 Okay, guys. Good morning, everyone. Okay, thanks. Thank you. So, I just wanted to remind you guys that we have Quiz 4 on Friday. The online people who are here, we have Quiz 4. I'm going to be posting it tomorrow, okay, for you guys. So, you'll have Thursday and Friday to take it. The Practice Quiz 4 solutions are posted. And, of course, the Practice Exam 3 has been posted for about a week and a half now. I'll be posting the solutions for that maybe sometime next week or something. Are there any other questions before we get started? If you haven't picked up your test yet, I still have a bunch of tests from people who haven't picked them up. Okay, so I think last time we essentially ended our discussion talking about these reaction diagrams. And, if you recall, is this an exothermic or endothermic reaction? Do you guys can tell? Yeah, exothermic. How can you tell? Because, what, the reactants are at a higher energy than the products, right? Okay, so let's draw, let's draw this up on the board. Okay, so if we look on the y-axis, remember that's talking about energy increasing, right? And the x-axis, I always call it time. And these reaction diagrams, a lot of times they'll call it reaction progress. Okay, that is essentially saying, okay, we started with our reactants, and then when we mix them up, the reaction is going. Okay? So, recall that if we've got an exothermic reaction, our reactants are at a higher overall energy level or average energy level than our products are. Recall also that just because this reaction is spontaneous, doesn't mean that it's going to happen on its own. Okay, you gotta kind of push it a little bit, right? And that little push is an increase in energy, and we call it what? So that's our increase in energy, right? So this is going to be called from, here, let's mark it with a different color chalk. This point here, the highest energy point to where the reactants started, that's called the EA or the activation energy, right? Okay, and then as the reaction progresses, of course, it quickly goes down in energy because, of course, most spontaneous, all spontaneous processes want to go down in energy. So it goes down relatively quickly after the initial activation of the process. Remember, we said this is an exothermic reaction. Okay, so, do you guys recall? What do we call the kind of complex that's found at the top of the energy diagram? The transition state, right? You guys are awesome this morning, good job. So the transition state? Remember, the transition state, the transition state isn't an actual molecule, okay? It's like two molecules with partial bonds to each other, okay? So, if we think about it, right? If we've got, say, AC, BD, like this, right? And we want to react those to form AB and CD, like this, okay? What we'll find is that, of course, this doesn't instantly happen, right? We've got to go through this transition state. So what we'll find is that the transition state for this complex, remember, these things have to hit each other in this orientation or they won't form this AB bond, CD bond, okay? So, if we looked at what the transition state may look like, oops, here, let's draw it, it's still in blue, okay? So we've got this AB and CD, right? But in the transition state, the AC bond is partially broken now, right? Because we want to be going from AC to AB, so we've got to break that covalent bond. So we could represent that like a dashed bond like that, okay? Also, the AB bond is partially being formed right now, okay? So we could represent that as another dashed bond like that, okay? So you could imagine this would be one portion of what the transition state would look like. Overall, the whole transition state would actually look like this, right? With partial bonds between all of those, the forming bonds being, which one are we, this one here, those ones are going to be forming those partial bonds. And then these partial bonds here are the breaking bonds, okay? And even though I marked them as solid lines, remember, they're partial bonds, okay? Covalently linked, okay? So this thing doesn't actually exist ever, okay? It's just kind of a theoretical two molecules sitting together forming two other molecules, okay? So there's some more portions to this reaction diagram that we can talk about. Recall, if we talked about the difference in energy from the reactants to the product, so just from here to here, does anybody know what value that would be called? Yeah, the delta H, delta H, right? Or does anybody remember enthalpy, right? The enthalpy. Yeah. So we call that delta H or enthalpy, okay? So for this reaction, is delta H going to be negative or positive? So I heard both, negative or positive? Negative. Why is it going to be negative? Because the energy is coming off of the reaction, right? Energy is coming off of the reaction. We can say that. So the vessel will, what, heat up or cool down if we're holding it. It'll heat up, okay? It'll heat up. So yeah, I guess you can think of it that way, yeah. But since you can also think of it the opposite way since this is an exothermic reaction, you know it's going to have a negative delta H, okay? And this is shown by this graph, okay? So let's just really quickly draw the, I think, let's see what we've got here. Activation energy, let's see if we've got some more things. Okay, yeah. So let's just look at these pictures representatively. So you can see here we've got a relatively high activation energy relative to the enthalpy here. So this reaction is actually going to go very slow, okay? So reactions that have high activation energies, it takes a lot of external energy stores to get those reactions started, okay? So in other words, they're going to go slow. Of course, once you get to this point, it's just like any other time you get to that point. It goes really fast. It's like going down the roller coaster or whatever, okay? Notice here the relation between the activation energy, EA and delta H. EA is very small relative to delta H. So this reaction will progress quite quickly, okay? So the lower the activation energy, the faster the reaction, okay? There's the activated complex or transition state, okay? Those are equivalent terms. So if one is used instead of the other, don't make sure you guys don't get confused. Remember, it's an extremely unstable, short-lived, intermediate complex. Reaction proceeds from reactants to products via the activated complex. So in order to get from NO plus O3 here to NO2 plus O2, you've got to go through this kind of partially bonded activated complex or transition state. So remember, because it doesn't actually exist, it can't be isolated from the reaction mixture. And this formation of this activated complex or transition state is what the energy in the activation energy, this little push of energy is actually forming. Remember, these molecules don't necessarily like to be in contact with each other. They'd rather be kind of far away from each other. So getting them in close proximity and the right orientation, which we're going to talk about a little bit more extensively today, does take some energy. And that's energy is found in this activated energy from the reactants to the transition state or the activation energy, okay? Again, here's an exothermic reaction. We can tell because the reactants are higher than the products. Slow, because the activation energy is high. Notice this. We can look at a reaction from the forward or the reverse from the left or from the right, I guess I should say. So here you see we've got the forward activation energy saying that this is the reactants and this is the products. But we could push the reaction in an opposite direction, okay? In that case, this would be the reactants and this would be the products, right? And now our activation energy would be from the average energy of the reactants down here all the way up to the average energy of the transition complex, okay? So you can see that activation energy for the reverse reaction is very high relative to the activation energy for the forward reaction, okay? Notice also the enthalpy of the reaction, the magnitude of this number stays the same but the sign switches, okay? So going from an endothermic to an exothermic reaction. In this case, the delta H for the exothermic reaction is negative 392 kilojoules, okay? So the delta H for the endothermic reaction would be positive 392 kilojoules because you need to gain that much energy to go back to your reactants, okay? So go over this slide a little bit because it really does kind of take everything and put it into one little picture. There's your endothermic reaction. Again, your activated complex, endothermic reactions almost always take place very slow because of course the reactants are always at a lower energy state than the products and you've got to get up to this very high activation transition state so that much energy takes a long time to get, okay? So unless you're heating these things up to a very high temperature, you're going to have very slow endothermic reactions. Okay, so we've been talking about reactions, the rates of reactions for the last couple of days so we know that at a certain temperature, in this case, at STP, standard temperature pressure, reactions will proceed at what is known as their characteristic rate, okay? So for example, this reaction here is a very fast reaction. If you're looking for some of these slides, I did put a couple more in this morning. So this reaction is very, very fast and this reaction at standard temperature pressure is very slow. So you can imagine at the same temperatures and pressures you'll find different reactions having different speeds, okay? So let's look at the five factors that affect the rate of the reaction. Okay, I essentially just expanded this portion in your notes. So if you look, the first of those factors is the concentration of these reactants. Of course, these molecules must collide to react. We've talked about that extensively over the past couple of days. They can't just shout to each other and say, okay, we want to react. They have to actually come into contact with each other, make and break bonds. So if they're not doing that, then you can't have a reaction, right? That's why I can have two things that if I mix them together, they can explode or whatever, but if I have them in two separate containers, they'll be perfectly safe, right? Okay, so let's talk about the concentration reaction, reactants. So the reaction rate is proportional to the concentration of the reactants. That should make sense to you. And you can see that graphically here. Here, we have this magnesium file in what is an evacuated container containing no oxygen, okay? And you can see that it's just glowing. It's not doing very much, okay? We take that same file at that same temperature and put it into a flask containing only oxygen, right? And of course the concentration of oxygen is very low here, very high here, right? And you can see the difference in the relative reaction rate, okay? That's because reaction rate is proportional to the concentration of reactants. In this case, the reactants are magnesium and oxygen. If we have very little of oxygen here, it's not going to react very fast. If we have a lot, it's going to react very fast. Okay, why is this? Well, if a reaction occurs between A and B and the reaction mixture contains mostly A molecules like here, most of the collisions participated in A molecules will be with other A molecules, okay? In this case, definitely, because it's a solid, so they're just kind of vibrating in place. So therefore, if you're only hitting A molecules, the reaction rate will be low. So if you can imagine you've got a low concentration of B and you've got A here, A is trying to hit B's, okay? Well, I'll have an effective collision if I hit there, there. But if I hit there, I won't have an effective collision. If I increase the concentration of B, right? A can hit B there, there, there, there. So I increase the concentration by two times. So I get twice this quick of a reaction. So again, higher concentration means more reactant molecules per unit volume, and more reactant molecules means more collisions per time. Does that make sense to everyone? Cool, cool, okay. So again, you can see in this, well, kind of display, this is the same reaction between iron and oxygen, okay? But in this case, we are just letting the iron sit out and only the surface pieces of iron can react with oxygen to rust, okay? That's why when you've got a solid piece of iron, it takes years and years for it to rust. But if you've ever washed dishes with steel wool or something, you can see that the steel wool rust quite readily, right? It's because the surface area of the steel wool is much greater than the surface area of, like, I don't know, one of these iron, I don't know, whatever they are, clamps or whatever, you know? So what'll happen is that this will rust much faster because the oxygen is able to touch more of the iron surfaces, okay? So the more surface area you have, the faster the thing will react, okay? So in this case, we can say that the effective concentration of the iron is low, okay? And in this case, the effective concentration is high, right? So it says, however, wire wool and finely divided iron power rust more rapidly because their surface area and effective concentrations is much greater. Okay? So that was the first factor, concentration. Increase it. It makes it go faster. Decrease it and make it go slower. The physical state of the reactance is the second factor that will affect the rate. So of course, molecules must mix to collide. So if they're not mixing, they're not going to collide. Just like we said, if we've got two separate containers, they can't mix, so they won't react, right? So what you find is that when reactants are in the same phase or a homogenous reaction, they collide throughout their entirety. Same phase being liquid or gas, okay? Solid and solid, right? If I wanted to react this and this together, it would, even if I'm touching them, right, it would take a long time because you can't mix them very well. So when we're talking about homogenous reaction, we're talking about liquid, liquid, aqueous, liquid, aqueous, aqueous or gas, gas, okay? So, but when they're in different phases, as you can imagine, heterogeneous reaction, they collide only at the phase interface, just like what was happening with iron bars or whatever. They were on the last slide, right? So let's just graphically represent what I'm talking about, right? So say we've got some sort of iron bar in a beaker. We want it to rust, right? Well, we pump a bunch of oxygen in this beaker or flask, cover it up. What will happen is the oxygen can only react with the surface molecules, right? So you only have reactions here. If I wanted to, if you can imagine being in the surface or in the center of this thing, the iron atoms in the center will take a very, very long time to react, okay? So this would be like a heterogeneous mixture, the, this being a solid, this being a gas. So it can only react at the phase interface there, okay? That's what that's saying. Reactions between oppositely charged ions on the other hand in solution, like it's happening right here, is almost immediate, okay? Because, of course, ions that are of opposite charges are fairly strongly attracted to each other and once they get into a media where they can flow freely, they'll kind of stick to each other almost immediately. So it says this is because the ions are strongly attracted because of their opposite electrical charges. So you can see this reaction taking place essentially, instantaneously, once you dump these two solutions together, okay? So let's just make, make the points again. Reactions occur when reactants can collide frequently with sufficient energy. So in the solid state, atoms, ions, and compounds are so close together, but they're restricted in motion, right? So they can't react with whichever molecules they come into contact with because they're only in contact with their surrounding ions and atoms. This is in the solid state. In the gaseous state, you would expect reactions to go very quickly, right? And they do relative to solid state, but in the gaseous state, particles are free to move but are often very far apart, okay? So the collisions are very infrequent. Very, that's a relative term, okay? Again, gaseous reactions are much faster than solid state reactions. On the other hand, if you think about what the molecular nature of liquids are like, right? Liquids in the liquid state, particles are free to move and are in close proximity with each other. So they move all about rolling on top of each other, right? So they have free range of motion and they're in close contact with each other. So what you'll find is that reactions tend to be fastest in the liquid state and of course slowest in the solid state, okay? That's a good reason for us to work with liquids in labs, yeah? So we don't usually take two solids and mix them together, right? Although we have done that, done a reaction like that in lab. Remember the sulfur and the iron that we mixed together to form pyrite or fool's gold, right? Yeah, so you remember that? We heated it up and, you know, kind of mixed it up. Okay, so liquids much faster, gasses a little slower, solids almost don't go at all. And it looks like I have the same slide twice, okay? So let's skip that other slide and go to the third factor, which is the temperature of the reaction. So of course we've been talking about molecules hitting each other, but just like we were talking about last time, they have to hit each other with enough energy, right, in order to react. So remember temperature and energy are essentially the same thing. So if I have a higher temperature, I'm at a higher energy state, right? So if I'm at a higher energy state, right, and I'm flying around hitting other molecules, I'll be hitting those molecules with more energy, right, with more power, right? So I'll have more effective collisions. And what you find is that temperature actually has a major effect on the speed of the reaction. You probably, we've looked at these pictures before, not in this context, but you might not be able to see it very well, but it says 0.2 degrees Celsius here, so that's very cold, almost freezing the water here. But I don't know if you can see, but these, so these guys outside are in room temperature, okay? And we're comparing them to the ones inside of the cold water here, and hopefully you can see that the light is very low relative to the ones outside in room temperature. And then when we heat the solution up to 59 degrees or the water up to 59 degrees and we compare them to the ones that are at room temperature, they're brighter, okay? So you can see it goes, there's this kind of progression from very dimly lit to intermediate lit to brightly lit. And these glow sticks are kind of like those reaction mixtures that I was talking about. Has anybody ever used a glow stick before, right? So what's the first thing you have to do in order to, yeah, you got to break it, right? So what are you breaking? In actuality, what's, how it's happening is that there's two compartments in these things and there's a glass piece in between them, right? And you break it and once those particles mix up, that's when the reaction occurs, okay? So when we cool these particles down after we break it, right, they don't have very much energy even though they're both in the liquid state, right? And they're rolling on top of each other just because they're rolling on top of each other doesn't mean they're hitting each other with enough energy, so they're still not being able to react effectively, okay? Increasing the temperature, of course, will let them react more effectively thereby giving us from hardly any light to much more light and then if we heat them up even more, right, they produce even more light. You can see this again. Okay, so here's another representation of what the molecules behavior is when we're looking at the temperature, okay? So what we can say is the general rule is that the rate increases as the temperature increases. Why is this? This is because increased temperature relates directly to the increased average kinetic energy. Remember I said the temperature and energy are essentially the same thing, okay? So if we have greater kinetic energy, that means the speed of the particles are effectively faster, okay? So if the speed of the particles are faster then the likelihood of collision is greater and of course the likelihood of collision or effective collisions is even greater than that. So higher average kinetic energy means a higher percentage of these collisions will result in product formation, okay? So hopefully that makes sense. Let's look at it graphically here. So if we look at this graph, what we see is that the mean or the average, if you will, of the cooler particles, so that's the particles under the line blue, okay? It's going to be about here where the big hump is, right? Okay? So does everybody, can everybody understand this graph? Okay? So most of the particles, this is saying how many there are and how much energy they have, okay? So most of the particles have that much energy, right? If I heat the solution up, right? I get a more expanded range of temperatures, but what you find is that the average temperature increases to here or the average kinetic energy increases to here, right? So it goes from here to here, right? And so what you'll find is that since most, more of them have higher average kinetic energy, then you're going to have higher effective collisions, okay? So that's what this is showing represent, representatively. What it's really saying here is where the activation energy has become overtaken, right? So we went over the little hump here, right? And this thing not working. Whatever. The hump, right? So over the hump right there, you can see if we're cold, there's only that many that get over the hump. If we're hot, right? We have more, okay? So does that make sense? Okay, cool. Okay, so increased temperature, increased effective collisions, increased reaction, right? Catalyst. So a catalyst is something that will also increase the reaction rate. How does it increase the reaction rate? It increases it by lowering the activation energy. So it's lowering the hill, right? That the molecules have to climb. So if I lower the hill, I can get over it faster. So I can make the reaction faster. So it's graphically represented here, although this is a more detailed picture than you guys really need to understand. So let's just look at it over here. What you find is a catalyst. When you put a catalyst in, you'll have actually two transition states. One transition state to grab the two reactants and one transition state to release the products, okay? But as far as we're concerned, you can just say the catalyst lowers the activation energy and you can just do kind of like a dotted line like that, okay? Giving a new pathway, okay? So this would be like burrowing, like if you could imagine instead of having to climb a mountain, you could burrow a tunnel through that mountain, right? And what you'll find is that you get your cars through the mountain faster than it would take to go over the mountain, okay? So that's kind of like what a catalyst is. A catalyst is actually, what it really is, is like something that has the right structure to actually grab both of the reactant molecules and put them in close proximity together in order to form an effective collision, okay? So that's how it lowers the activation energy. So what you find is that instead of this being our activation energy, we have a new activation energy, right? And its symbol is EA cat, okay? So cat being the catalyzed activation energy. So again, a catalyst is a substance that increases the reaction rate but undergoes no overall change in the reaction. So a catalyst does not alter the final product of the reaction. It gives you the same product, it just gives you that product much quicker, okay? So homogenous catalysts are substances that are distributed uniformly throughout a reaction mixture. So you can imagine they're like in the same phase as your reaction mixture. A heterogeneous catalyst is a substance that normally is used in the form of solids that have large surface areas, okay? So like a lot of times your reactions, again, are in the liquid media. Sometimes your catalysts are solids, so we'll put a solid brick in the bottom of your liquid media and we call this a heterogeneous catalyst. So again, just to emphasize it, catalysts provide an alternate reaction pathway that requires less activation energy than the normal pathway. It's proposed that solid catalysts provide the surface which reactant molecules absorb. Absorb means like being stuck into it, okay? So it kind of can grab things. And then puts them in favorable orientations relative to each other, okay? And then absorbed molecules with favorable orientations are located close enough to each other to react. So then there's such a thing as a negative catalyst or what we know as an inhibitor. So an inhibitor lowers the activation energy of the reaction by placing the reactants and not in close proximity, okay? So this should just cross that out. And not in the correct orientation. So an inhibitor is a substance that decreases the reaction rate but undergoes no overall change in the reaction and does not alter the final product of the reaction. So it's the same thing as a catalyst just backwards, okay? So you can see, well, inhibitors, they're like a lot of things that are poisonous to us are inhibitors like carbon monoxide poisoning and carbon monoxide inhibits your hemoglobin to bind oxygen because it binds to it better, okay? So you can see, well, you've got a substrate here. Substrate means the thing that the thing is supposed to bind, okay? So this is its natural binding thing. But then you've got this inhibitor here. This is like what carbon monoxide does to oxygen. If you can imagine this being hemoglobin down here, carbon monoxide bonds to hemoglobin faster and better than oxygen does. So it sticks there and doesn't allow the oxygen to bind in that site, okay? Or you could have a different type of inhibitor where the inhibitor binds at a site that's not what we call the active site of the enzyme. So it can bind outside the active site, but once it binds there, it kind of manipulates the shape of the enzyme in order to close the binding pocket for the natural substrate, thus allowing or not allowing the natural substrate to get in there, okay? So this one would be like putting a gum in a key lock, right? Okay? So you get it in there. Now you can't stick your key in there, okay? This one would be like taking a hammer and smashing the, you know, lock in order to deform it so the key can't fit in there, okay? So there's two different ways that you can do this by gumming it up or by like kind of, you know, manipulating the structure of the thing, okay? And the last thing that affects the rate of reaction is the structure and orientation of the reactants. So we keep talking about the same things over and over because we have to to talk about all of them. So it's kind of like what we talked about up here. These things have to be oriented in this fashion in order to make that bond and that bond, right? What if I add them oriented like this? Will we have a reaction? No, right? If this thing's going this way, this thing's going this way because when we try to react, those things don't react together so we won't have a reaction, okay? So they have to be oriented in the right way. So the right orientation, they've got to have the right energy and it's got to be between the product or the reactants, right? If a reactant hits a product, it's not going to form the proper reaction. So notice here, you've got an effective collision because it's got a lot of energy here. We're either hitting the things in the wrong place or not enough energy. So remember, oppositely charged species react very quickly, okay? So dissociated ions in solution whose bonds have already been broken have a very low activation energy. In fact, it just takes them to get into contact with each other. Ions with the same charge do not react with each other. Bond strength, of course, will play a role. In covalent molecules, bonds must be broken. Using that extra energy before the bonds can be formed. So the magnitude of the activation energy is related to the magnitude of the bond strength, right? So if we have very strong bonds, it's going to be very hard to break, right? And the size and shape influence the reaction. So large molecules may obstruct the reactive part of the molecule, okay? So let's talk about that. So let's say we've got a molecule or two molecules that want to react with each other. But one of the molecules is very big, say, that's what one of the molecules look like, okay? And the reactive portion, we'll say, is right there in the middle of it, okay? And then we have this other molecule that wants this other particle that wants to react with it. So it's got to hit it, it's got to get through all of this junk, right? And hit it in the exact right place in order to react, okay? In order to form a good reaction and go to product. If this thing hits it there, it's not going to react, hits it there, it's not going to react, hits it there, hits it there. So a lot of times what you find is that big molecules obstruct their reactive portions and don't allow other molecules to react with them, thereby making the reaction rate decrease, okay? And again, only the correct orientation, just like what we were talking about, leads to product formation. This is essentially the same thing looking at it kind of the way we did up here. Let's introduce equilibrium and then we'll save the major equilibrium discussion for Friday and Monday, I guess, okay? Okay, so equilibrium, what is equilibrium? Well, equilibrium is the dynamic balance between forward and reverse reactions and the study of how to influence this boundary by outside forces. So what is an equilibrium reaction? This is a reaction that does not go to completion, okay? So let's look at a representation of this. So if I say A goes to B, at the beginning of this reaction we'll only have A in solution, right? And at the end we'll only have B, okay? So this reaction goes to completion, so this reaction is not in equilibrium. The reaction that is in equilibrium, show that, okay? Notice the difference in arrows, okay? This is called a forward arrow, okay? This is called an equilibrium arrow. In the beginning of this reaction, it's just going to have C, but at the end, because C goes to D and D goes back to C, we're not only going to have D in the reaction mixture at the end, we'll have both C and D, okay? Because the reaction goes back and forth, back and forth. So there are various types of equilibrium reactions. Some reactions go almost to completion, some go halfway to completion, and some go very little of the way towards completion. So we can represent these reactions like this, okay? So the ones that almost go to completion will be represented like that with that type of equilibrium arrow. Ones that go to an intermediate completion value would be like that, and ones that go very little to completion would be like that. So when we're looking at these two different reactions here, HCl in water, what we find is that this reaction goes to completion, like that. But this reaction, acetic acid in water, notice does not go to completion, okay? But both of these reactions take less than one second to get to their final equilibrium concentrations, okay? But even though they're both very fast, one of them goes to completion the other doesn't, okay? The last thing we'll talk about is physical equilibria. So physical equilibria are always what we can call reversible reactions or reversible processes. So some reversible processes that are physical equilibria that you should be familiar with would be like dissolved oxygen in a lake, ice from water, formation of ice from water, and sugar dissolved in water. So remember a reversible reaction is a process that can occur in both directions and uses the double space equilibrium or the double arrow equilibrium arrow. A dynamic equilibrium is once you get to the state of equilibrium, it's when the rate of the forward process in a reversible reaction is exactly balanced by the rate of the reverse process. So notice here, at the beginning of a reaction, like this reaction here, we only have C and we have none of D, right? So the rate of C going to D is very fast at first and the rate of D going to C is also very fast at first. But once you get to equilibrium, the rates become equal. So you have just as many C's going to D as D's going to C, okay? So even though the concentration might not be the same, right? We might have a very low concentration of these things. We still have the same amount going back and forth, okay? So it's just like this. If we look at the two first desks or benches here, we've got three people in bench one and six people in bench two, right? So there's a higher concentration of people on bench two, right, than there are on bench one. If I said, okay, we're at equilibrium, so these are your reactants, these are your products. And there always has to be three to six ratio, but they can't be the same people. What we would find is that the people would be climbing back and forth, back and forth at the same rate, but we would find, right, that the people would be all different always, okay? If we took a snapshot after every, like, five minutes or something, the people would all be rearranged. It's not, so what we'll find is that there will always be three here and always be six there. This is kind of like what happens in a dynamic equilibrium. So even though the concentrations aren't the same, you'll have this forward and reverse process with the rate being exactly equal. So just emphasize it. Continuous change is taking place, but no observable change in the amount of, well in this case, solid sugar or dissolved sugar is being shown, right? This would be like if you got a bunch of sugar that's at the bottom of your cup undissolved, right? What you find is that that sugar is not static. It's not staying just sitting there, right? It's going back and forth to solution and back to solid, okay? Thanks a lot, guys, for listening. Hopefully my battery didn't die.