Lecture 26: Acids and Bases

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Let's get started. One announcement. And that is the reminder about the upcoming celebration Wednesday. There is the coverage. It is up here on the screen. It starts midpoint Lecture 17 starting with Bragg's Law and goes through to the end of November 8th, Lecture 24, Diffusion.

And that will be the coverage. Let's get on with today's lesson. It is a continuation of what we began talking about on Wednesday. We started looking at solution chemistry, and we recognized that bonding was the key to understanding why thing mix, why things don't mix.

And, along the way, we came up with some metrics, including the solubility product which was superior to simply saturation solubility because it allowed us to look at what happens when there is a plurality of solutes.

And we came to know the common ion effect which in the presence of a common ion we observed repressed solubility. Today I want to talk about a subset, some specialized solution chemistry. And that takes us to acids and bases, which are pervasive.

Perhaps you got up this morning and washed your hair with pH balanced shampoo and treated yourself to some orange juice with citric and ascorbic acid. Maybe you had the radio playing powered by zinc-alkaline batteries.

I started my car thanks to a lead acid battery. And I had some appliances running, electricity-generated coal fired plant which was spewing sulfur dioxide generating acid rain. We are off to a good start.

Acids and bases are everywhere. What I wanted to do today was to go a little bit deeper into acids and bases. And, unlike last day, today we will have some history. We are going to go back in time.

And we are going to go way, way back because acids and bases have been known into antiquity. In fact, humans have used acids in materials processing and in the processing of food. The whole notion of pickling involves denaturing of protein by a shift in acidity.

Acid comes from the Latin word. Acid derives from the Latin word acidus. And acidus means sour or tart. And that indeed is the taste of acid to us. And then modern chemistry, we go to just the predawn of the French Revolution to France and Lavoisier.

And it was Lavoisier in 1779, you know, I am going to be talking about a number of people from different countries. A lot of them are from Europe, so what I thought I would do, to keep everybody straight, I would use the oval sticker you see on the back of a car.

Lavoisier would have an F from France. He would be driving a Peugeot or Renault undoubtedly. And Lavoisier tried to understand acids and bases, and he reasoned that oxygen was the key, that oxygen is present in acids.

And we know this to be wrong now, but he spent much of his career studying combustion. In fact, there was an intense rivalry between Lavoisier in France, Joseph Priestley in Great Britain and Scheele in Sweden to try to understand combustion.

What was it about air that sustains combustion? And they eventually figured out that it was a constituent of air which they named oxygen. And it is named oxy. This comes from the Greek which means sharp as in tart.

Oddly enough, and of course the gen particle, you understand, is meaning to be born, or as we say to generate and so on. Oddly enough, the name oxygen is a complete irony. Because it is named by someone who thought it was a constituent of all acids.

And it is not, but the name remains. That is the way things were in 1779. And then Lavoisier subsequently perished in the French Revolution. Then we go to Britain and Sir Humphrey Davy in 1810. He would have a GB, driving probably a Jaguar or maybe an Aston-Martin.

And he reasoned that it was hydrogen present in all acids. And that was a good insight, and that is where it stayed. He didn't talk about anything beyond that. He didn't say what the form of hydrogen was.

He simply said that it was present in all acids. Then the next milestone comes in 1887. None other than Arrhenius. Arrhenius in 1887. And he was in Sweden so he has a S. He is probably driving a Volvo.

What he did is said not only is hydrogen present in all acids, but the acid dissociates in water in order to donate protons. Acid is a substance that dissociates in water giving the proton, H plus.

And he further talked about the compliment of the acid which he called the base. And he defined the base as a substance that dissociates in water to give the OH minus, the hydroxyl. We have hydroxyl ion and proton.

This is what Arrhenius told us. This was all part and parcel of his major contribution that won him the Nobel Prize, which was the theory of electrolytic dissociation. And this was really important because it set the stage for electrochemical processing.

What he reasoned is that when you inject charged species into water, you do the same as we do when we dope a semiconductor and we raise the conductivity. We saw evidence for that last day. Let's look at two examples.

This is HCl as a gas. Hydrogen chloride as a gas. This is a polar molecule. You have done the analysis of this many times. If we bubble this through water, it will dissolve. And, according to Arrhenius, dissociate to give us the proton which is now dissolved in water denoted aq for aqueous and chloride ion.

We can see injection of charges, pluses and minuses. And sodium hydroxide as a prototypical example of a base. It is a solid at room temperature. And, if it dissolves in water, it gives us sodium ion plus hydroxyl.

Furthermore, Arrhenius said that there is an overarching reaction that involves reconstitution of the solvent. Water, in this case, is acting as the solvent. We can run the reaction vertically now.

We can take HCl aqueous plus NaOH aqueous to give us NaCl aqueous plus H2O. What we are doing is reacting the acid with the base to get the solvent back - water - plus salt. And this is the neutralization reaction.

That is to take us away from either acidic or basic solution. Neutralization involves recombination of the solvent. Everything I am going to talk about today is in reference to aqueous solution chemistry, acids and bases.

But these definitions of proton donor and so on apply to nonaqueous solvents. But for 3.091 we are going to stay in the aqueous phase. Now, what are the shortcomings of Arrhenius' theory? It was good for the late 1880s, but shortcomings always manifest themselves through data.

And people had known for quite some time that they could dissolve ammonia, another molecule that we have seen in 3.091. They could dissolve ammonia in water. And when they dissolved ammonia in water they found they got an aqueous solution that neutralizes acid.

Then they concluded that ammonia dissolved in water is acting as though it is a base, but there is no hydroxyl here. There is no oxygen so you cannot make OH minus here. Something was incomplete. How to explain in the absence of OH minus? Well, you had to wait until the 20th century.

And the explanation came from two places simultaneously. Bronsted, 1923 in Denmark. I suppose he is driving a Volvo, too. And Lowry in the UK. Bronsted and Lowry both independently in the same year enunciated an enhanced definition, a broader definition of acid and base which is as follows.

Acid remains the same as Arrhenius. It is a substance that is a proton donor. That is the same as Arrhenius. But then, to capture the notion that an aqueous solution of ammonia can act as a base, they define the base in terms of something that is chemistry-free.

And they said this is something that is a proton acceptor. Now, that is different. No mention of hydroxyl. Anything that accepts proton would fall under the definition of Bronsted-Lowry base. Here is the prototypical reaction.

Any substance that has a proton, I am going to write proton plus everything else, so A represents the rest of the chemistry of the compound where H is a hydrogen that can be dissolved in water and liberated.

This is a proton donor. And for the rest of the lecture, instead of writing H plus, I am going to write "p+" to indicate proton. HA is a proton donor, and it reacts with some Bronsted-Lowry base, which is a proton acceptor.

And when it reacts, B accepts the proton and becomes BH plus. And HA has lost a proton, and it is now simply A minus. If you walked in the room, and I know this never happens, but if you had momentarily dozed off and hadn't caught the last thing that I said, you might look at the right-hand side of the equation and say, well, BH plus has a proton that it can give away and become naked B.

This BH plus is also a proton donor and A minus, we know from looking at the left side of the equation, is perfectly capable of bonding to H. This A minus must be also a proton acceptor. Now what do we see? We see that the equation comes in conjunction.

That B and BH plus are donor and acceptor, and they are associated with one another so I am going to denote that, that B and BH plus are associated with one another and HA and A minus are associated with one another.

And we call such pairs conjugate pairs. These are conjugate pairs. Con is the Latin for with and jugara is the Latin for to marry and is also the same word for yoke. I think if you pronounce the j as a y, you can see how you get yoke in modern English.

And, in fact, I will designate these with yoke to show that they are conjugate acid-base pairs. And just to be clear about definitions, let's look. HA, this is a proton donor, so this is both a Bronsted-Lowry acid and it is also an Arrhenius acid.

It conforms to the old definition of Arrhenius. Now, this is a proton acceptor B. Therefore, it is a Bronsted-Lowry base. But it is not an Arrhenius base because it has no hydroxyl. You can see this is a case of in some cases there is an overlap and others there is not.

These are both Bronsted-Lowry. This is Bronsted-Lowry acid. This would be an Arrhenius acid because it has a proton. It can give away a proton. This is both a Bronsted-Lowry acid and an Arrhenius acid.

And this one here, of course, is simply a Bronsted-Lowry base. It is not an Arrhenius base because it has no proton. You can see there is a nice contrast between the two. That means, in the light of Bronsted and Lowry, we view acid-base reactions are, in fact, proton transfer reactions.

Follow the proton - that is the message here. Follow the proton. In fact, the proton is the bearer of acidity. Follow the bouncing ball. Follow the bouncing proton, which is the bearer of acidity.

Where the proton goes that is where the acid is. Now let's go back to ammonia and see if we have solved the problem. Now I will write the ammonia reaction. NH3, which is now dissolved in water, is now aqueous, plus water, H2O.

What ammonia can do is neutralize water. What it does is neutralizes water, not by donating hydroxyls but by drawing up, taking out of circulation protons. Because acid and base is really a ratio. Acid has an excess of protons.

If I want to get rid of the acid, I can either flood it with base or somehow get a vacuum in there and draw up all the protons. That is what ammonia is doing. And leaving behind hydroxyl. It is generating hydroxyl indirectly.

And so let's call these what they are. This is a proton acceptor. And here is its conjugate acid. This is obviously a proton donor. And, if we come up with a new, improved theory and we do not declare hydroxyl a base, we failed.

We better make sure that is the case. And this indeed is a proton acceptor. And leaving water. Water is acting as a proton donor. Pure water acting opposite ammonia is acting as an acid here. This is Bronsted-Lowry base.

We solved the thorny problem of the observation that ammonia has the capacity to neutralize some solutions, and this water is acting as a Bronsted-Lowry acid. And then you see the conjugate acid and base pairs as follows.

Here water and hydroxyl are conjugates, and ammonia and this ion here which is called ammonium. Ammonium is one of the few polyatomic ions that is positive. Most of the polyatomic ions, things like carbonate, sulfate and phosphate are negative.

But this is one of the few that is positive. I think we should have special respect for ammonium, for its rarity. It is a rara avis. It is a rare bird. Now let's go into the chemistry. How do we identify substances that are going to act as Bronsted-Lowry bases? Whenever I ask you how, that is your queen of diamonds.

What do you do? He said how, I go let's look at electronic structure. I am going to look at electronic structure of ammonia and of proton, because ammonia is a proton acceptor. Let's look at it. Here is proton.

Actually, I said I was going to write it only as P plus, but I am going to do it this one last time. What is the Lewis structure of this? Where are the electrons? There are none. This brings nothing.

This is proton, and proton contributes nothing when it enters into bonds. It is like a needy friend. It just takes. It does not give. It takes your time, drains your emotional energy. That is proton.

We all have protons in our lives, I am sure. And I am not just talking about the orange juice. Now let's look at ammonia. Ammonia is NH3. Nitrogen has five valence electrons. Three of them are shared with the three hydrogens.

And there are two valence electrons sitting up here in their own orbital. And, in the past, we were circling these in blue and calling them nonbonding electrons. This is a nonbonding pair. Well, guess what happens? You have a situation where the proton has no electrons, and it wants to glom onto something that will be the base because it is a proton acceptor.

The only thing that can accept protons must come up with both electrons. It is axiomatic. The only substances that could possibly act as Bronsted-Lowry bases must be substances endowed with lone pairs or nonbonding electrons.

To find Bronsted-Lowry bases look for nonbonding pairs. All you need is one. Let's look at some other substances that could do this. How about water? What about water? Well, we could do the Lewis structure of water, H-O-H.

Oxygen has six valence electrons. Two are in the orbitals sharing with hydrogen leaving us with not one but two nonbonding pairs. We know that this tells us that water could possibly act as a Bronsted-Lowry base.

And what is the conjugate acid? If this is not Bronsted-Lowry base, it allows a proton to attach here. That means we are going to have three hydrogens here. And the conjugate base is shown as follows.

It is going to be H-H-H. And then the last nonbonding pair. And this has the chemical formula of H3O plus and has the name hydronium. Hydronium is the conjugate acid to water which is acting as a Bronsted-Lowry base.

We can write the reaction and show that water is very versatile. I am going to take water and react it with water. Water plus water, if I wanted to just waste your time, I would write 2H2O on the right-hand side and leave the auditorium, but I decided I want to keep my job.

And so what I am going to do instead is write H3O plus to give you the conjugate acid leaving behind OH minus as the conjugate base. This is acid here and this is base. I am looking at the two waters.

I am just designating them arbitrarily. Let's make this acid. And, of course, hydroxyl must be a base. And then we can group them in conjugate pairs. H2O is a conjugate to hydronium and H2O is a conjugate to hydroxyl.

We have the two conjugate pairs here. And we say that such substances that can be both proton donors and proton acceptors have this dual nature associated with them. And we call these amphiprotic. They behave in two ways with respect to proton.

It is sort of like amphitheater. If you are looking top down, a Roman theater looks like this. Here is the stage and here are all the terraces, the screaming people and everything else. What you can do is take two theaters and put them together.

Now you have theater in the round. That is an amphitheater. This is amphiprotic because now you can look at the stage from both sides and scream. It turns out that both hydronium and hydroxyl are very strong.

They have a very high chemical potential. That means it does not take much of them to express themselves. Both have high chemical potential. And this chemical potential is analogous to gravitational potential.

The higher the chemical potential the greater the chemical reactivity, the greater the chemical power. They have a very high chemical potential, certainly much greater than that of pure water. Pure water is relatively stable and calm, and so it takes very little for them to express themselves.

And it turns out that the extent of that reaction that I have written is really very minimal. And at 25 degrees C you expect that reaction to give about one part in ten million. The degree of dissociation of water is about ten to the minus seven.

And, obviously from the stoichiometry, whenever water dissociates you get equal numbers of hydronium and hydroxyl. And this reaction in which water decomposes, dissociates is called the self-dissociation reaction.

Or some people also refer to it as self-ionization. We start with neutral water, it dissociates and we get the hydronium and the hydroxyl. And we know that pure water is a very poor conductor. In fact, it is an insulator.

We saw that last day. And this is proof of it. Even though we have carriers here, these are both charge carriers, we have so few of them that it does not do much to give us electrical conductivity.

Analogous to a solubility product, we can write a constant called Kw, which is analogous to a solubility product. And it is the water dissociation product. And it is simply the product of the concentration of hydronium ion and the concentration of hydroxyl ion.

And why are we doing this? Because we saw last day that if we express solubility by a single number that would only work in one-solute solutions. If we use the solubility product, we could answer questions what happens when there is a second solute coming in with a common ion.

The same thing here. If all you have is pure water, I could just tell you that the dissociation constant is ten to the minus seven, end of story. But if I use this product and then throw in a second source of acid, this product will remain the same, but the hydroxyl will move up and down.

This is setting the stage for acid-base equilibria. And, before I draw the double line, let me point out that this is a vanishingly small number. It is the square of ten to the minus seven. It is ten to the minus fourteen at room temperature.

These are pitifully small numbers. We can see that if we add another source of acid then the proton level will go down and we end up with something that is acidic or vice versa. We can then define an acidic solution as one that is out of equilibrium with it.

This is a neutral solution. I started with pure water. It is self-dissociated. An acidic solution has another source of proton. In that case, the concentration of hydronium ion exceeds the concentration of hydroxyl ion because of another source.

This is not from self-dissociation. Not self-dissociation. Not self-ionization. We have some other source. And the alternative is the basic solution. And, in that case, the concentration of hydronium is less than the concentration of hydroxyl.

Again, not in self-dissociation. We have to have some other donor here. The acidic solution is proton-rich. Whereas, the basic solution is proton deficient. How do we maintain charge neutrality? Well, we can put in some other negative.

We can put in some anion. We can maintain charge neutrality in other ways. By the way, sometimes we call this alkaline solutions, basic. We do not call it the zinc basic battery. We call it the zinc alkaline battery.

And that comes from Arabic al qaly which goes back to about the 10th century where there was a recognition that if you took the calcined ashes of certain plants and dissolved them in water they made this tart solution that we now know to be the same as an alkaline solution giving us the higher.

We can also call it alkaline. That is the same thing. Now what we can do is look at how this varies. I draw your attention to the trace here. This is simply the plot of this equilibrium. All I am doing is plotting the Kw at 25 degrees C.

And what you see is that exactly when we have a neutral solution, the concentration of proton equals the concentration of hydroxyl. They are both at ten to the minus seven. If we end up with something that has an excess of proton then necessarily if the product is constant, if proton number goes up hydroxyl number goes down, and vice versa.

This is how this system operates. And I don't like this one because it is nonlinear, and I really don't like nonlinearity because we basically have this. I cannot do anything but eyeball it. It is xy equals constant.

It is a rectangular hyperbola. No good. What I would like to do is use some kind of transformation and convert this into a straight line. I would like to have some kind of f of x and a g of y. And, doing so, I would end up with something that is a straight line.

And that offers me two advantages. First of all, I can take a look at some data set and look at, with the naked eye, goodness of fit to see if my system is behaving, if my data are good. And the second thing is if I understand how to construct the transformation, this may give me clues as to the underlying science.

That is why we try to get away from these nonlinear representations and do something that is linear. And for that we go to Denmark, 1909, a young biochemist by the name of Sorensen. In keeping with our tradition today he gets the Denmark sticker.

He was a biochemist working at the Carlsberg Brewery in Copenhagen. Carlsberg Brewery had a research biochemist working. Why? When you are brewing beer, you want to control the acidity of the mash in order to make sure that your brewing is on chemical target.

What he did, being a good chemist, was looked at the situation and said I do not like this nonlinearity. He said I am going to, if you will pardon the pun, straighten things out. And so what he did was say I am going to define a quantity that will represent the chemical potential of hydrogen, the chemical potential of let's say hydronium.

He used the symbol lowercase p and the uppercase H for the chemical potential of hydronium. And he defined this in a logarithmic fashion. It is log base ten of the hydronium concentration. Furthermore, being practical, he recognized that these are always numbers less than one.

The log of a number less than one is a negative number. Who wants to drag negative numbers around? He defined it with a minus sign in front of it so that a ten to the minus seven concentration becomes a pH plus seven.

And he furthermore defined a chemical potential of hydronium ion, pOH as minus log base ten of the concentration of hydroxyl. If you take this and put this to the plot you will see the following. You end up now with a straight line.

We have accomplished our mission of getting something that allows us easily to determine goodness of fit. And the second thing is look at the range. We move here from ten to the fourteen down to one.

Whereas, on this plot, we started at ten to the minus seven and move barely a decade. By linearizing on a log-log plot, we have a much, much greater range of chemistry to express. And so now we talk about acid, which is something that has low pH because the pH is defined as minus the log of the hydrogen ion concentration.

Proton rich is low pH and the base is something that is high pH, according to this definition. And now we have, instead of that xy equals constant, we have x plus y equals constant. And this is now very, very nice to master, where this is the pH and the ordinate is the pOH.

Let's look at some values, put some values on it. Here are some common substances. We have here water in the center, milk, blood. These are very nearly neutral, mildly acidic and mildly alkaline. If you drank coffee this morning, you drank something that was more acidic.

Tomato is more acidic. I know you don't know anything about this, but you have probably read in the newspapers or in magazines people describing wines as being mildly acidic and so on. And indeed the pH is down here.

If the wine spoils it becomes sour wine, vin aigre. Aigre, it means eager, but the Medieval meaning of eager was something that was rather fresh, rather impetuous, tart. This is vinegar. Colas are down here thanks to benzoic and phosphoric acid.

Lemon juice is here. If you drink a lot of Coke or Pepsi, you are coming in at about pH 3, but your stomach is down around pH 1.5. Some of us just cannot take a lot of acidic media because they just drive our pH even lower because we keep contributing more and more protons.

And, if our stomach wall is not up to it, it will get ulcerated. What do we do? We shift the pH back. How do we shift the pH back? We introduce something that is a proton acceptor, a vacuum cleaner for the protons.

And so the classical formula is something in the liquid form. It is the suspension Milk of Magnesia or in the tablet form things like Rolaids, Tums and so on. All they are doing is contributing proton acceptors and driving the pH in the positive direction.

I suppose if you were really aggressive you could try household ammonia, but I would counsel against it. Be patient. I counsel against doing that. And this gives you some sense of scale. Now we know what we have.

So far we have been assuming if I introduce an acid it dissociates and I get protons. All acids are not created equal. Some are strong and some are weak. And what do we mean by that? Let's first of all look at the strong acid.

If I have a solution of one molar HCl, hydrochloric acid, I can assume that this dissociates fully to give me one molar hydronium. The concentration of hydronium is exactly. I get total dissociation.

But that is not always the case. We can look at something that is a little bit weaker. I am going to look at acetic acid. This is the constituent of vinegar. Its formula is given as follows, CH3COOH.

This frontal part is acetate and then plus proton. I want to break this into two steps. First of all we have, if you like, an acetate, hydrogen acetate. And then what we will do is dissolve it in water to get CH3COOH.

And I am just going to write aq. All I have done is dissolved the compound in water. And now what I want to do is look at its extent of dissociation. Let's just call this dissolution. All things that dissolve do not necessarily dissociate fully.

Let's look at its now dissociation reaction. For that we write CH3COOH which is now in solution plus water. And water is going to contribute in the following. We have H3O plus. It makes the hydronium ion and then leaves behind the acetate ion.

Now, compare. In one molar HCl, we have one molar hydronium. In one molar acetic acid, we have only about a half a percent. 0.4% reacts to give H3O plus and the acetate ion. If we write then an acid dissociation constant, it is going to be the product of hydronium and acetate over water, we will end up with hydronium times acetate divided by the undissociated acid.

And, in this case, the number is ten to the minus five. There is very little dissociation. Ten to the minus five is down around ten to the minus seven which was self-ionization of water. This is a very weak acid.

This is a very weak poor proton donor. It is a poor proton donor. What am I showing? I am showing that it dissolves but it does not dissociate. What we need, in order to have full acidity, is to have not only the substance dissolve but it has to dissociate to give us protons.

This we call a weak acid. And we see we have a very low value of the Ka which is termed the acid dissociation constant. And it is analogous to the solubility product that we met last day. Acid dissociation constant for HCl, just for reference, Ka for HCl is equal to the proton concentration times the chloride ion concentration over the dissolved but undissociated HCl.

There is almost none of this. All the HCl virtually dissociates. And this number is ten to the plus six. There is a ratio of ten to the eleventh. Look at this. This is ten to the minus five. This is ten to the plus six.

It is ratio of ten to the eleven. In six molar HCl we have 99.96% dissociation, conversion to H3O plus. We call this a very, very strong acid, and this is a weak acid. Strong acids, Ka is greater than one.

And in weak acids, Ka is less than one. And then you have these moderate acids right around the middle. And I have some charts here to illustrate this. This is a very primitive graphic to show that in the case of a strong acid, you get 100% dissociation.

All of the H becomes H3O plus. In a weak acid, you only get partial dissociation. You still have a lot of this undissociated neutral stuff, which is not active. There is no proton. There is no acidity.

And then a very weak acid essentially does not dissociate. It goes in a solution and you have a molecular liquid. There are no protons. And so no protons, this is a poor conductor of electricity. Conductivity will allow you to track the amount of dissociation.

This is taken from your reading. This is Table 11.3. You can see the acid dissociation constants. There is HCl at ten to the plus six. HBr. HI. There is HF. Hydrofluoric acid is actually a mildly weak acid.

And then down here you have citric and so on. There is carbonic which is the seltzer and so on. This is an interesting one. Why hydroiodic acid is even stronger than hydrochloric acid is because you have here a stronger bond strength.

Fluorine is smaller, it pulls proton in tighter, and so the degree of dissociation is not as great as it is here. These end up scaling as the acid dissociation constants. In general, equal acid strength does not mean equal concentration.

Now let's go to the last definition. Also 1923, but we are going stateside now. We are going to the United States. 1923, G.N. Lewis, the same person that gave us the Lewis Structure Notation. We will put USA on the back of his undoubtedly Chevrolet.

He gave a definition that goes way beyond Bronsted and Lowry and is free of all constraints of composition. He said if you recognize that what you are looking for is something with a nonbonding pair then let's talk about a base as something that has the nonbonding pair.

That is to say, in the past we said it was a proton acceptor. But why don't we look at the nonbonding pair. Remember how I gave you that analogy with the traffic? Don't look at the car, look at the car vacancy.

Instead, don't look at the proton, look at the nonbonding electrons. What we had before is we said that the Bronsted-Lowry base had a nonbonding pair. What Lewis says is don't talk about this as a proton acceptor, let's talk about this as an electron pair donor.

He is following the vacancy instead of the car. Anything that is an electron pair donor he is going to call a base. And then he is going to call what is the mate to this? It does not have to be a proton.

It could be anything that is a capable of accepting electrons, so I am going to call that a hollow orbital. My acid is anything that is an electron pair acceptor. And now look at this. This is the highest conceptualization.

My neutralization reaction, acid plus base gives solvent. Electron pair nonbonding. Empty orbital. What happens if I take an electron pair nonbonding and mate it with an empty orbital? What do I form? A bond.

This is very, very high level. It is gorgeous. It is absolutely gorgeous. And it is not restricted to aqueous solutions. This is Darwin. He is rising out of the water. He can talk about gas reactions, about solid state reactions.

This is free of all constraints. This is electron pair plus empty orbital gives bond. All dative chemistry, all dative bonds are captured here. This is huge. Let's take a look at an example where that would come into play and we will wrap into some environmental stuff as well.

I mentioned earlier about burning coal. In the United States, about 50% of our electrical energy is generated in coal fired power plants, 17% natural gas, 3% petroleum. There is very little that is non-carbon right now.

And industrial coal contains sulfur at the ratio of about 1%. It is an impurity in coal. And one ton of coal will burn to give you about 25 million British thermal units or 2.6 times ten to the tenth joules of energy.

Here is a nice figure to remember. Three tons of coal gives you one megawatt day. A megawatt is a power unit. You take power times time and you have energy. If you generate one megawatt for 24 hours that is an energy unit.

You need three tons of coal. And, just for comparison, you would need one gram of uranium. Think three tons coal, one gram uranium. You make policy. A ten megawatt plant burns about 30 tons of coal a day, given that ratio, generating a third of a ton of sulfur which makes two-thirds of a ton of SO2 because it goes up the stack and burns.

We can reduce sulfur dioxide emissions. Why do we care? Because sulfur dioxide eventually becomes H2SO4. This is a precursor to acid rain. What we can do is trap sulfur dioxide on lime, CaO, to form calcium sulfite.

I am going to do that thanks to G.N. Lewis. Here is the reaction. Here is sulfur dioxide. It is sulfur with two oxygens. This is a double bond and a single bond, so this is resonant. Each of these bonds is really about one and a half order.

And calcium oxide, as you know, is an ionic oxide. It is calcium cation and oxide anion. Oxide anion has nonbonding pairs to beat the band. How many are nonbonding pairs? Four. What it can do is it can sidle up next to the SO2, if SO2 is made to pass over a bed of lime.

And here is what happens. One of these electron pairs is donated to the sulfur which then breaks this double and forms three bonds. Why does it form three bonds? Because three bonds is stabler than two bonds.

Thanks to this, we have calcium oxide acting as a Lewis base. Actually, the O double minus is a Lewis base, according to this definition. Base is an electron pair donor. SO2 is a Lewis acid. It better be.

You know SO2 leads to H2SO4. That is acidic. If I have a new definition that tells me that it is basic, I don't like that. This is consistent. SO2 is a Lewis acid. It accepts the electron pair. And, instead of having a fugitive SO2, it is now a solid calcium sulfite, the volume is dramatically reduced and now we can safely dispose of the calcium sulfite and take advantage of what we have learned from G.N. Lewis. And on that happy note I will say have a good weekend. We will see you on Monday.

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