A lot of us keep collections of things we think are cool and interesting, like drink
koozies, movie stubs, or seashells.
But if we try to compare our collections, we can’t say the action movie ticket stub
is better than a fancy koozie, because your rank of those two might be different from mine.
We need a unifying measurement, like an objective third party rating, to be able to compare them.
Chemistry works the same way. We can’t compare atoms from different elements directly to
each other, because they’re different weights and have different properties.
To compare them, we need a unit of conversion that equalizes all our different substances,
and that’s what we’ll get into in today’s episode.
Hi, I’m Will Comar, and welcome back to Study Hall Chemistry, presented by Arizona
State University and Crash Course.
Let’s dive in!
An important unit of measurement involved in equalizing different substances is called a mole.
If you’ve taken some chemistry already, you might recognize this term, but as a refresher,
a mole is a way of describing the quantity of a chemical substance.
In the same way we measure distance in meters or mass in grams, we measure amounts of chemicals in moles.
It’s not the only way we represent amounts of a substance, though.
We usually represent the smallest units of matter as atoms, which have the properties
of the element they’re from.
And we can measure atoms by their atomic mass - the mass of one atom of that element.
We can find that number on the Periodic Table under the element name, in atomic mass units, or amu.
You might see atomic mass expressed in “daltons” or no units at all on different tables, but
they all tell us the same thing.
The exact mass might vary slightly between periodic tables as well, so you might see
the numbers rounded to different decimal points.
For simplicity, in this episode we’ll round to the nearest whole number, but just know
that other people might have different expectations for rounding.
So, if we have one atom of hydrogen and one atom of carbon, we can write out their atomic
masses as 1 amu of hydrogen and 12 amu of carbon.
Knowing the atomic mass of an element is a great start, but we can’t really calculate
anything yet without knowing what that mass actually means.
We first need to convert them to some new, unifying term.
Think about this like if we needed to exchange money from euros to the same value in yen or US dollars.
The money we’re converting maintains the exact amount it’s worth, it’s just represented
differently so that it’s accepted in the country we’re visiting.
Likewise, we convert the atomic masses of different elements to common units instead,
and that unit is the mole.
In any conversion, we need some sort of ratio that translates from the units we have to
the units we want.
We need to know how much one mole is, across the board, before we calculate how much one
mole of hydrogen or one mole of carbon will be.
Which...well, the idea of even trying to figure that out is daunting, but luckily we don’t have to!
An Italian physicist and professor named Amadeo Avogadro already did, and his contributions
will make this process way easier for us.
Not only does his name consistently conjure the image of an avocado, but he’s also the
person we have to thank for paving the way to the mole constant, or the value of one mole.
He did lots of experiments on the properties of gases, and eventually hypothesized that any two gases
in containers of equal volume at equal temperature and pressure contain the exact same number
of particles, whether they’re present as atoms or molecules.
This hypothesis was published in 1811, and although his efforts were not really well
known or appreciated until after his death, we now refer to this idea as Avogadro’s law.
Using this law as a springboard, other scientists eventually calculated the exact number of
particles in those equal volumes of gases,
now known as Avogadro’s Number: 6.022 x 1023 particles per mole.
In other words, there are 6.022 × 1023 particles in one mole of any substance.
This number is absolute, meaning it is always the same, regardless of what substance we’re talking about.
So one mole of elemental carbon would be 6.022 × 1023 atoms of carbon.
One mole of carbon dioxide would be 6.022 × 1023 molecules of carbon dioxide.
Even one mole of koozies would be - you guessed it - 6.022 × 1023 koozies. That’s a lot of koozies.
Avogadro’s number is huge, but remember, we use it to measure very tiny molecules,
which are a lot smaller than koozies, so it takes a lot of them to reach the scale of a gram.
And grams are our goal here, because we need to get from atomic mass to a unit we’re
more familiar with.
The mass of one mole of a given thing is called its molar mass, which is expressed in grams per mole.
For example, one mole, or 6.022 x 1023 atoms of carbon weighs 12 grams, and that means
its molar mass is 12 grams per mole.
And we know this because one atom of an element has a molar mass that is numerically equivalent
to its atomic mass.
If it’s an element on its own, the molar mass is its atomic mass in units of g/mol.
If it’s a compound, we’d add all the atomic masses of the elements that make up our substance
to get its molar mass.
Now that we have Avogadro’s number at our disposal, we can calculate exactly how much
of any substance we’d need for a reaction.
For example, if we wanted to find out the molar mass of glucose, or C₆H₁₂O₆,
we need to add up each of the atomic masses of the elements that make up its chemical structure.
We’d have six carbon atoms multiplied by 12 grams per mole, twelve hydrogen atoms multiplied
by 1 gram per mole, and six oxygen atoms multiplied by 16 grams per mole.
If we add all that up, we’ll get the molar mass of glucose, which turns out to be 180 grams per mole.
From the perspective of Avogadro’s number, we could then say that one mole, or 6.022
x 1023 molecules of glucose, would weigh 180 grams.
And here’s where molar mass gets super useful.
If we had, say, three moles of glucose in a reaction, it’d be represented by the coefficient
before the term, so we’d say 3C₆H₁₂O₆.
Coefficients in our reactions are the number of moles of those substances, and this is
how we compare substances to each other in common units.
To find the molar mass of 3 moles of glucose, we’d have 3 moles times 180 grams per mole.
3 times 180 is 540, and since we’re multiplying grams per mole by moles, we can cancel moles
out of our equation.
That leaves us with just 540 grams!
If we wanted to expand this idea to calculate the amount of each substance participating
in a photosynthesis reaction, for example,
we’d examine the balanced chemical reaction and perform the same molar mass calculations
for each substance until they’re all in common units of grams per mole.
Then we multiply their mass by their coefficients, which represent the number of moles of each
substance that we have.
So we have six moles of carbon dioxide, six moles of diatomic oxygen, and so on.
Our end result is the amount of each substance we’d need, in grams, for a successful reaction,
and how much of our product would be produced.
Let’s try something a little harder by jetting on over to TestTube.
Let’s say we’re on a beach vacation, and have some extra time on our hands.
We choose to spend it calculating how many moles and how many atoms are in one seashell.
To simplify, we can assume our seashell is made of pure calcium carbonate.
If we calculate the molar mass of calcium carbonate, we end up with 40 grams per mole
of calcium and 60 grams per mole of carbonate to get a total seashell molar mass of 100 g/mol.
And, because we scientists are always prepared, we can pull out our portable scale from our
beach bag to measure the shell’s mass in grams.
Let’s say that number is 5 grams.
We can use the calculation we did earlier to get our number of moles, but first we need
to shuffle it around to get what we’re looking for.
Originally, we were calculating mass in grams by multiplying the substance’s molar mass
by the number of moles the reaction called for.
Let’s flip that equation around with a little bit of algebra to get one that solves for
the number of moles instead.
Once we plug our known numbers, 5 grams of shell and 100 g/mol, into the equation, we
can cancel out the grams and see that our result is 5/100 moles, or 0.05 moles in one seashell.
If we wanted to know how many atoms are in our seashell before we toss it back into the
waves, all we need to do is multiply our 0.05 moles by Avogadro’s number.
Our mole units will cancel out, and we’re left with 3.011 x 1022 atoms in our seashell.
Thanks, TestTube!
It’s super important to be able to figure out how much of a substance a reaction requires or produces,
so it’s worth putting in the time to work some similar problems until we can surf through them.
And we’ll put more time into moles in upcoming videos!
Now, if you’re feeling confused about why Avogadro’s number is that specific constant, you’re not alone.
Actually, chemists today are still trying to find better ways to define the mole.
In the past, the constant was defined with equipment that wasn’t as precise as it is now.
But with new technological advances, research is being done to redefine the constant based
on a universally accepted prototype
in order to ensure the measurement is as accurate as possible.
This matters because the mole dictates all kinds of important decisions chemists need to make.
Avogadro’s number is used to determine how much rare materials are worth, how much of
a substance goes into a medicine,
or how much of a certain pollutant is permitted by environmental regulations before it’s deemed harmful.
It’s interesting that the tiniest details of chemistry often end up being the most important.
A single atom, a molecule, or a mole of a substance doesn’t seem like it holds up
the world, but together, they do.
Learning about moles is often a good way to shift our view: even the smallest units we
discuss in chemistry define nearly every aspect of life.
Next time, we’ll continue widening that perspective by going into more detail on how
to solve problems using moles.
Since they’re a tricky subject, we want to take our time and allow this concept to sink in.
Thanks for watching Study Hall: Chemistry, which is produced by Arizona State University
and the Crash Course team at Complexly.
If you liked this video and want to keep learning with us here in Study Hall, be sure to subscribe.
You can learn more about ASU and the videos produced by Crash Course in the links in the description.
See you all next time!