 In this video, we're going to look at concentration terms and we'll take an example to see how we can derive a relationship between these terms. So let's start to the first concentration term that is mole fraction. So let's say if we have a solvent A of a molar mass MA and there are NA moles of A and a solute B is added to the solvent to create a solution and we know that the molar mass of B is MB and the number of moles of B is NB. So now with this information, we can define our first concentration term that is mole fraction which is given as the mole fraction of A will be equal to the number of moles of A divided by the total number of moles that is NA plus NB. Now here because there is only one solute, the total number of moles will be NA plus NB. If let's say there are two solutes B and C, this total becomes NA plus NB plus NC. So this denominator is the total number of moles and similarly for B, we have the mole fraction of B which is denoted by XB will be equal to the number of moles of B divided by the total number of moles that is NA plus NB. And if you look closely, you can see something about XANXB here. You'll notice that the sum of XANXB is equal to 1. So if we are given the mole fraction of let's say only the solute, we can use this relation to find the mole fraction of the solvent or vice versa. And also again, if we think of this in general terms, if we had another solute C, so then we could write this as XA plus XB plus XC is equal to 1. That is the sum of mole fraction of the solvent and all the solutes will be equal to 1. The next concentration term that we're going to discuss is molarity, which is defined as the number of moles of solute in moles divided by the volume of the solution in liters. Now this liter part is important because in most iterations or lab experiments, the volume of the solution that we use is typically in mls. But for calculating molarity, which is this capital M, the volume of the solution should be in liters. Then next we have a very similar sounding term called molality and it is denoted by a small m and molality is defined as the number of moles of solute divided by the mass of solvent in kg. So in case of molarity, we use the volume of the solution in liters. In case of molality, it is the mass of the solvent which is specified in kg. Again, the unit is something that we need to keep in mind. So in calculations, this mass that we use has to be in kgs just like this volume which has to be in liters. And finally we have mass percent, which is defined as the mass of the solute divided by the mass of the solution in 200. Now the only thing to be careful of in calculating this is that both of them should be in the same units. So let's say if you have 10 grams of solute in 1 kg of solution, you need to make sure that either both of them are in grams or both of them are in kilograms and so this was mass percent. These are the common concentration terms that we use in the lab, mole fraction, molarity, molality and mass percent. Now sometimes in calculations, it becomes easier if we know a direct relationship between any of these two terms. So one very common usage is expressing mass percent in terms of the mole fractions of the solute and the solvent. So let's take that as an example and see how we can calculate the mass percent if the mole fractions are given. So let's start with the definition of mass percent, which is mass of the solute divided by mass of the solution times 100. Now we know that a solution has two components, a solute and a solvent. So instead of writing this as mass of solution, we can write it as mass of the solute plus the mass of the solvent and we know that this will be equal to the mass of the solution. So instead of writing mass of the solution here, we have just broken that down into these two parts. Now we know that the number of moles is defined as mass in grams divided by molar mass in grams per mole. So if you rearrange this, we can see that the mass will be equal to the number of moles times the molar mass and we can use this relation here. So we can rewrite the mass of the solute as the number of moles of the solute times the molar mass of the solute. And similarly, we can calculate the mass of the solvent. So if we plug in these values, we can rewrite the mass as number of moles of B times the molar mass of B, which is our mass of the solute, divided by the mass of the solute plus the mass of the solvent, which was A times 100. So now as we saw before, the denominator of the mole fractions had the sum of the number of moles, that is NA plus NB. So let's do one thing. Let's divide both the numerator and the denominator throughout by NA plus NB. So if we do that, we get something like this where the numerator is NB divided by NA plus NB times the molar mass of B, another denominator. We have the same term plus a similar term for A, but we just now saw that this term that is NB divided by NA plus NB is equal to the mole fraction of B and this term that is NA divided by NA plus NB or the number of moles of A divided by total number of moles is equal to the mole fraction of A. So all of these terms in the large brackets can be replaced by the mole fractions. So this becomes mole fraction of B. This becomes mole fraction of B and this becomes mole fraction of A. So if we plug them in, we get the mass person as equal to the mole fraction of B times the molar mass of B divided by this term again plus mole fraction of A times the molar mass of A into 100. So now if you look at this relationship, we have expressed the mass person as a function of the mole fraction of the solute that is B and the mole fraction of the solvent that is A.