 In an earlier video we looked at molar conductivity represented by this lambda m and we saw how it varies with concentration. So in this video what we're going to do is we want to plot this variation on a graph and try to graphically understand how molar conductivity varies with concentration. So before we go to graph this let me give you a quick recap of how these two are related. So the first thing is when we talk of concentration we know that decreasing the concentration is the same as increasing the dilution and when we think of molar conductivity you can think of it as basically the conductivity of one mole of an electrolyte. So how molar conductivity varies with concentration or dilution depends on the type of the electrolyte as well and we've seen before that an electrolyte can be a strong electrolyte or a weak electrolyte depending on how they dissociate. So if you have some electrolyte HA which is dissociating into some H plus and some A negative. Now if this is a weak electrolyte the extent of this dissociation will be very less and if it's a strong electrolyte this dissociation will be 100%. So what we saw before was that in case of a strong electrolyte the dissociation is 100% and when you increase the dilution or when you decrease the concentration the molar conductivity increases and for weak electrolytes where the dissociation is not 100% even then when you increase the dilution the molar conductivity increases but in the case of weak electrolytes on dilution the increase of molar conductivity is much higher because what happens during dilution is that on dilution of a weak electrolyte the degree of dissociation which is this alpha increases or do we know that let's take this example. So if HA is a weak acid let's write down the equilibrium constant for this reaction it will be given as this concentration of H plus into concentration of A minus divided by the concentration of HA. Now let's say you have reduced the concentration by a factor of 10 or you could say that you have increased the dilution by a factor of 10. So we have seen when we deal with equilibrium constants that if the reaction conditions change we can calculate the reaction quotient or Q and in this case I am saying that the concentration has reduced by a factor of 10 for all three. So now this will be H plus divided by 10 times A negative divided by 10 divided by HA divided by 10. I can cancel off these 10s and if I rearrange this I can write this Q as 1 by 10 times concentration of H plus times concentration of A negative divided by concentration of HA. So if you look at this the Q or the reaction quotient is one tenth the equilibrium constant or the Q is less than K and we know that when the reaction quotient is less than the equilibrium constant the reaction shifts to the right and that means we would have more of H plus and A negative forming which means that the dissociation of this weak electrolyte HA will increase on dilution and again this will not happen with a strong electrolyte because the definition of a strong electrolyte is that it is already dissociated completely but in case of weak electrolyte which does not dissociate fully on dilution the dissociation increases so when the dissociation increases the number of ions also increase and we know that when we talk of molar conductivity it is the ions that are actually conducting the electricity in the solution so because now there are more ions in the solution the molar conductivity increases much more than in the case of a strong electrolyte and so the increase in molar conductivity is much higher in case of a weak electrolyte but the question is how will this change or how will this variation look graphically let's see how we can plot this so I want to plot the variation of molar conductivity with concentration and again we'll take two cases one for a strong electrolyte and one for a weak electrolyte so on the y-axis I have the molar conductivity here which is this lambda m and on the x-axis I have this under root C which is the square root of the molar concentration and one reason why we are not directly plotting this against C is that when we look at the experimental data it is easier to fit the data points into a straight line as you will see in a second so first let's take the case of a strong electrolyte so for a strong electrolyte if we calculate the molar conductivity at different values of concentration and if we plot this on this graph we see a trend that looks like this so these blue dots are data points for a chosen set of concentrations so to see the trend if you try to fit these points you will see that they will fall on a straight line so let's check this trend with what we know from before so we know that in case of a strong electrolyte when we increase the dilution the molar conductivity increases and we know that increasing the dilution is the same as decreasing the concentration so if we look at this plot as we go from right to left the concentration is decreasing because this is the origin and this is the positive x-axis so as we go to the left the concentration is decreasing or the dilution is increasing and accordingly we can see that the points along the y-axis increase so from the plot also we can see that when the dilution increases or the concentration decreases the corresponding molar conductivity increases now this was the case for a strong electrolyte for a weak electrolyte the trend is again the same that is on increasing the dilution the number of ions increase and therefore the molar conductivity increases so here also if we plot the experimental data we see that they follow this hyperbolic type curve and here also as we move from right to left the concentration is decreasing which means the dilution is increasing and the corresponding lambda m points which are these marked with the pink dot here increase as we go from right to left so even for weak electrolytes the effect of dilution that we saw before is reflected in this trend and there is one more thing to note here we discussed how in the case of weak electrolyte since the number of ions increase the increase in molar conductivity is way higher and you can see that here in the case of a strong electrolyte when we go from point say 1 to 2 and 3 and 4 the increase in molar conductivity is very gradual but at the same time if we look at the curve for the weak electrolyte as we go from these points from 1 to 4 you can see that the change in these values is much higher which is the same as we saw before so this is what a graphical representation of the trends look like now there is some more information that we can get from these curves now since this is on a straight line if we just extrapolate this towards the y-axis let's say it is intersecting the y-axis at this point so what would this mean so if you look at the equation that we use for molar conductivity it was given as kappa divided by c where c is the concentration so as we go towards the origin the value of c is decreasing so this value of lambda m is the value that we get when c goes almost to 0 so if c will tend to go to a very small value which is next to 0 the corresponding value of lambda m will be called lambda m infinity which is basically the molar conductivity at infinite dilution and if you are wondering where this infinite dilution is coming from so we saw before how when we decrease the concentration the dilution increases so when the concentration is reduced to a very very small number the corresponding dilution will be very large which is why we are calling this value the molar conductivity at infinite dilution so now based on this information i want to write the equation of this straight line i know that it will be in the form of y is equal to mx plus c and m is the slope and i can see here that the slope is negative so let's say this slope is some value which is minus b and the c is the intercept which is basically this length and we define this length or this point to be the molar conductivity at infinite dilution so the value of c here is this lambda m infinity and we already know the y and the x which are this lambda m and this under root c so based on this we can write the equation of this straight line as lambda m is minus b under root of c plus lambda m infinity or we can rearrange this to write lambda m is lambda m infinity minus b under root c so this is the equation of this straight line and the important point to note is that this straight line trend is only for a strong electrolyte