>> narrator: In this
Closer Look, we'll investigate
mass to mass stoichiometry
and then learn how
to calculate percent yield.
First, let's talk about
mass to mass stoichiometry.
When there is
a balanced equation,
mass to mass stoichiometry
allows you to convert
from grams of one substance
in a chemical reaction to grams
of a different substance
in the same reaction.
The most likely reason
you would need to perform
mass to mass stoichiometry
is to determine
the "theoretical yield,"
in grams of a product
in a chemical reaction.
Theoretical yield is
the maximum amount of
a particular product
that can be formed
in a chemical reaction,
given a specific amount
of a starting reactant.
Now, here's an example
of a mass to mass
stoichiometry problem.
Hydrogen and oxygen gas
can be generated through
the electrolysis of water.
The balanced chemical equation
is two waters react to form
two hydrogens and one oxygen.
What is the theoretical yield,
in grams, of oxygen
from the decomposition
of 11 grams of water?
Start this problem
by taking what's given,
in this case 11 grams of water,
and place that in
the upper left hand corner
of a conversion chart.
Next, bring down the units,
in this case grams of water,
and in this first step,
convert to moles of water
using the molar mass
of water, 18.02 grams,
which we get from
the periodic table, and put
that in the denominator,
and one mole of water
in the numerator.
Since 18.2 is the molar mass
of water, use that,
which will allow you to cancel
the units of grams of water.
Now at this point,
you've effectively converted
to moles of water,
but the question is to
determine grams of oxygen.
That means you need to keep
going with the conversion.
So, bring down the units,
the moles of water,
and convert from
moles of water
to moles of oxygen.
Notice from the balanced
equation that there are
two moles of water
that are decomposing
for every one mole of oxygen
that is forming.
That means you put a two
in front of water
and a one in front
of the oxygen.
Then cancel the units
of moles of water.
You're almost there now,
but you need to get
to grams of oxygen,
not moles of oxygen,
so set up another
conversion box to go
from moles of oxygen
to grams of oxygen.
The molar mass for oxygen
is 32.0 grams,
which in the case of O2
is determined by taking
the molar mass
from the periodic table
and multiplying it times 2.
Carry out the math
by multiplying 11
times one times one times 32,
which gives you 352.
Then divide by 18.02
times two,
which equals 36.04.
and when you divide 352
by 36.04,
you get 9.8, after rounding
it to the correct number
of significant figures.
So 9.8 grams of oxygen
can be produced using
11 grams of water,
according to
the balanced equation.
This amount is known
as the theoretical yield,
because on paper,
based on the stoichiometry,
it is the maximum amount
of product that can
be produced.
Percent yield,
on the other hand,
is a calculation
that measures
the reaction's efficiency.
It is the ratio between
what is actually recovered
by experiment in the lab,
the actual yield,
and the theoretical yield,
which as you just saw
is calculated through
stoichiometry.
To get the percent yield,
we take the ratio
of those two, the actual
and the theoretical yield,
and we multiply it
times a hundred to convert it
to a percentage.
Here's an example of a problem
in which percent yield
is calculated.
Sodium chloride is
produced by the reaction
between sodium metal
and chlorine gas.
The balanced chemical equation
is two sodiums
plus one chlorine yields
two sodium chlorides.
What is the percent yield
for an experiment
that recovers 75.50 grams
of sodium chloride
when 47.00 grams
of chlorine gas reacts
with an excess of sodium?
In this problem,
you are told that you have
an excess of sodium, so you
can focus your attention,
and the calculation,
off of the 47.00 grams
of chlorine you are given
in the problem.
So the first thing
you need to figure out is
what the theoretical yield
of sodium chloride is,
when 47.00 grams of chlorine
are used according to
the balanced equation
for this reaction.
You already have
the actual yield,
because it was given
in the problem.
So once you have
the theoretical yield,
you can compare
the actual yield
to the theoretical yield
to figure out
the percent yield.
So now, take what is given
and put it in
the upper left hand corner
of a conversion chart.
In this case it's
47.00 grams of chlorine.
Then, bring the units down,
the grams of chlorine,
and convert that
to moles of chlorine.
To do that, use 70.91 for
the molar mass of chlorine.
There are two atoms
of Chlorine present
in a Cl2 molecule,
which doubles the molar mass.
Notice the units of grams
of chlorine cancel,
and then go from
moles of chlorine
to moles of sodium chloride.
This is the mole ratio step,
so use the coefficients
from the balanced equation,
that's an understood
one for chlorine
and a two for sodium chloride.
So put a one in front
of the chlorine
and a two in front of
the sodium chloride, and now
you can cancel the units
for moles of chlorine.
And you have converted
to moles of sodium chloride.
But you're not done
because you're trying to get
to grams of sodium chloride.
So this last step, convert
from moles of sodium chloride
to grams of sodium chloride
using the molar mass,
58.44 grams,
and you can cancel the units
of moles of sodium chloride.
And what you find is that
77.47 grams of sodium chloride
could be produced if you used
47.00 grams of chlorine,
according to this balanced
equation for this reaction.
To get there, you take
47.00 times one times two
times 58.44,
which is 5,493.36.
Then you divide that
by the product of 70.91
times one times one,
which is just 70.91,
and you get to 77.47,
after rounding
to four sig figs.
The 77.47 is
the theoretical yield,
and remember, when calculating
percent yield, you take
the ratio of the actual yield
over the theoretical yield,
and multiply it by 100.
So the actual yield
is here, 75.50,
and you just calculated
the theoretical yield, 77.47.
Now use the equation to
determine the percent yield.
So take the actual yield,
the 75.50, and put that
over the theoretical yield,
77.47, and multiply
that ratio times 100
to convert it to a percentage.
And what you find is
the percent yield is 97.53%,
which would be pretty good
if you were to
actually carry this out
as an investigation
in the lab.
Now here's one for you
to try.
Sodium chloride is
produced from the reaction
between sodium metal
and chlorine gas.
The balanced chemical equation
is listed below.
Two moles of sodium react
with one mole of chlorine
to produce two moles
of sodium chloride.
What is the percent yield
for an experiment
that recovers 205.0 grams
of sodium chloride
when 83.00 grams of sodium
reacts with excess
chlorine gas?
When you're ready,
press pause and give it a try.
Then, press play
and check your answer.
The correct answer for
the percent yield is 97.16%.
If you got that, that's great,
if you didn't, let's go back
and look at how we got here.
We took the 83.00 grams
of sodium and started
a conversion chart.
We brought down our grams
of sodium, we converted
to moles using the molar mass
of sodium, then we then brought
the moles of sodium down,
and using the coefficients
from the balanced equation,
we converted from
moles of sodium
to moles of sodium chloride,
canceling units as we go.
Then we brought down
the units of moles
of sodium chloride,
and using the molar mass
of sodium chloride,
we converted to grams
of sodium chloride.
This set us up to calculate
our theoretical yield,
which we found
by multiplying everything
in the numerator first,
and then dividing that
by the product of everything
in the denominator.
So that gave us our
theoretical yield, 211.0.
The actual yield was given
in the problem.
It was 205.0.
And to calculate percent yield,
we took our actual yield,
205.0 and divided it
by the theoretical yield
that we just calculated,
which was 211.0,
and multiplied that by 100.
And that's how we got
our percent yield of 97.16.
Again that would be
a pretty good percentage
in a lab.
That's a closer look
at mass to mass stoichiometry
and percent yield.
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is available to you.