in this video we're going to look at the ionization of water and how that affects the pH of your solution and also look at buffers and ionizable groups uh when we're looking at biological molecules so we'll start by just looking at the ionization of water so we know that water can react with another molecule of water and that one of those water molecules can act as a base and grab a hydrogen and then the other water molecule can act as acid and donate its hydrogen those two electrons and the oxygen hen Bond will come down to this oxygen giving us our hydroxide ion so we'll make this hydronium ion and hydroxide ion in water now this doesn't happen to a large extent which is why we see this double-headed arrow with the bigger arrow pointing towards water so there will be small amounts of hydronium ion and hydroxide ion in your water solution now um one thing to keep in mind remember is that we know anytime we see hydronium h3o+ it's the same as H+ in water all right this happens to a very small extent so our KQ or the amount that our reaction is going to proceed to product is 1 * 10-14 um and remember that KQ or KW is found by looking at the concentrations of our products over our reactants but we do not include liquids as part of our equation so water would not be part of our equation so our KW which again is just KQ we call it KW because we're dealing with water is going to be our H+ or h3o plus concentration time our hydroxide ion concentration so our KQ or KW is 1 * 10 -4th which means in a neutral solution our H+ and our hydroxide ion concentration are equal and have a concentration of 1 * 10- 7 molar so it's a very small amount of hydroxide and hydronium ion that are present in a water solution okay so this brings us to our pH scale remember pH is the negative log of our H+ concentration and the way that our pH scale works in case you have forgotten is that as we are going down on the scale we are becoming more acidic so if something has a pH of zero it is exceptionally acidic whereas if something has a pH of 14 it is very basic an acidic solution is going to have a lot of H+ or h3o plus ions hydronium ions whereas a base solution is going to have a lot of hydroxide ions and very little h plus ions a neutral solution is going to have equal amounts of hydroxide and hydronium ions and we'll have a ph of 7 we get that pH of 7 taking this 1 * 10us 7 and taking the negative log of it so we'll put 1 * 10us 7 here and the negative log of that is 7 now the pH scale is a log scale which means going from 7 to 6 is actually a factor of 10 times more acidic going from 7 to to 5 would be 100 times more acidic now when we're looking at biological Solutions the pH of our body fluids is generally ranging from between 6.5 to 8 so most of our biological processes are going to take place in this neutral region and we have buffers in our body that are designed to keep the pH at this point so you can see we've got egg whites pancreatic juice blood sweat tears milk saliva all of these things are going to be around a neutral pH that said we do have some places in our body where things get a little bit more acidic for example gastric juice has a very acidic pH between one and two um and so there are some places in the human body and in other biological systems where you will see very acidic conditions all right so these acidic conditions are actually going to be affecting um how our proteins work so our enzymatic activity so enzymes are protein with a function our enzymatic activity is going to be very sensitive to pH so here we see two different proteins pepsin and Tron now pepsin and Tron both have a very similar job their job is to break down proteins um but pepsin its enzymatic activity is highest at a very low PH whereas tron's enzymatic activity is more active towards a neutral pH it's still a little bit acidic but around maybe 6.2 2 6.3 whereas pepsin acidic or pepsin activity is going to be more active at a pH of around two and why they have different functioning PHS is based on where they're located in the body so Tron is going to break down proteins in the pancreas which has more neutral pH whereas pepsin is going to break down proteins in the stomach where we have a more acidic environment right just to remind you are strong acids and strong bases when you put them into water they're going to dissociate completely to make ions whereas your weak acids and weak bases are only going to dissociate partially and so these weak acids and weak bases are going to play a very important role in our protein structure and function because they're going to be these weak acids and bases are what's going to allow our proteins to work at different PHS all right so let's look at a acid some acid conjugate based pairs so remember our weak acid equilibria we've got weak acid generically written as ha when we put it into water it's going to have equilibrium so our acid is going to donate its hydrogen to water to make its conjugate base a minus water will accept the hydrogen from the acid so this will be our base in this case and we'll make hydronium ion we can simplify this or sometimes you might see it written as ha is in equilibrium with a minus and H+ it is the same thing as saying ha+ water is in equilibrium with a minus and h3o+ they mean the exact same thing so ha is our acid and a minus is our conjugate base so we can write our equilibrium expression for this so our Ka is equal to our H+ concentration times our a minus concentration so those are our products and again you could write it as h3o Plus instead of H+ if you'd like divided by the concentration of our conjugate acid remember we do not include water in our equilibrium expression because it is a liquid so this is our Ka or weak acid equilibrium expression so if we have large amounts of product that's going to give us a large Ka value if we have small amounts of product that's going to give us a smaller Ka value remember when we looked at the KA water it was very small it was 1 * 10us 14 and that's because we had very little products very little H+ and hydroxide in that case in our solution if we wanted to find out the pka of our acid the pka of our acid would be found by taking the negative log of the KA value a smaller PKA value is going to mean that you have a stronger acid a larger PKA value is going to mean that you have a weaker acid okay so we can determine PKA by titration so this is actually two different titrations overlayed on the same graph so I don't want you to get too confused looking at this figure the most important thing um to remember is is that it's it's actually two graphs combined into one so let's first look at this weak acid here so this is formic acid so H so this is a carboxilic acid with a hydrogen on it so when we have formic acid in solution and we've added no base the pH of our solution is going to be right here around two then we can add um base to our solution so this is adding a quarter equival a half equivalent 3/4 equivalent and a full equivalent and so these would be M equivalents so if we had one Mo of formic acid we would then need to add one mole of Base in order to get to this one equivalent so it's molecule for molecule so as we are adding in base the base is going to start removing the acidic hydrogen and as we add more and more base it's going to remove more and more hydrogens the pH of our solution is going to start to in increase until we get to the point where we've added one equivalent and at one equivalent now all we have is formate we have removed all of that acidic hydrogen the midpoint this halfway point is where we have removed half of the hydrogens and half the hydrogens remain so that means that we've got equal amounts of formic acid and formate at this midpoint this would be the pka of our formic acid when we have a 50 50 mixture of both the acid and its conjugate base so we can look here at this other titration this is for the ammonium ion so we can see before we add any acid we have a pH of around five so ammonium ion is a weaker acid than formic acid is because when it's in Solution by itself it by itself it has a higher pH now we add in our equivalence of base and very quickly our pH starts to rise and we're going to continue adding in equivalents of Base once we have one equivalent now we have ammonia so we've got ammonium ion and going to ammonia our Midway point where we've added half equivalent of base is going to be where we have equal amounts of ammonium ion and ammonia and that pH at that point is the pka of our ammonium ion so let's look mathematically at why this happen happens um oh sorry here's before we do that I forgot we had this here this is one a a molecule that has three ionizable groups so this is the phosphate ion so it if we look at the structure phosphate it has three ionizable hydrogens the first Hydrogen that comes off they use this one but it doesn't matter which one comes off it's just the first one we call that pka1 so here's our pH of just phosphate by itself we add in half equivalent of Base that is going to be our first PKA and then we'll get to our first equivalent of Base so at this point we have removed all of our first acidic hydrogen we're going to keep adding base now we've added one and a half equivalents of Base so we have removed all of our first hydrogen and half of our second hydrogen so we're midway between h24 minus and hpo4 2 minus we keep adding that second equivalent of base and now we will have only this hpo42 minus so there's only one acidic hydrogen remaining and two of those hydrogens have been removed we can continue to add base we'll get to our third PKA point and you can see that this happens at a much higher pH and then eventually we will completely deprotonate it and get phosphate ion so whether we've got one ionizable group two ionizable groups or three ionizable groups we keep continuing to add equivalents of strong base and we can find the pka for each of those ionizable groups so the reason we can do all of this is because of buffers now we think of buffers typically as a solution that is resistant to pH change but as we are looking at each of these um areas especially around our PK a points these are also buffers because we've got a weak acid and we have a weak base that are both in solution so this is what we would call the buffering region where we've got these plateaus in our pH titration so these are buffers so a buffering system consists of a weak acid and its conjugate base so in this case our weak acid would be phosphoric acid and um hydrogen dihydrogen phosphate would be its conjugate base and at that midpoint we have equal concentrations of both so this would be a buffering region or a buffer solution an effective buffer is going to occur when we have that flat region on our titration curve around our PKA and most buffers are only effective within one pH unit of the pka so if we go back this um buffer right here of phosphoric acid and dihydrogen phosphate it has a pka of around 2.2 which means that the buffer for this would only be effective between about 1.2 and 3.2 at maintaining P pH after that you would want to use a different buffering system the equation that we use to do calculations regarding buffers is called the Henderson hosle block equation and this goes through just how we can derive it from our um equilibrium expression so we just rearrange it we do some negative logs here we do an equation flip which switches whether ha or a minus is on top and changes the sign and that gives us our final equation here um which is that the pH of a solution is going to equal the pka of the solution plus the log of the conjugate base over the weak acid so we're going to use this to describe the relationship um between pH PKA and buffer concentration please keep in mind that this equation will only work with weak acids and weak bases it will not work with strong acids and strong bases all right so let's look at our Henderson hosel boach equation in a case where we've got 10% acetic acid sorry 10% acetate and 90% acetic acid so we're right here at the very beginning of our titration we've added in 0.1 equivalents of Base to get to this point now because it's just 10% acetate and 90% acetic acid uh what I've done is I've just assumed a one molar solution and 10% of one m is .1 mol 90% of 1 molar is .9 mol just make our calculation simple but we could choose any marity and then do 10% of that marity and 90% of that marity to get these concentrations all right so the pka of acetic acid is 4.8 really it's 4.76 if we take it out here to two two significant figures so our PK is 4.76 and then our conjugate base is a concentration of 0.1 because it's 10% acetate and our acetic acid is a concentration of9 so the log of9 over sorry 0.1 over9 is going to be a95 so the pH of our solution is going to be 3.81 and we can see that as we look at the graph it is slightly below four so it makes sense that it would be acidic we also haven't added much base so it makes sense as well that the pH of our solution would be less than the pka of our solution our next case would be our 50/50 concentration so again I'm assuming a one molar solution 50% of one M would be 0.5 um so the concentrations of each are 0.5 the log of 0.5 over .5 which is the log of one is just zero so that is that that case where pH equals the pka so this would be our midpoint we've added we're exactly halfway through our titration curve if we go to the other end where now we've added 0.9 equivalents of Base we've got mostly acetate ion and very little acetic acid um we can put in the log of 0.9 over .1 and that will give us a pH of 5.71 so we're almost at the end of our titration and we can see that at this point in that buffering region we're nearing the effectiveness of our buffer so this has a pH of 5.71 now which is one pH unit above our PKA um after this point we're probably going to be getting out of the effectiveness of our buffer and into where we just have acetate ion so this is going to be cases where our buffering is going to fail if we have in this case 99 um so this top one is looking at this first case over here which is 99% acetate ion 1% acid in this case our pH is 2 units higher than our PKA so our buffer would not work there is not enough acid to be able to neutralize any base that you might add the same thing happens at the other end where we've only added 1% or 0.1 um equivalent sorry 01 equivalents of our base in this case um we would be subtracting two pH units and so our pH would be 2.76 in this case there's not enough weak base in order to counteract any acid that you might have so our ideal buffer is going to be about 1 pH unit from the P just to make sure that we have enough acid and base in our solution weak acid or weak base in our solution to counteract any buffer or any acids or bases you might add okay let's look at this now in terms of a biological molecule so we're going to look at glycine so this is an amino acid our amino acids are going to have um a carboxilic acid they're going to have an amine and then in this casee we've got this C ch2 group that are connecting them so glycine it's R Group it's an amino acid it's R Group is a hydrogen so this is our most simple amino acid so if we proteinate every protonatable group in glycine it will protonate our ammonium in our nitrogen in and it will proteinate our carboxilic acid when everything is proteinated this nitrogen will have a positive charge because it's proteinated this hydrogen on the carboxilic acid will be neutral because it's proteinated giving the overall molecule a net charge of postive 1 this is going to happen in very acidic conditions when all of our hydrogens are or all of our ionizable groups are proteinated so this is going to be down here at a pH close to zero so fairly acidic you know in the maybe 0.5 region we have had added no equivalence of Base to our glycine as we add hydrogens the ionizable group that is the most acidic is going to be the one that is dep protonated first so our pka of a carboxilic acid is going to be around 2 to 4ish depending on the carboxilic acid where's the pka of a hydrogen that is on an amine is going to be around 8 to 9 maybe up to 10 Again depending on the amine so that means the one with the lower PKA is going to be deprotonated first it is the stronger acid so as we add an equivalent of Base the base is going to remove the more acidic hydrogen first which is on the carboxilic acid so that will give us this species here so we can see that this PKA 1 is for the carboxilic acid and so this is going to be again around 2 and 1 half approximately so here we have our halfway point where we've removed half to the half of our um hydrogens from our carboxilic acid and then as we continue to remove hydrogens we'll get to this point where we will have this species here so what is special about this species is that it has no charge overall so it does have this nitrogen with a positive charge and has this oxygen with a negative charge but overall it is neutral because the positive and the negative charge are going to cancel it out cancel each other out this will happen when we have added one equivalent of Base for glycine other amino acids it will be a different number of equivalents of acid or base depending on their side chains now as we keep adding equivalents of base and we get to 1 and a half equivalent of Base we will reach our second PKA value and now this is where we'll have 50% removed um the hydrogen on your um your NH3 group and then 50% deproteinated as you continue and add your second equivalent of Base you will now get to fully deprotonated glycine in which case your carboxilate has a negative charge your amine has a neutral charge and overall it has a charge of1 so this case here where you've got charges but it is neutral this is called a zwitter ion so this zwitter ion is a fairly important thing to be able to find for an amino acid where do you have a an amino acid that is neutrally charged but it still has charges in it positive and negative charge the pH at which you get your zerion is called the pi so what we have here is just the population in solution of these species so you can see we start out with all fully proteinated and then as we add our equivalents of Base we get less and less of the fully proteinated until we don't have any left as we are making or as we're getting rid of this fully protonated what we're forming is the zwitter ion and so we start out with no zerion but as we add equivalence of Base we get to our zerion until we get to a pH where we have all zerion as we continue to add equivalents of Base the amount of zerion is going to go away as we increase the amount of the fully deprotonated form so the pH at which you have this zwitter ion is called our pi value this pi value or isoelectric point is going to be found by taking the pka of the two groups that the two ionizable groups that are the the acid that you lose first and then the acid that you lose second in order to get to the zwitter ion so in this case we have to lose our carboxilic acid hydrogen to get to the carboxilate um that will give us our negative charge and then next we would have to lose this hydrogen on the ammonium ion to get to our um our neutral group so the PKS of those two groups averaged will give you your pi value