If chemical equations are like little recipes for doing
chemical reactions, then stoichiometry is your mom looking over your shoulder
telling you that you need to add more salt. And moles are your measuring
cups. The good news is that chemical reactions are easier to ignore than
your mother, but the bad news is that you get graded on them. All in all,
I think chemical equations come out ahead.
What’s a mole?
So, you’ve finally heard about moles. I’m not talking
about those little creatures that live underground and come up to feed on the blood
of the innocent at night – I’m talking about the chemistry type that comes up
to feed on the blood of chemistry students at night.
What’s a mole?
Pop quiz: If I’m wearing a pair of shoes, how many shoes
am I wearing?
Answer: If you said “two shoes”, you’re absolutely right!
Give yourself a gold star!
Other things that come in pairs include glasses (it has two
pieces of glass), a pair of pants (each leg used to be called a “pant”¹), and a
pair of binoculars contains two monoculars.² If you think about it, the word
“pair” really just means “two.”
If I were to tell you that I bought a dozen eggs, you’d probably
assume (rightly) that I bought 12 eggs. Likewise, if you go down to
Krispy Kreme and buy a dozen doughnuts, they’ll give you a box containing 12
doughnuts.³ In fact, if you refer to a dozen of anything, people know
you’re talking about 12 of them. In other words, “dozen” = “12”.
Similarly, the word “score” refers to 20 of something (“four
score and seven years” is just 87 years) and the word “gross” refers to 144 of
something.
Now, let’s turn our attention to the word “mole.” Just
like a pair of shoes has two shoes in it, a dozen doughnuts contains 12
doughnuts, and a gross of pencils contains 144 pencils, the word mole just
refers to a number. This number is 602,214,129,000,000,000,000,000.
Which is a really, really big number. You can make it seem a little
easier to manage by putting it into scientific notation (we usually round
to 6.02 x 10²³), but that doesn’t change the fact that 1 mole = a whole
lot of things.
How many things is it? Let’s have a look:
§ 1 mole
of moles (the little furry animals) would cover the earth to a depth of about
80 km or, if shot into orbit, make a small planet about the size of the moon
(check out this
article for the calculations).
§ 1 mole
of unpopped popcorn kernels would form a sphere about the size of Florida (an
interesting article is here).
§ 1 mole
of basketballs would form a sphere the size of the Earth (a good video about
moles can be found here).
You
are here
You get the idea: 1 mole is a great big bunch of stuff.
Which is why you’ve never
heard of a mole until now. It’s not like you can walk down to the store
and buy a mole of candy bars, or go play with that mole of Legos that Uncle Al
gave you for Christmas. If you can see individual things, it’s not really
possible to get a mole of them together in one place. Even the universe
only holds about a tenth
of a mole of stars, and it’s a really big
place.
Simply put, moles have been completely irrelevant to you before
now.
So why should I care about
moles all of a sudden?
It turns out that, while
a mole of hot dogs is way more than you could ever eat, a mole of water isn’t
the same way. If you have 6.02 x 10²³ molecules of water, that’s a
moderate-sized sip of water. Though one mole is a really really big number,
molecules are really really small. Unlike
eggs, where collecting a mole of them would be insane, a mole of molecules is
something that you can work with in the laboratory.
And, because molecules and atoms combine with each other in
whole-number ratios during chemical reactions, it’s handy to know how many
we’ve got in one place. We could use the actual number of molecules that’s
present (the math would be the same), but people have lots of problems
visualizing 602,214,129,000,000,000,000,000 atoms. It’s much easier
on our little brains to just say that we have a mole of them.
In the next tutorial, I’ll discuss how to use moles in
calculations. For now, please remember that the chemical idea of the mole
just refers to a number. It’s nothing mysterious or scary.
Mole calculations
§ Molar masses
§ Grams – moles – molecules
calculations
§ How to calculate ions
As I mentioned in the past
tutorial, the word “mole” refers to 6.02 x 10²³ things. Because this is a
really really big number, the only thing we use this number for is to count
really really small things like atoms or molecules. In other words,
Santa’s not bringing you a mole of wheat for Christmas, no matter how good a
baker you are.
However, if your chemistry
teacher is really nice, maybe you’ll get a mole of something toxic in your
stocking instead!
Molar masses:
If you guessed that the
term “molar mass” refers to the mass of a mole of something, you’re right.
For example, if you have a mole of water molecules, the molar mass won’t
be very big. On the other hand, if you have a mole of those chewy hard
candies your grandma gives you, the molar mass will be a lot bigger.
To understand how to
calculate the molar mass of a compound, we first have to look at the periodic
table. I’ll wait while you go get one.
OK. Now that you’re
back, let’s take a look at the little box for oxygen. It should look
something like this:
I think my graphics skills are
coming along nicely.
This little box tells you
the following information:
§ The element oxygen has the
atomic symbol “O”
§ The atomic number of oxygen
is 8, which also means it has 8 protons.
§ The average atomic mass of
oxygen is 16.0.
It’s that last thing that
we’re interested in. We usually like to have units to go along with our
numbers, but the “16.0” doesn’t really have any units, nor is there a single
answer that I can just tell you. Instead, it means two different things:
§ The average atomic mass of
a single atom of oxygen is 16.0 atomic mass units (amu). In other words,
if you were to take all of the oxygen atoms in the whole universe and average
their weights, the average would be 16.0 atomic mass units.
§ The mass of a mole of
oxygen atoms (unsurprisingly, the “molar mass”) is 16.0 grams. In other
words, if you have 16.0 grams of oxygen atoms, you’d have 6.02 x 10²³ atoms in
your sample.¹
The
reason we can do this is because of a number known as Avocado’s
Anyway, let’s find the
molar mass of water, H₂O:
§ In a single water molecule,
there is one atom of oxygen. As we saw above, oxygen weighs 16.0 amu per
atom, or 16.0 grams per mole. We’ll go with the mole one from now on.
§ In this single water
molecule, there are two atoms of hydrogen. Given that the molar mass of
hydrogen is 1.0 g/mol (check out the periodic table), the mass of both oxygen
atoms together is 2.0 grams.
If you add the mass of
oxygen (16.0 grams) to that of hydrogen (2.0 grams), you end up with a molar
mass of 18.0 grams/mol.
Here are some other
examples for you to figure out (answers are given below):
Find the molar mass of:
1. HNO₃
2. Ca(NO₃)₂
3. NH₄NO₃
Answers:
1. Nitric acid has one
hydrogen atom (1.0 g/mol), one nitrogen atom (14.0 g/mol), and three oxygen
atoms (3 x 16.0 g/mol). If you add them up, you get 63.0 g/mol for the
molar mass of nitric acid.
2. Calcium nitrate has one
calcium atom (40.1 g/mol), two nitrogen atoms (2 x 14.0 g/mol), and six oxygen
atoms (6 x 16.0 g/mol). If you add them up, you get a molar mass of 164.1
g/mol.
3. Ammonium nitrate has two
nitrogen atoms (2 x 14.0 g/mol), four hydrogen atoms (4 x 1.0 g/mol), and three
oxygen atoms (3 x 16.0 g/mol). This makes the molar mass 80.0 g/mol.
Converting between moles, grams, and particles
Now that you’re A-OK with
the world of molar masses, it’s time to teach you how to use moles to do actual
chemistry. After all, you’ve got to measure things using grams with a
balance – if you tried to either count the particles you’re working with, it
would take a very long time for you to get started with your experiment.
To do these conversions,
you’ll need the following chart:
In case it’s not
intuitively obvious what this chart means (and why would it be?), here’s how to
use it:
If you’re converting
between particles and moles, you’ll use “6.02 x 10²³” as your conversion
factor.
If you’re converting
between moles and grams, you’ll need to know the molar mass of the compound in
question.
You can’t convert between
particles and grams without first converting to moles.
That said, doing mole
calculations is no different than doing any other unit conversion – after all,
you’re just converting from grams to moles instead of from inches to
centimeters. The specifics may change, but the idea is exactly the same.
An example: Convert 97.4 grams of NaCl to moles.
Step 1: Draw a t:
Step 2: Put whatever you know in the top left corner.
Since the problem actually
says “97.4 grams of NaCl”, write “97.4 grams NaCl” in the top left:
Step 3: Put the units you already wrote into the bottom
right corner.
Step 4: Put the units of what you’re trying to find in the
top right corner.
Since we’re trying to
convert grams of NaCl to moles, put “moles of NaCl” in the top right corner:
Step 5: Put the conversion factors in front of the units on
the right side of the t.
This
seems like it would be hard, except that we have the following rules that
you always need to
follow when doing simple mole calculations:
§ Always write “1” in front of “moles”
§ Always write “6.02 x 10²³” in
front of “atoms” or “molecules.”
§ Always write the molar mass of the compound in front of “grams.”
If
you always follow these steps, you can’t go
wrong. Let’s do them here!
§ In front of “moles of NaCl”
we need to write a “1”. Why? Because “1” always goes in front of “moles.”
§ In front of “grams of
NaCl”, we need to write the molar mass of NaCl (it’s 58.5 g/mol). Why?
Because we always write the molar mass of the compound
in front of “grams.”
Step 6: Do the math.
These t-chart things that I
mention here are just fancy ways of writing fractions. Specifically, the one
above is another way of writing the calculation:
The
answer to this is 1.66 moles NaCl.
Cows are often known to lick
blocks of our friend NaCl – another way of demonstrating that they’re dumb as
all get out.²
Let’s do another, more awesome example: Convert 77.2 grams
of CH₄ to molecules.
As you can see from the
chart above, this will require two calculations. The first calculation
will be used to convert grams of methane to moles, while the second calculation
will convert moles of methane to molecules. This doesn’t make the problem
any harder – it just adds another step that looks just like the others.
Let’s see:
Step 1: Make a t:
Step 2: Put the thing you know from the question in the top
left:
Step 3: Put the units of what you know (the thing you put in
the top left) in the bottom right of the t:
Step 4: Put the units of what you want to find in this step
in the top right:
Step 5: Put the conversion factors in front of each unit.
Remember: “1” always goes
in front of moles and a molar mass (for methane, it’s 16.0 grams) always goes
in front of grams!
Step 6: Since we have one more calculation to do (to convert
to molecules), add another section to the t:
Step 7: Put the units of whatever is in the top left at the
bottom right:
Step 8: Put the units of whatever you’re trying to find in
the top right:
Step 9: Put conversion factors in front of each unit.
“1” goes in front of moles,
and “6.02 x 10²³” goes in front of molecules:
Step 10: Since this finished t-chart represents a fraction…
Just
solve this calculation to find that you’ll have 2.90
x 10²⁴ molecules of
methane.
Finding numbers of ions:
Let’s say that instead of
finding number of molecules, your teacher gives you a problem which asks for
the number of ions present in an ionic compound. This is a reasonable
question, because our calculations give answers in “molecules”. However,
ionic compounds don’t come in the form of molecules, so we need to find the
ions instead.
It turns out that this is
pretty simple. Just multiply the number of molecules by the number
of ions present in the compound’s formula.
Let’s say that you were
told to find the number of ions in some quantity of NaCl and you used the above
method to find that you had 1.00 x 10²³ “molecules”. Since NaCl is an ionic
compound and doesn’t contain molecules, we have to take our final answer and
multiply it by the number of ions that’s present in the formula “NaCl”. As you
can see, NaCl has two ions, so our final number of ions in this calculation
would be 2.00 x 10²³ ions. Likewise, if the formula was CaF₂,
we’d
have 3.00 x 10²³ ions because calcium fluoride has a total of three ions (one
calcium, two fluoride).
As my son says, easy peasy
lemon squeezy.
I’m guessing that lemons don’t
use the same expression.
Some common questions and problems that students have:
§ Question: Is there a
simpler way of doing this?
§ Answer: Not a
reliable one. This will work, guaranteed.
§ Question: Should I just
memorize each type of calculation?
§ Answer: No. If
you forget one, you’ll be out of luck, but if you know the steps, you don’t
need to memorize anything. This method is also handy for stoichiometry,
which you’ll be seeing a lot of.
§ Question: Why do I need
to find the number of molecules in anything? It’s not like I can
count them or anything.
§ Answer: It’s
traditional, and as far as I know, there’s no reason you’d ever need to know
this. It is handy to find the number of ions in an
ionic compound, but not for the type of calculations shown here.
§ Question: Did they name
the mole after an actual mole?
§ Answer: No, it’s
named after the German word molekül,
which means “molecule.” I’m guessing you’d already figured that out,
though.
After weighing,
newly-manufactured babies are shrink-wrapped and shipped to their waiting
families via first class mail.
Footnotes:
1. You wouldn’t believe the
terminology controversies that surround the terms “average atomic mass”,
“atomic mass”, “relative atomic mass”, and about a million other things that
are out there. I’m using the terms “average atomic mass” for elements
because that is the simplest and most common, and using “molar mass” for moles
of anything because that’s pretty common, too.
2. Though cows are, indeed,
dumb as all get out, salt licks are actually used to ensure that cows get the
necessary nutrients they need to survive. In the Prose Edda (a 13th
century work of Icelandic mythology) we also hear the story of a divine
cow named Auðhumla, who created the ancestor of
the gods from a salt lick, which was apparently activated with the cow’s
tongue. I didn’t just make that up. Check for yourself: Icelandic / English / Wikipedia page
|
All chemical reactions
can be placed into one of six categories. Here they are, in no
particular order:
1) Combustion:
A combustion reaction is when oxygen combines with another compound to form
water and carbon dioxide. These reactions are exothermic, meaning they
produce heat. An example of this kind of reaction is the burning of
napthalene:
C10H8 +
12 O2 ---> 10 CO2 + 4 H2O
2) Synthesis:
A synthesis reaction is when two or more simple compounds combine to form a
more complicated one. These reactions come in the general form of:
A + B ---> AB
One example of a
synthesis reaction is the combination of iron and sulfur to form iron (II)
sulfide:
8 Fe + S8 --->
8 FeS
3) Decomposition:
A decomposition reaction is the opposite of a synthesis reaction - a complex
molecule breaks down to make simpler ones. These reactions come in the
general form:
AB ---> A + B
One example of a
decomposition reaction is the electrolysis of water to make oxygen and
hydrogen gas:
2 H2O ---> 2 H2 + O2
4) Single
displacement: This is when one element trades places with another element
in a compound. These reactions come in the general form of:
A + BC ---> AC + B
One example of a
single displacement reaction is when magnesium replaces hydrogen in water to
make magnesium hydroxide and hydrogen gas:
Mg + 2 H2O
---> Mg(OH)2 + H2
5) Double
displacement: This is when the anions and cations of two different
molecules switch places, forming two entirely different compounds. These
reactions are in the general form:
AB + CD ---> AD + CB
One example of a
double displacement reaction is the reaction of lead (II) nitrate with
potassium iodide to form lead (II) iodide and potassium nitrate:
Pb(NO3)2 +
2 KI ---> PbI2 + 2 KNO3
6) Acid-base:
This is a special kind of double displacement reaction that takes place when
an acid and base react with each other. The H+ ion in the
acid reacts with the OH- ion in the base, causing the
formation of water. Generally, the product of this reaction is some ionic
salt and water:
HA + BOH ---> H2O
+ BA
One example of an
acid-base reaction is the reaction of hydrobromic acid (HBr) with sodium
hydroxide:
HBr + NaOH ---> NaBr + H2O
|
|
Mrs. Jordan’s Handy Checklist for figuring out what type of
reaction is taking place:
Follow this series of
questions. When you can answer "yes" to a question, then stop!
1) Does your
reaction have oxygen as one of it's reactants and carbon dioxide and water as
products? If yes, then it's a combustion reaction
2) Does your
reaction have two (or more) chemicals combining to form one chemical? If yes,
then it's a synthesis reaction
3) Does your
reaction have one large molecule falling apart to make several small ones? If
yes, then it's a decomposition reaction
4) Does your
reaction have any molecules that contain only one element? If yes, then it's
a single displacement reaction
5) Does your
reaction have water as one of the products? If yes, then it's an acid-base
reaction
6) If you
haven't answered "yes" to any of the questions above, then you've
got a double displacement reaction
|
|
Sample Problems (the solutions are in the next section)
List what type the
following reactions are:
1) NaOH + KNO3 -->
NaNO3 + KOH
2) CH4 +
2 O2 --> CO2 + 2 H2O
3) 2 Fe + 6 NaBr
--> 2 FeBr3 + 6 Na
4) CaSO4 +
Mg(OH)2 --> Ca(OH)2 + MgSO4
5) NH4OH
+ HBr --> H2O + NH4Br
6) Pb + O2 -->
PbO2
7) Na2CO3 -->
Na2O + CO2
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|
Solutions to the Sample Problems
1) double
displacement
2) combustion 3) single displacement 4) double displacement 5) acid-base 6) synthesis 7) decomposition |
The magic of stoichiometry
So, you’ve finally, done it: You’ve entered the realm of
stoichiometry. Or as some people pronounce it, “stoi-shee-oh-met-tree.”
Don’t pronounce it that way, it’ll make you sound silly. The actual
pronunciation: “stoy-key-ah-meh-tree.”
Now that we’ve got that out of the way, let’s learn about the
magical world of stoichiometry!
The magical world of stoichiometry
What is stoichiometry?
One time I was making sandwiches for some of my children’s
friends who had inexplicably been invited over to my house on a “playdate”.
All I had was crackers and cheese in the house, and the kids all decided
that the proper way to eat them was to put one piece of cheese between two
crackers to make a little sandwich. It’s a miracle I didn’t kill any of
them.
Anyway, I looked in the fridge and found about a
zillion pieces of cheese, and the package of crackers had a sleeve of 20
remaining. The question: How many cracker sandwiches can I make?¹
Here’s the math:
§ If I
have 20 crackers and assume that I have infinite quantities of cheese, I can
make 10 cracker sandwiches.
Because I run out of crackers at 10 cracker sandwiches, that’s
the maximum quantity I can make. And that’s what I made them. And
the biggest kid one cried.²
The
fat kid had to go home because he threw up.
Believe it or not, this story actually answers the question of
what stoichiometry is. Here’s a more explicit version for those of you
who didn’t like the story:
Stoichiometry is a set of
calculations you perform to figure out how much stuff you can make in a
reaction, or how much stuff you will need to make the reaction occur.
In other words, stoichiometry is used to figure out if you’ve
got enough crackers to make 30 sandwiches, or how much cheese you’ll need to
make 15 sandwiches. Of course, since chemistry uses fancy symbols, we’ll
deal with all of that in a second. However, that’s the basic idea.
How to do stoichiometry
Before we do anything, we’re going to make a modified version of
the diagram we saw back when we were doing mole calculations:
Let’s see what it all means using the following example:
Example: Using the
equation 2 H2 + O2 →2
H2O, determine how many grams of water can be formed from 45.0 grams of oxygen
and an excess of hydrogen gas.
So, where do we begin? We begin by figuring out what that
diagram above means:
§ The box
that says “grams of what you’ve got” refers to the number of grams that you’ve
been given in the problem. In our example, we literally see “45.0 grams
of oxygen”, so that’s where we start.
§ The box
that says “moles of what you’ve got” means that before we even start talking
about water, we’ve got to figure out how many moles of oxygen we have.
Since you already know how to do mole calculations (using the molar mass
of what you’ve got, shown above), you should be OK.
§ The box
that says “moles of what you want” refers to the fact that, using the equation
for this reaction, you can convert “moles of oxygen” to “moles of water.”
We do this using the mole ratio, which literally just consists of the
numbers written down in the equation. We’ll get back to that in a sec.
§ The box
that says “grams of what you want” refers to what is likely your desired
answer. To get this value, convert the moles of water to grams of water using water’s
molar mass. When you’re finished with this, you’re done!
Let’s just go ahead and do this example, using the methods
you’ve seen before to do conversions: The T-chart method:
Step 1: Draw a t
There
it is!
Step 2: Put whatever the
problem tells you in the top left of the t.
In this case, the problem tells you that you have 45.0 grams of
oxygen, so write “45.0 grams of oxygen” in the top left of this t.
Step 3: Write the units
of whatever was in the top left at the bottom right.
Since “grams of oxygen” was written at the top left, write
“grams of oxygen” at the bottom right.
Step 4: Write the units
of whatever the next step is on the top right.
In the first step of this calculation we use our table to see
that we’re converting from grams of oxygen to moles of oxygen. As a
result, write “moles of oxygen” in the top right:
Step 5: Put numbers
before each blank on the right side of the t, corresponding to the conversion
factors you need.
This is exactly the same as grams/moles conversions, except
that we’ll do more later. What this means is that we’ll put “1” in front of
“moles” (because we always do during mole calculations) and the molar mass of
O2 in front of “grams” (it’s 32.0 g for those of you playing at home):
Step 6: Repeat these steps
until you’re done.
You’ll get the hang of what to do before long, but I’ll keep
going through all of these steps in this example to make sure
you’re comfortable with the calculations.
Step 7: Add another
section to the t, and write the units of the thing in the top left on the
bottom right:
Step 8: Write the units
of the thing you want to find in this step in the top right.
We’re converting from moles of oxygen to moles of water here, so
write “moles of water” in the top right:
Step 9: Add the conversion
factors in the blanks on the right.
Now, given that we have “moles” on both the top and the bottom,
it doesn’t really make sense to put “1” in each spot as we usually do.
Instead, realizing that the equation gives us a ratio of the number of moles
of oxygen to number of moles of water (these are the coefficients in the
equation), we’ll put these numbers in front of each number. This ratio is
called the “mole ratio”, because it’s a ratio of moles.
Step 10: Do the last
conversion from moles of water to grams of water, using the standard t-chart
method.
Step 11: Do the math:
The whole t-chart thing you just did is just a big bunch of
fractions being multiplied together, so think of it like this:
And that’s how you do stoichiometry!
Is that all?
Of course not. But it’s all for now, so you’ll have to
wait for limiting reagents to find out more.
Footnotes:
1. The
other question: Did I really care? No.
2. For the
record: He didn’t cry because he was the biggest kid. He cried
because he was a crybaby.
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