Calculate your own osmolarity | Lab values and concentrations | Health & Medicine | Khan Academy

Now let's say that you
have a vial of plasma.

And I'm actually going
to label it as we go.

We've got some sodium
floating in here

and you've got some anion
in purple over here.

And this could be anything
that really binds to sodium.

So if this is some negatively
charged ion, maybe chloride,

or bicarb, those are
the two most common.

And you've also got, let's
say, some glucose in here.

And maybe some urea, or we
call it urea nitrogen as well.

So you've got a few things
floating around the plasma

and someone asks
you, well, what is

the total osmolarity
of the plasma?

And you know that
this is in units

of osmoles per liter
blood, Actually,

I should write liter
plasma to be more accurate.

Since that's what we're
talking about here.

So per one liter of plasma.

And these are the units
that we have to think about

to answer this
question, is, what

are the osmoles per
liter of plasma?

So let's go through this.

And I'm going to give
you some lab values

and we'll see how based on just
a few lab values and really

just four of the most
representative solutes,

or most important
solutes, we can

get a pretty close
guesstimate of the osmolarity.

So you don't actually need to
know every single osmole that's

in your plasma.

You can figure it
out based on four

of the most important ones.

So let's go with the
first one, sodium.

And let's say the lab tells
you, well, your sodium value--

and I'm going to write the labs
in kind of this grey color,

somehow that reminds
me of the lab--

let's say they say the sodium
value is 140 milliequivalents

per liter.

So how do you take that and
make it into osmoles per liter?

Well, our denominator
is already OK.

But immediately, you can
say, OK, well 140 millimoles

per liter is what that equals.

And you know that because
sodium is a monovalent.

It's only got one charge.

If it's monovalent,
then that means

that the equivalents
equal the moles.

And now that you're
in moles, you

can actually go
across to osmoles.

You could say 140 osmoles
or milliosmoles per liter.

And you know that because
once sodium is in water,

it acts the same way that
you would expect it to act.

It doesn't split
up or anything like

that because it's one particle.

So it acts as a single particle.

One particle.

So if it's one
particle, it's going

to have 140
milliosmoles per liter.

And we've effectively gotten one
quarter of this problem done.

Because all we need to do is
take the four different solutes

that we've identified
and add them up together.

So we've figured out sodium.

And now let's move
on to the anion.

And the trick to the anion is
just thinking of it as sodium.

It's almost the same as
sodium, but just the reverse.

So we know that it's
going to be 140.

We're going to use 140
as the number here.

Because our assumption is that
sodium is a positive charge

and for every one
positive charge,

you need one negative charge.

So we're going to assume that
all the negative charges are

coming from these anions.

And these would be
things like we said,

things like chloride or
bicarb, something like that.

So again, we don't
actually get these numbers

or even need these
numbers, we simply

take that 140 and
we multiply by 2

and assume that the other half
is going to be some anion.

Now we actually have
to convert units still.

We have to get over to
milliosmoles per liter.

And so we know that the anion
is going to be monovalent

and that gets us to millimoles.

And we use the same
logic as above.

We just say, OK, well
if that was millimoles

and it's still one particle,
meaning it's not splitting up

when it hits water and going
in two different directions,

in a sense, having
twice the effect,

we're going to end up with
140 milliosmoles per liter,

just as before.

So this is our second
part done, right?

So two parts are done.

We figured out the sodium
and we figured out the anion.

Now let's go over to glucose.

So let's figure out how to
get glucose as units from what

the lab gives us, which I'll
tell you in just a second,

into something more usable.

So how do we actually get
over to something usable?

Let me actually, switch over.

There we go.

Make some space on our canvas.

So let's say we have
our glucose here.

And the lab calls us
and says, hey, we just

got your lab result, it was
90 milligrams per deciliter.

It's actually a very,
very common lab value

or common range for
a glucose lab value.

One thing we have
to do right away

is figure out how to get
from milligrams to moles.

And you know that this is
what glucose looks like.

This is the formula for it.

So to get the overall
weight, the atomic weight,

you could say,
well, let's take 6,

because that's how
many carbons we have,

times the weight of
carbon, which is 12,

plus 12, because that's
what we have here,

times the weight of
hydrogen, which is 1,

plus 6, times the
weight of oxygen.

And that's going to equal--
this is 72, this is 12,

and this is 96, and add them all
up together, and we get-- 180.

So we have 180 atomic mass
units per glucose molecule.

Which means, if you
think back, which

means that one mole of
glucose equals 180 grams.

And since these
are way, way bigger

than, I mean this is grams, and
we're talking about milligrams

over here, so I'm going to
just switch it down by 1,000.

So one millimole of glucose
equals 180 milligrams.

All I did was divide by 1,000.

So now I can take this unit and
actually use our conversions.

I could say, well, let's
multiply that by 100

and-- let's say, one
millimole rather,

one millimole per 180
milligrams, that'll

cancel the milligrams out.

And I also have to get from
deciliters to liters, right?

So I've got to go 10
deciliters equals 1 liter.

And that'll cancel
my deciliters out.

So I'm left with-- and this
10 will get rid of that 0--

so I'm left with
90 divided by 18,

which is 5 millimoles per liter.

And, just as above, I
know that the glucose

will behave as one particle
in water, in solution.

So it's going to be 5 osmoles,
or milliosmoles, actually.

5 milliosmoles per liter.

And that's the
right units, right?

So I figured out another
part of my formula.

And I'll show you the actual
formula at the end of this,

but I wanted to work
through it piece by piece.

So we've done glucose now and
we're ready for our last bit,

so let's do our last one,
which is going to be urea.

Specifically, the lab is not
going to call us about urea,

it's going to call us
about blood urea nitrogen.

And actually, it
matters what this means.

So what that exactly
means is that they're

measuring the nitrogen
component of urea.

And so they'll call you and
say, well, we measured it

and the value came to 14
milligrams per deciliter.

Something like
that, so let's say

that's the amount
of urea we find

in our little tube of plasma.

How do we convert that to moles
per liter like we did before?

Well, again, it'll be helpful if
I draw out a molecule of urea.

So we have something like this.

A couple nitrogens.

And this is what
urea looks like.

It's a pretty small molecule.

A couple nitrogens,
carbon, and oxygen.

And these nitrogens have an
atomic mass unit of 14 apiece.

So that's 14.

And this is 14
over here, as well.

So what the lab actually
measures is just this part.

It's just measuring
the two nitrogens.

It's not measuring the weight
of the entire molecule.

So all it's going to give you
is the weight of the nitrogens

that are in the molecule.

So what that means is that we
say, OK, well, that tells us

that one molecule of urea is
going to be 28 atomic mass

units of-- I'm going to put
it in quotes-- urea nitrogen.

Because that's the part of
urea that we're measuring

and that means that
one mole of urea

is going to be 28
grams of urea nitrogen.

And because, again,
this is much, much more

than what we actually have,
let me divide by 1,000.

So one millimole equals 28
milligrams of urea nitrogen.

So that's how we figure
out the conversion.

And I do the exact
same thing as above.

I say, OK, well, let's
times-- let's say,

I want to get rid of
the milligrams, right?

So 1 millimole divided
by 28 milligrams,

and that'll get rid
of my milligrams.

And I'll take, let's say,
10 deciliters over 1 liter

and that'll help me get
rid of my deciliters.

And so then I'm left with
14 over 28, which is 0.5.

And then times 10, so that's 5.

5 millimoles per liter.

And as I've done
a couple times now

and we know that it's
the urea nitrogen

or the urea is going to act and
behave like one molecule or one

particle when it's
in water, it's

not going to split up
or anything like that,

so that means that
it's going to basically

be 5 milliosmoles per liter.

And so I figured out the
last part of my equation.

So going back to the
top, we have sodium.

And this turned
out to be a total

of 140 milliosmoles per liter.

And then for our anion, we had
140 milliosmoles per liter.

And then for our glucose, we
had 5 milliosmoles per liter.

And for our urea, we had
5 milliosmoles per liter.

So adding it all up, our total
comes to 140 times 2 plus 10.

So we get, if I do
my math correctly,

I think that's 290
milliosmoles per liter.

That's the answer
to our osmolarity.

Our total osmolarity
in the plasma

is 290 milliosmoles per liter.

Now that was kind of the
long way of doing it.

Let me give you a very,
very quick and dirty way

of doing it.

Let me actually make
some space up here.

You could do the exact same
problem, you could say,

well, this osmolarity
equals, you could say,

sodium times 2, plus
glucose, divided by 18,

plus BUN divided by 2.8.

And that takes all
of those conversions

and simplifies it down.

So if you ever get your sodium
value, your glucose value,

and your BUN, and you
want to quickly calculate

your osmolarity, now you
know the fast way to do it.