Leah here from leah4sci.com/mcat.
And in this video we're going to look at the definition and calculations for density.
According to google, density is the degree of compactness of a substance.
Say what? you come across density in both chemistry and physics where chemistry will
use the letter d and physics will use the greek letter rho that looks like a lower case
p.
I'm gonna be using rho but recognize you can also use D. Density is equal to mass over
volume.
Recall the definitions that mass tells us how much matter of how much stuff.
And volume tells us how much space it takes up which gives us a more logical understanding
of density, how much space stuff takes up.
We're looking at this intuitively, how much stuff is in there?
meaning, how heavy?
And then how much space it takes up.
If you think of a balloon that's filled with air and a bag that's filled with rocks.
They could be the same size, they take up about the same amount of space but that balloon
filled with air, you can probably just hold it with two fingers but that bag of rocks
will require two hands and then it may even still be too heavy.
I like to think of density almost as thickness, like how thick something is on the inside.
Maybe this is where the concept of having a thick head nothing gets through because
it’s so compact comes from , but that's not what we're referring to.
Density tells us how much space matter occupies.
So how do we measure that?
If Density is equals to mass over volume and mass is measured in units of grams or kilograms.
But what about volume?
Isn't volume measured in liters or in cubic meters? which one do we use for density? and
the answer is both.
You will typically come across density in units of grams per milliliter or grams per
cubic centimeter recognizing that 1 milliliter is equal to 1 cubic centimeter which is something
we worked out on the conversion series linked below.
Here's how I like to think of it.
A milliliter is typically referring to fluids and fluids can move around take the shape
of their container so I can have a milliliter of water in the form of a big drop of water
and that takes up a certain amount of space.
But if I were to take that same amount of water and force it into a tiny box, I would
get 1 centimeter each for the length, width, and height which gives me 1 centimeter times
1 centimeter times 1 centimeter or 1 centimeter cube as the volume for this box that can hold
1 milliliter of water.
It's easy enough to find density if you know what you're looking for.
We know that density is equal to mass over volume so let's start with a solid.
Say I have a brick of metal, a perfectly shaped brick.
All I have to do is find the mass by weighing it and then finding the volume by measuring
the length times the width times the height.
Plug it in and I get grams per cubic centimeter or whatever units you're using.
If I have a liquid I can just as easily find the density.
The only thing you have to make sure is that you account for the weight of your baker.
The way to do that is to first find the mass of the empty baker then add the water in and
find the mass again.
The total mass is going to represent the mass of the water which you want but also the mass
of the beaker which we don't want.
Sow what you do is you subtract empty beaker from the total mass and that will give you
the mass of your water or the mass of the fluid.
Then you look at the volume,so hopefully you're using something like the graduated cylinder
which gives you a very clear reading of the volume and once again grams per milliliter
or similar unit to find the density.
But what if you're trying to find the density of something not so easy to measure because
it's not in liquid form so you can't put it in a beaker but the solid is not that easy
to measure because it got a lot of different pieces.
For example the crown in the Archimedes story, the story goes something like this; A king
commissioned a crown to be made with pure gold and when he got the crown and it was
beautiful he was still worried that the artist mixed in an inferior metal and took some of
that gold for himself to figure out if the crown was indeed pure gold he went to Archimedes.
Now Archimedes thought about this but the problem was, in order to find out what it
was ideally you will have to melt the crown and do the typical mass over volume calculation.
But, that would destroy the beautiful crown!
Archimedes didn't know what to do.
And the story goes to figure out how to do this by taking a bath so if you ever stuck
on an mcat problem, maybe what you need is a bath.
And what he realize was, if he fills a container with water and then submerges the crown he
can simply note how much the water volume increases when the crown is placed inside.
Any displaced water would represent the volume of the crown and this is what he is able to
use when figuring out density is equal mass divided by volume of the water displaced or
volume of the crown.
And if the density is equal to that of` gold, the crown was pure but if wasn't let's just
say, I wouldn't wanna be that guy.
You'll see a lot more of this when you're looking at density in physics including specific
gravity.
Specific Gravity is a ratio of densities commonly used with water.
So we would look at the density of an object compare that to the density of water.
And since the density units will cancelled, we get a unitless ratio that tells us this
thing is x many times as dense as water.
The logic here is something more dense than water is going to the sink or partially submerged.
And something less dense than water is going to float.
You don't have to memorize these values but as an example, the specific gravity of cement
is equal to 3.15, this tells you that cement is 3.15 times as dense as water, then if you
look at something like wood which we know floats we expect it to be less dense than
water.
And while different woods vary for example if I look at oakwood, it has a specific gravity
of 0.75 telling us it's 0.75 times as dense as water meaning it's three quarters density
of water.
And here's a fun one, blood has density that is slightly greater than 1 which is why if
you ever bleed over water you'll notice it floats for a bit but then slowly mixes in
it as it dissolves in water.
The density that you absolutely should memorize for the MCAT is the density of water which
is equal to 1 gram per milliliter or 1 kilogram per liter.
Memorize both of these numbers but you can see this worked out in the conversion link
below.
Another one to note, the density of sea water or salt water is 1.03 kilograms per liter
which would be 1.03 grams per milliliter.
On the MCAT close enough is` good enough but it's important to remember that sea water
is saltier and that means it's going to be slightly more dense and this may come up as
the logic behind figuring out some of your passages.
One more that I wanna point out is the density of diethyl ether ET2O which is equal to 0.7
grams per milliliter.
This is 70 percent as dense as water and while you don't have to know the number I want you
to recognize this when you're looking at chemical extractions.
In extractions where you have 2 layers in a separatory funnel, how will you know which
layer is the aqueous layer and which layer is the organic layer.
If you're using something like diethyl ether which has a density that is less than water,
we know that something less dense is going to float.
This means that your aqueous layer which is water is gonna be the layer on the bottom
the one that comes out of that separatory funnel first and the organic layer your ether
is going to remain on top because of its lower density.
Say you're asked to find the volume in milliliters occupied by 21 grams of ethanol given that
the density of ethanol is 789 kilograms per meter cube.
First, figure out what you're asked for.
We wanna find the volume, we're given a mass, and we're given a density.
This should clue you in, density problem is equal to mass over volume, but we're ask to
find the volume given everything else.
We have to isolate volume by bringing it to the other side which gives me volume times
density is equal to mass.
Divide both sides by density and that tells me that volume is equal to mass over density.
Now we plug it in, we have a mass of 21 grams and we have a density of 789 kilograms per
meter cube.
The problem with this is kilograms is not grams and we're asked to find the volume in
milliliters not meter cube.
So we have to convert kilogram per meter cube into grams per milliliter.
We'll set this up using given times ratio taught in the conversion series linked below.
This is something you should get comfortable, either doing it in your head or writing out
minimal steps.
The given in this case is 789 kilograms over 1 meter cube.
What do we use for our ratio?
You should know that 1 gram per milliliter is equal to 10 to the 3rd kilogram per meter
cubed.
How do we set this up?
Remember, we want the units that are given to cancel out the units in the ratio so let's
set this up as a fraction over another fraction, that's the worst.
What do we put at the top? the new unit.
And what are the new units?
gram per milliliter divided by the ones we know 10 to the 3rd kilogram per meter cube.
This allows us to cancel out kilogram per meter cube giving us our answer in units of
grams per milliliter.
But we have to divide by 10 to the 3rd.
From here we simply use the decimal trick.
When dividing by 10 to the 3rd, we just move the decimal back 3 spaces which gives us 0.789
grams per milliliter. if you were overwhelmed by this Math, I am too.
So let's see if there's another way to do this.
You can try to look at this a little more logically.
We know that 10 to the 3rd kilogram per meter cube is a gram per milliliter so every thousand
kilogram gives us 1 gram, we have just under a thousand kilogram which means we have just
under 1 gram and how much less?
well .789 of a thousand which would give us .789 of a gram.
Then we go back to our original problem and plug it in.
We have 21 grams divided by 0.789 grams per milliliter.
Units of grams cancel giving us an answer in 1 divided by per milliliter which is simply
just milliliters but what about the math?
Don't let the math scare you, try to find shortcuts, try to find simplifications cause
you can't have a calculator on the MCAT.
What we're looking at is 21 divided by .789`.
First thing we want to do is round.
21 is approximately 20, .789 is approximately .8 and from here we use the decimal trick.
By moving the decimal to the right on top and bottom giving me 200 divided by 8.
If you recognize that 8 quarters will give you 2 dollars then you can say 200 divided
by 8 is 25.
Or you can simplify a little.
You can divide both 2 and 8 by 2 giving us a hundred over four and a hundred over four
you should definitely recognize as 25 for an answer of 25 milliliters.
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