydrogen =

grams
grams · (100%) = 2
...
Sometimes, the sum may total to 99% or
101% due to rounding, but if it totals to 96% or 103%, you have made an error
...
Consider the formula for the compound
iron(III) oxide, Fe2 O3
...

Example:
What is the percent composition of iron(III) oxide, Fe2 O3 ?
Solution:

Element Atomic Mass Number of Atoms
Product
per Formula
Fe
55
...
6 daltons
O
16
...
0 daltons
Formula mass = 159
...
6
159
...
9%
daltons

48
...
6 daltons

· (100%) = 30
...
0 daltons) + 3 · (32
...
0 daltons) = 342
...
0 daltons · (100%) = 15
...
0 daltons
342 daltons
192
342

· (100%) = 28
...
1%
daltons

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Chapter 1
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• Percent composition can be determined either from the masses of each element in the compound or from the
formula of the compound
...

• http://www
...
com/chemzone/05chemical-reactions/
This website has lessons, worksheets, and quizzes on various high school chemistry topics
...

• http://www
...
org/gcurran/sho/sho/lessons/lesson58
...

• http://www
...
com
...
html

Review Questions
Determine the percent composition of the following compounds
...

2
...

4
...


BF3
Ca(C2 H3 O2 )2
FeF3
CrCl3
(NH4 )3 PO4

11

1
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Empirical and Molecular Formulas

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1
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• determine the empirical formula of a compound given either percent composition or masses
...


Vocabulary
molecular formula a formula indicating the actual number of each kind of atom contained in a molecule

Introduction
The empirical formula is the simplest ratio of atoms in a compound
...
Molecules such as benzene, C6 H6 , would have an empirical formula of CH
...
Consider the following
example
...
50 gram sample of a compound contains 0
...
60 grams of chlorine
...
We can calculate the number of moles of calcium and chlorine atoms
in the compound
...
From this, we can determine
the empirical formula
...

0
...
1 g/mol = 0
...
60 g
35
...
0451 mol Cl

At this point, we have the correct ratio for the atoms in the compound
...
0224 Cl0
...
We need to find the simplest whole number ratio
...

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Chapter 1
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0224
= 1
...
0224

Cl =

0
...
01
0
...


Finding Empirical Formula from Percent Composition
When finding the empirical formula from percent composition, the first thing to do is to convert the percentages into
masses
...
0% carbon, 6
...
3% oxygen
...
Suppose we choose a sample size of 100
...
The masses
of each of the elements in this sample will be 40
...
71 grams of hydrogen, and 53
...
These masses can then be used to find the empirical formula
...
grams is usually most convenient because it makes the arithmetic simple
...
0% carbon, 6
...
3%
oxygen
...
grams and multiply this 100
...
This would yield 40
...
71 grams of hydrogen, and 53
...
The
next step is to convert the mass of each element into moles
...
0 g
moles of C = 12
...
33 moles C
moles of H =

6
...
01 g/mol

= 6
...
3 g
16
...
33 mole Ca

Then, we divide all three numbers by the smallest one to get simple whole number ratios:

C=

3
...
33

H=

6
...
33

O=

3
...
33

Finally, we can write the empirical formula CH2 O
...

Whenever the subscript for any element in the empirical formula is 1, dividing each of the moles by the smallest will
yield a simple whole number ratio, but if none of the elements in the empirical formula has a subscript of 1, then
this technique will not yield a simple whole number ratio
...

Example:
Determine the empirical formula for a compound that is 66
...
0% phosphorus
...
grams and multiply the 100
...

This yields 66
...
0 grams of phosphorus
...
0 g
moles of Ca = 40
...
65 moles Ca
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Empirical and Molecular Formulas
moles of P =

34
...
0 g/mol

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= 1
...


Ca =

1
...
50
1
...
10
= 1
...
10

In this case, dividing each of the numbers by the smallest one does not yield a simple whole number ratio
...
If we multiply each of
these by 2, we get a whole number ratio of 3 Ca to 2 P
...


Finding Molecular Formulas
Empirical formulas show the simplest whole number ratio of the atoms in a compound
...
When you find a empirical formula from either masses
of elements or from percent composition, you are finding the empirical formula
...
If we want to determine the actual molecular
formula, we need one additional piece of information
...
In order to get the molecular formula for N2 H4 , you must double each of the subscripts in the
empirical formula
...
The formula mass for NH2 is 16 g/mol, and the
molecular mass for N2 H4 is 32 g/mol
...

Example:
Find the molecular formula for a compound with percent composition of 40
...
1% hydrogen, and 53
...
The molecular mass of the compound is 180 g/mol
...
Earlier,
we determined the empirical formula of this compound to be CH2 O
...
0 g/mol
...
As a result, the molecular formula
for this compound will be C6 H12 O6
...
6% carbon and 14
...
The
molecular mass of the compound is 42
...

Solution:
We choose a sample size of 100
...
This yields 85
...
5 g of H
...
13 moles of C
and 14
...
Dividing each of these by the smallest yields a whole number ratio of 1 carbon to 2 hydrogen
...

The formula mass of CH2 is 14 g/mol
...
1 g/mol yields a multiplier
of 3
...

14

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Chapter 1
...

• The empirical formula of a compound can be calculate from the masses of the elements in the compound or
from the percent composition
...


Further Reading / Supplemental Links
This website has solved example problems for a number of topics covered in this lesson, including the determination
of empirical and molecular formulas
...
sciencejoywagon
...
Lesson 5-5 is on
empirical formulas
...
fordhamprep
...
htm
The website below reviews ow to calculate empirical formulas
...
chem
...
edu/lucid/tutorials/empiricalform
...

2
...

4
...

6
...

8
...

10
...
What is the molecular formula
of this compound?
A compound has the empirical formula C2 H4 NO
...
1 g/mol, what is the molecular
formula of the compound?
A sample of pure indium chloride with a mass of 0
...
2404 grams of chlorine
...
0 grams of rubidium and 5
...

Determine the empirical formula of a compound that contains 58
...
50%N, and 32
...

Determine the empirical formula of a compound that contains 33
...
0%O, and 26
...

Find the molecular formula of a compound with percent composition 26
...
1%N, and 61
...


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