Chem143 Density and Specific Gravity

Density and specific gravity.

>> In this video, we're talking

about density and
specific gravity.

So first of all, let's
see what density is.

You probably already know this.

But anyway, the definition
of density is the mass

of an object divided by its
volume, mass over volume.

In terms of symbols, we
say d is equal to m over v.

This is an algebraic
equation really,

and it has three
variables in it.

And you will need to, every
now and then, solve for one

of these three different
variables.

So if you know the mass
and the volume and you want

to find the density,
you just take the mass,

divide by the volume.

It gives you the density.

The most common unit
that we will see

for density is grams
per milliliter

or grams per cubic centimeter,

which are exactly the
same as each other.

Now you could have any unit for
mass and any unit for volume,

but these are just the most
common ones you guys will see.

You'll see grams per liter
every now and then also.

So if we rearrange this and
solve for the mass, which is m,

if we know the density and we
know the volume of the object,

all we have to do to get its
mass is take its density times

its volume.

And likewise, if we know
the mass and the density

of an object, we can find
the volume of an object.

So memorize this.

Well, memorize the
density equation.

Density is equal to
mass over volume.

And be able to rearrange
it to get any

of the three variables
by itself.

So the units of grams per
milliliter are exactly the same

as the units of grams
per centimeter cubed

because a milliliter is the
same as a cubic centimeter.

That's really important to know.

You'll use it throughout
this course really.

So memorize that 1
milliliter is exactly the same

as 1 cubic centimeter.

These are exact numbers here.

And also, while we're
memorizing stuff,

you should memorize
the density of water,

to at least three
significant figures

at a round room temperature.

And all those are
qualifiers, aren't going

to really matter to
us at this point.

But the density of water
is 1, simple right,

1 gram per milliliter.

So memorize that.

That's the only density of any
substance that I will ask you

to memorize, but I
want you to know that.

So if you have different
objects, different substances

and you place then
into a liquid,

if the substance has
a greater density

than the liquid, it'll sink.

And if it has a lower density
than the liquid, it will float.

And if it has roughly
the same density,

it'll be suspended in there.

You know, so in this
picture here, right,

cork has a density
less than water.

So let's assume this
liquid here is water, okay.

So its density is 1 gram
per milliliter; 0.26 is less

than 1, so the cork floats.

Ice, solid ice, which is
different than liquid water,

has a little bit lower
density than liquid water,

about 0.92, so it floats.

It floats on liquid water.

Water is 1 gram per milliliter.

Oh, yeah, we don't
have to assume.

Now aluminum and lead, both
of these guys have densities

that are greater than water,
so, of course, they sink.

Now the human body made
up of, well, mostly water.

And you know if you've ever gone
swimming, been in the water,

that if you just lie
in the water, you'll,

you know, more or less float.

You might sink.

You might float.

But, you know, it's
pretty close, right.

And what that tells
you is that the density

of the human body is roughly
the same of that as water,

1 gram per milliliter.

Now if you've ever been in the
ocean where it has a lot of salt

and things dissolved in it, the
density of seawater is greater

than the density
of regular water.

It's higher than 1
gram per milliliter.

And so, the human body
definitely floats in seawater.

So now, let's just do
a couple of examples.

Let's say we have an object.

We know its mass, 2.718 grams.

And we know what
volume it occupies,

3.141 cubic centimeters.

We want to find the density
in grams per milliliter.

So if we know the mass
and we know the volume,

all we have to do
is take the mass

and divide it by the volume.

That's the density
formula, right.

Now the units here, you have

to be careful about,
but it's no big deal.

We have the mass
in grams already

and we want grams
over milliliters.

But we're given the volume
in cubic centimeters.

However, remember that
a milliliter is the same

as a cubic centimeter.

And so, what I do, and you
certainly should do it too,

is whenever you need to, you
can just interchange cubic

centimeters and milliliters.

Just swap them out.

Here, because we want the
density in grams per milliliter,

we can just write that the
volume is 3.141 milliliters

because it's exactly the same.

So here we are just plugging

into the density
formula, mass over volume.

We get this number.

Each of these measurements
had four sig figs.

So that means because
we're dividing,

we can keep four sig figs.

So we don't round at first.

But we get 0.8653 sub
3, maybe something else.

And then rounding
to four sig figs,

we get 0.8653 grams
per milliliter.

Easy as that.

Just another example.

And we're going to just throw
a little bit of extra in here.

So to do this problem, you
should remember that for a cube,

a cube is a rectangular solid
whose lengths all have the same,

excuse me, whose sides
all have the same length.

And so, here we go.

We have a cube, okay,
and its mass is --

Well, mass is what
we're trying to find.

We're given its density,
1.414 grams per milliliter.

And we're given the
lengths of its sides.

Because we know it's a cube,

we know they each
have the same length.

And you also know that the
volume of a cube is the length

of its sides to the third
power, the length cubed.

And so, because we
know here the density

and we can find the volume,

density times volume
is equal to mass.

Remember that?

So to find the volume, we just
take the length of an edge,

0.7298 centimeters, cube it.

And when we cube this,
we cube the number

and that cubes the dimension.

And so, we get 0.3886 sub 9,

four sig figs, cubic
centimeters.

Please, pause this for a minute,
put this in your calculator

and just make sure you're
getting the same number I am.

All right.

Now we know the volume.

All we have to do is
multiply it times the density

to get the mass.

And let's see.

So we have a volume
in cubic centimeters.

But remember, that's exact to
the same as the milliliters.

So I just write it as 0.3886 sub
9 milliliters so that it cancels

with the milliliters here.

And multiplying that out, we get
0.5496 grams to four sig figs.

Now specific gravity,
it's really no big deal.

The specific gravity of a
substance, it's just the density

of that substance divided
by the density of water.

And we saw that it
leads to three sig figs

at the temperatures we're
going to be dealing with.

The density of water is
1 gram per milliliter.

And so, the specific gravity

of an object will
just be the same value

as its density but
with no units.

It's dimensionless.

And so, if we had an object
whose density was 4.72 grams per

cubic centimeter, its specific
gravity would just be 4.72.