Leah here from leah4sci.com/mcat and in this video we're going to look at the mole concept
in avogadro's number.
What is a mole?
We're not referring to a little rodent and we're not referring to that thing that can
show up on your skin and definitely not referring to a spy though that would be a fun chemistry
video.
Now, in general chemistry a mole is just a big number.
A very very, very big number.
According to google, a mole is a mass in a substance containing the same number of fundamental
units as there are atoms in exactly 12.000 of Carbon 12.
Ouch!
right?
This is why the topic scares so many students, it sounds overwhelming.
But if you think of it, it's just a big number and understand the math, the entire thing
becomes easier.
Let's take a step back.
Say I tell you i have a pair of shoes.
You're thinking I have two shoes.
If I tell you that I have a dozen eggs.
You're thinking I have 12 eggs.
If I tell you I have a gross of pencils, you may recognize that I have a 144 pencils.
And if I tell you I have a mol of carbon atoms, you should recognize that I have 6.02 x 10^23
carbon atoms or for the MCAT just 10 x 10^23 because on the MCAT, close enough is good
enough.
The concept is simple, the Math is also pretty simple, it's the story behind it that confuses
students.
The number 6.02 x 10^23 is also referred to as Avogadro's Number which you'll see sometimes
written as N sub A or N sub 0.
This is to honor the Italian scientist and lawyer Avogadro who helped us understand the
molecule volume relationship specifically that equal volume of a gas under the same
conditions will have the same number of molecules.
But don't worry about it now because we'll cover it in detail in MCAT physics.
So what does this number tell us?
The back story, the confusing part is something you don't even need to know for the MCAT.
As long as you know the takeaway.
But in summary, say I tell you about carbon 12, this is a specific isotope of carbon,
the most abundant isotope of carbon that has a mass of 12 atomic mass units.
If we do the math, carbon has 6 protons, this isotope group of carbon has 6 neutrons, each
of this weigh 1 atomic mass unit giving us a total mass of 12 amu.
But, if I want to use 12 amu as a small scale and 12 grams on the large scale, I weight
out 12 grams of carbon which is mostly carbon 12, how many atoms do I have?
If I weigh out 12 grams of carbon 12 we'll end up with a ridiculous amount of carbon
atoms specifically 602214085700000000000000, phew!
can you imagine if the MCAT dealt with molecules in this format?
The Math would be insane!
Thankfully, we have a much easier way to look at this.
First of all we turn it into scientific notation.
Remember we have an invisible decimal at the end of the last 0, so if we move it all the
way over here, what do we get?
6.02, ignore the other numbers, in fact on the MCAT we can even just call it 6 times
10 the what power?
to the 23rd power because I had to move the decimal 23 spaces over to the left.
But more than scientific notation, we can just refer to this entire thing as one mol
and that makes life so much easier.
1 mol of any atom on the periodic table will give you the number of grams specified on
the periodic table.
If I take 1 mol of iron, I will get 55.845 grams of iron.
If I weigh out 22.99 grams of sodium, I will get 1 mol of sodium.
If i weigh out 32 grams of sulfur, I get 1 mol of sulfur.
And if I weight 1 mol of bromine, I will get 79.904 grams of bromine.
So even though 1 mol is equal to 6x10^23 atoms or 1 mol of molecules is 6x10^23 molecules,
the substance itself is different.
It's unique to what it is.
Sodium, very different from Iron.
Iron very different from sulfur, very different from bromine.
Think of our initial example.
If I gave you a dozen papers, eggs, and pencils, those are each 12 of something but they're
so different.
Good luck drawing on your dozen papers with a dozen eggs, very messy compared to the pencils
right?
they're unique and therefore very different.
And that should be your takeaway for the MCAT.
In fact, calculating the number of atoms in a mol or how many moles for a certain number
of atoms is less likely to show up on the MCAT compared to what we get out of it and
what we can get out of it is molar mass or molecular weight calculations.
That is what you have to master on the MCAT.
Now we've already done some of that in the previous video on molar mass so let's look
at some simple conversions.
But first, biological question, which has more atoms, 2 grams of carbon or graphite
that has 1 x 10^15 carbon atoms?
We can't compare grams of carbon to carbon atoms because they're completely different
units.
The typical MCAT student instinct is to do the math to figure it out which you can but
it's a waste of time.
See if you can think it through logically before applying before applying the calculation.
What do we know about the relationship between carbon atoms and mass of carbons?
We know that 12 grams of carbon is equal to 6x10^23 atoms.
If we have 2 grams of carbon, 2 of 12 is a 6 so we have a 6 of this number.
6 times 10 to the 23rd divide by 6 gives me 1 x 10^23 which is way, way larger than carbon
atoms on the order of 10 to the 15th.
Remember that every factor represents unit of 10 so we're dealing with a much much larger
amount carbon in just 2 grams of carbon atoms.
Let's solve this mathematically to prove it to make sure that you understand by converting
the 2 grams to atoms of carbon.
We'll solve it using the given times ratio method that I teach you on the conversion
series linked below where our given is 2 grams of carbon and the ratio compares mass of carbon
to atoms of carbon.
We put grams of carbon on the bottom so that the units can cancel giving me atoms at the
top then plug in the numbers giving me 6x10^23 atoms divided by 12, no units because we cancelled
that.
Our answer is going to be in the unit of atoms.
And now we do the Math but we really don't do the Math because on the MCAT, always try
to simplify before doing the calculation.
6 and 12 both divide by 2 that gives me 1 over 2 and guess what?
2 and 2 cancels giving me the final Math of 1 times 1 divided by 1 times 10 to the 23rd
as we already predicted which once again is way greater than 1 x10^15.
Let's try a more Mathy problem.
Say I ask you to find the number of atoms in 0.67 mols of water.
Once again we want to set this up as a given times ratio where the given is 0.67 mols of
H2O.
What's the ratio?
What are we converting here?
We know that 1 mol is 6x10^23 but that's not enough.
1 mol of water is 6x10^23 water molecules.
We are asked for the number of atoms so we need that second ratio where every 1 H2O is
equal to 3 atoms.
2 atoms of Hydrogen and 1 of Oxygen so that means we add a second ratio entire setup.
Our given has units of mol H2O so let's send up the ratio mols of H2O where we know that
1 mol of H2O is equal to 6x10^23 molecules of water.
And the next ratio where we take just 1 H2O, 1 molecule of water is equal to 3 atoms.
Water molecules cancel, mols of water cancel giving us a final answer in unit of atoms
which is what we were looking for.
With the Math of 0.67x6x3.
Looks scary, but ask yourself, are there any patterns that I recognize? 0.67 is a decimal
that should instantly recognized as 2/3 so what we really have is 2 over 3 times 6 times
3.
The 3s cancel and you should be able to do this in your head, I'm drawing it out to show
you.
The 3s cancel giving me 2x6 which is 12x10^23 atoms.
This is improper scientific notation so we do the move the decimal trick thought in the
Math video linked below.
We make 12 smaller giving us 1.2 and 23 bigger giving us 10^24 for a final answer of 1.2x10^24
atoms.
For even more practice on this topic and Stoichiometry in general, first give this video a thumbs
up then try the stoichiometry and reactions practice quiz on my website leah4sci.com/reactions.