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# Buffers and Henderson-Hasselbalch

## Video transcript

let's say I have some weak acid I'll call it h a H a a is a placeholder for a really a whole set of elements that I could put there could be fluorine it could be an ammonia molecule if you add an H it becomes ammonium so this isn't any particular element I'm talking about this is just kind of a general way of writing a an acid and it's it's an equilibrium it's in equilibrium with of course and you've seen this multiple times a proton and all this is in an aqueous solution aqueous between this proton jumping off of this and its conjugate base a minus and we could have also written a a base equilibrium where we say the conjugate base could disassociate or it could essentially grab a hydrogen from the water and create O age and we've done that multiple times but that's not the point of this video so let's just think a little bit about what would happen to this equilibrium if we were to stress it in some way and you can already imagine that I'm about to touch on le chatelier's principle which essentially just says it look if you stress an equilibrium in any way the equilibrium moves in such a way to relieve that stress so let's say that the stress that I apply to this system let's say that the stress that I apply is I'm going to add I'm going to add let me do a different color I'm going to add some strong base that's too dark I'm going to add some na o H and we know this is a strong base when you put it in an aqueous solution the sodium part just kind of disassociates but the more important thing you had all this o H in the solution which wants to grab hydrogen's away so when you add this Oh H to the solution what's going to happen for every mole that you add so for every not even just mole for every molecule you add of this into the solution it's going to eat up a molecule of hydrogen right so for example if you had one mole of hydrogen molecules in your solution and you added 1 mole of sodium hydroxide - your solution right when you do that all of this is going to react with all of that and it's and the OHS are going to react with the h's so just so you be and form water and they'll both just kind of disappear into the solution they didn't disappear they all turned into water and so all of this hydrogen will go away or at least the hydrogen that was initially there that one mole of hydrogen's will disappear so what will what should happen to this reaction well we know this is an equilibrium reaction so as these hydrogen's disappear as these hydrogen's disappear because this is an equilibrium reaction or because this is a weak base more of this is going to be converted or the more of this is going to be converted into these two products to kind of make up for that loss of hydrogen or you can even play with it on the mat so this is going to so this hydrogen goes down initially and in all of this equilibrium then it starts getting to equilibrium very fast but this is going to go down this is going to go up and then this is going to go down less because sure when you put the sodium hydroxide there it just ate up all of the hydrogen's but then you have this you can kind of view is this this the spare hydrogen capacity here to produce hydrogen's and when these disappear this weak base will disassociate more the equilibrium will move more in this direction and then you'll have so immediately this will eat all of that but then when the equilibrium moves in that direction some of the hydrogen will be replaced so if you think about what's happening if I just threw if I just threw this sodium hydroxide in water so if I just did NaOH in an aqueous solution so that's just throwing it in water that disassociates completely into the sodium sodium cation and hydroxide anion and so you all of a sudden you would immediately increase the the quantity of OHS by essentially the amount of the number of moles of sodium hydroxide you're adding and you would immediately increase the pH right remember when you increase the amount of Oh H you would decrease the POA right and that's just because it's the negative log or so if you increase your decreasing Poh and you're increasing pH and just to think Oh H is you're making it more basic more basic and a high pH is also very basic if you have a mole of this you end up with a pH of 14 and if you had a strong acid not a strong base you down with a pH of zero you and and you know hopefully you're getting a little bit familiar with that concept right now but if it confuses you just play around with the logs a little bit and you'll eventually get it but just to get back to the point if I if you just did this in water you immediately get a super high pH because the O H concentration goes through the roof but if you do it here if you apply the the sodium hydroxide to this solution the solution that contains a weak acid and its conjugate base the weak acid and its conjugate base what happens sure it immediately reacts with all of this hydrogen and eats it all up but then you have this extra supply here that just keeps providing more and more hydrogen's and it'll make up a lot of the laws so essentially the the stress won't be as bad and over here you you you dramatically increase increase the pH when you just throw it on water here you're going to increase the pH by a lot lot lot less and in future videos we'll actually do the math of how much less it's increasing the pH but the way you can think about is it's kind this is kind of a shock absorber for pH it even though you threw the strong base onto this into this solution it didn't increase the pH as much as you would have expected and you could make it the other way if I just wrote this exact same reaction is a basic reaction and remember this is this the same thing so if I just wrote this as a minus I just wrote its conjugate base is in equilibrium with the conjugate base grabbing some water from the surrounding aqueous solution everything we're dealing with right now is in an aqueous solution and of course that water that it grabbed from is now going to be an OHA remember these are just equivalent reactions here I'm writing it as an acidic reaction here I'm writing it basic reaction but their equivalent now if you were to add a strong at a strong acid to this solution what would happen so if I were to throw hydrogen chloride into this well hydrogen chloride if you just throw it into straight-up water without this solution it would complete this associate into a bunch of hydrogen's and a bunch of chlorine anions chlorine anions and it would immediately make it very acidic you would get though you'd get to a very low pH if you had a mole of this if your concentration was one molar then this will go to a pH of zero but what happens if you add hydrochloric acid to this solution right here this one that has this weak base and it's conjugate weak acid well all that all of these hydrogen protons that disassociate from the hydrochloric acid are all going to react with these OHS you have here and they're just going to cancel each other out they're just going to merge with these and turn into water and become part of the aqueous solution so this the OHS are going to go down initially but then you have this reserve of weak base here and we've shut Ali A's principle tells us look if we have a stressor that is decreasing our overall concentration of O H then the reaction is going to move in the direction that relieves that stress so the reaction is going to go in that direction so you're going to have more of our weak base turning into a weak acid and producing more o H so the so the pH won't go down as much as you would expect if you just threw this in water this is going to lower the pH but then you have more o H that could be produced as this guy grabs more and more hydrogen's from the water so the way to think about is it's kind of like a like a cushion or a spring on in terms of what a strong acid or base could do to the solution and that's why it's called a buffer a buffer buffer because it provides a cushion on acidity if you add a strong base to water you immediately increase its pH or you decrease its acidity dramatically but if you add a strong base to a buffer because of the of letelier's scible essentially you're not going to affect the pH as much same thing if you add an acid to that same buffer it's not going to affect the pH as much as you would have expected if you thrown that acid in water because the the equilibrium reaction can always kind of refill the amount of Oh H that you lost and the if you're adding acid or it can refill the amount of hydrogen you lost if you're adding a base and that's why it's called a buffered provides a cushion so it gives some stability to the solutions pH and so the actual definition really is just a solution of the definition of a buffer is just a solution of a weak acid in equilibrium with its conjugate weak base that's what a buffer is and it's called a buffer because it provides you this kind of cushion of pH it's kind of a stress absorber or a shock absorber for the acidity of a solution now with that said let's explore a little bit the math of a buffer which is really just the math of a of a weak acid so if we rewrite the equation again so H a is in equilibrium everything's in an aqueous solution with hydrogen and its conjugate base we know that there's an equilibrium constant for this we've done many videos on that the equilibrium constant here is equal to the concentration of our hydrogen proton times the concentration of our conjugate base when I say concentration I'm talking molarity moles per liter divided by the concentration of our weak acid now let's take the log or let's take the negative log of both sides of this equation let me do something let's solve for hydrogen concentration because what I want to do is I want to figure out a formula and we'll call it the Henderson Hasselbach formula which which a lot of books want you to memorize which I don't think you should I think you should always just be able to go from the this kind of basic assumption and get to it but let's solve for the hydrogen so we can figure out a relationship between pH and all the other stuff that's in this formula so if we want to solve for hydrogen we can mulch by both sides by the reciprocal of this right here and you get hydrogen concentration and I'm flipping it well let me just do ka times I'm multiplying both sides times the reciprocal of that so times 8 the concentration of our weak acid divided by the concentration of our weak base is equal to our concentration of our hydrogen fair enough now let's take the negative log of both sides so the negative log do that negative log of all of that stuff of your acidic equilibrium constant times times make sure let me see what green was I using times H a our weak acid divided by our weak base is equal to the negative log of our hydrogen concentration which is just our pH right negative log of hydrogen concentration is that's the definition of pH and I'll write the P and the H in different colors so you know that p is just means negative log minus log that's all at base 10 let's see if we can simplify this anymore so our logarithmic properties we know that when you take the when you when you take the log of something and you multiply it that's the same thing as taking the log of this plus the log of that so this can simply simplified to minus log of our ka minus minus the log minus the log of our weak acid concentration divided by its conjugate base concentration is equal to the pH now this is just the pKa of our weak acid which is just the negative log of as each of its equilibrium constant so this is just the pKa and the minus log of H a over a if you what we can do is we could take make this a plus and just take this to the -1 power right that's just another logarithm property and you can review the logarithm videos of that confused you and this to the -1 power just means invert this so it could say plus the logarithm of our conjugate base concentration divided by the weak acid concentration is equal to the pH and this right here this is called the Henderson Hasselbach equation Henderson Hasselbach and I really encourage you not to memorize it because if you do attempt to memorize it you're and within a few hours you're going to forget whether this was a plus over here you're going to forget this and you're going to forget whether you put the a minus or the H a on the numerator the denominator and if you forget that it's fatal the better thing is to just start from your base assumptions and if you weren't and trust me it took me a couple minutes to do it but if you just do it really fast on paper and you don't have to talk it through the way I did it'll take you no time at all to come to this equation it's much better than memorizing it and you you won't forget it when you're 30 years old but what's useful about this well it immediately relates pH to our PKA and this is a constant right for an equilibrium plus the log of the ratios between the at the acid and the conjugate base so if I the more conjugate base I have and the less acid I have the more my pH is going to increase right if this goes up and this is going down my pH is going to increase which makes sense because I have more base in the solution and if have the inverse of that my pH is going to
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