Stoichiometry: Chemistry for Massive Creatures – Crash Course Chemistry #6


Chemists need stoichiometry to make the scale of chemistry more understandable – Hank is here to explain why, and to teach us how to use it.


Transcript Provided by YouTube:

00:00
By now, you’re probably starting to see how chemistry can change your view of the world.
00:04
Chemistry explains everything you can see, how it looks, the way it feels, why it behaves the way it does,
00:10
by describing everything that you can’t see.
00:12
It helps us understand the biggest stuff in the universe by helping us understand the tiniest.
00:17
And that’s why chemistry can be kind of hard to understand sometimes.
00:20
Because we are, on a chemical scale, huge.
00:24
Chemistry traffics in infinitesimal particles, but we are made of quadrillions of those things.
00:29
They are the building blocks of mass; we are literally massive.
00:34
So mass is how we massive beings tend to understand the world.
00:39
In our day-to-day dealings with substances,
00:41
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.
00:47
For example, chemistry will be happy to tell me that the atomic structure of the sugar in this packet is
00:52
12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms in every molecule.
00:57
But I don’t have any idea how many molecules of sugar I want to put in my tea!
01:02
Or how that one molecule will react with other chemicals in my body.
01:07
To understand that kind of stuff, I need to know the mass of the sugar that I’m dealing with.
01:12
In other words, I need to measure it.
01:14
And that, is why there’s stoichiometry,
01:17
the science of measuring chemicals that go into and come out of any given reaction.
01:22
In Greek, it literally means measuring elements,
01:25
and, in essence, it allows us to count up atoms and molecules by weighing them.
01:30
Stoichiometry, yes, contains a fair bit of math, but it’s one of the most important decoders that we have as chemists.
01:35
It’s what we use to translate from the very small to the very big,
01:40
to parley the stuff that we can’t see into the stuff that we can.
01:44
And because of that, chemists use it all the time.
01:48
Including, yes, for sweetening your tea. Ow… hot. It’s… it’s quite hot.
01:55
[Theme Music]
02:05
Now if you’ve been with me for a couple of weeks, and I do hope you have, you’re probably thinking to yourself,
02:10
“Wait, wait, now, don’t… don’t we already have a way of measuring elements?”
02:13
And you’re right. We do.
02:14
The real coin of the realm when it comes to measuring stuff in chemistry is relative atomic mass.
02:19
The average atomic mass of all of the naturally occurring isotopes of a given element.
02:24
So for example, all of the natural carbon on earth occurs as one of 3 and only 3 isotopes:
02:30
C-12, C-13, and C-14.
02:32
They all have six protons, but the number of neutrons vary.
02:35
And these isotopes show up on our planet in totally different proportions.
02:39
So the relative atomic mass of carbon is a weighted average of these three masses, which comes out to 12.01.
02:46
But 12.01 what?
02:48
Well, remember when we’re talking about units of measurement, we’re talking about arbitrary talk.
02:53
Most, units, except for the ones that we use to measure time, aren’t based on any real, objective value.
02:58
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.
03:04
The same goes for atomic mass. We measure atomic mass in atomic mass units.
03:08
We made them up, and the value for a single amu is — bear with me now —
03:12
1/12th of the mass of an atom of carbon-12.
03:16
Why? Funny story.
03:18
Until the mid-1800s, chemists in different parts of the world used different yardsticks for measuring elements.
03:22
One of the most intuitive and therefore most common was to use the smallest, simplest element, hydrogen, as a base line.
03:28
But in the 1850s, some chemists, led by German Wilhelm Ostwald, proposed using oxygen instead.
03:34
They preferred oxygen mainly because it combined readily with so many other elements,
03:38
so they figured it would be easier to determine the weights of lots of compounds.
03:41
So a bunch of guys stroked their beards, agonized over this for years,
03:45
until in 1903, they decided that atomic weight, as it was called, should be measured in 1/16ths of an oxygen atom.
03:52
Until in 1912, isotopes were discovered and chemists realized that you can’t talk about
03:57
an element like it’s all the same thing!
03:59
It turned out there was an oxygen-16, and an oxygen-17, and an oxygen-18!
04:03
And suddenly, everyone was walking around like, “I don’t know how much this such weighs anymore!”
04:07
This was so crazily disruptive that it took another 50 years of strokey-beard meetings
04:12
for everyone to decide to use another standard — carbon-12.
04:15
Like oxygen, carbon is common, and kind of promiscuous, when it comes to what it bonds with.
04:19
And since it has 12 protons and neutrons,
04:21
the mass of other, similar elements would be expressed as some fraction of it.
04:26
So, since 1961, science has pegged one amu as 1/12th of an atom of carbon-12.
04:32
Which means that carbon has a relative atomic mass of 12.01 amu.
04:37
Oxygen, 16 amu, and hydrogen, 1.008 amu. So that’s how we way atoms.
04:43
But, none of this solves my tea sweetening problem.
04:46
Like, I don’t know how many amus of these molecules together are going to make this taste good to me,
04:51
or how many other molecules of sugar I can consume while maintaining my slim yet robust physique.
04:56
This doesn’t happen by itself, you know.
04:58
And in order to make these calculations and predict reactions,
05:00
I first need to be able to convert the atomic mass of this sugar, into a standard amount of substance.
05:07
Not weight, not volume, just purely, objective amount of stuff. You heard me, stuff.
05:13
That, my friends, is what moles are for. Not those moles, though those are nice-looking moles.
05:19
A mole is arguably the most important unit in all of chemistry,
05:23
because it allows us to express a chemical’s atomic mass in terms of grams.
05:26
And to define what a mole is, no matter what it’s a mole of, we use our old standby, carbon-12.
05:32
There are 6.022 x 1023 atoms in 12 grams of carbon-12,
05:38
and by definition, that number of anything is a mole of that thing.
05:42
That’s a lot, and it is known as Avogadro’s number, one of the most important constants in chemistry,
05:48
and although Avogadro isn’t the one that arrived at this number,
05:51
it’s named in his honor because he used this basic principle of comparing amounts of substances
05:56
to first weigh atoms and molecules.
05:58
So there are this many carbon atoms in a mole of carbon-12
06:01
and there are the same number of anything in a mole of anything else.
06:05
Like a dozen roses is twelve roses, but a mole of roses is 6.022 x 1023 roses,
06:11
which would be enough roses to cover the surface of the earth quite deep.
06:14
A mole of sand would be 6.022 x 1023 grains of sand and if they were each one millimeter long,
06:20
a mole of them would stretch 100 quadrillion kilometers.
06:25
So you get the picture, it’s a big number, but in chemistry the thing to remember is this:
06:30
a mole of any element contains 6.022 x 1023 atoms of that element no matter what.
06:37
This is what lets us translate number of atoms into grams. It lets us weigh the elements.
06:43
All right, follow me here.
06:44
One mole of carbon-12 contains 6.022 x 1023 atoms and weighs 12 grams, right?
06:49
So one mole of oxygen also contains 6.022 x 1023 atoms but because oxygen atoms are
06:55
more massive it weighs 16 grams and you’ll recall that oxygen’s relative atomic mass is 16 amus.
07:02
The number of atoms per mole remains the same,
07:05
but the mass of a mole depends on the average mass of the element.
07:08
This simply means that one mole of any element equals its relative atomic mass in grams.
07:13
So now you’ve got it, 1 mole of hydrogen weighs 1.008 g, a mole of iron is 55.85 g,
07:19
and a mole of natural carbon is 12.01 grams.
07:23
This is known as an element’s molar mass.
07:25
And now that we know the molar mass of elements we can calculate the molar mass of any compound.
07:30
All we have to do is add up the molar masses of its component elements.
07:34
So for instance, the formula for this sugar or sucrose is C12H22O11.
07:39
One mole of sucrose, by definition contains 6.022 x 1023 molecules,
07:44
and since each molecule contains 12 carbon atoms and 22 hydrogen atoms and 11 oxygen atoms,
07:50
then one mole of sucrose contains 12 moles of carbon, 22 moles of hydrogen, and 11 moles of oxygen.
07:57
Multiply the number of moles of each element by its molar mass and add them all up,
08:01
that’s the molar mass of the whole compound.
08:03
See, the mole is like our chemical Rosetta Stone;
08:06
with it, we can translate anything from the level of atoms and molecules to the level of grams and kilograms.
08:11
And we can use it to describe not only elements and compounds, but reactions.
08:15
And you don’t need a lab full of samples to do it, just a pencil and a calculator.
08:20
To get back to my tea problem, let’s say, y’know, hypothetically, that I’m watching my weight,
08:24
so I want to know what it’ll take for me to burn a certain amount of sugar that I consume.
08:29
That’s a reaction! And it’s a pretty simple one.
08:31
My body uses sucrose by combining it with oxygen to create energy plus CO2 and H20 as waste.
08:37
You can write this out as an equation,
08:38
in which the reactants combine on the left to yield the products on the right.
08:41
But there’s a problem here: this equation doesn’t reflect chemical reality.
08:45
During a reaction, bonds are broken and new ones are formed but the number of atoms of
08:49
each element remains the same.
08:50
The sugar and oxygen molecules may be busted apart and mixed up,
08:53
but the number of each kind of atom that you start with ends up being exactly the same after the reaction.
08:59
Conservation of mass, yo.
09:00
So when writing a reaction out as an equation,
09:02
the number of atoms of each element has to be exactly the same on both sides.
09:06
Reconciling the reactants with the products is called equation balancing,
09:10
and it’s a good bit of what stoichiometry is all about.
09:12
Because from a chemical perspective an unbalanced equation is pretty useless.
09:16
It doesn’t tell you how much is going in and how much is coming out.
09:20
Without balancing the equation it’s like saying,
09:21
“When a mommy and a daddy love each other very much, a baby appears and that’s all you need to know.”
09:26
But that’s not all you need to know!
09:27
So how do you do it? Not make a baby, balance an equation. I did biology last year.
09:33
Well the best way is to start with the most complicated molecule, which in this case is,
09:37
of course, the sucrose.
09:39
For every molecule of sucrose that goes into the reaction, you know that you’re gonna have 12 carbon atoms,
09:43
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,
09:49
because that’s the only molecule where those carbon atoms end up.
09:52
Now let’s deal with the hydrogen,
09:53
because that also shows up in only one molecule on both sides of the equation so that’s easier.
09:58
You know that at least 22 atoms of hydrogen go into the reaction
10:01
and the product contains some multiple of 2 hydrogen atoms (that’s the H2 in the water molecule).
10:07
So if there were 11 water molecules produced,
10:09
that would balance the hydrogen with 22 hydrogen atoms on each side.
10:12
Finally, the oxygen.
10:14
Since we know we have 12 CO2 molecules and 11 water molecules as products so far,
10:19
we also know that we’re gonna end up with thirty-five oxygen atoms.
10:22
If you look at your reactants, on the left, you see that you have 11 oxygen atoms in the
10:25
sucrose molecule and 2 in the molecular oxygen, O2.
10:29
The carbon and hydrogen are balancing nicely with only one molecule of sucrose, so let’s leave that alone.
10:34
But there could be any number of paired oxygen atoms involved.
10:36
Since you need 35 and you know you have 11 to start with in the sucrose,
10:40
you just need 24 more, which would equal 12 molecules of O2.
10:45
And now, the equation is balanced! You know exactly what my body is producing.
10:48
For every molecule of sucrose I’m metabolizing I have to inhale 12 molecules of oxygen and in return,
10:55
in addition to a little sugar buzz, I’ll produce 12 molecules of carbon dioxide and 11 molecules of water.
11:00
This is incredibly useful in helping us to understand the proportions of chemicals as they react at the molecular level.
11:07
But in a lab, or in life, you have to work with measurable amounts of stuff,
11:11
so the last stoichiometric trick you need up your sleeve is to calculate specific masses
11:15
of the reactants and products.
11:17
So for instance, how much oxygen will I need to inhale in order to burn 5 grams of sugar?
11:21
To figure that out, we just need to focus on the left part of the equation,
11:25
because we only need to quantify the reactants.
11:27
First, convert your balanced equation into molar masses;
11:30
in order to get from molecules to grams, you need to go through moles first.
11:33
When you figure out the molar masses, you see that the ratio of sucrose to oxygen is actually pretty close:
11:38
384 grams of oxygen for every 342.3 grams of sucrose.
11:42
Then you simply compare this ratio to the masses of reactants in your experiment,
11:46
5 grams of sugar to X grams of oxygen, and hopefully you know how to solve for X.
11:52
For every 5 grams of sugar I ingest I’ll need to inhale 5.6 grams of oxygen,
11:57
which I happen to know is about 35 breaths’ worth.
12:00
So as long as I manage to stay alive for the next minute and a half or so,
12:03
I’ll manage to burn off this five grams of sugar. Down the hatch!
12:07
Today, we learned about two of the most important units of measure in chemistry, atomic mass units and moles.
12:12
We also learned how to calculate molar mass and how to balance a chemical equation and finally,
12:16
we talked about how to use molar ratios to calculate the amount of stuff that goes in and out of a reaction.
12:22
Thank you for watching this episode of Crash Course Chemistry,
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which was filmed, edited, and directed by Nick Jenkins.
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This episode was written by Blake de Pastino and edited Dr. Heiko Langner.
12:30
Sound design was by Michael Aranda, and our graphics team is Thought Cafe.


This post was previously published on YouTube.

Photo credit: Screenshot from video

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