Unit 5 Lesson 9 Activation energy vs temperature

greetings ap chemistry students want to go over in particular problems two and six on this worksheet here about the steady state approximation just to kind of review things the first thing want to point out is that when trying to determine the rate law you cannot just look at the overall reaction and say hey there's one hydrogen and one bromine so it's first order in hydrogen first order in bromine you can only look at coefficients on elementary steps in reaction so to find the rate law for this reaction we need to direct ourselves to the slow step which is right here and what we'll find is that what we find first is that there's actually problem with this mechanism this should just be br not br2 and that should not be part of that step three it's not going to affect our rate law but it is problem with that mechanism but anyways to find the rate law we need to direct ourselves to the slow step where we can look at the coefficients to get the rate law which would say that rate equals times the concentration of br times the concentration of h2 now this cannot be the rate law for the overall reaction because there's no br there's the bromine diatomic molecule instead this reaction has an intermediate of br it also has an intermediate of we can't have an intermediate in our rate law so we need to go back to the first step this fast equilibrium step where the vr came from and look at it and for that reaction the rate of the forward reaction equals the of the forward reaction times the concentration of br2 and the rate of the reverse reaction equals the of the reverse reaction times the concentration of squared because it's got coefficient of 2 there so this makes for something interesting because what we can do is we set these rates equal to each other and so we get the times the concentration of br2 equals times the concentration of br squared we then want to solve for bromine by itself so we move the kr over to the other side and when we do that we end up with over which will just become another constant and then to get bromine by itself we need to take the square root of both sides this is going to say that the concentration of bromine is going to equal the square root of constant divided by constant which is going to be yet another constant we'll just call that prime and then it's also going to give us bromine the square root of that or to the one-half power so we'll plug all of that in for br up here and so what we get is that our overall rate law is rate equals times the concentration of bromine to the one-half power times the concentration of hydrogen in other words it's half order so if you double the concentration of bromine the rate increases by the square root of two if you quadruple the concentration of bromine the rate would increase by factor of two if you increase the concentration by factor of nine the rate would go up by factor of three and so forth so this is really interesting one where we have fractional orders so if that problem gave you some trouble you may want to pause this video and try this problem number six again and then come back and watch as go through the solution on this one all right so for this one we are going to once again direct ourselves to find the order of the reaction to the slow step where we get that rate equals times the concentration of times the concentration of two that's problem because in the reaction we have b2 and then we have a2 so is an intermediate so we need to go back to step one which is fast equilibrium step and so for that the rate of the forward reaction equals times the concentration of a2 the rate of the reverse reaction equals of the reverse reaction times the concentration of squared at equilibrium the rates are equal so we have times a2 equals times squared we move kr to the other side so that's going to give us kf over kr which is going to just essentially be new constant prime and then we take the square root of those the square root of constant is yet another constant times 2 to the one-half power and that equals so now we will take this and plug it into our rate law for which gives us that rate equals well constant times constant is another constant times a2 to the one-half power times b2 all right so hopefully that helps you out little bit now for our one new piece of information today we're going to look at something called the arrhenius equation this is an equation that you do not need to know mean it is an equation it appeared on your kinetics and crystal violet lab sheet where essentially if you record at different temperatures then if you take the natural log of and versus one over the temperature and you graph them then the slope of the line equals your negative activation energy over but we're not going to actually be doing that the college board doesn't expect you to do that but what they do expect you to be able to notice here is that the temperature dependence of is related to the activation energy in other words if we go back to these graphs right here right the rate of reaction depends on the ability of the molecules to overcome the activation energy barrier in order to have successful collisions and react and the activation energy barrier depends upon the temperature of the molecules in other words how much energy they have because if you increase the temperature then you're going to have more molecules that can overcome this activation energy barrier and so the reaction happens faster and so there if the reaction happens faster then in your rate law has to change because if you consider standard rate law like rate equals times the concentration of for whatever this reaction is the reaction happens faster when the temperature increases and the only way that we can account for that is when you change the temperature the value of itself also changes the temperature goes up gets bigger the temperature goes down gets smaller and so temperature and the value of are related mathematically through that arrhenius equation but that's because of the fact that as you increase the temperature more molecules can overcome the activation energy