>> Welcome to a Screencast, an Introduction to Molarity.
When chemists use solutions, we typically don't weigh them out, we don't measure their masses,
but instead we measure the volume of solution we use and this means that we also need
to know what the concentration of the solution is.
Now there are lots of concentration units that one can use,
but for chemists probably the most common solution unit is something called molarity.
And molarity is defined as moles of solute, so this is going to be the substance
that we dissolve into the solution, divided by liters of solution,
which is going to be our volume of total solution plus --
or solute plus solvent to make the solution.
We often abbreviate this by capital M for molarity, n, represents moles of solute
and we're going to have to remember that this is moles of solute.
And then V represents volume of solution, and we're going to have to remember
that that's going to be in liters.
So let's look at an example.
A solution contains 58.87 grams of potassium bromide,
it's dissolved in 750 milliliters of solution.
What's the molarity of this solution?
Well, we have to remember the definition of molarity,
moles of solute divided by liters of solution.
And we know the milliliters of solution, so that's easy to convert to liters.
And then we know the grams of the solute potassium bromide,
but we're going to have to convert that to moles.
So we take our grams of potassium bromide.
Use the periodic table, find that one mole of potassium bromide has a mass of 119.0 grams.
That's the conversion factor that allows us to convert from grams of solute to moles of solute,
and that gives us 0.4947 moles of KBr.
Now to get the molarity, we're going to have to take the moles of the solute KBr
and divide it by the liters of solution.
So this is going to be 0.4947 moles KBr divided by 0.7500 liters.
Remember, we have to convert from milliliters to liters, and then we divide and get our answer
of 0.6596 moles of KBr per liter of solution.
And it's very common to instead of moles per liter to simply use the symbol capital M.
So we would report this as 0.6596 molar KBr solution
and the capital M represents the moles per liter or molarity.
Now here's how we actually do this.
Potassium bromide is not orange, but here it's shown, the substance shown
in the image is orange just so you can see it better.
But what you would do is you would determine the amount of solute you need,
you would add it to a typically a volumetric flask because we're going to need
to measure the volume of solution pretty accurately.
It's pretty common to have some of our -- typically our solvent it's going to be water,
so have some water in here before we add the solute or in this case,
we can just add solute to an empty flask.
Then we're going to add our solvent and again, typically it's going to be water
and we don't measure out the amount of solvent we add, we simply add enough
to get the desired solution volume.
And typically in a volumetric flask, there will be a line that represents your total volume
that you want to get and you will mix up your solution and achieve
that desired total solution volume.
OK, now some things you're going to need to be able to do with regard
to molarity is not only calculate molarity just straightforward from its definition
like the previous example, but also use known concentration solutions,
solutions of a known molarity to determine the volume of that solution that you will need
to get some number of moles, and vice versa different permutations
of this type of calculation.
So here we have a question what volume of a 0.6596 molar potassium bromide solution,
the one that we just figured out how to make.
How much of this do we need to provide 0.1500 moles of potassium bromide?
Maybe we need this for a reaction.
And we note what our definition of molarity means, moles of solute per liter of solution.
And specifically, we're going to apply it to the known concentration of solution we have,
which is 0.6596 moles of potassium bromide per one liter of solution.
And here I'm writing it explicitly as a ratio, which can be use as a conversion factor.
So we want 0.1500 moles of KBr, so that's the first thing we'll write down.
And then our conversion factor allows us to convert from moles
of KBr into liters of KBr solution.
And notice, we're going to be writing the molarity ratio, sort of quote unquote,
upside down because we want to cancel moles of KBr and we want to get a volume.
So there's our setup, we're going to take 0.1500 multiply it by one and divide it by 0.6596.
That will give us our answer, in this case, 0.2274 and it's in liters
of the potassium bromide solution and specifically,
it's of the 0.6596 molar potassium bromide solution.
And of course, we could do a similar calculation, but turned around a little bit
if we were trying to find out the number of moles
in a particular volume of solution, for example.
Now, what often happens is we have an existing solution of a particular substance,
but we need a different concentration of that solution.
And if what we need is a solution that's more dilute than our existing solution,
then there's a fairly straightforward way to figure out how
to make the more dilute solution starting with the existing more concentrated solution.
And here's an example, we have 0.6596 molar KBr and we'd
like to make 500 milliliters of 0.2500 molar KBr.
Now, we want 0.500 liters or 500 milliliters of this KBr solution,
this new KBr solution we want to make.
And it needs to be a concentration of 0.2500 moles of KBr per liter of solution.
And that conversion factor and those two bits of data allow us to determine
that what we need is 0.1250 moles of KBr in the 500 milliliters
of 0.25 molar KBr solution we're going to make.
Now where are we going to get that 0.1250 moles of KBr?
Well, we'll get it of course from the more concentrated solution.
And so what we do is we say well, we need 0.125 moles of KBr,
the more concentrated solution has 0.6596 moles of KBr per 1 liter of solution.
So we can use the molarity value as a conversion factor.
It's kind of upside down in the sense because we want to cancel out moles and we want
to get liters and when we do this calculation, we find that we need 0.1895 liters
of this more concentrated 0.6596 molar KBr solution.
And if we use that, add water to it and dilute it appropriately,
then we will make the amount we want of the more dilute 0.2500 molar KBr solution.
So the actual how we make it description is we would combine 0.1895 liters
of the more concentrated 0.6596 molar KBr with as much distilled water as is needed.
So enough distilled water to get a total solution volume of 0.5000 liters.
Again, take a look with a not exact representation.
Here we have a solid, when in fact we're using a liquid but just for visual purposes,
what you'd be doing here is taking a known quantity,
calculated quantity of our concentrated solution.
Put it in a flask of the right size, add enough distilled water
until we make the total solution volume that we want.
Now this is a very common thing for chemists to do, to take a more concentrated solution
and to add water to it to make a more dilute solution.
And the calculation involved in this type of dilution is going
to pretty much always be the same type of thing as we just did in the previous example.
And for this reason, we often use a sort of shortcut calculation.
This is fairly easy to show that's true in general, but for dilution,
if we have a more concentrated solution and a less concentration --
less concentrated solution we'd like to make, then the molarity times the volume
of the more concentrated solution is equal to the molarity times the volume
of the less concentrated solution.
And this M1V1 equals M2V2 equation, it's true for dilution in general,
it's not true for everything in the world so be careful about that.
And if you remember this, you can always do kind of a plug and chug type of dilution calculation.
So let's go back to the problem we just looked at, and let's do it that way.
So our equation is M1 times V1 equals M2 times V2.
And we could do it either way, but we're going to pick for this case, we're going to pick
that solution two is our more dilute solution.
So it has a volume 500 milliliters that we want and a concentration of 0.2500 molar.
And then the more concentrated solution, we're going to call solution one,
and we know its molarity 0.6596 molar, but we don't know its volume.
So what that means, of course, is we need to solve for the volume of solution one,
which of course is molarity times volume of solution two, over molarity of solution one.
Molarity of solution two is 0.2500 molar and volume of solution two is 500 milliliters.
So we're going to make that liters 0.500 liters
and then molarity of solution one is 0.6596 molar.
And notice molarities cancel leaving us with liters and when we do our calculation,
what we get is 0.1895 liters and then we have to remember that this is 0.1895 liters
of the 0.6596 molar KBr solution.
And so, how we would make this solution is as before, combine the 0.1895 liters
of the 0.6596 molar KBr solution with enough distilled water.
So DI, deionized water to make a total of 500 milliliters or 0.500 liters of total solution.
So that is our final answer for the description of how to do this
and of course it agrees with what we did previously.
And that's it for an introduction to molarity.