[MUSIC]
Lighthouse Scientific
Education presents a lecture
in the Mole series.
The topic;
the Mole as a Quantity
Material in this lecture
relies on an understanding
of the previous lectures
Dimensional Analysis
and Scientific Notation.
This lecture focuses on
the mole as a counting unit.
It begins with a look at
other counting units that
are more familiar to
give some perspective.
These familiar counting
units are used to
demonstrate how counting
units can be formed
into conversion factors.
Conversion factors
facilitate the changing
of units from one
type to another.
Specifically, the definition
of the counting unit
is used create unit factors.
Conversion factors and unit
factors are essential tools
in dealing with moles and
the student should have
a modest understanding
of them moving forward in
their study of chemistry.
If this is already
the case then skip this
subject and the practice
problems that use
familiar units in conversions.
Then it is onto
an introduction of
the main topic, the mole.
The definition of the
mole is also used to create
and use unit factors
as conversion factors.
The lecture ends with a
quiz using the definition of
the mole in conversions.
Counting; larger units.
When common items are
dealt with in large numbers
they are not
counted individually.
Appropriate size terms that
are called counting units,
are used for counting.
For example,
12 eggs are generally
counted as one dozen eggs.
Dozen is a counting unit.
Large numbers of eggs
are counted in dozens.
24 soda cans is referred
to as a case of soda cans.
In this circumstance
the term 'case' means 24.
Consider a package of
500 sheets of paper.
That is a large number
which is more easily handled
as a ream of paper.
In each case, a new
counting term is used to
handle larger numbers.
Each term is derived from
the practical counting or
availability of the item.
A ream of eggs is
not a realistic amount
to be sold in grocery store.
The value of the counting
unit is only to reduce
the size of the number
of the individual count.
Percent plays the same
role with fractions.
For example, 5 reams
is easier to understand
and process than 2500.
Plain and simple
collection terms allows for
the use of smaller numbers.
People feel more
comfortable with numbers that
they intuitively understand.
We like our numbers
to be between 1 and 10.
Few people have an intuitive
understanding of 2500.
Most 1st graders have
mastered the number 5.
We will return to these
counting units in a moment
but first a review
of conversion factors.
Conversion factors are a
tool for changing units of
a measured or given
value into different units
WITHOUT CHANGING THE VALUE!
For that to be true the
units in the conversion
have to be of the same type.
That is, they are both units
of a kind of measurement.
Such as length;
inches can be converted
into centimeters.
Or units of weight;
grams can be
converted into pounds.
Moving between different
units doesn't alter
the amount or length
it merely changes how
that amount is presented.
1 inch can equally be
described as 2.54 cm.
There is a conversion
factor that mathematically
allows the conversion.
Conversion factors are
covered in detail in the
'Dimensional Analysis'
lecture which is part of
the 'Measurement
and Numbers' series.
Conversion factors will
be reintroduced here
because of its necessity
in dealing with the topic
of the lecture, moles.
In the 'Dimensional
Analysis' lecture the
description for converting
from one form of units
to another form of units,
of the same measurement type,
used the generic terms of
'current units' for the
unit type before
the conversion and
'desired units' for the unit
type after the conversion.
The mathematical expression
of a conversion has
the given, or the starting,
or the current unit type
on the left hand side
of the equal sign and
the wanted or the
desired unit type on the
right-hand side of equal sign.
Following the
current units will be
the conversion factor.
Its role is to change
unit type and to provide
the numerical difference
between the units.
Let's look at its first role,
changing unit type.
It does so by canceling
out the term current units.
To help clarify the process,
which is going to involve
fraction math, the current
unit term is made into
a fraction with a
denominator of 1.
Anything can be made into
a fraction by dividing
it by 1.
What this highlights is
that the term 'current units'
can be considered as
being in the numerator of
a fraction even if it is
not written in fraction form.
Now, in fraction
multiplication if the
same thing is in the
numerator of one fraction
as is in the
denominator of another.
it will be canceled out.
All that is left is
the desired unit and
the equation is complete.
All conversions will seek
to cancel out current units
leaving desired units.
That is the underlying
principle of conversions.
With that in mind we return
to those counting units
and show how the
definition of unit is used
to create conversion factors.
A conversion factor, from
dozen into number of eggs,
might look like 12
eggs over a dozen.
24 cans over 1 case
is a conversion factor
into cans from case and
500 papers over 1 ream
is a conversion factor
into paper from ream.
If the opposite conversion
is wanted than the
conversion factor
is the reciprocal;
1 dozen over 12 eggs will
go from eggs to dozen.
1 case over 24 cans goes
from cans to case and
1 ream over 500 paper
would go from paper to ream.
The reason that these
ratios, or fractions,
can be used as conversion
factors is that in each
and every case the
ratio is equal to 1.
These conversion factors
are known as unit factors.
A unit factor is a fraction
that has the same value
in the numerator as
in the denominator
and is therefore equal to 1.
It will be helpful to
describe the construction
of a unit factor
since unit factors and
conversions surround
the use of the mole.
Take this 12 eggs over 1
dozen conversion factor.
Its construction begins
with its definition as
an equality. And that equality
is 1 dozen equals 12 eggs.
We could use donuts if we
wanted to but this is not
about the object,
it's about the units.
To get a unit factor divide
both sides of the equation
by the value on
one of the sides.
Here we will divide
both sides by one dozen.
Shortly we will return
to this step and divide
both sides by 12 eggs.
For now we have this
modified equation.
Since both sides were
divided by the same value
we've maintained the equality.
The final step is to solve
or simplify the expression.
One dozen divided by
one dozen equals one.
There are no units
the dozens cancel out.
Another way of looking at
the simplification is to
ask how many '1 dozens'
are there in '1 dozen' ?
That answer is 1.
The other side the equation
that still remains is unchanged
and we have the unit factor
that we set out to get.
Taking a step back we
can construct a different
unit factor by dividing
both sides of the equation
by 12 eggs.
In simplifying this
expression we ask
how many '12 eggs' are
they are in '12 eggs'?
getting the value of 1.
The other side of the
equation is unchanged
and the second
unit is produced.
These unit factors
are reciprocals
or flips of each other.
They both equal 1 and
are therefore
equal to each other.
Any equality can be made
into a unit factor by
the simple step of dividing
both sides the equation
by one of the sides.
We can solidify our
understanding of conversions
with a couple of examples.
The format of the
conversion, current units
times unit factor
equals desired units
will be our guide.
First example, 60 cans is
equal to how many cases?
A set up of 60 can
is the current unit
and the case is
the desired unit.
What's needed here is
a unit factor with the
correct orientation of units.
Bringing up the definition
of the case we can
construct the appropriate
unit factor by recognizing
the need to cancel out
the current unit of cans.
Since the 60 cans
is essentially in the
numerator, the unit
factor will need to have
cans in the denominator.
Inserting this unit factor
and verifying that the
units of cans cancel
out gives us a correct
mathematical equation
for the conversion.
Taking these values to
calculator and dividing
60 by 24 will give a value
of 2.5 cases.
60 cans equals 2.5 cases.
The next conversion
gives 78 donuts and asks
for the number of
dozen doughnuts.
Beginning with
equality, 12 donuts
equals one dozen donuts.
The correct orientation
of the unit factor to be
inserted in as a conversion
factor will be the one
that has single count of
donuts, the current unit,
in the denominator.
The orientation of this
unit factor is correct
because the unit
donuts cancels out
leaving the unit dozen.
Proper use of the calculator
will show that 78 donuts
is equal to 6.5 dozen donuts.
We see that it is a smart
practice to literally
draw a line through the
units to cancel them out
because it double
checks our orientation.
A final conversion is
5.5 reams of paper into
an individual count of paper.
Starting with equality,
500 papers equals 1 ream,
the correct unit factor will
have the current unit reams
in the denominator so that
the current units cancel out
leaving the unit papers. The
math is multiplication this time,
the other two examples
involved division,
and the final answer
is 2750 papers.
Students who are still not
comfortable with conversions
should review the
'Dimensional Analysis' lecture.
Now it is time to get
after counting very
small particles.
Particles on the atomic scale
are so small that vast
numbers are required
to even see them.
For example, it takes
about 1 times 10 to the 24th
water molecule to
fill a shoot glass.
That's how small
water molecules are.
As there is a need for
dozens, cases and reams
there is a need for
a chemistry unit.
The chemistry unit will
have to be a very large in
order to bring the number
of atomic scale particles
into the realm of
comfortable numbers.
And it is.
The MOLE is the counting
unit for chemistry.
To be inclusive, some
textbooks shorten mole
to just m o l.
Either way, they both
represent the same thing
and that is a number.
It is the counting unit.
Counting units reflect
the size and dimension
of particular items.
Dozen is used for items
that are the size that
regularly come in 12.
The case is for items
that regularly come in 24
and ream for items
that regularly come in
larger collections like 500.
The mole is used for
items that come in
very very large numbers.
It is a number that
is easier to write in
scientific notation.
One mole equals
6.022 times 10 to the 23rd.
Some textbooks just use
6.02 and not the 6.022.
Either way, it is multiplied
by 10 to the power of 23.
6.022 times10 to the 23rd
is called Avogadro's number
after the Italian scientist
Amedeo Avogadro.
Additionally, the symbol
N subscript 'a', is used
for Avogadro's number.
So there is 4 ways
to express this value.
(1) 6.022 times 10 to the 23rd,
(2) just calling it a mole,
(3) calling it
Avogadro's number and
(4) that shorthand N sub 'a'.
Avogadro's number will
follow us the rest of
the way through the
study of chemistry.
Just how big is 6.022
times 10 to the 23rd?
Well, 6.022 times 10
to the 23rd seconds is
14 quintillion years.
That is millions times
longer than the
existence of the universe.
A mole of pennies would
be a stack that made
3.5 round trips to the moon.
There are about N sub
'a' milliliters of water
in the pacific ocean.
The entire pacific ocean.
Note that we used 3
different representations
of Avogadro's number
and also note that
Avogadro's number is an
inappropriate unit for time,
coins or any amounts that
we can see with our eyes.
But try this out;
how much is 1.66 moles
of the molecule H2O?
It is that shot glass
of water which we saw
contains 1 times 10 to
the 24 molecule of water.
So the mole is good
counting unit for:
subatomic particles like
electrons, protons, neutrons.
It is good for atoms, ions,
molecules and compounds.
It is good for atomic
scale particles.
An expansion on the
notion of moles comes when
dealing with compounds.
We know that the molecular
formula or the formula unit
gives the ratio of atoms
or ions in the compound.
1 mole of compound
will therefore have that
ratio of moles
of atoms or ions.
For example, 1 mole of the
compound barium chloride,
Ba Cl 2, will have 1
mole of Ba 2 plus cations
and 2 mole Cl minus anions.
That follows from the
formula unit ratio of 1
barium ion to 2 chloride ions.
1 mole of the polyatomic
ion C O3-2, carbonate,
will have 1 mole
carbon atoms and
3 moles oxygen atoms.
The -2 charge plays
no role here. 1 mole of
carbonate has 4 moles of atoms.
1 mole of the sugar
molecule C6 H12 O6
will have 6 moles
of carbon atoms,
12 moles of hydrogen atoms,
and 6 moles oxygen atoms.
Some math with these
numbers shows that
1 mole C6 H12 O6 is
comprised of 24 moles
of atoms. This is consistent
with the sugar molecule
having 24 atoms.
As with the other
counting units covered in
this lecture, the mole can
be made into a unit factor
as long as it is a
fraction with the same value
in the numerator as
in the denominator.
Repeating the process of
generating a unit factor;
begin with an equality.
1 mole equals 6.022
times 10 to the 23rd.
Divide both side of the
equation by one of the sides.
For example divide
both sides by 1 mole.
Solve or simplify expression;
1 mole divided by 1 mole
is equal to 1.
The second fraction
remains unchanged. This is
the first of 2 unit factors
that can be used in moving
between count and moles.
The other unit factor is
made by dividing both sides
by Avogadro's number and
simplifying the fraction
on the right to
1 and leaving the
other fraction.....unchanged.
These two unit factors are
equal to one and therefore
are equal to each other.
These unit factors can
be put to work converting
from individual count
to moles or vice versa.
They are based on the
definition of a mole as
a counting unit.
But the count needs to be
of something........
like atoms.
A mole of atoms is
Avogadro's number of atoms.
A mole is not a mole of atoms.
A mole is a number.
A dozen is not a dozen eggs.
It is the number, 12.
The unit factor based
on the definition of mole
should include what is
being counted like atoms.
The first unit factor says
1 mole of atoms is equal
to 6.022 times10
to the 23rd atoms.
But the mole is
not just for atoms.
The count can be of ions
which can be included
in the unit factors.
The second unit factor
reads as 6.022 times 10 to
the 23rd ions over
one mole of ions.
Same logic with a
count of molecules.
Molecules are added to
the unit factor producing
a couple of equalities.
The point here is that
the mole is a number not a
number of atoms or number of
ions or number of molecules.
It is just a number.
There is a general term
that comes up in mole
conversion problems.
It is inclusive of atoms, ions
and molecules.
It is the particle.
A mole of particles is
Avogadro's number of particles.
Unit factors follow from the
definition and serve to convert
between number of particles
and moles of particles.
We will see that
conversions using moles are
fundamentally no different
than those for dozens.
Consider the conversion
of 10 to the 24th atoms
into moles of atoms.
The definition of a
mole of atoms leads
to these two unit factors.
In the problem atoms are
the current unit and
moles are the desired unit.
Which unit factor is
the appropriate one
for the conversion?
As with all conversions
that is decided by which
unit factor cancels
the current units out.
Count of atoms is
the current unit and
can be considered
in the numerator.
Therefore, this unit factor
has the correct orientation
because its count of
atoms is in the denominator
and will cancel out
leaving the desired units
moles of atoms.
What's left is a division
problem but one that
involves some
pretty big numbers.
A review of inputting
scientific notation values
into a calculator
might be helpful here.
A more thorough
demonstration of
scientific notation with
the calculator is given
in the 'Scientific
Notation' lecture.
Remember, different
calculators can use
different sequence
of keystrokes.
We will use a generic
calculator to solve
this problem. There
are two points that need
to be made before
the calculation.
The first is inputting
the 10 to 24 or the
10 to the 23.
Most calculators have
a button that specifically
sets this up so all
that needs to be
added is the exponent.
On the generic calculator
it is an exp button.
Some calculators have
that as an 'ee' button.
Here is the exp bottom.
The second point is that
10 to the 24 is easier
to input as 1 times
ten to the 24th.
The division of 1 times
10 to 24th by 6.022 times
10 to the 23rd........input 1
then exp button, the
exponent 24 as 2 4, divide,
6.022, exp button,
(exponent 23) 2 3, equal sign.
Now, this yields
a very long number
but it begins with 1.66.
The answer to the
conversion is 1.66 moles.
For completion seek we
can reverse this problem
and have the 1.66 moles
of atoms as the given
or current unit and
the count of atoms as
the desired unit.
A different unit factor
is needed in this set
up because there is a
different current
or given unit.
Since moles of atoms is
technically in the numerator,
the correct unit factor
will have moles of atoms
in the denominator.
Canceling out units
leads to count of atoms
which is the desired unit.
A second calculator
demonstration introduces
a second helpful key.
It is called the F-E key and
it toggles between numbers
written in decimal form
and that same number written
in scientific notation. Really
small and really large numbers
are difficult to
read in decimal form.
The math of this equation,
1.66 times 6.022 times
10 to the 23rd
is done by...first
inputting 1.66, hit multiply,
then 6 . 022, go to the
exp button, and hit the
exponent 23, and then equals.
Now go back to the F-E button
which brings it back
to scientific notation
and we have 9.99
times 10 to the 23rd.
We will round this term,
9.99 times 10 to the 23rd
rounds to 10 to the 24th.
Practice these
two demonstrations
on your calculator to verify
the necessary sequence of
keystrokes that will get
the appropriate answer.
This lecture ends
with review in
the form of a quiz.
The definition of the mole,
and the two unit factors
derived from the definition
will be our key to solving
the following
conversion problems.
First problem, calculate
the number of moles
that contain 3.5 times 10
to the 24th molecules of H2O.
Identification of
this question as a
conversion problem
is the first step.
Determining the given
value with the current units
and the wanted value
with the desired units
is the next step.
From the question we see
that 3.5 times 10 to the
24th molecules is
the given value,
which is written on the left
hand side of the equation.
And moles of water is
the desired unit which
is written on the right-hand
side of the equation.
The selection of the
appropriate unit factor
is the next step.
The unit factor must have an
orientation that cancels out
the current units which
is count of molecules.
Inserting the unit
factor and verifying its
correct orientation
by canceling out count
of molecules leaves the
desired units of moles.
Correctly entering the
numbers of this division
problem into the calculator
will yield a value of
5.8 moles of water.
3.5 times 10 to the 24th
molecules of water
is 5.8 moles of water.
A second problem asks
us to find the number of
protons in 2.88
moles of protons.
Again we identify
this question as
a conversion problem.
A close look at the problem
shows 2.88 mole of protons
to be the given or current
units. Insert that value
on the left hand side
of the equal sign.
The desired unit is
the number of protons.
Insert that on the right
hand side of the equation.
Since the current unit is
moles, and it is technically
in the numerator, the
correct unit factor
that will cancel out
moles must have moles
in the denominator
like this.
Indeed, moles protons cancel
out leaving 'count' of proton.
The calculated
solution comes to
1.73 times 10 to
the 23rd protons.
The final question
is one involving the
generic term particles.
How many moles particles
are there in 2.0 times 10
to the 22nd particles?
Identify the question as one of
converting between units
and set up an equality.
Referring to the
problem we see that the
given units are numbers
of particles which we write
on the left hand
side of the equation.
The desired units are
moles which we write
on the right-hand
side of the equation.
The conversion between
number of particles
and moles of particles
requires the definition
of moles and the unit
factors that follow.
The unit factor that
completes the conversion
has to have Avogadro's
number of particles
in the denominator so
that count of particles
cancels out with count of
particles as the given unit.
This leaves moles
of particles which
is the desired unit.
The calculated answer is
0.033 moles of particles.
A lot better than
dealing with 10 to the 22.
To recap the lecture
When items are dealt
within large numbers they
are NOT counted individually.
Appropriate size terms
(counting units) are used.
This is solely done to
bring numbers into a more
comfortable range.
The mole is a number.
It is a very large number
which can be represented
in scientific notation as
6.022 times 10 to the 23rd.
Some textbooks will
use the coefficient 6.02
instead of the 6.022.
Being such a large number
the mole is only used
with atomic scale
particles such as
sub-atomic particles,
atoms, ions and compounds.
For 1 mole of a compound,
the molecular formula
or the formula unit gives
the ratio of the moles
of the atoms or ions that
make up that compound.
Conversion factors are
a tool for changing units
of a measured or given
value into different units.
These different units are
referred to as the wanted
or the desired units
and have to be same
kind of measurement.
Conversions requires a unit
factor. This is a fraction
that has the same value
in the numerator as in the
denominator and is
therefore equal to 1.
In a conversion the unit
factor is oriented such
that the current
units cancel out
That concludes our lecture.
The moles is a fundamental
concept in the
study of chemistry.
Make mole conversions a tool
and it will greatly reduce
the complexity
of future topics.
[MUSIC]
