Description (Edit): Principles of Chemical Science/n * Email this page/nVideo Lectures - Lecture 21/nTopics covered:
/nAcid-Base Equilibrium/nInstructor:
/nProf. Catherine Drennan/nTranscript - Lecture 21/nOK./nGood afternoon./nI think these clocks may be a little bit fast, but we will get started anyway. All right. Last week we moved the transition from thermodynamics and talking about delta Gs and delta H and chemical equilibrium./nWe started talking about Ks./nAnd we talked about Le Chatelier's principle of applying a stress to the system. That the system will respond in such a way to minimize that stress. Today we are going to start talking about acids and bases./nAnd this is acid-base equilibrium. We are continuing to talk about chemical equilibrium, but chemical equilibrium as applied to acids and bases./nAnd acid-base equilibrium is of particular importance in biological systems because the pH at which a reaction occurs is very important./nIn the body, if the pH is not maintained there are serious problems. A lot of enzymes use acid-base catalysis to catalyze their reactions. These are, again, fundamental principles of biological systems and a direct application of chemical equilibrium./nToday we will continue with this./nAnd we will also, throughout this part, go back and talk about how this relates to thermodynamics so there will be a little review for the test on Wednesday somewhere in the middle of the lecture where we go back and talk about how this relates to delta Gs./nAre there any questions about the exam on Wednesday, any technical things? That will be in the same place as last time. Instructions for the exam should be posted on the Web, as well as extra problems./nAnd all the TAs have special office hours./nMany of the TAs are handing back problem sets, so you might want to check with your TA before you leave class today to see if your problem set is available to help you review. And, of course, there will be recitation tomorrow, which we will talk more about the exam on Wednesday./nAll right. Let's get started with acid-base equilibrium. And this is in Chapter 10 of your book./nAnd there are a number of topics that we hope to get through today. This is sort of all the introductory material to acids and bases, and it will be the build up for what you need for the next couple lectures./nWe have three lectures on this topic. When we start sort of a new unit, the first thing we look at are definitions. And there are several different definitions of acids and bases./nSome are more narrow to the ones that are really quite broad./nWe are going to start with the most narrow definition and build our way up to the broadest definition. In the most narrow definition just consider an acid as any substance that when dissolved in water increases the concentration of hydrogen ions or also known as protons in solution and a base is something that would increase the amount of hydroxide ion concentration when that base is put in water./nThat is the narrowest definition./nWe can go on with the Bronsted-Lowry acid and base. And this is mostly what we will be using in this part of the course where an acid is defined as something that donates a hydrogen ion or a proton and a base is something that can accept that hydrogen ion or proton./nLet's look at an example./nLet's take something, CH3COOH in aqueous solution./nPut it in liquid water./nAnd there will be an equilibrium that is formed, arrows back and forth. That will form H3O+ and CH3COO-. Now, according to this definition here, the acid is the substance that is donating the hydrogen ion or proton./nIn this case, this would be the acid./nIt is donating this proton or hydrogen atom ion to a base. And this is the base. The base is doing the accepting. And when this base accepts the hydrogen ion it forms this, which is its conjugate acid./nAnd the original acid, when it loses the hydrogen ion, forms a base over here./nAnd so these then are what is known as conjugate acid-base pairs./nConjugate acid-base pairs. Note that instead of forming H+ here we are forming hydronium ion because that is more accurate as to what is actually happening in solution./nHydronium ion./nAll right./nLet's look at a little movie that shows this happening where the hydrogen ion or the proton is given up by the acid and accepted by a base. This starts out, this little movie, these are just water molecules./nIn red is oxygen and the hydrogens are in white. And the acid is going to come in, in green, and it has hydrogen ions or protons on it./nHere it is reacting with the water and now you have formed hydronium ion./nAnd now one water reacted with another and you have a hydronium ion there. Once one water has accepted it, it can pass it along. Let's just look at that one more time. And you can see the interaction of that acid./nHere water is acting as the base. It is accepting that hydrogen ion and it now forming hydronium./nAll right. This means that you have to have these conjugate acid-base pairs. When an acid donates its proton, it is going to form a conjugate base./nWhen a base accepts a proton, it is going to form a conjugate acid. The conjugate base of an acid is a base that is formed when the acid has donated its hydrogen ion. The conjugate acid of the base is the acid that forms after the base accepts the hydrogen ion./nThese then, as indicated on the board, you have a conjugate pair here, the acid in its conjugate base./nAnd here we have the base and its conjugate acid, another conjugate acid-base pair./nNow let's look at two more examples and consider in these reactions which are the conjugate acid-base pairs./nWhat is acting as the acid? What is acting as the base?/nHere we have a reaction of something with water and it is forming hydronium ions and CO3 minus two./nAll right. Is this acting as an acid or a base? It is acting as an acid so it is giving up a hydrogen ion or a proton to the water which is acting as the base. And when it gives a proton to this, it forms the conjugate acid./nThis is like the example we saw before. And what is left, when you take the proton or hydrogen ion off of this acid, is the conjugate base over here. Now, let's consider another example./nIf we take the same two things but write different products --/nNow, if this equation was presented to you and you look at the products formed on the other side and you are asked is this acting now as an acid or a base, what would the answer be? Now it is acting as a base so it is accepting a hydrogen ion from this water which is acting as an acid./nAnd when it acts as an acid and it gives up a hydrogen ion or proton, it forms this conjugate base, and when this molecule accepts an extra hydrogen then it forms this conjugate acid over here./nYou see that water can act as an acid or a base, and it will do this in a number of occasions./nAnd that has a special name when that is possible. You have to look at each equation to see what is going on and always ask the question what is donating the hydrogen ion or what is accepting, which will tell you whether it is acting in that particular example as an acid or a base./nSeveral things can act as both, and so your amphoteric molecule can function as either an acid or base depending on the conditions./nAnd water is a good example of that./nFinally, let's look at our third example, which we actually are going to not talk about too much in this unit but will come back to later in the course, but just so you have all the definition up front./nAnd after we go through this definition we are going to go back and talk more about water. Water is very important in these acid-base equilibriums./nThe final definition is the Lewis acid and base./nHere it is more general because it is not even considering a hydrogen ion. Here a base is defined as a species that can donate loan pair electrons and an acid is a species that accepts those electrons./nHere could be an example of things acting as Lewis acids and Lewis bases./nHere this base is a species that could donate loan pair electrons and over here you have something that could accept those loan pair electrons./nThis is the most broad definition because it doesn't even include a hydrogen ion. We are going to come back to this later when we talk about mechanisms of catalyzing reactions, catalysts, because some catalysts act as Lewis acids./nWe will come back to this later, but just so you know all of the various different definitions now./nAll right. Now we are going to back to this sort of more Bronsted-Lowry definitions when we talk about what is donating protons or hydrogen ions and what is accepting./nWe saw that water has some fairly unique properties. And so if water can act as an acid or a base, water seems like it could react with water and do a reaction, this up here./nIf you had water acting as an acid and water acting as a base, you could be forming a conjugate acid hydronium ion and also the conjugate base hydroxide./nThis raises the question then, if you have a glass of water, how much H2O are you going to have in that glass of water and how much hydronium ion and how much hydroxide ion would be in water?/nWe can consider that, how much water is in water./nHere is our equation again. What we are really asking is what is K? If we are at equilibrium conditions, we want to know how do the ratio of products compare to reactants?/nHow much of these ionized species do you have? How much product over the liquid water? That is K./nHow do we figure this out? How do we find K for this particular reaction? Well, here are some of our old familiar ways of relating terms involving K./nWe have delta G knot equals minus RT times the natural log of K./nIf we know delta G knot then we can find K at a particular temperature knowing the gas constant, so we can rearrange this expression here to solve for K in terms of delta G knot. And we are going to do this at room temperature./nAnd just a reminder that is the gas constant./nFirst we need delta G knot. There are a couple of different ways one can calculate delta G knot. And you might want to just sort of think in your head for a minute what are those ways because that is an important useful thing to know on Wednesday./nThis is one of the possible ways. If you know something about the delta G knot of formation, of products minus reactants./nWhat is the other equation that you might use to find delta G?/nYeah, I heard it./nThis one. That one should look familiar to you as well. This will be on Wednesday's, or this is material on Wednesday's exam. I haven't seen the exam, but that is certainly something that should look familiar to you for that exam./nAnd it also shows the connection between the material that was covered on exam two and the material that we are doing now, so everything that you are learning for exam two will be useful in the future./nAll right. Let's just calculate this one way. And I have done the math out here for you. If we look up all of these values and we plug them in, we find that this delta G knot is plus 79.89 kilojoules per mole./nIt is a fairly large positive number./nIf we have a fairly large positive number for delta G knot, what do we predict about the size of K? Is it going to be a big number or a small number? It will be a small number. And so you could actually calculate that from this equation or just sort of remember the relationship if you are just asked qualitatively if it should be large or small./nBut we can actually go through and calculate what K would be at room temperature./nAnd the answer is 1.0 times 10 to the minus 14th at room temperature. And this number you will see a lot for quite a while in the next problem set and in many lectures. That will become a familiar number to you./nAll right./nThat means this is a fairly small number. That means that most of the water is actually H2O. A very small percentage of water is ionized at room temperature, so there isn't that much in terms of hydronium ion or hydroxide ions in your water./nA small percentage of the water molecules are ionized or are in this charged form, so not much of this at equilibrium compared to this./nLots of water in a glass of water one hopes. All right. This equilibrium constant has a special name which is why it is going to become very familiar to you as the lectures go on./nAnd this name is Kw, w for water, so the equilibrium constant for water. And pretty much all of the acid-base things that we will be doing are at room temperature to make your life easier./nThat is why it will become particularly familiar./nKw can be expressed in terms of the concentration of hydronium ions times hydroxide ions. And I just wanted to make a point, and I think you have talked a little about this before perhaps, but here we are not including this bottom term so we don't have the water down here./nThe Kw is just equal to these two not over the two water molecules in liquid. And that is because if you have a material that is nearly pure, you don't include it in your equilibrium expressions./nIf it something solvent, the concentration in water is the solvent, it is just not changing very much under these conditions so it gets left out. This is something that you will see many times./nAll right./nKw is the equilibrium constant and is the product of hydronium ion times hydroxide ion. And it always going to be 1.0 times 10 to the minus 14th at room temperature. Now we are going to look at definitions of pH and pOH and come back to this Kw./nI think I will do that over here./npH equals minus log of the hydronium ion concentration./nAnd pOH equals minus log of the hydroxide ion concentration. We just saw that Kw equals the hydronium ion concentration times the hydroxide ion concentration./nNow, if we take this expression and put logs on both sides and minus signs on both sides, we can come up with minus log of the KW equals minus log of hydronium ion concentration minus log of hydroxide ion concentration./nAnd find that pKw equals pH plus pOH./nAnd that is going to equal 14.00 at room temperature./nYou see that there is a relationship between pKw, pH and pOH that is derived from this equation from Kw being equal to the hydroxide times the hydronium ion concentrations. These are all useful things to remember in doing the problems./nBecause if you are given the pOH and asked for a pH at room temperature, you can use those equations to interconvert./nIt also turns out to be important in terms of thinking about the strengths of acids and bases. Let's look at strengths of acids and bases in terms of pH, the relationship between pH and acids and bases./nThe pH of pure water should be 7, and that is neutral./n7 is neutral pH. An acid solution is anything less than pH of 7, a basic solution is anything greater than 7, and the EPA defines corrosive as substances that yield pH lower than 3 or higher than 12.5./nHere, on the pH scale over here and on the other side it has hydronium ion concentrations, we are neutral in the center here at 7, we are acidic anywhere below neutral and we are corrosive below 3, and we are basic above 7 and we start to get corrosive above 12.5./nNow we are just going to look at the pH of a couple of different things to give you a sense of where they fit in, in terms of whether some of the things that you commonly use are acids or bases or corrosive./nWhat I am going to do is ask for a couple of volunteers. We have some pH paper. This is not accurate to very many significant figures./nBut you can dip it into the material and then look to see what pH it is by the color change./nHere we have some glass cleaner, which is basically ammonia. And we also have some lemon juice./nDo we have a volunteer here who wants to measure pH? OK. Thanks. We have soda, Dr. Pepper. And Dr./nPepper happens to be my favorite, so I am not trying to draw any bad conclusions for any particular soda product. Does someone else want to measure a pH./nAll right. And I also got some tap water from MIT./nWe have to get the pH paper back./nLet's see. I have trouble getting this open./nLemon juice. MIT water. We need the ammonia, too. Do you have a measurement over here? Three. And that was for the soda?/nDoes someone want to do the ammonia in there? Do you want to pass that down? I can take that./nHere, I can take this./nWhat? 6 for MIT water./nWhat do we have for the ammonia?/n10? 10 or 11? 10 or 11 for ammonia./nOK. This shows that it is safer to clean than it is to drink soda./nThat gives you some general sense./nOnly lemon juice is really in the corrosive range, although soda is kind of right on the borderline./nAnd so the MIT water is not totally neutral, according to this. Now, we don't have a lot of significant figures in these measurements./nAnd, actually, a better way to measure a pH are these pH electrodes, which we will talk about later, but actually measuring a lot of significant figures for pH doesn't work even when you have something better than the pH paper./nAnd so if on any of your problem sets or tests you seem to have a lot of significant figures for pH, it probably indicates that there is some problem there because it would actually be highly unlikely that it could be measured that well./nJust a little tip for proofreading your problems. One reason why the water might not be neutral is that it may have some salt in it. And so we are going to be talking about problems of salts in water./nAnd, depending on what the salt is, it can give rise to a slightly acidic or a slightly basic pH of the water./nWe are going to be talking about that as these lectures go on. This gives you a little bit of a sense of the strengths of particular materials in terms of pH./nLet's do some definitions of acids and bases in water. All right. First we are going to look at an acid in water. And we are going to be defining a new form of equilibrium constant./nAnd then we are going to lead into talking about strengths of particular acids and bases./nHere we have an acid in water situation. We will take our acid./nAnd it is dissolved in water. And an acid dissolved in water, if it is an acid, it is going to be giving up its hydrogen ion to the water./nYou are going to be forming hydronium ion and you are going to be forming a conjugate base of that acid./nNow, if you are going to talk about the equilibrium of this reaction, which is a way of getting at the strength of the particular acid that is in water./nIf you are talking about an equilibrium constant, you are talking about a K./nBut here we are going to talk about a special kind of K, which is a Ka, which is often called the acid ionization constant, which is just the equilibrium constant for an acid in water. We will have a lot of Kas./nAnd, as you will see in a few minutes, we are going to have some Kbs as well as a base reaction in water./nKa, you are going to do it the same way you have done other equilibrium constants, products over reactants./nWe have hydronium ion, the conjugate base, which is a product, and over reactants. And here, with reactants, we are not including the liquid water because that is the solvent./nAnd it is not changing very much./nIts concentration is not changing much during this equilibrium so it gets left out of the expression. This is the complete expression then. And we could look up the value of Ka, or we could determine it if we were given concentrations at equilibrium, but a lot of these we can look up./nAnd so this value is 7.6 times 10 to the minus 5 at room temperature, which is pretty much where we are going to do all of these types of problems./nThis is a fairly small Ka, and so what that is going to mean is that this acid, when put in water, is not going to ionize very much./nIt is not forming many of these products here, so this is a small number, not a lot of products./nJust a little ionization. Not too much ionization when this acid is put in water. That is going to mean that it is a weak acid./nA weak acid is something that doesn't ionize very much when it is put in water. A strong acid is something that ionizes quite a bit. And so this acid in water is not going to make the pH all that low./nYeah?/nSorry, 1.76./nI just copied that down wrong. So either one is pretty small because of the 10 to the minus 5. That is really the thing you are going to be looking at, is what is over here in terms of whether it is greater than one or less than one./nLet's just give you that definition right now./nA strong acid is going to be something where the Ka is larger than one and weak is going to be less than one. And almost all the acids we talk about are going to be weak acids. There are only a handful of strong acids./nAnd this is even more true with bases. There is basically one strong base we are going to talk about, and everything else is kind of weak./nIt has to be a very strong acid for this to be true, greater than one./nSee, down here it says 10 to the minus 5. That is a fairly weak acid. Let me just give you some generic ways that these acid and water problems will be written. The way that we wrote this example on the board, we could write this as H in front of an A where A stands for the acid in water./nIt is going to go to hydronium ion concentration and the conjugant base, which is indicated by the A minus./nNow, you may also see this another way. And so I wanted to point this out now, that this BH+ is also an acid the way that this expression is written./nHere it is giving up its hydrogen ion or proton to water, which is forming the conjugate acid over here. And here you are forming a base./nBoth of these could be considered acids because they are both giving up their hydrogen ion to a base forming a conjugate base./nOver on the top you have neutral two negatively charged or plus to neutral on this side. And it can be written both ways. Often the bottom one is indicating when you take the conjugate acid of a base and put it in water./nSo don't get confused if you see these written these different ways./nAnd, in any case, if you are talking about anything being a strong acid, you are wondering whether the Ka is a bigger number than one, which means that pretty much you are ionizing completely./nYou are putting that acid in water and it is going all the way, it is ionizing completely. It is forming as much hydronium ions as the amount of acid that you put in water, so it ionizing completely./nAnd a weak acid means that you are not ionizing that much./nYou are not forming that much hydronium ion when you put the acid in water. And you could also consider whether something is a strong acid in terms of its pKa as well, not just its Ka./nAnd remember the relationship here. pKa equals minus log of Ka as we saw with the pKw before, so these are the same expressions./nAnd so if you have a small value less than one here, if this is small, you are going to have a higher value for pKa./nAnd so the higher the value the weaker the acid. You can think about whether something is a weak acid in terms of its Ka or in terms of its pKa depending on what information is given to you, and that is the relationship between those terms./nHere are some examples of acids./nAnd there are a bunch of these that will be in your book. Up here we have the strong acids. You can see these Ka numbers are enormous. They are very big. You go pretty much all to product and go all to hydronium ion concentration so they ionize completely up here./nAnd the ones you will see the most are probably hydrochloric acid, hydrobromic acid. Those will be the ones that you will probably see in problems sets in the book./nAnd then we go from the strong acids down here to weak./nThese are Kas of less than one. And so here you do not have nearly as much ionization. And, of course, when these numbers get small the pKa also gets bigger. And we can keep going, there are a lot of acids, down here to where you have really truly small Ka numbers and quite large pKas./nThese would be very weak, very little ionization when you put that acid into water. Let's do the same thing for bases./nLet's look at a base in water./nLet's take NH3 in water. The base will accept a hydrogen ion forming NH4+ and the water becomes hydroxide./nWhen you have a base in water, you are going to form hydroxide. When you have an acid in water, you are going to be forming hydronium ions./nIn this base in water, you are going to be talking about the base ionization constant, which is you will be talking about Kb./nAnd so Kb is going to be equal to the concentration of products at equilibrium over the concentration of reactants./nAgain, water is not included. It is our solvent in this case. And the Kb here is equal to 1.8 times 10 to the minus 5, so it is a fairly small number again at 25 degrees./nAgain, it is a fairly small number. You have a small Kb. Then it is a weak base./nYou don't have much ionization for form the hydroxide ion concentration, so it is fairly weak if it doesn't ionize very much./nIf it has a small K, it means it doesn't ionize very much. This would not give rise to a corrosive in the basic category because you are not ionizing that much. You are not forming that much hydroxide ion./nWe can do the same thing then for bases as we did for acids./nAnd we can write generic equations. And you should get used to writing these equations. In fact, on exams, sometimes the molecules are given as acids and bases are fairly long./nAnd so if you want to just write it as a generic equation rather than considering the whole molecule, I will give you full credit for that if you write it correctly. It can be written in terms of the base B in water going to BH+ and hydroxide ion./nBase B in water./nYou could also talk about base A- in water going to HA, the conjugate acid and hydroxide. A base in water should always give you hydroxide, otherwise you have written something incorrectly. Then how strong the base is depends on how much it ionizes to give the hydroxide ion./nAnd so if you have a large number it is a strong base./nAnd, really, the only strong base we are going to talk about in this class is when you actually add something like sodium hydroxide to your solution. That is very strong. That will ionize completely./nIt already is a hydroxide ion. You can also use the same equation when you talk about pKbs instead of pKas. These are a little less common./nIn biochemistry, organic chemistry, you are going to talk a lot about pKas./nYou don't see pKbs that much, so most of the time you are just going to convert them over to pKas. But it has the same expression, and so these are again inversely related. If you have a large pKa you have a weaker base./nAnd here are some examples of bases in the book. And there are a lot fewer of these that you actually work with./nAnd there are none on this table that you would consider truly strong. You have weak bases here that don't ionize very much and they get a bit stronger down here./nWhat else is true about these is that there is a relationship between the conjugate acid and the conjugate base./nIf you have a strong acid its conjugate is going to be weak. If you have a strong base its conjugate acid is going to be weak./nYou are not going to have something that is strong and strong. That is just not possible. And I will prove that in a few minutes. But if you look at this table, if you have something that is like a really strong acid here, HCl, then its conjugate is Cl-./nAnd that is ineffective as a base. It does not do anything./nHere, if you have really strong, basically its conjugate is worthless for anything. Then, as you go down, if you are sort of moderately weak on one side then you will have very weak on the other side./nYou don't have to worry too much about this. If you just want to say it is going to be weak and it is going to be weak to make things a little bit easier. And if you have something that is a really strong base on this side then its conjugate acid is also going to be completely ineffective as an acid./nWhen we are defining things as strong is where they basically push the equilibrium all the way to the ions, and it is not going to come back the other way at all./nWhen it is strong, you are really talking about a reaction that is all the way driven to the ionized forms. Now I am going to prove to you that you that they cannot both be strong./nAll right. Let's look at an example./nIf we have NH3 in water going to NH4 plus hydroxide ion, and I want to write an equilibrium constant for this, what am I writing, a Ka or a Kb?/nIs this a base in water or an acid in water? Base./nAnd how did I know that? Because you are forming hydroxide ion, right. This is a Kb. And so Kb is going to be equal to the products of the base in water over the reactant./nAnd, again, water is not included./nNow I am going to write an equation for this guy, the conjugate acid of this base in water. And now I am forming hydronium ions and the conjugate base. Here I have the base in water and here I have the conjugate acid in water./nNow I am talking about the Ka, which is going to be equal to the products hydronium ion and NH3 over the reactant, which is NH4+./nAgain, water is not included. And now I am going to take those two and multiply them together, the Kas and the Kbs./nAnd if I did that, if I multiplied Ka times Kb then NH4+ is going to drop out because it is on the top here and it is on the bottom here and NH3 is going to drop out because it is on the top and the bottom./nAnd we will find that Ka times Kb is equal to hydroxide concentration times hydronium ion concentration./nAnd what else is that equal to, hydroxide ion concentration times hydronium ion concentration? Yeah, that is equal to Kw./nAnd we can write another expression here which then is pKa plus pKb is equal to pKw. And that is equal to 14.00 at 25 degrees./nThere is a relationship between the conjugate acid and the conjugate base./nThey cannot both be very large numbers. These guys have to add up. That is a mathematical way to think about the fact either the equilibrium is going to rise in one direction or in the other direction./nIt cannot be kind of going in both directions to a large extent. These things all come together and add up together./nAll right. Maybe I can use this board right here. Just in terms of defining a strong acid, if you have the NA in water, then if it is strong, it is basically all going to the conjugate base and hydronium ion./nThere is really not much coming back here./nIt is very small or sort of nonexistent. If this is strong, this is sort of ineffective. It is not pushing back this way. You are pretty much all going to your conjugate. And if you have a strong base in water, it is again pretty much all going to that conjugate acid and hydroxide ion./nThere is really not much coming back in that direction./nWe are going to assume, for strong acids and strong bases, that however much of this we are adding, we are creating pretty much the same exact amount of this and the same exact amount of that. All right./nWe will stop there for today. Good luck on Wednesday.
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