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# Keq intuition

## Video transcript

let's see if we can develop some intuition as to why the equilibrium constant equation looks the way it does and just as a review this is it equilibrium constant it would be the concentration of our molecule Y raised to its coefficient power or if we're thinking in moles raised to the number of moles if we think of these as kind of them the the mole ratios or the molar ratios or we could just view them as the molecular ratios either way times the concentration of our molecules Z now we're not doing some calculus here D is just the number of the number of moles we need of Z for every C moles of Y B moles of X and ay moles of e so Z to the D power divided by the concentration of V to the a power and X to the B power so the question is why it's a nice little clean equation but why does it look this way and I actually made a video earlier today where I started exploring this with natural logs and I think I got someplace but that one started to break down and I think I've come up with a much simpler reason why this looked this way so I've deleted that video and I think I've come up with a much more intuitive one that that explains more of why this works and actually some of the other things we're gonna learn about about the equilibrium constants in future videos so what makes any what makes a reaction happen or what what does equilibrium mean it means that the rate at which the forward reaction is happening so that means that the rate of the rate of this happening of a V Plus X turning into y plus Z can't forget the coefficients all right is equal to is going to be equal to the reverse reaction is equal to the rate of the reverse reaction so our C moles of Y plus D moles of Z turning going the other way turning into the V and the X with certain ratios right it doesn't mean to say that the concentrations are the same because we could have one where we end up with you know a heavily favoring the forward reaction we end up much more with much higher concentrations of y&z or we might heavily favor the backwards reactions where we have more V and X but when we're in equilibrium we're saying that our concentrations have reached a stability point which implies that the rate of going in this direction is equal to the rate going into that direction so let's just think a little bit about what drives these rates what drives these rates of reactions in order for this forward reaction to happen that I drew in purple what needs to happen we have to have a molecules of V roughly and it's let's say in any volume of space we have to have some V molecules and preferably AV molecules being in the being in the vicinity of BX molecules so being so there's got to be B of these X molecules and they have to be in the right configuration and in the right place and kind of close enough in order for the reaction to happen so the reaction is really going to be driven by if you think about it the probability of finding a V molecules and B molecules all within a closed enough set of close enough confines that they can actually react so you could say that there the rate is going to be it's going to be driven by maybe it's going to be proportional it's say it's just equal to let's say some constant that takes into account things like temperature and the molecular how the molecules are actually configured because it's not dependent just on them being there you have to have worry about their kinetic energies you have to worry about their shape because some shapes are going to be more conducive to reaction than others so let's just let that be taken into account with a K and let's say we're talking about the forward reaction right so in order for the forward reaction happened let's call that K plus for the forward reaction we have to have some we have to have a molecules of V there and B molecules of X so what's the probability of having a molecules of X or what's a rough approximation of the probability well the concentration right concentration the way we've so let's think about this a second when rewrite the concentration of the molecule V which I think when I did this was the blue one right here what is that given in that is given in moles per liter so this is telling us moles is just a number so this tells us look in any given volume roughly how many of the molecules do you expect to find that's what concentration is so if I wanted to figure out the probability of finding a of these molecules because that's how many I need I need to multiply this by itself a times because I need a of them the probability of having just one molecule and some in some in just some small fraction you would just use the concentration once but you're going to use it a times because you want a of those molecules there right it's like though you could look at what's the probability of having five heads well you multiply the probability of one heads five times so the forward reaction probability is going to be the concentration of V to the a power and then of course you have to is that's not enough to have the reaction happen you also need to have a B of the X molecules there so you the concentration of X to the B power and I want you to make sure you make sure you understand this this I'm saying or my my step my claim is that this is approximation or actually it's a pretty good way of calculating the probability probably so let me write it this way the rate is equal to some constant that takes into account the temperature and the molecular figurations times the probability of having a V molecules V molecules and and B X molecules in a sufficiently small area all at the same time and the best way to approximate that is with their concentration obviously the higher the concentration the higher the moles per liter the more likely you're going to find and that many of molecules in the in kind of that little small space that you care about in the temperature and the configuration are going to matter more but if you use if you use the concentration as the probability of a if the probability let me switch colors if the probability of having of having a V molecule in some volume if we assume that the solution is is is homogeneous that it's the V molecules are roughly evenly distributed it's going to be this is even approximation it's going to be the concentration of the V molecules times the volume under which we we care about and if we want the probability probability of a so where a is a number it could be five V molecules a V Mott or let me just write AV s in some volume some volume it's the probability of finding of this a times so it's going to be equal to and this is just from the probability from the probability concepts that we learned in the whole probability playlist so if you want it if you want to have five heads in a row it's one-half to the fifth power if you want to have V molecules there five or a you know five of them at the same time in some volume or a of them it's going to be V to the a power times the volume if you also want care about the probability if you also care about the probability so you want all of that so a V's and B X's in some volume well then you're going to multiply all of them together so it's going to be it's going to be equal to the concentration of V to the a power times the concentration of X to the B power times the volume so the probability of finding a finding the right number of V particles and X particles in the right place and some volume is going to be proportional to exactly this and we're saying that the the reaction rate the forward reaction rate is also proportional to this thing so that's where we get the forward reaction rate so the rate forward is equal to the concentration of our V molecules to the a power times the concentrations of our X molecules to the B power now if we want to find the reverse rate so this is the rate forward if we want to find the rate of the reverse reaction rate reverse let's say that that's so cool to some other constant let's call that K - same exact same exact logic olds we're just going in this direction now we're going if we look at our original one we're going in that direction so for this reaction we do the same thing we literally just do different letters so the reverse reaction is just going to be the concentration of the concentration of the Y molecule to the C power because we need C of them they're roughly at the same time times the concentration of the z molecule to the D power now just at the beginning of the video we said that equilibrium is when these rates equal each other I wrote it down right here so if the reverse rate is equal to some constant times this and the forward rate is equal to some constant times that then we reach equilibrium when these two are equal to each other so let me clear up some space here right there let me clear this up - so what are they going to be equal to each other when the forward rate forward rate is this that's our forward constant which took into account a whole bunch of temperature and molecular structure and all of that times the concentration of our V molecule to the a power that you can kind of view that as what's the probability of finding in a certain volume and that certain volume can be factored into that k factor as well but what's the probability of finding V things V V molecules in some volume or or a V molecules in some volume and it's the concentration of V to the a power times concentration of X to the B power that's the forward reaction and that has to equal the reverse reaction so K - times the concentration of Y to the C power times the concentration of Z to the D power now if we divide both if we divide both sides by let me erase some more space nope not with that all right so let's divide both sides by K minus and both sides by this so you get K plus K plus over K minus sorry over K minus is equal to that is equal to Y to the C times Z to the D all of that over that V to the a times X the concentration of X to the B let me put this in magenta just so you know this was this K minus right here and then this these are just two arbitrary constants so we could just replace them and call them the equilibrium constant and we are where they're where we need to be we're at the formula for the equilibrium constant I know this was really hand wavy but I want you to at least get the sense that this isn't this doesn't come from out of the blue and there is at least I think there is there's an intuition here that these are really calculating the probabilities of finding of the this is kind of you can this is the forward reaction rate probability it's proportional to this because the more V concentration you have the more likely you're able to find it although if if you need more of those particles around you have to multiply that that concentration by each other because the probability is going to get a lot lower because you need more of them together in order for the reaction happen same thing for everything there but all this is derived from is that the forward reaction should be equal to some constant times the reverse reaction or actually their rates should be equal but then when you actually calculate the probability you'll have a constant in there anyway hopefully I didn't confuse you but I just wanted to give you that this isn't you know just some random equation it really does I think come from the the reality that the higher the concentration you have the more the probability you have of the actual molecules bumping into each other
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