By now, you're probably starting to see how
chemistry can change your view of the world. Chemistry explains everything you can see, how it looks, the way it feels, why it behaves the way it does, by describing everything that you can't see. It helps us understand the biggest stuff in the universe by helping us understand the tiniest. And that's why chemistry can be kind of hard
to understand sometimes. Because we are, on a chemical scale, huge. Chemistry traffics in infinitesimal particles,
but we are made of quadrillions of those things. They are the building blocks of mass; we are
literally massive. So mass is how we massive beings tend to understand
the world. In our day-to-day dealings with substances, we need to have some sense of how much of it there is before we can use it or predict how it's going to act. For example, chemistry will be happy to tell me that the atomic structure of the sugar in this packet is 12 carbon atoms, 22 hydrogen atoms, and 11
oxygen atoms in every molecule. But I don't have any idea how many molecules
of sugar I want to put in my tea! Or how that one molecule will react with other
chemicals in my body. To understand that kind of stuff, I need to know the mass of the sugar that I'm dealing with. In other words, I need to measure it. And that, is why there's stoichiometry, the science of measuring chemicals that go
into and come out of any given reaction. In Greek, it literally means measuring elements, and, in essence, it allows us to count up
atoms and molecules by weighing them. Stoichiometry, yes, contains a fair bit of math, but it's one of the most important decoders that we have as chemists. It's what we use to translate from the very
small to the very big, to parley the stuff that we can't see into
the stuff that we can. And because of that, chemists use it all the
time. Including, yes, for sweetening your tea.
Ow... hot. It's... it's quite hot. [Theme Music] Now if you've been with me for a couple of weeks, and I do hope you have, you're probably thinking to yourself, "Wait, wait, now, don't... don't we already
have a way of measuring elements?" And you're right.
We do. The real coin of the realm when it comes to measuring stuff in chemistry is relative atomic mass. The average atomic mass of all of the naturally
occurring isotopes of a given element. So for example, all of the natural carbon
on earth occurs as one of 3 and only 3 isotopes: C-12, C-13, and C-14. They all have six protons, but the number
of neutrons vary. And these isotopes show up on our planet in
totally different proportions. So the relative atomic mass of carbon is a weighted average of these three masses, which comes out to 12.01. But 12.01 what? Well, remember when we're talking about units of measurement, we're talking about arbitrary talk. Most, units, except for the ones that we use to measure time, aren't based on any real, objective value. We just pick a unit, like the kilogram, and we agree for a standard on what a kilogram is, and then we run with it. The same goes for atomic mass. We measure
atomic mass in atomic mass units. We made them up, and the value for a
single amu is -- bear with me now -- 1/12th of the mass of an atom of carbon-12. Why?
Funny story. Until the mid-1800s, chemists in different parts of the world used different yardsticks for measuring elements. One of the most intuitive and therefore most common was to use the smallest, simplest element, hydrogen, as a base line. But in the 1850s, some chemists, led by German
Wilhelm Ostwald, proposed using oxygen instead. They preferred oxygen mainly because it combined
readily with so many other elements, so they figured it would be easier to determine
the weights of lots of compounds. So a bunch of guys stroked their beards, agonized
over this for years, until in 1903, they decided that atomic weight, as it was called, should be measured in 1/16ths of an oxygen atom. Until in 1912, isotopes were discovered and
chemists realized that you can't talk about an element like it's all the same thing! It turned out there was an oxygen-16, and
an oxygen-17, and an oxygen-18! And suddenly, everyone was walking around like, "I don't know how much this such weighs anymore!" This was so crazily disruptive that it took
another 50 years of strokey-beard meetings for everyone to decide to use another standard
-- carbon-12. Like oxygen, carbon is common, and kind of promiscuous, when it comes to what it bonds with. And since it has 12 protons and neutrons, the mass of other, similar elements would
be expressed as some fraction of it. So, since 1961, science has pegged one amu
as 1/12th of an atom of carbon-12. Which means that carbon has a relative atomic
mass of 12.01 amu. Oxygen, 16 amu, and hydrogen, 1.008 amu.
So that's how we way atoms. But, none of this solves my tea sweetening
problem. Like, I don't know how many amus of these molecules together are going to make this taste good to me, or how many other molecules of sugar I can consume while maintaining my slim yet robust physique. This doesn't happen by itself, you know. And in order to make these calculations and
predict reactions, I first need to be able to convert the atomic mass of this sugar, into a standard amount of substance. Not weight, not volume, just purely, objective
amount of stuff. You heard me, stuff. That, my friends, is what moles are for. Not
those moles, though those are nice-looking moles. A mole is arguably the most important unit
in all of chemistry, because it allows us to express a chemical's
atomic mass in terms of grams. And to define what a mole is, no matter what
it's a mole of, we use our old standby, carbon-12. There are 6.022 x 1023 atoms in 12 grams of
carbon-12, and by definition, that number of anything
is a mole of that thing. That's a lot, and it is known as Avogadro's number, one of the most important constants in chemistry, and although Avogadro isn't the one that arrived
at this number, it's named in his honor because he used this
basic principle of comparing amounts of substances to first weigh atoms and molecules. So there are this many carbon atoms in a mole
of carbon-12 and there are the same number of anything
in a mole of anything else. Like a dozen roses is twelve roses, but a
mole of roses is 6.022 x 1023 roses, which would be enough roses to cover the surface
of the earth quite deep. A mole of sand would be 6.022 x 1023 grains of sand and if they were each one millimeter long, a mole of them would stretch 100 quadrillion kilometers. So you get the picture, it's a big number,
but in chemistry the thing to remember is this: a mole of any element contains 6.022 x 1023
atoms of that element no matter what. This is what lets us translate number of atoms
into grams. It lets us weigh the elements. All right, follow me here. One mole of carbon-12 contains 6.022 x 1023
atoms and weighs 12 grams, right? So one mole of oxygen also contains 6.022
x 1023 atoms but because oxygen atoms are more massive it weighs 16 grams and you'll recall that oxygen's relative atomic mass is 16 amus. The number of atoms per mole remains the same, but the mass of a mole depends on the average
mass of the element. This simply means that one mole of any element
equals its relative atomic mass in grams. So now you've got it, 1 mole of hydrogen weighs
1.008 g, a mole of iron is 55.85 g, and a mole of natural carbon is 12.01 grams. This is known as an element's molar mass. And now that we know the molar mass of elements
we can calculate the molar mass of any compound. All we have to do is add up the molar masses
of its component elements. So for instance, the formula for this sugar
or sucrose is C12H22O11. One mole of sucrose, by definition contains
6.022 x 1023 molecules, and since each molecule contains 12 carbon atoms and 22 hydrogen atoms and 11 oxygen atoms, then one mole of sucrose contains 12 moles of carbon, 22 moles of hydrogen, and 11 moles of oxygen. Multiply the number of moles of each element
by its molar mass and add them all up, that's the molar mass of the whole compound. See, the mole is like our chemical Rosetta
Stone; with it, we can translate anything from the level of atoms and molecules to the level of grams and kilograms. And we can use it to describe not only elements
and compounds, but reactions. And you don't need a lab full of samples to
do it, just a pencil and a calculator. To get back to my tea problem, let's say, y'know, hypothetically, that I'm watching my weight, so I want to know what it'll take for me to
burn a certain amount of sugar that I consume. That's a reaction!
And it's a pretty simple one. My body uses sucrose by combining it with oxygen to create energy plus CO2 and H20 as waste. You can write this out as an equation, in which the reactants combine on the left
to yield the products on the right. But there's a problem here: this equation
doesn't reflect chemical reality. During a reaction, bonds are broken and new
ones are formed but the number of atoms of each element remains the same. The sugar and oxygen molecules may be busted
apart and mixed up, but the number of each kind of atom that you start with ends up being exactly the same after the reaction. Conservation of mass, yo. So when writing a reaction out as an equation, the number of atoms of each element has to
be exactly the same on both sides. Reconciling the reactants with the products
is called equation balancing, and it's a good bit of what stoichiometry
is all about. Because from a chemical perspective an unbalanced
equation is pretty useless. It doesn't tell you how much is going in and
how much is coming out. Without balancing the equation it's like saying, "When a mommy and a daddy love each other very much, a baby appears and that's all you need to know." But that's not all you need to know! So how do you do it? Not make a baby, balance
an equation. I did biology last year. Well the best way is to start with the most
complicated molecule, which in this case is, of course, the sucrose. For every molecule of sucrose that goes into the reaction, you know that you're gonna have 12 carbon atoms, so right off the bat you know that you're gonna have to end up with at least 12 molecules of CO2 as a product, because that's the only molecule where those
carbon atoms end up. Now let's deal with the hydrogen, because that also shows up in only one molecule
on both sides of the equation so that's easier. You know that at least 22 atoms of hydrogen
go into the reaction and the product contains some multiple of 2 hydrogen atoms (that's the H2 in the water molecule). So if there were 11 water molecules produced, that would balance the hydrogen with 22 hydrogen
atoms on each side. Finally, the oxygen. Since we know we have 12 CO2 molecules and
11 water molecules as products so far, we also know that we're gonna end up with
thirty-five oxygen atoms. If you look at your reactants, on the left,
you see that you have 11 oxygen atoms in the sucrose molecule and 2 in the molecular oxygen,
O2. The carbon and hydrogen are balancing nicely with only one molecule of sucrose, so let's leave that alone. But there could be any number of paired oxygen
atoms involved. Since you need 35 and you know you have 11
to start with in the sucrose, you just need 24 more, which would equal 12
molecules of O2. And now, the equation is balanced! You know
exactly what my body is producing. For every molecule of sucrose I'm metabolizing I have to inhale 12 molecules of oxygen and in return, in addition to a little sugar buzz, I'll produce 12 molecules of carbon dioxide and 11 molecules of water. This is incredibly useful in helping us to understand the proportions of chemicals as they react at the molecular level. But in a lab, or in life, you have to work
with measurable amounts of stuff, so the last stoichiometric trick you need
up your sleeve is to calculate specific masses of the reactants and products. So for instance, how much oxygen will I need
to inhale in order to burn 5 grams of sugar? To figure that out, we just need to focus
on the left part of the equation, because we only need to quantify the reactants. First, convert your balanced equation into
molar masses; in order to get from molecules to grams, you
need to go through moles first. When you figure out the molar masses, you see that the ratio of sucrose to oxygen is actually pretty close: 384 grams of oxygen for every 342.3 grams
of sucrose. Then you simply compare this ratio to the
masses of reactants in your experiment, 5 grams of sugar to X grams of oxygen, and
hopefully you know how to solve for X. For every 5 grams of sugar I ingest I'll need
to inhale 5.6 grams of oxygen, which I happen to know is about 35 breaths'
worth. So as long as I manage to stay alive for the
next minute and a half or so, I'll manage to burn off this five grams of
sugar. Down the hatch! Today, we learned about two of the most important units of measure in chemistry, atomic mass units and moles. We also learned how to calculate molar mass and how to balance a chemical equation and finally, we talked about how to use molar ratios to calculate the amount of stuff that goes in and out of a reaction. Thank you for watching this episode of Crash
Course Chemistry, which was filmed, edited, and directed by
Nick Jenkins. This episode was written by Blake de Pastino
and edited Dr. Heiko Langner. Sound design was by Michael Aranda, and our
graphics team is Thought Cafe.