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CHEMICAL KINETICS Four factors affect reaction rates Concentration of reactants Temperature of reaction Presence or absence of a catalyst Surface area of liquid or solid reactants Reaction Rates Reaction speed defined as the change that occurs per unit time o It is determined by measuring the disappearance of a reactant or the appearance of a product o The speed of a reaction is the reaction rate For reaction AB : Avg rate = change in the number of moles of B / change in time o B= moles of B at final time- moles of B initial o At t= 0, there is 1 mole of A and no B o At t= 10 min, there is .74 mol A and .26 mol B o At t=20 min, there is.54 mol A and .46 mol B o Avg rate= B/ T= Mol B at 10min- Mol B at 0 min/ 10min –0 min= .026mol/min o Or Avg rate= - Mol A / t ; note the negative sign. It means reactants are disappearing Rates in Terms of Concentration The most useful measure is molarity Since volume is constant, molarity and moles are directly proportional Units for average rate are mol/L sec or M/sec The average rate of a reaction decreases over time. Why? The rate at any specific point in time is the instantaneous rate If we plot the concentration of a reactant vs time, the rate at any instant is the slope of the straight tangent to the curve at that point Stoichiometry For the reaction : C4H9Cl + H2OC4H9OH + HCl Rate= - [C4H9]/t = [C4H9OH] /t What if stoichiometry is not one to one? 2HI H2 + I2 Rate = - [HI]/ 2 t = [H2]/ t = [I2]/ t Generalized : For the reaction aA + bB cC + d D Rate = - [A]/at = - [B]/ b t= [C]/ct = [D]/dt Dependence of rate on concentration In general, rate increases with increased concentration of Reactants and decreases with decreasing concentration We often examine the effect of concentration by measuring the reaction rate at the beginning of a reaction Consider A + B C + D We find that if we hold [B] constant and double [A], the rate doubles. Therefore , the rate is directly proportional to [A]. If we hold [A] constant and double [B], then the rate doubles. Therefore, the rate is directly proportional to [B] The overall concentration dependence is given by the rate law. For this example the rate law is: Rate = k [A] [B] where k is the rate constant Reaction Order For any reaction with rate law: o Rate= k[A]m [B]n, the exponents are called reaction orders. The overall reaction order is the sum of the exponents. o This reaction is first order in[A] and first order in [B] And second order overall Reaction orders must be determined experimentally o They do not necessarily correspond to stoichiometric coefficients o They are typically 0,1 or 2 o However , they can be fractional or negative Units of rate constants Units of the rate constant depend on the overall reaction order For a second order reaction: Units of rate = (Units of rate constant) (units of concentration) (units of concentration) Therefore : Units of rate constant= Units of rate/ (Units of concentration)2= M/sec/M2= M-1 S-1 Using Initial Rates to determine rate laws To determine the rate law, we observe the effect of changing the initial concentrations o If the reaction is zero order, changing the concentration has no effect on rate o If the reaction is first order, doubling the concentration will double the rate( change is directly proportional) What if concentration is halved? o If the reaction is second order, doubling the concentration will result in a 4X increase (22). Tripling the concentration will cause a 9X increase o A reaction is nth order if doubling the concentration causes a 2n increase in rate o The reaction rate, NOT THE RATE CONSTANT, depends on concentration. First order Reaction ln[A]t = -kt + ln[A]0 is the equation for a first order reaction. Note the similarity to y = mx + b. In this case , a plot of ln[A]t vs t yields a straight line with a slope –k and an intercept of ln[A]0 Half-life is the time required for the initial concentration of a reactant to decrease to one half its original value T1/2 = .693/k Note that the half life of a first order reaction is independent of the initial concentration of the reactant Second order reactions 1/ [A]t = kt + 1/[A]0 A plot of 1/[A]t versus t is a straight line with a slope k and an intercept of 1/[A]0 For a second order reaction a plot of ln[A]t is not a straight line T1/2 = 1/k[A]0 Half life is dependent on initial concentration Note that a second order process can have the form : Rate= k[A] [B] . The reaction is second order overall but first order in reactant concentration Temperature and Rate As temperature increases, the rate increases Since the rate law does not have temperature in it, the rate constant must be temperature dependent The Collision Model Rates of reaction are effected by concentration and temperature The collision model, which is based on kinetic molecular theory, explains this o In order for molecules to react they must collide o The greater the number of collisions the faster the rate o If you have more molecules the probability of collision increases and the frequency of collision o Higher temperature ( higher KE ) gives the molecules higher energy and increases the number of collisions(moving faster) o However , not all collisions lead to reaction. Only a small fraction of collisions lead to reaction Activation Energy Arrhenius: molecules must possess a minimum amount of energy to react. Why? o To form products , bonds in the reactants must be broken o Breaking bonds requires energy o Molecules moving too slowly, KE too low, do not react Activation energy, Ea is the minimum energy required to start a reaction o Ea varies with the reaction Consider the rearrangement of methyl nitrile to acetonitrile o Energy is required to stretch the bond between the methyl group and the nitrile group and to allow the nitrile group to rotate o The carbon carbon bond forms o The energy associated with the molecule drops o The energy level between the starting molecule and the highest energy state found along the reaction pathway is the activation energy. The chemical species at the top of the barrier is the activated complex or the transition state The energy change for the reaction is the difference in energy between the products and the reactants o Erxn has no effect on reaction rate The activation energy is the difference in energy between the reactant and the activated complex. o Rate depends on activation energy. The lower Ea , the faster the reaction How does this relate to temperature o At any particular temperature, molecules present have an average kinetic energy associated with the population o In the same population , some molecules have more energy than average , some have less. The fraction of molecules with energy equal to or greater than Ea is given by f = e-Ea/RT As we increase temperature, f becomes larger Orientation Factor Orientation has a major effect on whether or not a reaction will occur Consider the reaction between NOCl and Cl Cl + NOCl NO + Cl2 If the Cl collides with the Cl the reaction proceeds If the Cl collides with the O, no reaction occurs Arrhenius Equation Arrhenius discovered that most reaction rate data obeys an equation based on 3 factors o Number of collisions per unit time o Fraction of collisions with the correct orientation o Fraction of molecules that have energy greater than or equal to Ea lnk = -Ea/RT + ln A where k is the rate constant, Ea is the activation energy, R is the gas constant(8.314J/Kmol) T is the temperature in K A is the frequency factor. It is related to the frequency of collision and the probability that the orientation will be correct Both A and Ea are specific to a reaction Rearranging the equation we get lnk = -Ea/RT + lnA. Once again , if you graph the lnk vs 1/T you get a straight line with a slope –Ea/R Reaction Mechanisms Balanced chemical equations provide information about substances present at the beginning and end of a reaction The reaction mechanism is the process by which the reaction occurs Elementary Steps Any process that occurs in a single step The number of molecules present in an elementary step gives the molecularity o Unimolecular-one molecule o Bimolecular- two molecules o Termolecular- three molecules A multistep mechanism consists of a series of elementary steps o Elementary step must give a balanced reaction o Some multistep reactions include intermediates Species that appear in an elementary step but not as a product or reactant Intermediates are formed in one elementary step and consumed in another They are not found in the balanced equation for the reaction Rate Laws for Multistep Reactions Rate laws of the elementary steps determine the overall rate law Rate law of the elementary step is determined by molecularity o Uni- processes are first order o Bi- processes are second order o Ter- processes are third order Most reactions have more than one elementary step o Often one step is much slower o This step limits the reaction rate and governs the rate law Consider: NO2 + CO NO + CO2 The experimentally derived rate law is : rate = k[NO2]2 A proposed mechanism is o Step 1 : NO2 + NO2 NO3 + NO slow o Step 2 : NO3 + CO NO2 + CO2 fast Note NO3 is an intermediate The rate law for the slow step is rate = k[NO2]2 This theoretical rate law is in agreement with the experimental This supports(does not prove) a proposed mechanism Mechanisms with an initial fast step Consider the reaction 2NO + Br2 2NOBr The experimentally determined rate is : Rate = k[NO]2 [Br2] Proposed Mechanism o Step 1 : NO + Br2 NOBr2 fast o Step 2 : NOBr2 + NO 2NOBr slow o The theoretical rate law for the slow step is : rate = k2 [NOBr2] [NO] Problem: this rate law depends on the concentration of an intermediate o Intermediates are usually unstable and have low/unknown concentrations o We can express [NOBr2] in terms of NOBr and Br2 by assuming an equilibrium in Step 1 o In a dynamic equilibrium the e forward rate equals the reverse rate Therefore we get k1 [NO] [Br2] = k-1[NOBr2] Rearranging : [NOBr2] = k1/k-1[NO] [Br2] Substituting in the rate law : rate = k2 k1/k2 1[NO] [Br2] [NO] = k[NO] [Br2] This is consistent with the experimental rate law Catalysis A catalyst is a substance that changes the rate of a reaction without undergoing a permanent change There are 2 types of catalysts : homogeneous and heterogeneous Homogeneous Catalysts A catalyst that is present in the same phase as the reactants How do catalysts increase rates? o By lowering the activation energy o Increasing the number of collisions o Catalysts provide a completely different mechanism for reaction Heterogeneous Catalysts A catalyst that exists in a different phase from the reactants. Ie. Solid catalyst and gas reactants: the catalytic convertor on a car