In the last episode we introduced the concept of the mole - a unit of measure that allows
us to compare elements and the compounds they form to each other.
To recap, the periodic table lists the atomic mass of every element underneath its chemical symbol.
That atomic mass is the mass in atomic mass units, or amu, of one atom of that element.
The molar mass is the mass of the substance in grams per mole.
For single elements, the atomic and molar masses are numerically the same, but expressed
in different units.
For compounds, we’d add all the atomic masses of the elements that make up our substance
to get its total molar mass.
Avogadro’s number, which is 6.022 x 1023 particles per mole, is what chemists use to
determine how many particles are in an amount of moles, or vice versa.
This number can be used for calculations with any substance.
It’s the same for any element or compound.
One mole of lead is 6.022 x 1023 atoms of lead.
One mole of mercury is 6.022 x 1023 atoms of mercury.
Or, flipping it the other way, there are 6.022 x 1023 particles of strawberry ice cream in
one mole of that ice cream.
Last time, we used Avogadro’s number to do those conversions back and forth, but now
we’re going to take things a little further.
It’s time to talk about dimensional analysis - the way we make sure our calculations give
us a number at the end that’s in the right units.
Hi, I’m Will Comar, and welcome back to Study Hall Chemistry, presented by
Arizona State University and Crash Course.
Let’s dive in!
We’ve already been kind of using dimensional analysis unofficially, but it’s nice to
have a name for it.
What we end up doing in dimensional analysis is writing ratios called conversion factors,
which we use to convert things from one set of units to another.
They have one unit in the numerator and one in the denominator.
As we calculate, the units we’re using should cancel each other out, until we get to the
end, where our final answer will have whatever units are left over.
There are five steps we can walk through for this process, so let’s do an example.
Let’s say we need to convert 3.05 grams of potassium to moles.
First, let’s start with our givens.
We have 3.05 grams of potassium.
We also know from the periodic table that the atomic mass of potassium is about 39 amu.
Like we talked about before, for simplicity, we’ll be rounding our atomic masses to the
nearest whole number on this series.
Second, we need to write out what we need to find.
We need to know how many moles of potassium there are in 3.05 grams of it.
Third, we should identify our conversion factors.
For this one, we’ll call our molar mass of potassium a conversion factor since it
has its units in a ratio of grams per mole.
This is basically another way of saying there’s 39 grams of potassium in one mole.
Fourth, we set up our conversion, with the units we’re going from on bottom, and the
units we need to get to on top.
Here, we want grams on the bottom, and moles on the top.
In order to do that, we need to invert our conversion factor so it reads one mole per
39 grams of potassium.
Fifth, we multiply our given by the conversion factor and solve for the correct units.
So we could multiply 3.05 grams by 1 mole over 39 grams potassium, then divide the result.
There is a faster way to do this though - we can just divide 3.05 by 39.
The grams will both cancel out because of the rules of fractions - something divided
by itself becomes one.
We’ll do this as a shortcut in all our calculations.
3.05 divided by 39 becomes 0.0782, and the only units left in our calculation are moles,
so our answer is that there are 0.0782 moles in 3.05 grams of potassium.
Also, we’ll need to be sure to keep our answers rounded to the proper amount of significant
figures, or sig figs.
This helps scientists know how accurate our measurements and calculations are.
We will know how many digits to include in our answers by noticing how many sig figs
are in our given values, and from those, using the lowest number of sig figs in our answer.
Our givens here were 3.05 g, which has 3 sig figs, and 39 amu, which has 2.
We need to round our final answer to two sig figs then, because that’s the lowest
number of sig figs this time.
Since leading zeroes are not significant, our answer is 0.078, with just the seven and
eight counting toward our total of 2 sig figs.
This kind of conversion is also reversible - we can find an amount of grams from
a number of moles given to us.
If we were to do that for a compound like carbon dioxide, it would follow the same steps,
just this time we’re solving for something different.
So, let’s say we’re given 0.50 moles of carbon dioxide, and we’re asked
to find out how many grams that is.
We’ll apply the same steps.
First, our givens are 0.50 moles of carbon dioxide, and the atomic masses of carbon and oxygen.
Second, we need to find the molar mass of carbon dioxide, and for our final answer,
we need to find out how many grams of carbon dioxide are in our given amount.
For the formula CO2, we have one carbon atom and two oxygen atoms.
We can sum the atomic masses of these to get 44 grams per mole as the molar mass of carbon dioxide.
Third, we need to pick out our conversion factor.
Like last time, our molar mass will probably be our conversion factor because its units
include both the units of what we’re given - moles - and what we need - grams.
Fourth, our conversion needs to be ordered so that our units of moles will cancel out
and leave us with grams of carbon dioxide.
So if we lay out our known values, we have 0.50 moles of carbon dioxide multiplied by
our molar mass conversion factor, with grams on top and moles on the bottom.
Fifth, we multiply and solve for our proper units, and round to the proper number of sig
figs, which in this case would be two.
Our moles cancel out, and we’re left with 22 grams of carbon dioxide, our answer.
Now that we’ve got the hang of this 5-step process, we can always apply it to other calculations.
Dimensional analysis is really versatile, and scientists use it for all kinds of things in chemistry.
Especially when we’ve got multiple conversion factors, it helps us organize and line up
what we’re seeing.
That way, we don’t commit any math crimes.
One way we can apply dimensional analysis is to convert between particles and moles.
Here’s where we can bring back Avogadro’s number.
If we are trying to find the amount of atoms in 5.889 moles of tin, we can lay out our
steps the same way as before.
We are given 5.889 moles of tin, and we need to find the number of atoms in that amount.
So, let’s talk conversion factors.
We know Avogadro’s number has the units of particles per mole.
That can be atoms, molecules, or whatever else we’re working with.
The units of Avogadro’s number depends on the problem, but here we can refer to it as
atoms per mole.
It accounts for both the units we currently have and the units we need, so it seems like
a good choice here.
Now we can lay out our calculation with all our terms.
We’re starting with 5.889 moles of tin, which we can multiply by our conversion factor
in atoms per mole.
So we’d multiply 5.889 moles of tin by 6.022 x 1023 atoms, divided by one mole.
Next we should multiply our terms and cancel out our moles units, leaving our answer in atoms of tin.
In other words, 5.889 times 6.022 x 1023 which gives us our answer in our desired units of atoms.
But...okay, 6.022 x 1023 is a huge number, so big we write it in scientific notation.
Scientific notation takes big terms and converts them to decimal numbers multiplied by 10 to
a given power, like 10^23.
Nobody in chemistry is going to expect us to do this in our heads.
I mean, we could try.
But there’s an easier way to do this calculation.
Let’s take a tour of a calculator on TestTube.
On most calculators, there’s a way to multiply terms with exponents.
There’s also a specific button for scientific notation, sometimes shown as EE or 10^x for
terms that are ten to an exponential power.
If we wanted to type our tin calculation in, we’d enter 5.889 times 6.022 like normal,
then the multiplication button, the EE button, and 23.
We’ll end up with the answer given to us in scientific notation.
If your calculator doesn’t automatically give you an answer in that format, there’s
a way to change it in your settings.
With our calculator doing the heavy lifting, our answer here is that there are 3.5463558×10^24
atoms of tin in 5.889 moles.
Rounding this to four significant figures, we have 3.546 x 1024 atoms as our final answer,
since the 10 to a power doesn’t count.
We’ll use the same process when working with compounds.
There’s still the same conversion setup, because Avogadro’s number is universal whether
we’re dealing with elemental manganese or a glucose molecule.
And the fact that it’s reversible means we can do these conversions in the opposite
order if we needed to.
We just have to be mindful when using a calculator if it doesn’t automatically use order of operations.
In this case, we’d need to put parentheses around our scientific notation expressions and press enter.
We’d then round to four sig figs again, since we only do that at the very end of our calculation progress.
We end up with the number we started with, 5.889 moles of tin.
Thanks, TestTube!
There are lots of cool ways to use our understanding of atoms and moles in real-life chemistry too,
including some that use fancy instruments.
Most of the examples we’ve done in this episode have come from known substances.
But if we’re handed a sample and told to find out the mass of its components, a process
called mass spectrometry is one way to do that.
Mass spectrometry helps us learn more about the components of a substance by separating
them out by mass and electrical charge.
It’s widely used in fields like pharmaceutical research, water quality analysis, and biomedicine.
It relies on a machine called a mass spectrometer.
A mass spectrometer ionizes a sample so it accelerates into a beam that can be projected onto a detector.
Components with smaller masses or more ionic charge hit the detector first, followed by
heavier or not as charged ones.
The spectrometer provides us with an awesome plotted chart that shows which components
are present in what quantities, and their masses.
And as we’ve learned in this episode, we can do a lot of valuable calculations if we
know the mass of a substance -
we can determine how many particles are in it using Avogadro’s number, we can determine
its molar mass, and we can convert it to moles.
Building up some brain muscle memory with this mole conversion process will go a long
way for us, because next time, we’ll be covering multi-step mole problems.
It wouldn’t be chemistry if we didn’t eventually make it more complicated, but complicated
doesn’t always mean harder.
Now that we know the steps to take, we just have to apply and expand them, and we’ve
already got the tools we need to approach them logically.
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!