Chapter 12: Stoichiometry
Introduction: What is stoichiometry?
Unlike in chemistry class, in the real world, chemists perform reactions to
make useful chemical compounds such as medicines. When we learned
about chemical reactions, we learned about how to figure out what chemicals
and conditions will be needed to make reactions take place.
However, the real world also has another limitation: Things are expensive.
Though we can make the products we want by putting huge amounts of
chemicals together, we’ll end up wasting a lot of reactant if we just guess at
how much we need. Imagine the following reaction:
2 slices of bread + 1 slice of ham  1 ham sandwich
Now, it’s fine for your parents to go to the store and buy a loaf of bread and a
package of sliced ham, even though they know that the amount of ham they
buy won’t be the exact amount of ham needed to make an entire loaf of
bread’s worth of sandwiches – after all, ham is cheap. However, if ham cost
twenty bucks a slice, they’d be a lot more careful about buying exactly what
they need and no more. That’s what industrial chemists worry about – in
many cases the reactants they work with are very expensive.
As a result, chemists spend a lot of time making sure that they use only the
bare minimum of chemicals necessary to make the amount of product that
they need.
Stoichiometry: The determination of how much stuff you can make in a
reaction from some given amount of reactant.
In the kitchen, we do a very simple kind of stoichiometry whenever we make
ourselves lunch. For example, when we make a ham sandwich using the
equation:
2 slices bread + 1 slice ham  1 ham sandwich
We know that to make two ham sandwiches, we will need four slices of bread
and two slices of ham. All we need to do is to look at the equation (usually in
our heads, though) to know that.
In chemistry, the same thing is true. If we do the reaction:
2 H2 + O2  2 H2O
and want to make 2 moles of water, we know that we’ll need to start with 2
moles of hydrogen and two moles of water. Likewise, if we want to make 4
moles of water, we’ll use 4 moles of hydrogen and 2 moles of oxygen. This is
why chemical equations are handy!
Of course, there’s more to it than that. We already know that “moles”, while
handy for chemistry, aren’t terribly handy for doing calculations. After all, if
we’re going to work only with moles, we’ll have to count out 6.02 x 1023 things
every time we do a reaction. The unit “grams” is a lot more practical in the
real world, so we’ll learn how to work with them instead.
Fortunately, this doesn’t require you to learn anything new.
Example: Ammonium sulfate is made by the reaction:
2 NH3 + H2SO4  (NH4)2SO4
If we want to make 150 grams of ammonium sulfate, how much ammonia
will we need?
From what we just saw, we can figure out what we want by doing the following
calculations:
Convert grams of ammonium sulfate to moles (we already know how to
do this).
Convert moles of ammonium sulfate to moles of ammonia (which we just
learned can be done directly from the equation).
Convert moles of ammonia to grams of ammonia (we already know how
to do this).
To make life easier for us, here’s a handy chart that you can use to keep
everything straight for both mole calculations and stoichiometry calculations:
grams
known
molar
mass of
known
moles
known
mole
ratio
(from
equation)
moles
unknown
molar
mass of
unknown
grams
unknown
What’s a mole ratio? It’s the conversion factor between
moles of product and reactant that you find from the
coefficients in the equation.
Back to our example: To solve, set this thing up exactly as you would a
regular T-chart calculation:
150 g (NH4)2SO4 1 mole (NH4)2SO4
132 g (NH4)2SO4
2 mol NH3
1 mol (NH4)2SO4
17 g NH3
1 mol NH3
= 38.6 g NH3
Another example: How many grams of carbon dioxide will be made when
100 grams of CH4 burn in oxygen?
CH4 + 2 O2  CO2 + 2 H2O
(answer: 275 grams)
Percent Yield Notes:
When we do chemical reactions, we NEVER make as much of our desired
product as stoichiometry says we should.
Why? Experimental error!
Types of experimental error:
Human error: You screwed something up (biggest cause!)
Instrumental error: The equipment screwed up (not usually significant)
Unknown error: Something else screwed up the experiment (though
this can be almost anything, it frequently is found to be human error on
further investigation).
Whatever the reason, experimental error is a significant part of chemistry and
cannot be ignored.
To indicate how much error was present in a chemical reaction, we compare
the amount of product that was formed in the reaction to the amount of
product that stoichiometry predicted we should have formed. This quantity is
called the percent yield.
percent
yield
=
actual yield
theoretical yield
x 100
Example: If stoichiometry predicts that we’ll make 50 grams of a substance
and we make only 30 grams, the percent yield is 60% (show the math so
they see how this works)
Important note: The percent yield of a reaction should NEVER be over
100%, because that violates the law of conservation of mass.
This doesn’t mean that it won’t happen – however, when it does, you
should realize that it’s because of something else that’s been
inadvertently added to what you’re making – perhaps the product has
water in it, etc.
Another example: Consider the reaction:
Ca(OH)2 + 2 HCl  CaCl2 + H2
If I start with 60 grams of calcium hydroxide and an excess of hydrochloric
acid, what’s my percent yield if I make 10 grams of water?
29.2 grams of water is the theoretical yield.
(10/29.2) X 100 = 34.2% yield
Limiting Reagent Notes
Up until now, whenever we have done a stoichiometry problem we’ve always
assumed that in addition to our starting quantity of reactant, we also have
enough of the other reactant to make the reaction go to completion.
However, this isn’t always the case. Consider the problem:
2 H2 + O2  2 H2O
How many grams of water can I make if I start with 1,000 grams of hydrogen
and 10 grams of oxygen?
Clearly, this isn’t like our other problems. Not because you can’t solve this
question, but because there’s so much of one of the reagents that there will be
some of it left over after the reaction is complete.
The reagent that runs out first is called the limiting reagent (called the
limiting reactant in the book) because it puts a limit on how much product
can be formed.
The concept of limiting reagent can be seen when you’re trying to make
sandwiches for a big picnic:
Let’s say that you make a sandwich by using two pieces of bread and
one piece of cheese. The equation for this process would be:
2 pieces bread + 1 piece cheese  1 cheese sandwich
Let’s say that when you check your refrigerator, there are 100 pieces of
bread and 10 slices of cheese. How many sandwiches can you make?
(pause and let them figure out that it would be 10 sandwiches).
The thing that ran out first is the limiting reagent. Because the cheese
ran out before the bread did, the cheese is the limiting reagent.
How to solve limiting reagent problems:
1)
Find out how much product you can make from each of the reagents,
assuming that you have an infinite number of the other reagent.
Going back to our earlier example, this means making the one question
“How much water can we make from 1,000 grams of hydrogen and 10
grams of oxygen” into two different questions (and then solving these
questions):
How much water can we make from 1,000 grams of hydrogen,
assuming we have plenty of oxygen?
9,000 grams of water
How much water can we make from 10 grams of oxygen, assuming
we have plenty of hydrogen?
11.3 grams of water
2)
The reactant that causes the smallest answer is the limiting reactant,
and is completely consumed during the reaction. The answer that we
get from the question involving this reactant is the correct one.
In our example, O2 is the limiting reagent. 11.3 grams of water will be
formed.
3)
To find out how much of the excess / nonlimiting reactant is left over
after the reaction is complete, use the following equation:
In our example:
= 1000 g H2 – 1000 g H2 (11.3 grams / 9,000 grams)
= 1000 grams – 1.26 grams
= 998.74 grams H2 left over
Another (less extreme) example: How many grams of water can be formed if
10 grams of hydrogen react with 32 grams of oxygen? How much of the
excess reactant will be left over?
Answer:
72 grams of water
4 grams of H2 left over
Example: 2 HCl + Ca  H2 + CaCl2
If we start with 100 grams of each reagent, how much hydrogen will
be formed and how much of the excess reagent will be left over?
Answer: If you use 36.5 as the MW of HCl, you end up with 2.74
grams of H2 formed (HCl is the limiting reactant) and 45.2 grams of
Ca (the excess reagent) left over.