 In an earlier video we looked at conductivity to help us understand how the flow of electrons takes place in the solution of an electrolytic cell. Now because the actual charge transfer happens via ions, the number of ions in the solution or the concentration of ions is an important factor that will affect the conductivity. So we want to know how conductivity changes when we change the concentration of the solution. We have looked at conductivity in detail in an earlier video. So if you remember there we compared the flow of electrons in this solution to the flow of electrons let's say in this wire and here we know that the resistance is given by rho L over A where the length and area are shown here for this wire and this rho was the resistivity. So we defined conductivity as 1 over resistivity. If you take the length to be 1 centimeter and the area to be 1 centimeter square or in other words we take this volume to be 1 unit volume. So the resistivity is essentially the resistance of a unit volume. So by same reasoning conductivity which is the inverse of resistivity is the conductance of a unit volume. So if we use the same values here let's say if this area is 1 centimeter square and this length is 1 centimeter we can think of a unit volume of the solution which is occupied between these two plates. So for this unit volume and here you can see that the volume is 1 cubic centimeter or 1 cc which is 1 ml. So for this 1 ml solution you can think of the conductivity as the ability of this 1 ml solution to conduct electricity. But unlike in the case of this wire in the case of the solution the actual transfer of electrons is done via ions. So if you are looking at conductivity in solutions we need to think about the concentration or the amount of ions which are present in this unit volume and that will be an important factor which is controlling this conductivity. So how does conductivity vary with concentration? And fun fact this idea of how conductivity varies with concentration is used in water purification systems in labs. So I'll tell you later about how that is done but for now let's try to think of what will happen to the conductivity when the concentration of ions in this unit volume decreases. So when we say that the concentration decreases. Another way to say the same thing is that the dilution increases. So dilution is basically adding more of the solvent. Effectively there is less solute in more of solvent. So what happens when we decrease the concentration or increase the dilution? If you think of the number of ions in the solution like let's say we have three ions here in this unit volume and when I decrease the concentration let's say now I only have two ions. So what's happening is since the number of ions are decreasing the charge transfer will also decrease. So effectively the ability of this unit volume to conduct electricity decreases which means therefore our conductivity that is kappa also decreases. So if the concentration decreases or the dilution increases the conductivity kappa also decreases. Now instead of reducing the number of ions here we can also think of this in terms of dilution. Let's say I have three ions as before but this time instead of reducing the number of ions I'm increasing the dilution. So let's say I add more solvent such that now the volume is doubled. So if you think of the distribution if you average it out and look at only one unit volume the effective number of ions in each of these unit volumes is reduced. So you had let's say three ions in one unit volume. Now the same three ions are distributed for two unit volumes. So individually for each of these unit volumes the amount of ions is reduced and so the conductivity reduces and this idea is sometimes used in water purification systems. So if you take some impure water the impurities in such water are usually things like salts which are basically good electrolytes. So impure water which contains these impurities would mean more number of ions and we know that if the number of ions is more the conductivity is more. So for impure water the conductivity is high and conversely if we take pure water the idea is now these salts and other impurities which were the source of ions in the solution are removed and so with fewer ions in the solution the conductivity decreases as the water becomes more pure and so you can see how this can be used in purification because as the water is purified the conductivity will decrease. So this is a quick and easy way to monitor the water purification process and so that's the application I told you about before and this was based on the relationship between conductivity and concentration. Now let's see what is the relationship between molar conductivity and concentration. This here is how molar conductivity which is denoted by this lambda m is defined. So it is the conductivity kappa divided by the molar concentration or the molarity and so you can think of the molar conductivity as the conductivity on a per mole basis. We'll get to understanding this in detail in a bit but before that I want you to look at this relation and tell me something. I know that there is a concentration term in the denominator. So if I think that I want to look at the variation of molar conductivity and concentration and they seem to be inversely related would it be correct here to say that if we decrease the concentration the molar conductivity will increase take a few seconds to think about this and we'll continue after that. So on a first look it does seem like concentration and molar conductivity are inversely related. So if I decrease the concentration it looks like the molar conductivity should increase but this is wrong because this kappa that is a conductivity is also dependent on concentration. So we just saw before how when we decrease the concentration kappa also decreases and so just by looking at this relation itself we cannot understand the variation of molar conductivity with concentration. For that let's go back to our definition of molar conductivity. So before when we were talking of conductivity we considered some small amount of ions in a unit volume and the argument was that when the number of ions in this unit volume decreases the concentration decreases and so fewer number of ions are available for conducting electricity and so the conductivity decreases. But now when we talk of molar conductivity we can think of it as conductivity per mole or in other words instead of taking a unit volume we are saying that the molar conductivity is the conductivity of a volume V such that this volume will contain one mole of the electrolyte. So again look at the difference between these two definitions. Here we took unit volume and we were looking at the amount of electrolyte in this unit volume whereas here we are taking one mole so we are talking about the conductivity per unit mole. So in the way that molar conductivity is defined we are not concerned about the volume occupied. We are fixing the number of moles or the amount of the electrolyte which is there in this volume and we want that to be one mole. So as soon as you add this one mole of electrolyte there are two possibilities. So first if the electrolyte dissociates easily it will be a strong electrolyte and if it does not dissociate so easily or if the dissociation is not complete it will be a weak electrolyte. So let's take both of these cases one by one. First let's take the case of the weak electrolyte. So from Ionic equilibrium we know that a weak electrolyte is one that does not dissociate completely and we also know that when we increase the dilution the alpha or the degree of dissociation also increases. So this means in the case of a weak electrolyte when we increase the volume more of the electrolyte dissociates forming more ions. So the effect of dilution in the case of a weak electrolyte is that the overall number of ions increases and we know that if the number of ions increases the molar conductivity will also increase. So for the case of a weak electrolyte on increasing the dilution the molar conductivity increases. Now let's look at the case of a strong electrolyte. Now for a strong electrolyte the degree of dissociation is 100% because by definition these are strong electrolytes. So as soon as you add this one mole of electrolyte it dissociates fully to form the ions. So now when you increase the dilution unlike the case of the weak electrolyte the number of ions is not going to increase because all of them have already dissociated. So then what is happening on dilution? So let's say you have these ions which have dissociated from a strong electrolyte and already the number of ions is maximum because it has fully dissociated. So when these ions are within this volume there will be some electrostatic interaction between these ions. So some of them are positively charged, some of them are negatively charged and because of these interactions the ions are not able to move freely in this sort of cramped space. So what is happening when you increase the dilution? As soon as you increase the dilution you can think of this as adding space between these ions. So now the electrostatic force between these ions decreases because the gap between them has widened and so they are able to conduct electricity better which is why in case of strong electrolytes on dilution because the effect of these electrostatic forces is minimized and the ions can move freely now the molar conductivity increases. So in both cases for a strong electrolyte as well as a weak electrolyte on increasing the dilution the molar conductivity also increases but in the case of weak electrolytes the number of ions increases on dilution. So you can think that after dilution charge transfer will be much higher because there will be more ions but in the case of strong electrolyte the number of ions is already at maximum because the dissociation was 100 percent and so in the case of weak electrolyte the increase in molar conductivity is much higher than in the case of strong electrolyte. In both these cases the molar conductivity is increasing but in the case of the weak electrolyte the molar conductivity increases much more because more ions are introduced because of increase in dissociation.