 So in the last video, we saw that the strength of a base is measured by its KB values, right? Now instead of using KB, chemists generally use the PKB values, the PKB values to measure the strength of a base. So what exactly is this PKB? Let's find out in this video. Now before we do that, before we talk about PKB, let's do a quick recap and try and recollect what this KB really stood for. So whenever we dissolve a base in water, there's actually a reversible reaction that's going on and the extent of this reversible reaction, that is how far forward or backward this reaction is, can actually be experimentally determined by calculating the equilibrium constant K of this reaction. Now the equilibrium constant K in fact out here is called KB, the base dissociation constant. Now greater the value of KB, this means more forward this reaction goes. And if this reaction is more forward, then we can say that the base is in fact good at abstracting this H plus from water. So we say that the strength of the base is higher, it's a relatively strong base. While on the other hand, if this KB value comes out to be very low, then this means that the reaction hasn't moved much in the forward direction. So this means that the base is in fact not that good at abstracting an H plus from water. So the strength of the base is going to be lower and it's going to be a relatively weak or a relatively poor base, right? So greater the value of KB, stronger is the base. So therefore, if you look at a table, things like the MI diene that has a KB of almost 10 to the power 21 or something like HC2 minus that has a KB of almost 10 to the power 12, these are much stronger bases compared to something like say ammonia out here, that has a KB of only 1.8 into 10 to the power minus of 5 or something like any line which has an even lower value of KB, almost 10 to the power minus of 10. So greater the value of KB, stronger is the base. Now if you look into this table carefully and this by no means is an exhaustive list of all the bases out there. But even in this table, you can see that these KB values are wildly different, right? While MI has a KB of 10 to the power 21, water, which is right here, has a KB of 10 to the power minus of 14. So there's a difference of almost 10 to the power 35 between these two values, right? Now whenever we have data that spread across such wide ranges, it's actually better to report them in the logarithmic scale. So chemists generally report this data in the form of PKB, where PKB is nothing but equal to minus of log of log base 10 minus of log of KB. Now I'm sure you must be having a question, why is there a minus sign out here? In fact, what does this expression even mean? Let's find out. So what we're actually trying to do out here is that we're trying to convert all this data and as you can see, a lot of this data is less than one. So what we're really trying to do is we are trying to convert all these KB values, all these KB values in the form of 10 to the power minus of something, 10 to the power minus of some value, let's say X. Now if you can do that, if you can write all of this in the form of 10 to the power minus of X, then we can simply report our KB values in the form of X and we call this the power of KB, the power of KB or PKB. So let's say I want to convert the KB of ammonia, which is 1.8 into 10 to the power minus of 5. So let's say I want to write 1.8 into 10 to the power minus of 5 in the form of 10 to the power minus of X, minus of X. So how do I do that? What will the value of X be? Well, if I use my logarithmic operator on both sides of the equation, so log of 1.8 into 10 to the power minus of 5, this is going to be equal to log of 10 to the power minus of X, right? And log of log base 10 of 10 to the power minus of X is going to be nothing but equal to minus of X, right? So this will be nothing but equal to minus of X. So therefore X can be written as minus of log of this value, right? So the power of KB that we are trying to figure out will be nothing but minus of log of KB, right? So PKB is nothing but the minus of log of KB. So coming back, if you do our calculations out here, minus of log of 1.8 into 10 to the power minus of 5, this will come out to be equal to 4.7447. So it's approximately equal to 4.75, right? So this will be approximately 4.75. So the value of X is nothing but 4.75. So 1.8 into 10 to the power minus of 5 is nothing but 10 to the power minus of 4.75. So if you look into the table, the PKB of ammonia is given as 4.75, right? Similarly, if I want to say write the KB of enylene, enylene has a KB of 7.4 into 10 to the power minus of 10. So if I want to write it in the form of 10 to the power minus of X, this PKB, if you do our calculations, will come out to be 9.13. So this will be nothing but 9.13. Let's take one final example. The KB of the amide ion is 1 into 10 to the power 21. So it's 1 into 10 to the power 21. And if I want to write it in the form of 10 to the power minus of something, then I need to write it as 10 to the power minus of minus of 21, right? So as you can see in this table, the PKB is given as minus of 21. So now instead of using this data directly, we can also present them in the form of PKB. And anyone reading this PKB values can easily find out KB by using this equation, right? So what's the advantage of presenting our data in this way? Well, while the KB values in this table range from 10 to the power 21 to 10 to the power minus of 14, which is a difference of almost 10 to the power 35, the PKB values only range from minus of 21 to plus 14, which is a difference of only 35. So our data now becomes much more compact. And say if you want to present this data in the form of a graph, then this range of values will be much easier to plot compared to values that have a difference of almost 10 to the power 35. In fact, presenting all this data in the form of a graph is actually going to be a nightmare. So PKB makes our data much more compact and much easier to present and manage. The one important thing that you should note out here is that while I go from the MI Dine to water, the KB values keeps decreasing, right? It goes from 10 to the power plus of 21 to 10 to the power minus of 14. So the KB values as presented in this table keeps on decreasing. But if you look into the PKB, the PKB goes from minus of 21 to plus of 14, right? So the PKB values are in fact increasing. The PKB in fact keeps increasing, right? Now of course this makes sense because if I say take a set of KB values that are in decreasing order because we are choosing to write our KBs in the form of 10 to the power minus of x because we are choosing to write it into 10 to the power minus of x. So the PKB for 10 square is actually going to be minus of 2. For 10 it's going to be minus of 1. For 10 to the power minus of 1 it's going to be simply 1. And similarly for 10 to the power minus of 2 it's only going to be 2, right? So therefore lower the value of KB, higher will be the PKB. Now of course you might ask why are we even choosing to do it in this way in the form of 10 to the power minus of x? We could have also done the same thing in the form of simply 10 to the power x. And that's a valid question. But remember that the vast majority of bases, especially organic bases are weak. So they have KB values less than 1. While bases like the hydroxide and the amide ions, this actually exists as any compounds like sodium hydroxide or sodium amide or calcium hydroxide and so on. And these inorganic bases are far fewer in number compared to the huge number of organic bases that are out there. So chemists have chosen to represent it in this way so that the vast majority of our data is positive rather than being negative. So now that we have understood what this PKB really stands for, how do you predict the strength of a base based only on these PKB values? Well, we have said that greater the value of KB, more forward the reaction goes. So stronger is the base. But a greater value of KB leads to a lower value of PKB. So in terms of PKB, we should say that lower the value of PKB, stronger will be the base. So if you want to compare the basic strength of ammonia, that is a PKB of 4.75 and say aniline that is a PKB of 9.13 because ammonia has a lower PKB so it will have a greater KB. So therefore ammonia will be a stronger base compared to aniline, right? So therefore lower the value of PKB, stronger will be the base.