in chapter 15 we're going to learn about chemical kinetics now chemical kinetics basically means the movement of the molecules with respect to time how fast is the reaction curring occurring and reaction rate so what is the reaction rate the reaction rate is the speed of the reaction and it could be measured by the concentration change of either the products or the reactants because as the as the reaction goes forward reactions or reactants are going to decrease and they're going to form products which will then increase so here's a very simple reaction where you have reactant a yields reactant B it changes to another substance now if you look at the reactant and product concentration percentages in terms of total moles in the sample you can see that as the reactant a is being removed from the sample meaning as it's being converted to product B the concentration percentage of the entire entire solution equals 100% as it decreases as reactant gets turned over to product at the exact same time product B is increasing so we see this kind of decrease of the reactants increase of the product so this chapter we're going to learn how we can Define this and use and mathematically figure it out as a term of in marity per second that's really going to be the main unit marity per second so how fast does the concentration change so we can Define the rate as being the change in concentration over change in time now for reactants that rate is always going to be expressed negatively because the change in the reactant concentration is always going to decrease as the reaction goes forward this means the rate is going to be the negative of the change in concentration of the reactant over the change in time whereas for the product it's going to be positive because you're going to be creating more product as the reaction goes forward now here's just you can look at this um just a schematic of what happens when you have a slow reaction versus a fast reaction and we're going to be able to calculate how fast the reaction is what we just talked about now another way you can determine the rate of reaction based on concentration of products and concentration of reactant curves is with in a function of time is by using a little bit of calculus and calculating the T line so the tangent line at a certain point would give you the slope at that point and the slope is going to be your rate of change right so the slope is the change in your Y versus your change in X in this graphical context the change in y is going to be your concentration in marity so marity and then your change in X is going to be your time so marity per second and that's another way graphically if you're given a graph you can figure out the reaction rate of either the products increasing or the reactants which would be decreasing and something you might be thinking of is how does the reaction rate change based on the coefficients that are in a balanced equation that's a good thought but we'll talk about that more later and there's equations that govern that as well so to calculate the average rate you can just say you can do a linear approximation of a curve so let's say we looked at the curve up here and we want to determine the average rate of the reaction from let's say 30 seconds all the way to 80 Seconds right we would take the two points 30 and 80 and do the change in y over the change in X and we'd have a slope put going from uh 30 seconds to to 80 Seconds and that would be a decent approximate I mean if you go the larger the time interval the worse approximate it is but overall rate it would tell you but there's a better way to represent this rate because look it's constantly changing over time and that's based on what order of a reaction it is so we can talk about that more in a few slides now the instantaneous rate that was the average rate where you take two points but the instantaneous rate can be figured out by a derivative so we're not going to talk about derivatives in this class that's calculus which you already hopefully had but basically it's a slope at the tangent line so at a specific point on a curve what is the slope of that point so that's how you can figure out the instantaneous rate now here is a very important equation this can relate the coefficient of the reactants and the products to their reaction rate or to their concentration change and to the rate of the entire reaction so let's look at this reaction H2 plus I2 equals 2hi now what's happening a lot of this happening so let's read this bold statement every mole of I2 used needs to form two moles of hi so it forms twice the amount of product in the same amount of time time because once this is completely removed once the one Mo once the one mole is gone the two moles will be completely formed meaning this process of the reactants decreasing and the products increasing happens in the same amount of time this means that the rate at which hi forms per mole meaning the concentration increase has to be double the rate of The Disappearance of I2 in order for it to catch up to so basically saying the time that one mole of I2 is removed or it goes away is the same time that two moles of hi need to be made therefore the reaction rate or the change in concentration of hi is double so um that can be represented and we can actually talk about the rate of the entire reaction in terms of the rate of disappearance of reactants or appearance of a product so for this example or for any example you'd have the rate equals let's say you had reactants A and B and products C and D the rate would be one over the concentration change of a over the time and then it would be negative and then for the products it would be positive right because the products are being formed so you can take some time to think about that now here's a conceptual question for the reaction a + 2 Bal C under the given set of conditions the initial rate of the reaction is .1 m m per second what is Delta B so what is the change in concentration of B over time so B is being removed right it's a reactant therefore it must be negative so it's either a b or c and let's just let's write this down let's write down what we know based on the equation we just saw is that the initial rate of reaction is 0.1 molar per second and this can be equal to one over the coefficient of B we'll call it little B times the concentration of B over the change in time but we already know that we already know the coefficient so we can just figure out the what is the Delta B over delta T so the coefficient of B is two so put a two there multiply two by both sides we get 0.2 molar per second is the change in concentration of B over time now it has to be negative because B is a reactant so the answer is C okay so I'm going to skip these for now this is a brief overview of the chapter so skip those let's talk about the um one of the main one of the two main factors that contributes to the reaction rate one of which is the concentration of reactants so you can imagine based on what we learned in chem 1 where we talk about the speed of molecules leading to more collisions we're going to learn more about that today is that the speed of the molecules actually and the amount of molecules can actually determine the rate and actually increase the rate in some cases so the general rate law we talk about is rate equals K times the concentration of a to the N power so n is called the order so whether that order has to do with the coefficients but just talk about it as the order and K is the rate constant so it's usually per second or per minute in this case where a yields a certain amount of product so the rate of a reaction is dependent on the concentration of reactants but it gets a little bit more complicated there's different orders of equations so n is this order now we can talk about order and for an example if we have our rate equals K times in some reaction that's not written here um n o or it would be 2 N plus O2 then our reactants it would be n^2 plus the concentration of or times the concentration of O and our exponents meaning there's a one here our exponents added up would equal the order of the reaction so order of the rate law so a very uh key component if you don't want to get too crazy with this add up the exponents for the rate law that determines the order of the rate law very important because a lot of questions will be asking you to figure out the rate law and what can this what can knowing the rate law tell you it can tell you that if the rate law is zero order meaning this n this n is zero that means the rate law the rate is just based on K this turns to one the a concentration of a to the N is becomes one and then rate equals K so what that means is if you double the concentration of a nothing will happen to the rate nothing will happen more products will be made but the rate at which they're produced will be identical so it'll be basically a straight line until the reaction is done then it becomes zero if it's first order meaning this is a one here what that means is the rate is directly proportional to the reactant concentration so if you double a rate doubles if it's second order meaning n is two or the sum of the coefficients of this reactant and another reactant are two that means the rate is directly proportional to the square of the reactant concentrations meaning if you double a you'll quadruple the rate of the reaction so there's actually a lot of equations that are we see Zero order first order and second order so here's how they look graphically speaking the rate of concentration of reactants versus time where the concent zero order the reactants just decrease linearly first order they decrease and then they slow the decrease slows down as concentration decreases and then for n equals 2 the rate slows down faster because you're having you're it's you're more related you're more uh dependent on concentration and then the rate of product being a rate of rate versus this is concentration this is the rate of the reaction versus the reactant concentration so zero order doesn't matter what the concentration of reactant is it's flat if you have an increasing concentration for first and second order the rate of the reaction would increase but in different manners by one is exponential and one is linear so here's a more another conceptual question for particular reaction in which a equals products doubling the concentration of a causes the reaction rate to double what order is the equation is the reaction so if it if doubling the concentration causes the rate to double not quadruple or not change at all but to double than its first order so how can we determine initial rates so we can determine these rates from uh data from data tables that are presented to us or we can use the integrated rate laws so there's a lot of questions on the homework relating to using the experimental data where we just do concentration 2 minus concentration one over time two minus time one which I mean we can do that but those are pretty simple but the rate laws are what we want to get after now there's going to be a whole set of rate law equations for zero order first order and second order but you do not need to memorize them I would say you need to be familiar with them and be familiar with the units because the units for the rate constant for the zero order first order and second order are different so for a first order rate law we'll do the easiest one first what we have is that the rate equals K times the reactant concentration to the one the integrated rate law how does that how do we figure that out we integrate this basically if you do the integral and the derivation for it is right here so I'm not going to go over the derivation but here's a link to it you integrate that and then you TR try to solve for um make it linear so you can do y equals this is kind of yal MX plus b you can calculate that the natural log of a equals KT where negative K is the slope of the resulting graph plus the natural log of the initial initial concentration of a so again we don't need to memorize this but it is the first order rate law integrated rate law so what we can say is is that like I said the graph of the natural log of a over time is a straight line and the slope is K based on this yal MX plus b so maybe so it's important to understand what the rate law means and the Y intercept is going to be the natural log of a initial so you can figure out the initial concentration um in that reaction for if if you know it's a first order rate law so what this means is that the rate constant is going to be in per second because you have the rate is going to be marity per second so here's what A first order integrated rate log looks like where natural log of the initial concentration of a is the Y intercept next so a reaction A to B has experimentally determined to be second order so think about that second order you automatically think all right I double the concentration of the reactant I quadruple the rate law so what we say the initial rate is 01 marity per second at an initial concentration of a equals 0.1 okay so the rate of the reaction is 01 at an initial concentration of a of 0.1 what is the initial rate at 0.5 okay so we can calculate this the initial rate is 0.01 and and this is going to equal since it's a second order it's going to equal the rate constant times the concentration of a squared so that means our 0.01 is going to equal K 0.1 squared we can use this to solve for our rate constant and then we can use that number to figure out the initial rate at a equals .5 mol so our 0.1 squared is 0.1 so we have K * 01 equal 01 this means K is equal to 1 so if that's the case if our initial rate is 0.5 so we have K time 0.5 squared equals our rate then we know K is 1 we can just say that. 5^ 2 * 1 is .5 SAR so 0.25 and that's going to be our rate so that would be our [Music] answer okay so you can also determine the rate law when there's multiple reactants and there's an overall order right is you add up the exponents now here's a question you can say that this reaction was experimentally determined to be first order with respect to o 2 and second order with respect to n o sometime most of the time they follow the uh coefficients actually but if you're stuck you can try that but not all the time the diagrams shown here represent reaction mixtures in which the number of each type of molecule represents its initial concentration which molecule is the fastest initial rate so if it's second order with respect to n this means that the more n o there there is the faster the rate will go it has more dependency on n o than it does for o so if we look here O2 there's three and three here there's more o2s and here there's more no o so therefore the one with the more no O's will go faster because the rate law has more of a dependence on two because it's just or on n o because it's no squar the concentration of no SAR times the concentration of o2 so it look like that all right now we can talk about second order so second order you have a bunch of different equations again which will be given in the derivations right here so the rate is your your K constant your rate constant times the reactant squar now what we can say is linear if once you integrate that you get 1 over aals kt+ 1/ a initial so using this rate law this integrated rate law we can determine the concentration we can determine the rate constant if given the initial concentration and then the a specific point concentration we can at a time we can determine the initial concentration we determine a lot of things basically Al solving for the unknown but what we can see from this is that it follows another y mx plus b in that the graph of one over the concentration of a over time has a straight L straight slope and the slope equals positive K this time and the Y because there a a positive slope the Y intercept is one over the a initial and it can be used to determine the rate constant and you can get the T half life from that so we're going to talk about half life in a minute half life basically means the time it takes for the concentration to have and it depends on the rate constant and it depends on the initial concentration for second order and and zero order does actually doesn't doesn't for for first order and in this case the K the rate constant for you the rate constant unit is going to be per mole per second so it's actually written in 1 over Ms like this 1/ Ms there is a second order integrated rate law and then we could talk about the zero order integrated rate law now in this case it has a constant reaction rate because if you look the rate constant equals or the rate equals the rate constant there's no dependence on concentration of a so on we integrate this it's pretty easy we can see it's a very simple linear equation that the concentration of a Depending on time the slope will be negative K again if it's just the graph of a versus time plus the initial concentration which is the Y intercept now think about it you're thinking about oh my God is all these equations what do I do if you see the equation be able to unravel it be able to to tell me which type of graph is linear in this case it's not there's no natural logs there's no one over it's just straight up the graph of the concentration of a versus T is going to be linear with the slope of negative K and the Y intercept of a initial that is very valuable information and then what you can say is to calculate the halflife meaning the time it takes for half of the initial concentration to be gone you can turn a concentration of a into 1 half of concentration of a initial and then solve for a initial or solve for sorry solve for T and then you would get the initial concentration of a over 2K again this will be given as well but even if it's not even if just the integrated rate law is given you should be able to determine halflife by setting a to a initial over two and then solving for T in this case in zero order the rate is what we're more used to in marity per second because it's identical the rate is equal to the rate constant so duh of course they're going to have the same units in the other cases we didn't have the same units we had one overs and we had natural logs so it was a little bit different so here's an the idea of halflife where the after every halflife half of the original concentration is now removed so here's a question the image images shown here depict the first order reaction A to B at various times during the reaction process the black circles represent a and the red circles represent product B what is the halflife so the halflife we want to see is all right this is initial concentration count how many there are and see which image are there exactly half and then what time is that image so let's see this 1 2 3 4 5 6 7 8 nine 10 so where are there five 1 2 3 4 five 6 1 2 3 4 five all right T equals 90 so 90 is the half life here's another one A first order reaction A to B has a half life of 25 minutes if the initial concentration of a is.3 what is the concentration of B after 50 minutes this one you have to think a little bit so I'll walk you through it if the half life is 25 minutes and initial concentration is.3 let's go through some half lives one halflife one I'll put h l is going to give you 0.15 five that's after 25 minutes now if you keep reading the question it says what happens to B after after 50 minutes let's figure out what happens to a after 50 minutes so 50 minutes is two half lives so after 50 minutes to HL we have 0.075 mol okay so if this is a simple first order a to B this means if you double the concentration of a you double the concent double the rate and a makes B every mole of a makes one mole of B so there's no it's very straightforward this means that whatever of a is removed it will become B it will be turned over into B and make that reaction happen so by two half lives we have the final a remaining is 0.075 so how much B is remaining we know that the total amount in the vessel or wherever the reaction occurs is 0.3 so 0.3 minus what's left over is how much got converted to to reactant or to product B which would be 0.225 mol so that's how that would work so here's a summary on the different rates for zero order first order and second order here you have the rate law the unit for K the integrated rate law the straight line slope graph and then the half-life equation so you can see how the half-life of of uh the first order doesn't is the only one out of is the only one that doesn't depend on the initial concentration of the reactant it's just the natural log of two which is 693 over K and here's just a summary of the kinetics we learned about and this is just part one of the video we can part two we're going to start talking about the effect of temperature which is the second important variable relating to reaction rate