>> host: Baking... one of
our oldest, most delicious,
and historically important
chemical processes,
reminds us that chemistry
isn't something
that only happens in a lab.
It also happens here,
in this bakery and in homes
around the globe.
From flatbreads,
to fancy cakes, a successful
and delicious product
is the result when you get
the proportions of ingredients
just right.
You see, ingredients
are the reactants,
and the bread is the product.
You have to mix the flour,
liquids, eggs,
and other components together
in amounts that will react
in a predictable way...
or you get this...
...or this.
But exactly how does baking
relate to chemistry?
We'll find out
in this episode
of Chemistry Matters.
♪♪
>> host: Welcome back
to Chemistry Matters.
This is the first video
on the playlist for Unit 6:
The Mole and Stoichiometry.
The mole is just a number...
a really, really large number.
And we'll talk more
about that shortly.
First, let's give you
a little more information
on stoichiometry.
In Greek,
stoikhein means element,
and metron means measure.
So you could literally
translate stoichiometry
to mean the measuring
of elements.
Whether you're a baker
trying to mix together
ingredients
for just the right ratio,
or a chemist
trying to get a specific
amount of a product to form
in a chemical reaction,
the proportions
of the ingredients
that are mixed together
make a big difference
in the final product.
[bell dings]
Bakers do this by measuring
the amounts of ingredients
they need very carefully.
And chemists do this
by taking advantage
of one of the most useful
problem solving techniques
you may ever learn.
It's known as
dimensional analysis,
or the factor-label method.
Let's go out to our classroom
where our students
are exploring
this very important
problem-solving technique.
>> professor: Before we formally
begin exploring dimensional
analysis, I'd like to ask you
a very simple question:
how many donuts are there
in a box that contains
one dozen.
>> student: That's easy. 12.
>> professor: Do you all agree?
>> student: Yeah!
A dozen is the same as 12.
So you would have 12 donuts
in a box that was labeled
as a dozen.
>> professor: Exactly,
and that's just something
that you know to be true,
right. One dozen equals 12.
If you were to go buy
some donuts,
you could order 12
or a dozen.
You'd get the same number
of donuts.
You'd just be using
different units
to describe them.
Chemists call statements
like "One dozen equals 12"
an equivalence statement.
And if used properly,
equivalence statements
can be powerful tools
whenever we have to do problems
in which conversions of units
are required.
Another example of
an equivalence statement
would be 1 inch equals
2.54 centimeters.
The distance is the same,
it's just a matter of
which unit we decide to use.
So, in this case,
we can use centimeters,
which are metric units,
or inches,
which are English units.
Of course chemists
always prefer metric units.
Let's get back to donuts
for a minute though.
What if I asked you
how many donuts you'd have
if you were to have
2.768 dozen donuts?
How could you solve for that?
Amaria?
>> student: Well,
if one dozen equals 12 donuts,
then you could just multiply
2.768 times 12, right?
>> professor: Yes, that's true.
But in a second I'll show you
how you can use
equivalence statements
to solve problems like this,
as well as those that are
much, much more complex,
using a technique known as
dimensional analysis.
Dimensional analysis,
also known as
the Factor-Label Method,
is a problem-solving method
that uses the fact
that any number or expression
can be multiplied by one
without changing its value.
It's a very useful technique.
So, let's go back to
the equivalence statement
we used earlier
so I can show you what I mean.
We used the equivalence
statement 1 dozen equals 12.
What if I were to rearrange
this equivalence statement
in the form of a fraction?
Let's say one dozen
divided by 12.
What would your answer be?
>> student: Wouldn't that
just be one?
I mean you'd still be
dividing 12 by 12,
and that would give you one.
>> professor: Absolutely,
And I'm glad you caught that.
Okay, how about this.
What if I wrote 12
in the numerator divided by
one dozen in the denominator.
How about that fraction?
What would that represent?
>> student: It's still one,
you're still dividing
12 by 12.
>> professor: Perfect!
What we've just demonstrated is
that an equivalence statement
can be written as a fraction.
Regardless of which unit
is placed in the numerator
and which unit is placed
in the denominator
it will always equal one.
When we write equivalence
statements this way,
in fraction form,
we call them conversion factors.
It allows you to change units
while maintaining
the original measurements.
The cool thing about
conversion factors
is that they allow you
to perform seemingly
very difficult problems
relatively easily,
as long as you follow
some very important steps.
>> host: Now that our teacher
has explained
what conversion factors are,
we're ready to apply them
and begin solving problems
using dimensional analysis.
Take a look at this example.
The first thing we need to do
is identify what information
the problem gives us.
Notice that "cm" appears
on the far left,
because that's the unit
we're starting with,
and on the far right
you see "in" for inches,
the unit we're converting to.
Next, it'll help to build
what's called
a conversion chart,
which is similar in shape
to the letter "t."
Then, start putting
the numbers and units
on the chart.
For instance, in this problem
we're told that the hairdresser
wants to cut 8.0 centimeters
of hair.
So put that number,
along with the units,
in the upper left hand corner
of your conversion chart.
The unit that you
started with, centimeters,
will now become
the denominator
of the second column.
The numerator
of the second column
will be the target unit--
the unit that
you're converting to.
In this case,
that's inches.
In this way,
we're letting the units
guide the conversion.
In this particular problem,
we'll choose
the conversion factor
that has one inch
in the numerator
and 2.54 centimeters
in the denominator.
We'll choose this
as our conversion factor
because, as we just saw,
centimeters became
the denominator
of the second column.
And we needed to solve
for inches, since that's
what the question
originally requested.
There will be problems
in which you'll have to
keep going,
meaning you'll have to draw
another line, and convert
another column
to convert additional units.
But in the case of
this problem,
there's only one step.
And we know that
because the target unit
is in the upper
right hand corner-- inches.
If a unit appears
in both the numerator
and the denominator,
the units can cancel
each other out.
In our example,
the centimeters
in the first numerator
cancel centimeters
in the denominator
in the next column.
Then, all we have to do
is multiply the numbers
found in the numerators
together.
And then we do the same thing
with all of the numbers
in the denominator.
Then divide the product
of all numerators
by the product
of all the denominators.
For this problem, that means
multiplying 8.0 times 1,
which is 8.0.
And since we only have
one value in the denominator,
2.54, we divide 8.0 by 2.54
to find that 8.0 centimeters
equals 3.1 inches.
Not every conversion
is as straightforward
as the one we just saw,
but there are
some basic steps we can follow
to help guide us anytime
we use dimensional analysis.
First, we always want
to identify what it is
that's given to us
in the problem.
We'll start the conversion
from this given value,
the number and the unit.
It's also helpful as you are
first reading over the problem
to make a note as to what
you're solving for.
In other words,
what units am I going to
have to convert to before
I can finish the problem?
And remember, if you do
the setup correctly,
the desired unit
you're solving for
will be what's left
in the upper right hand corner
of your conversion chart
at the end.
Next, place the number
that's given in the problem,
along with its units,
in the upper left hand corner
of a conversion chart.
Choose a conversion factor
that will get you
to the next unit.
Make sure the unit
from the upper left
also appears
on the lower right.
Let the units guide
the conversion by lining up
conversion factors
so units cancel.
You'll know your conversion
chart is complete
when you've canceled out
all units except for
what the question
asked for initially.
After canceling units,
multiply all the numbers
in the numerator together,
as well as all the numbers
in the denominator.
When you've got
both products,
divide the numerator
by the denominator.
Lastly, you'll want
to check units
and your answer.
Now let's go back out
to our classroom,
where our teacher is ready
to guide our students
through a dimensional analysis
calculation.
>> professor: Let's solve
a problem together step by step.
I have given you each
a copy of our list
of steps for using
dimensional analysis
to assist you.
It'll help you tremendously
if you learn to be
systematic when you work
on these types of problems.
Okay?
So, your high school
football team
needs 550 centimeters
for a first down.
How many yards is this?
According to our steps,
what's the first thing
we need to do in solving
this problem?
>> student: Well, first
we need to find our
starting and ending units.
We've got 550 centimeters,
and it looks like
we need to convert that
to yards.
>> professor: Great.
What do we do next?
Ciara.
>> student: We can create
a conversion chart.
So we will put 550 centimeters
up into the upper left
hand corner.
>> professor: That's right.
So now we've identified
what we're starting with,
and where we want to go.
So, What's the next step,
Robbie?
You want to take it?
>> student: Sure, we need to
choose a conversion factor.
>> professor: Perfect.
Okay, now this step
can be challenging.
We need to determine
which conversion factor
to use for this step.
We have centimeters,
but eventually we're going
to have to get to yards.
Does anyone have any ideas?
>> student: I do.
We have to put centimeters
on the bottom right.
>> professor: Good.
What else?
>> student: We know that
one inch is equal
to 2.54 centimeters.
So we use
that equivalence statement
as a conversion factor
for this column,
and that'll let us
convert our distance to inches.
>> student: Right.
And we bring the units
of centimeters down to
the right side's denominator,
because the units
guide the conversion.
>> student: Yeah.
We need to convert
from metric units
to English units,
and that conversion factor
does it.
>> professor: Well done,
everyone. Like Robbie said,
notice the conversion factor,
1 inch equals 2.54 centimeters,
has centimeters
in the denominator
because we're letting units
guide the conversion.
What should we do next?
>> student: Well, according
to the list you gave us,
the next step for
dimensional analysis
is to line up conversion
factors so the units
cancel each other out.
This will happen anytime
the units appear in both
the numerator
and the denominator.
>> student: Yeah.
So we can cross out
the centimeters.
>> professor: Great.
Okay, are we done?
>> student: No, because
if we stopped now,
our answer would be in inches.
We need yards.
>> professor: That's right,
so what's the next step?
>> student: Let the units
guide the conversion.
So we should bring down inches
into the next denominator,
and then we need to
convert inches to feet.
>> professor: That's
exactly right.
So what's
the equivalence statement
that you're going to use
as a conversion factor here?
>> student: Well,
1 foot is 12 inches.
So we put 1 foot
in the numerator and 12 inches
in the denominator.
>> student: Yeah,
that's when you can
cancel out the inches.
Then we only have one more
conversion factor to go,
because we can bring down
the unit "feet" into
the next denominator.
>> professor: There you go,
letting the units
guide your conversion.
>> student: So we put
one yard in the numerator
over three feet
in the denominator,
because one yard is equal
to three feet.
>> professor: Yes!
What next?
>> student: We need to
cancel out the units, too.
So now we can cancel
the "feet" on the top and
the "feet" on the bottom.
>> professor: That's right.
Remember, we know we're done
with the converting part
when the unit we're solving for
is in the upper right hand
corner of the conversion chart.
And there it is-- yards!
So all we have left to do
is the math.
Who wants to lead us
through that?
>> student: I can.
>> professor: Great.
>> student: Uh, we can start
by multiplying 550 times
one, times one, times one,
since those are the numbers
in the numerator.
And that equals 550.
Then, we multiply 2.54
times 12 times 3.
>> professor: Good.
I've done that math for you.
It equals 91.44.
>> student: Then, we just
divide 550 by 91.44.
>> student: I've got it-- 6.0.
>> student: And that's
our answer. 550 centimeters
is the same as 6.0 yards
for the first down.
>> professor: Well done,
everyone. Now you're ready
to handle dimensional analysis
in chemistry!
>> host: The dimensional
analysis problem solving
technique can be tricky
at first.
So make sure you follow
each step our teacher described,
because this is
a problem solving technique
you'll be able to use
for the rest of your life
in many of your science
and math classes--
really, anytime you need
to convert from one unit
to another.
We'll be using
dimensional analysis
extensively for the rest
of this unit, as we move into
the concept of the mole
and stoichiometry.
So keep those step by step
instructions handy.
You can find this document
in the Chemistry Matters
Toolkit.
And I'll see you at the top
of the next video
on the Unit 6 playlist,
where we'll use
dimensional analysis
to help us calculate
large numbers
of very tiny particles:
atoms.