Reactions in equilibrium

all of the reactions we've looked at so far have been of the form let's say lowercase a moles of the molecule uppercase a plus lowercase B moles of the molecule uppercase B's they react to form the product or the products let's just say they have a couple of products I could have had as many molecules here than want it let's say C moles of the molecule C plus D moles of the molecule capital D and the idea here is that they went in one direction and if we did a little energy diagram just going off of the kinematics video we just did if if this is if that's the reaction or how the reaction progresses you could imagine that here you have it at a higher energy state you have lowercase a moles of capital a molecule plus lowercase B moles of capital B molecule and you have some activation energy and then you get to a more stable state or a lower energy level here where it's lower say C moles of C molecule plus lowercase D moles of D molecule and of course you had some activation energy and only goes in this direction once you get here it's very hard to go back so that if you came back and looked at this if you had enough of a and B you'll just be sitting with molecules of C and D it'll only go in this direction but that's not how it happens in reality in reality well it sometimes happens like this in reality where the reaction can only go in one direction but in a lot of cases the reaction can actually go in both directions so we could have right instead of this one rate reaction we could write a two way reaction like this and just be you know not to confuse you too much these lower case and these are these are the number of moles or the ratios of the at of the molecules I'm adding up so and they become relevant in a second so let's have lowercase a moles of this molecule plus lowercase B moles of this molecule and then they react to form lowercase C moles of this molecule plus lowercase D moles of that molecule sometimes the reaction can go in both directions and to do that to show an equilibrium reaction you do these arrows that go in both direction that means that hey some of this is going to start forming into some of this but at the same time some of this might start forming into some of this and at some point I'm going to be reaching an equilibrium when the rate of reaction of molecules doing going in that direction is equal to the number of molecules going in the other direction that I'm going to reach some type of equilibrium equilibrium equilibrium equilibrium now why would this happen as opposed to that and I can think of one situation if we draw this energy diagram again maybe both of these have similar or not so different energy states there could be other reasons but this is the one that comes to my mind maybe the energy states look something like this so on this side you have the a plus B and then you need some activation energy and then maybe the C plus D maybe it's a little bit of a lower potential but it's not that much lower so you know maybe you're favored to go in this direction because this is a more stable state so this is the a plus B but here you have the C plus D but it's not ridiculous to go this way either so most of it might go that way but some of it might go this way that if enough of these if some of these molecules just have the right amount of kinetic energy they can they can surmount this activation energy and then go backwards to that side of it and the study of this is called equilibrium where you're looking at the concentrations of the different molecules and just to compare that to kinetics kinetics was how fast is this going to happen or what can I do to change the activation this hump here equilibrium is studying what will be the constants or what will be the concentrations of the different molecules that end up once the rate going in this direction is equal to the rate going in that direction and I want to be clear equilibrium is where the rate going in the forward direction is equal to the rate going in the reverse direction it doesn't mean that the concentrations of the two things are equal you might end up with with 25% of your eventual solutions concentration to be a and B and 75% here all we know is that at some point you've reached an equilibrium just means that those concentrations won't change anymore and just to give you an example what I mean here you know if I could have written let's see this is actually the Haber process I could write nitrogen gas plus three hydrogen gases these are all in gas form so I could put a little G in parenthesis results in actually it's an equilibrium reaction with and it produces two moles of ammonia it's called the Haber process we could talk about that in another video but just do one so in this case we could say a is just one this lowercase a capital a is the nitrogen molecule lowercase B is three uppercase B is a hydrogen molecule and then lowercase C is the number of moles of ammonia and uppercase C is the ammonia molecule itself I just want you to realize that this you know this is just an abstract way of describing a whole set of equations now what's interesting the equilibrium reactions is that you can define a constant called the equilibrium constant equilibrium constant is defined as the constant of equilibrium let me switch colors I'm using this light blue too much the equilibrium constant is defined as you take the products right or the right-hand side you know but if it goes in both directions you can obviously go in either direction but let's say that this is the forward direction going from a plus B to C plus D so you take the products you take the concentration of each of the products and you multiply them by each other and you raise them to the mole ratios that you're taking them so in this case it would be big C the concentration of Big C raised to the lowercase C power and the concentration of Big D raised to the lowercase D power and when I say concentration it's usually they usually in especially what you see in your in your intro chemistry classes the concentration is going to be measured in molarity molarity which just as a review is moles per liter and when I a couple of videos ago when I taught you what molarity was I said you know moles per like it so much because the the volume of your fluid or your gas you're dealing with its dependent on temperatures so I didn't like using molarity but in this case it's kind of okay because this equilibrium constant is also only true for given temperature so we assume it for a given temperature and I'll show you how we use it in a second but it's defined as the concentrations of the products to the towers and I also have time maybe I'll do it in the next video the intuition why you're raising it to the power divided by divided by the concentrations of the reactants are the things on the left hand side of the equilibrium reaction so capital a to the lowercase a divided by capital B to the lowercase B and what's interesting about this and this is a bit of a simplification because some of this doesn't apply to all reactions but to most things that you're going to encounter in a intro chemistry class this is true that once you establish this equilibrium constant for a certain temperature it's only certain true for a certain temperature then you can change the concentrations and then be able to predict what the resulting concentrations are going to be let me give you an example so let's say that after you did this equilibrium reaction or let me just do it oh no actually actually just to make things hit home a little bit let me take this Haber process reaction and write it in the same form so that if I wanted to write the equilibrium constant for the Haber reaction or if I wanted to calculate it I would let this reaction go at some temperature so this is only true let's say we're doing at 25 degrees Celsius which is roughly room temperature so what I would do is I would take the products so the only product is ammonia nh3 I raise it to the power of the number of moles is produced for every one mole of nitrogen gas and three moles of hydrogen's so if I raise it to the power of two so that's what that gets me and I divided by the reactants so one mole of nitrogen so I just put the concentration of the nitrogen plus three moles of hydrogen oh no I shouldn't write a plus there it's multiplied so times the hydrogen and I raise it to the third power because it for every one mole of nitrogen have three moles of hydrogen and then two moles of ammonia and if I were to calculate this and remember when I put these in brackets I'm figuring out the concentration so I would have to figure out the moles per liter or sometimes they say the you know well the molarity of each of these things that will get me some constant and if I change it I can go and calculate the rest so let me just do an example right now so let's say I have let me write a simple letter I have a some molecule a plus two one mole of molecules a plus two moles of molecule B are in equilibrium are in equilibrium with three moles of molecule C and let's say that once we're in equilibrium we see we go when we measure the concentrations and we figure out that the concentration of a the concentration of a is one molar which is equal to one mole per liter that's the concentration of a we figure out that once we're in equilibrium the concentration of B the concentration of B is equal to I'm going to think of a I don't know let's say it's equal to three molar which means three moles per liter and let's say once we're not equilibrium the concentration of C C is equal to let's just say it's it's all--it's a say it's equal to point I don't want to do something to let's say it's equal to 1 molar as well I should get rid of that point there because I want to say it point one molar so it's just one molar so if we wanted to calculate the equilibrium constant for this reaction I want to calculate the equilibrium constant we just take C the concentration of C over here so let's say the equilibrium constant constant equilibrium is equal to the concentration of C to the third power to the third power / the concentration of a to the first power because there's only one mole of a for every three of C and two of B times the concentration of I'll do it in that color of B to the third power so if we needed to calculate this concentration of C is one molar and we're right we're raising it to the third power divided by concentration of a is one molar times the concentration of B which is three molars times three molars to the third power so this is equal to one over twenty-seven so the fact that this well there's a couple of things we can think about it the fact that this is that this is less than one what does that mean well that means that our concentration of our reactants the concentration of the reactants is much larger than the concentration of the products we'll review just the products as whatever's on the right hand side of the equation so once this this reaction goes to equilibrium we're still left with a lot more of this than this and so if you're and because we're left with a lot more of that our equilibrium constant is less than 1 which will means that the reaction favors this direction it favors the backward direction it favors the backward direction right think about it because because there's more of this this must be happening more than the left-to-right reaction you know the right-to-left reaction the left-to-right it might be a small direction like this while more is happening that and that's what we're finding more reaction here and that causes the equilibrium constant to be less than 1 on the other hand if you had the equilibrium constant if the equilibrium constant was greater than 1 that means that this numerator is greater than this denominator which would imply that you have more concentration once you're an equilibrium you end up with a lot more of the stuff on the right then you end up with the stuff on the left so then that means the reaction would be going in the forward direction the other interesting thing is you can then figure out well what happens if I add if I add another mole of a to the reaction right so let's say I throw some a into the reaction I had I add one I make I I add some concentration of a so now my new a my new a is equal to my new a is equal to two let's say my new a is equal to two and let's say my new be my new B let's say that I want to well actually we can figure out the relation between the actually instead of going into this situation where I change the country so let me do that in the next video because I just realize that I'm running very low on time but hopefully you've got a good sense of what the equilibrium constant is all about and how its measured or how its defined and in the next video we're going to talk a little bit about how else it could be useful long you know in this video you just said oh if it's less than one that means that the backward reaction is favored if it's greater than one the forward reaction is favored in the next video we'll get a little intuition hopefully and why it is defined this way as opposed to say this way you know my intuition said hey why don't I divide the you know why isn't it three times the concentration of C divided by you know one times the concentration of a plus three times the concentration of B this might have been more intuitive to me but this isn't the case this is what actually is constant regardless of how you change the concentrations of the variance reactants so maybe we'll talk a little bit about why this is true and not and not necessarily this