- Today on Real Chemistry we're gonna talk
about something called molarity.
What's molarity?
Well, it's a measurement of what
you might call concentration
and to get a handle on what concentration is,
you can see that there is a range of drinks on this slide.
And they go from really, really light pink
to really, really dark red.
And you can imagine that these are all Kool-Aid
and the difference between all these different drinks
is how much of that red powder we used
when making them.
So we've used the same amount of volume of water
in each case but different amounts of powder.
And, it's nice to be able to look at this
and you can tell what's more diluted
and what's more concentrated.
But in chemistry, we want to come up with a number
that can exactly tell us how much powder there is
per volume of liquid.
So the goal of molarity is just to come up with a number
that can express the difference between these drinks.
So, there's all sorts of different ways to count
how much powder is there.
But you can imagine in chemistry we like to use moles,
because we use moles for everything apparently.
So, molarity is equal to the moles of a powder
that we have there,
divided by the liters of the water we've added.
So we can even get a little more specific than that.
Molarity is moles over liters
but it's moles of solute and that's the thing
that's being dissolved
so in this case it would be that Kool-Aid powder.
So we take the moles of that Kool-Aid powder
and we divide it by the volume of that drink in liters,
we get molarity.
Now, these units are really important.
You always, always, always have to have moles in liters.
Any other units for the amount of powder or the volume
of liquid, will give you the wrong answer.
It always has to be moles over liters.
That is the definition of molarity.
So let's take a look at some problems
where you're gonna calculate molarity.
This is the most basic type of problem
you can have for molarity.
It gives you the volume of your solution
and the quantity of stuff you're dissolving
and all of your units are right from the very beginning.
Let me show you what I mean.
Here it says, what is the molarity of a 1.2 liter solution
containing 2.4 moles of sugar?
So we already have liters of our solution
and moles of what's being dissolved.
So we're all set to just plug everything into our equation.
And our equation remember is moles is divided by liters.
Often you'll see this expressed in terms of symbols
so here you can see that we use this big "M" for molarity
and then we use "n" which stands for moles
and "L" which stands for liters.
So when you write it out in symbols you can write
M is equal to n over L
and that's what we'll do now.
And this is the equation we're gonna use
to calculate our molarity.
So M is equal to n over L
and since we're given our volume in liters
and our quantity of sugar in moles,
we can just go ahead and plug this stuff directly in.
So we have 2.4 moles up top,
and we have 1.2 liters on the bottom.
Notice we have moles over liters written there
so our units are all set.
And if we now divide that in our calculator
or just by looking at it,
we would get 2.0 and then the way we write
the units for molarity is just a big capital "M".
So what we could say, the way we could express
that concentration is the sugar solution
has a concentration of two molar.
So it's kind of a weird way to say it
but turns you can say as a concentration of 2 molar.
So that's how we calculate molarity, pretty straightforward.
The main complication comes in that they don't always
give you volume in liters or the quantity
of your solute in moles.
And so there's lots of time some conversion problems
you have to do beforehand
so we'll go through two more example problems
where we actually have to do some unit conversions
before we can calculate molarity.
So in this problem, it says what is the molarity
of a 120 milliliter solution containing 1.6 moles of sugar?
So, the very first thing we wanna do
if we want to calculate molarity is make sure
that we have moles of solute
so that's what I've put in our step one.
And you notice that in this problem we're actually
already given moles of sugar, so that's nice.
We're given 1.6 moles of sugar
so we don't even have to do step one in this case.
We already have moles.
We also wanna calculate liters of solution
and here we have some work to do,
because our volume is in milliliters and not in liters.
So what we're gonna do is say okay,
a 120 milliliters and we want to take that to liters.
This is a common conversion problem
you do in chemistry and all you gotta do is divide by 1000.
So 1000 milliliters are in one liter.
And when we do that division we're gonna get 0.120 liters.
So now we have our volume in liters,
we've done step two.
So the last step is just go ahead and plug that
into our equation.
Now that we have the right units,
the problem is just like it was before.
It's pretty easy, we plug it into our equation
and we'll get the right answer.
So our molarity is always equal to moles divided by liters
and our moles we know is 1.6 moles of sugar
and we're gonna divide that now by our volume in liters
which is not 120 milliliters but 0.12 liters
so 0.12 liters.
When we do that division, we're gonna get our 13 molar.
We got two sig figs there because our moles
only have two sig figs.
And, our concentration of sugar in this case is 13 molar.
All right, one more problem.
Well, now we're gonna have to calculate both the liters
of our solution and the moles of our solute.
So here you can see it says what is the molarity
of a 320 milliliter solution containing 78 grams of sugar?
And now we have a problem because we have grams of sugar
not moles of sugar
and we have milliliters of solution,
not liters of solution.
If you think about it, this is actually the way the problem
normally would be if you're actually doing stuff in the lab.
We can't directly measure moles, right?
We can only go to the scale and measure grams.
So more often than not when you're making a solution,
you're gonna be thinking about making it with grams
and if you wanna calculate its molarity
you have to go from grams to moles.
Now going from grams to moles we always do
with our molar mass.
For the sake of time, I've written our molar mass of sugar,
in this case it's glucose down here,
180.2 grams per mole.
And so that's the way we're gonna go from grams to moles,
just as we do in many other chemistry problems.
All right, so let's go ahead and do step one,
calculate moles of solute
and to calculate moles of solute
we're just gonna start with our 78 grams of solute.
And we're gonna multiply that by a conversion factor.
Well, we want to eventually get to moles
and that means we're gonna put moles up top
and we always have one next to our moles for our molar mass
and then we write in our molar mass in grams
in the bottom, 180.2 grams.
Remember that molar mass there is telling us
that 180.2 grams of glucose sugar
is exactly one mole of sugar.
And when we do that division we're gonna get 0.43 moles.
So that's our sugar in moles.
So we're halfway there to the right units.
Now we have to calculate the liters of our solution.
Again we're given milliliters and we got to take
that to liters.
You could be given anything.
Sometimes you could be given mega liters,
not very common measurement of volume there
but you should be prepared for any different measurement
of volume; gallons, cubic centimeters
and being able to take that to liters is always gonna be
how you're gonna calculate your molarity.
So 320 milliliters in this case,
we do the conversion in the same way
where we know there's a 1000 milliliters in a liter,
so we're gonna get rid of milliliters
by writing it on the bottom and we're gonna get out liters
and there's one liter in a 1000 milliliters.
We do that division and we're gonna get 0.320 liters.
Sweet, now we have our concentration of sugar in moles,
I'm sorry, our amount of sugar in moles
and the volume of our solution in liters
and now we can just go onto step three
where we just plug stuff in, plug it into the equation.
So again we know that molarity is always, always, always
equal to the moles of our solute,
the thing we're dissolving divided by the liters
of our solution.
And we calculated our moles to be 0.43.
And we calculated our volume to be 0.320 liters.
And when we do that division we're gonna get out 1.3 molar.
So that's our answer.
So you can see we had to do a little more work there
to get to molarity
because we were giving grams of our sugar and milliliters
of our solution.
But the basic way to calculate molarity
is always to just get moles and liters and divide them.
So thanks for watching this episode of Real Chemistry.
If you have any questions, please ask them below.
As always subscribe to get updates about my future videos.