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# UCCS CHEM 1010 - CHEMICAL KINETICS

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CHEMICAL KINETICSCHEMICAL KINETICS Chemical KineticsKinetics is the study of how fast chemical reactions occur. There are four important factors that affect rates of reactions:1. reactant concentration2. temperature3. catalyst4. surface areaReaction RatesSpeed of a reaction is measured by the change in concentration with time. Suppose A reacts to form B. For the reaction A B there are two ways of measuring rate:1. the speed at which the products appear (i.e. change in concentration of B per unit time), or2. the speed at which the reactants disappear (i.e. the change in concentration of A per unit time). average rate = change in concentration of B or A =  [ B] = - [ A] time required for this change  t  tThe units for average rate are mol/L.s or M/s.1The rate at any instant (instantaneous rate) is the slope of the tangent to the curve ( r =-d[A]/dt Instantaneous rate is different from average rate.We usually call the instantaneous rate the rateReaction Rates and Stoichiometry In general for aA + bB c C + dD rate = - 1 d[A] = - 1 d[B] = 1 d[C] = 1 d[D] a dt b d t c d t d d tDependence of Rates on ConcentrationIn general, rates increase as concentrations increase.For the reaction:NH4+(aq) + NO2-(aq) N2(g) + 2H2O(l)we note :as [NH4+] doubles with [NO2-] constant, the rate doubles,as [NO2-] doubles with [NH4+] constant, the rate doubles.We conclude rate  [NH4+] [NO2-]Rate law:Rate = k[NH4+] [NO2-]The constant k is the rate constantNote that the rate constant k does not depend on concentration.2For a general reaction with rate law:Rate = k[reactant 1]m[reactant 2]nwe say the reaction is mth order in reactant 1 and nth order in reactant 2.The overall order of reaction is m + n A reaction can be zeroth order if m, n are equal to zero.Note the values of the exponents (orders) have to be determined experimentally. They are not simply related to stoichiometry. The Change in Concentration with TimeFirst-Order ReactionsGoal: convert rate law into a convenient equation to give concentrations as a function of time.Consider the hypothetical reaction:A BFor a first order reaction, the rate doubles as the concentration of a reactant doubles. Therefore: rate = - d[A] = k[A]dt 1n[A]t - 1n[A]0 = - kt. Rearranging:1n[A]t = - kt + 1n [A]0 A plot of 1n[A]t versus t is a straight line with slope -k and intercept ln[A]0Half-life3Half life is the time taken for the concentration of a reactant to drop to half its original value. That is, half life, t1/2 is the time taken for [A]0 to reach 1/2[A]0Mathematically: ln [A]t = - kt [A]0 So for t = t1/2 and [A]t = 1/2[A]0, 1n 1/2[A]0 = - kt1/2. [A]0 1n 1/2 = - kt1/2. Therefore: t1/2 = - 1n 1/2 = 0.693 . k k Second-Order ReactionsFor a second order reaction, Consider the hypothetical reaction:A BRate = - d[A] = k[A]2 . dt Integrating gives 1 = kt + 1 . [A]t [A]0 A plot of 1/[A]t versus t is a straight line with slope k and intercept 1/[A]0For a second order reaction, a plot of 1n[A]t vs. t is not linear.We can show that the half life is:t1/2 = 1 k[A]0 Temperature and RateMost reactions speed up as temperature increases. (e.g. food spoils when not refrigerated.)4 As temperature increases, the rate increases. Since the rate law has no temperature term in it, the rate constant must depend on temperature.The Collision Model Goal: develop a model which explains why rates of reactions increases as concentration and temperature increase.The collision model: in order for molecules to react they must come into direct contact via collosion and must possess a minimum kinetic energy to reactThe greater the number of collisions the faster the rate.Complication: not all collisions lead to products. In fact, only a small fraction of collisions lead to product.Activation EnergyArrhenius: molecules must posses a minimum amount of energy to react. Activation energy, Ea, is the minimum energy required to initiate a chemical reaction .In order to form products, bonds must be broken in the reactants.Bond breakage requires energy5Example:Consider the rearrangement reaction of the conversion of methyl isonitrile CH3NC to methyl acetonitrile CH3CN. 6As the temperature increases the bond bends until the C-N bond breaks and the NC portion is perpendicular to the H3C portion. H3C N CH3CCN H3C C NThis structure is called the activated complex or transition state.The energy required for the above twist and break is the activation energy, Ea.Once the C-N bond is broken, the NC portion can continue to rotate forminga C-C N bond. The change in energy for the reaction is the difference in energy between CH3N C and CH3C N. The activation energy is the difference in energy between reactants, CH3NC and transition state. In order for reaction to occur the reactant molecules must collide with enough energy in the correct orientation to form products. Consider the reaction between Cl and NOCl:If the Cl collides with the Cl of NOCl then the products are Cl2 and NO.7If the Cl collided with the O of NOCl then no products are formed. We can qualitatively explain the various influence of concentration and temperature on the rate of reactions based on collosion model:Effect of Concentration:The more molecules present, the greater the probability of collisions and the faster the rate.Effect of TemperatureThe higher the temperature, the more energy available to the molecules and the faster the rate.8The Arrhenius EquationArrhenius discovered most reaction-rate data obeyed the equation: k = Ae-Ea/RTk is the rate constant, Ea is the activation energy, R is the gas constant (8.314 J/K-mol) and T is the temperature in KA is called the frequency factor.A is a measure of the probability of a favorable collision.Both A and Ea are specific to a given reaction.Ea can be determinedand graphically :1n k = - Ea + ln A RT Or Ea can be determined if the rates of chemical reactions are known for two given temperatures:1n k1 = Ea 1 - 1 k2 R T2 T1 Reaction MechanismsThe reaction mechanism gives the path of the reaction ; or the process by which a chemical reaction occursMechanisms provide a

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