0:14

So when we talk about the concentration,

Â it's a quantitative way of describing a solution.

Â A solution contains a solute or

Â more than one solute, which is present in a smaller amount.

Â It contains a solvent, which is a substance present in a larger amount.

Â And together they make up the solution.

Â 0:41

We are going to look at a variety of units of concentration including molarity,

Â molality, mole fraction, percent, parts per million and parts per billion.

Â While we see all of these used in chemistry,

Â the most common is probably molarity.

Â 1:01

Molarity is defined as the moles of solute over the liters of solution.

Â While most of our concentration units use the volume or

Â mass of solution in the denominator, please pay attention to the details,

Â because some of them do use the volume of solvent or the mass of the solvent.

Â 1:19

So let's look at an example to see how we would use this definition of molarity to

Â calculate the quantitative value for a solution.

Â What is the molarity of a solution prepared from 25 grams of Sodium Chloride,

Â or NaCL, in 250 millimeters of solution?

Â So the first thing I need to do is find the moles of my NaCl.

Â I see that this substance is present in the smaller amount.

Â So this will be my solute.

Â And so I need to find the moles of solute.

Â So I use 25.0 grams [SOUND] and divide by

Â the molar mass which 58.5 grams per mole of NaCL,

Â and I'm able to find the moles of sodium chloride,

Â which is 0.427 moles of NaCL.

Â I can then use my definition of molarity.

Â 2:19

0.427 moles of the NaCl, over the liters of my solution,

Â I see that I have 250 millimeters, so

Â that is going to be equal to 0.250 liters, because I divide by 1000 [SOUND].

Â Now I can take 0.427 and divide by 0.250, and

Â find that my molarity is equal to 1.71 molar.

Â Notice tha we use a capital M here, so

Â capital M represents molar or the molarity of a solution.

Â 2:51

The definition molality is moles of solute over kilograms of solvent.

Â Notice that this is difference than what we saw for

Â molarity, which was moles of solute over liters of solution.

Â So we have a different unit and a difference substance in the denominator.

Â Let's look at an example of how this would be used.

Â What is the molality of a solution prepared from 25 grams

Â 3:13

of NaCl in 175 mills of water?

Â So, I notice that in my definition of molality,

Â I have the units of moles of solute.

Â So the first thing I need to do is convert from 25 grams of NaCl,

Â [SOUND] to moles of NaCl.

Â And I do that using the molar mass of NaCl, which is 58.5 grams per mole.

Â 3:44

And I find that I have 0.427 moles of NaCl.

Â So I see if I have the moles of my solute.

Â Now I need to look for my kilograms of solvent and

Â I'm told that I have a 175 millilitres of water, which is my solvent, and

Â I remember that the density of water is 1.00 gram per millilitre, and

Â I need to get this into kilograms, and 1000 grams equals 1 kilogram.

Â So now millilitres cancel, grams cancel, and I'm left with units of kilograms.

Â 4:31

Now, I have both the moles of solute and the kilograms of solvent.

Â So, I can plug in those values, 0.427 moles,

Â over 0.175 kilograms, and

Â I get that the molality is 2.44 molal.

Â Notice we use a lowercase m to indicate molality.

Â 5:02

Now, we can look at mole fraction.

Â And a mole fraction is calculated similar to a percentage.

Â The main difference, is that we don't multiply by 100.

Â And the amounts going in to it, must be in units of moles.

Â But notice we have moles of our solute.

Â So relative to a percent, this is our part.

Â 5:19

Over moles of solute plus solvent, or

Â moles in the total solution, and that would be our whole amount.

Â But it has to be in terms of moles.

Â So what is the mole fraction of a solution prepared from 25.0 grams NaCl and

Â 175.0 milliliters of water?

Â Well, we've already seen from the previous examples that 25 grams of

Â NaCl is 0.427 moles of NaCl.

Â Now we have to figure out how many moles of water we have.

Â We know we have 175 millilitres of water.

Â 5:54

We can use our density of 1 gram per milliliter of water to

Â get into units of grams.

Â And then we can use the molar mass of water, 18.02 grams

Â per mole of water to find the moles of water.

Â And once we do the calculation which is 175 times 1,

Â divided by 18.02, we find that

Â we have 9.71 moles of water.

Â Now we can take the values we know, and plug in and find our mole fraction.

Â So we have the Greek symbol chi to represent mole fraction.

Â On the top I put our moles of solute, which is 0.427 moles.

Â And on the bottom I had to put both the moles of solute, the 0.427 moles,

Â plus the moles of the solvent, which we calculated and found to be 9.71 moles.

Â We don't multiply by the hundred, that's not the definition of mole fraction.

Â We can now find our mole fraction

Â of sodium chloride in this particular solution.

Â And so we get 0.0421 as our mole fraction.

Â Notice this is one of the few numbers that we write that do not

Â have a unit associated with them.

Â So our mole fraction of sodium chloride is 0.0421.

Â What i also know about mole fraction is that the mole fraction of sodium chloride

Â in this problem, plus the mole fraction of water, will equal to one.

Â So if I want to find the mole fraction of water,

Â I can do that as well by simply changing the value I put on top.

Â And what I should see is that the number I get for

Â the mole fraction of water, plus the mole fraction of sodium chloride,

Â should equal to one because that's the entire amount of sample.

Â The only two components are the solute and the solvent.

Â 8:02

There are other units of concentration other than molarity, molarity or

Â mole fraction.

Â Percent is also a common unit of concentration.

Â With percent we actually to have to m,

Â identify what type of percent we're talking about.

Â If we're looking at a mass percent,

Â then we're looking at mass of solute over mass of solution.

Â For a volume percent, we're looking at the volume of solute for

Â the volume of solution.

Â But for mass volume percent,

Â we have the mass of solute, then the volume of solution.

Â Notice because the percentages they're all multiplied by 100, and

Â we can't just say the percent of the solution,

Â we always have to indicate the type of percent it is.

Â 8:44

Two other concentration units that are much less common simply because they

Â measure very small amounts are parts per million and parts per billion.

Â We can think of these similar to a percentage, which is parts per 100.

Â What we usually see is that if we write something in terms of ppm,

Â it usually means milligrams per liter or milligrams per kilogram of solution.

Â So, where we see these most frequently, in our everyday lives,

Â is if you have a municipal water supply.

Â You may get a yearly statement from the company letting you

Â know how much of each contaminate is present in your water.

Â In general, these amounts are very, very small, so they're generally reported in

Â units of ppm, parts per million or ppb, parts per billion.

Â If I look at parts per billion instead of milligrams per liter, what I will see is

Â micrograms per liter or micrograms per kilogram of solution.

Â 9:43

When I look at a solution,

Â I need to remember what happens to ionic compounds in solution.

Â Now if I look at the concentration of BaCl2 and

Â I find that the concentration is equal to 1.25 molar, that

Â tells me how many moles of barium chloride I put in the solution to prepare it.

Â 1.25 moles per liter of solution.

Â 10:06

However, because barium chloride is an ionic compound and

Â therefore a strong electrolyte and it dissolves in water,

Â what I'll actually see in solution are my chloride ions and my barium ions.

Â I won't, I will no longer see barium chloride units.

Â As a result, we have to look at the concentration of

Â ions a little bit differently than we look at concentrations of our solute.

Â So this is our solute, and these are our ions.

Â And this is what's actually present in solution, you know, the ions.

Â So if I have 1.25 moles per liter of solution, what I find is

Â that also I have 1.25 moles of barium ion, per liter of solution.

Â So that's the same as saying 1.25 molar.

Â 10:51

If I look at the chlorine, however, what I see is,

Â I have twice as many chlorines as I had originally in my original molecule.

Â So here I would have 2.50 molar of my chloride ions.

Â Because, for every unit that broke apart.

Â Every unit of BaCL2 that broke apart.

Â I got one barium ion and two chloride ions.

Â 11:15

Because our concentrations actually show a relationship between two units.

Â For example, molarity shows us the moles per liter of solution,

Â ppm shows us the milligrams per liter of solution.

Â We can use these as a relationship to figure out some calculations.

Â 11:35

For example, we can figure out how many moles of HCl are in

Â 500 millilitres of 0.3 molar HCl.

Â I usually recommend that as soon as you see units of molarity or that capital M,

Â that you rewrite it to represent it as moles over liters.

Â So, for 0.30 molar, I would actually rewrite that as

Â 0.30 moles of HCL per liter of solution.

Â This allows me to look at it with both of it's units, it helps me to

Â figure out how to set up the problem so that my units cancel out correctly.

Â 12:10

Now when I look at molarity, I see that it's a relationship there,

Â there are two units combined into one, so

Â a compound unit, whereas if I had millilitres, I only have a single unit.

Â So I'm going to start with my 500 millilitres.

Â 12:25

And then I'm going to convert that to liters.

Â Because I see I have liters in my concentration.

Â So 1000 milliliters in one liter.

Â And then I can use my concentration.

Â 0.30 moles of HCl per liter of solution.

Â 12:44

Now, millilitres are cancelled, liters are cancelled and I'm left with moles of HCl.

Â And once I do my calculation, I find that I get 0.15 moles of HCl.

Â If I had chosen, I could have taken this problem one step further and

Â actually found the grams of HCl, but I didn't need to

Â go that additional step because it wasn't being asked for in the problem.

Â The point is, is that we can continue on past this, if we need to,

Â depending on what's being asked for in the problem.

Â 13:45

Then I want to use my 250 millilitres,

Â because that's the information I was given to start with.

Â I'm going to convert it into liters [SOUND].

Â Then I can use my molarity, or

Â 3.50 Moles of magnesium bromide, per liter of solution.

Â Now I'm going to use my molar mass of

Â magnesium bromide, which is 184.1 grams per mole of MgBr2.

Â Now millilitres cancel,

Â liters cancel, moles cancel, and I'm left with a unit of grams.

Â And when I do the calculation, what I find

Â 14:44

Now we can add another tool to our toolbox, or

Â values we can use as relationships to get between one unit and the other.

Â Here, I've shown moles to liters as an example and used the unit of molarity.

Â However, we can use different concentration units, including mole

Â fraction, percents, parts per million, parts per billion and molality.

Â To us relationships as well, to get from one set of units to another.

Â