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# Chapter 14 Chemical Kinetics.docx

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School
McMaster University
Department
Chemistry
Course
CHEM 1AA3
Professor
Pippa Lock
Semester
Winter

Description
Chapter 14: Chemical Kinetics Rate of a Chemical Reaction  The rate of reaction describes how fast the concentration of a reactant or product changes with time  Rate of formation o  Rate of disappearance o  Given the general equation aA + bB  gG + hH o The rate of reaction is o In this expression, we take the negative value of [X]/t, when X refers to a reactant to ensure that the rate of reaction is a positive quantity  Ex. A  2G o Average rate =  Rates are always positive Measuring Reaction Rates  Following a chemical reaction o Ex. H 2 2aq)  H O2l) + 1/2O (2) o We can follow the progress of the reaction by focusing either on the formation of O 2g) or on the disappearance of H2 2  Measure the volumes of O (g)2produced at different times and relate these volumes to decreases in concentration of H2 2  Remove small samples of reaction mixture from time to time and analyze these samples for their 2 2 content  One way to do this is by titration with KMnO4in acidic solution  Rate of reaction expressed as concentration change over time o When the rate of reaction is expressed as -[H O 2 2t, the result is an average value for the time interval t  Rate of reaction expressed as the slope of a tangent line o Graph time vs. [H O2 2and determine the slope of a line tangent to the graph o The rate of reaction determined from the slope of a tangent line to a concentration-time curve is the instantaneous rate of reaction at the point where the tangent line touches the curve  Initial rate of reaction o The initial rate of reaction is the rate of reaction when the reactants are first brought together (rate when t = 0)  Given by v0 o This rate can be obtained from the tangent line to the concentration-time curve at t = 0 o An alternative way is to measure the concentration of the chosen reactant as soon as possible after mixing, in this way obtaining [reactant] for a very short time interval at essentially t = 0  If average rate = o Instantaneous rate =  Experimental rates are always average rates  To approach instantaneous rates experimentally, use short measurement times and measure rates near t = 0 Effects of Concentration on Reaction Rates: The Rate Law  The rate law or rate equation is an equation that can be used to predict the relationship between the rate of reaction and the concentration of reactants  Consider the reaction aA + bB  gG + hH o We can express the rate of this reaction as m n o Rate of reaction = k[A] [B] o The terms [A] and [B] represent reactant molarities o The required exponents (m, n) are generally small, positive whole numbers, although in some cases, they may be zero, fractional or negative o They must be determined by experiment and are generally not related to stoichiometric coefficients  The term order is related to the exponents in the rate law and is used two ways o If m = 1, we say that the reaction is first order in A and if n = 2, the reaction is second order in B and so on o The overall order of reaction is the sum of all the exponents (m + n + …)  The proportionality constant k relates the rate of reaction to reactant concentrations and is called the rate constant of the reaction  Its value depends on the specific reaction, the presence of a catalyst and the temperature  The larger the value of k, the faster a reaction goes  The order of the reaction establishes the general form of the rate law and the appropriate units of k  With the rate law for a reaction we can o Calculate rates of reaction for known concentrations of reactants o Derive an equation that expresses a reactant concentration as a function of time  Methods of initial rate o If a reaction is first order in one of the reactants, doubling the initial concentration of that reactant causes the initial rate of reaction to double o General pattern of doubling the initial concentration of a particular reactant  Zero order in the reactant – there is no effect on the initial RoR  First order in the reactant - the initial RoR doubles  Second order in the reactant – the initial RoR quadruples  Third order in the reactant – the initial RoR increases eightfold o The order of a reaction, as indicated through the rate law, establishes the units of the rate constant k  If on the left side of the rate law the rate of reaction has the units M/time, on the right side the units of k must provide for the cancellations that also lead to M/time Zero-Order Reactions  An overall zero-order reaction has a rate law in which the sum of the exponents is equal to 0  Ex. A  products o If the reaction is zero order, the rate law is 0 o Rate of reaction (v )0= k[A] = k = constant  Other features of the zero-order reaction are o The concentration-time graph is a straight line with a negative slope o The rate of reaction, which is equal to k and remains constant throughout the reaction, is the negative of the slope of this line o The units of k are the same as the units of the rate of reaction (M s )-1  Another useful equation, called the integrated rate law, expresses the concentration of a reactant as a function of time o Starting with the general equation for a straight line, y = mx + b o Substitute y = [A] tconcentration of A at some time t), x = t (time), b = [A] 0initial concentration of A at time t = 0) and m = -k (slope of negative line) o [A] t -kt + [A] 0  For a zero-order reaction, half life decreases with decreasing reactant concentration  Examples of zero-order reactions o Evaporation/sublimation with constant surface area o Pseudo zero-order reactions  Reactions where catalyst is saturated with reactants (drug/alcohol mechanism) First-Order Reactions  An overall first-order reaction has a rate law in which the sum of the exponents is equal to 1  V =0k[A]  Characteristics of k o Constant regardless of concentration o Depends on identity of reactants, temperature, catalyst and solvent  A particularly common type of first-order reaction is one in which a single reactant decomposes into products  Ex. H O2 2q)  H O (2) + 1/2O (g)2  The rate of reaction depends on the concentration of H O ra2 2d to the first power o Rate of reaction = k[H O2 2  An integrated rate law for a first-order reaction o or o Because the logarithms of numbers are dimensionless (no units), the product –kt must also be dimensionless -1 o This means that the unit of k in a first order reaction is time  The half-life of a reaction is the time required for one-half of a reactant to be consumed  It is the time during which the amount of reactant or its concentration decreases to one- half of its initial value o T = t , [A] = ½[A] 1/2 t 0 o The integrated rate law takes the form o ( ) o o The above equation is only valid for first-order reactions  The equation indicates that the half-life is constant for a first-order reaction  Regardless of the value of [A] atothe time we begin to follow a reaction, at t = t , [1/2= ½[A] 0  After two half lives, t = 2 X t1/2[A] = ½ X ½[A] 0 ¼[A] 0  At t = 3 X t , [A] = 1/8[A] etc. 1/2 0  Reactions involving gases o For gaseous reactions, rates are often measured in terms of gas pressures o Ex. A (g)  products, the initial partial pressure, (P A 0nd the partial pressure at some point t, (P A t are related through the expression o  Examples of first-order reactions o Radioactive decay  Ex. Radioactive isotope iodine-131 Second-Order Reactions  An overall second-order reaction has a rate law with the sum of the exponents equal to 2 2  Rate of reaction = k[A]  Integrated rate law o o If plot 1/[A] tver time, the slope of the line is k and the intercept is 1/[A]0  The units for k are M t-1 -1  Half life for a second order reaction is given as o T 1/2= 1/k[A]0 o The half life depends on both the rate constant and the initial concentration o The half life is not constant o Its value depends on the concentration of reactant at the start of each half-life interval o Because the starting concentration is always one half that of the previous half- life, each successive half-life is twice as long as the one before it  Ester hydrolysis o Esters are synthesized from carboxylic acids and alcohols o Esters are broken down by hydrolysis nd o A 2 order reaction which becomes very slow as the reactants are depleted  Pseudo-First-Order Reactions o A second order reaction that is made to behave like a first order reaction by holding one reactant concentration constant is called a pseudo-first-order reaction o We can treat the reaction with the methods of first-order reaction kinetics o Ester hydrolysis  Run reaction in dilute aqueous acid  Change in [H O2 is negligible  Reaction appears to be first order  Behaves like v = k[ester] Reaction Kinetics: A Summary  To calculate a rate of reaction when the rate law is known, use the expression rate of reaction = k[A] [B] n  To determine a rate of reaction when the rate law is not given, use o The slope of an appropriate tangent line to the graph of [A] vs. time o The expression -[A]/t, with a short timer interval t  To determine the order of a reaction, use one of the following methods o Use the method of initial rates if the experimental data are given in the form of reaction rates at different initial concentrations o Find the graph of rate data that yields a straight line o Test for the constancy of the half-life (only good for first-order) o Substitute rate data into integrated rate laws to find the one that gives a constant value of k  To obtain the rate constant k for a reaction, use one of the following methods o Obtain k from the slope of a straight-line graph o Substitute concentration-time data into the appropriate integrated rate law o Obtain k from the half-life of the reaction (only good for a first-order reaction)  To relate reactant concentrations and time, use the appropriate integrated rate law after first determini-ktk o [A] =t[A] ·oe o [G] =t[A] (o-e )-kt Theoretical Models for Chemical Kinetics  Collision Theory o Only a fraction of collisions among gaseous molecules lead to a chemical reaction o For a reaction to occur following a collision between molecules, there must be a redistribution of energy that puts enough energy into certain key bonds to break them o The activation energy of a reaction is the minimum kinetic energy that molecules must bring to their collisions for a chemical reaction to occur  The higher the activation energy, the smaller is the fraction of energetic collisions and the slower the reaction o Another factor that can strongly affect the rate of reaction is the orientation of molecules at the time of their collision  In a reaction in which two hydrogen atoms combine to form a hydrogen molecule no bonds are broken and a H-H bond forms  The H atoms are spherically symmetrical and all approaches of one H atom to another prior to collision are equivalent  Orientation is not a factor and the reaction occurs about as rapidly as the atoms collide  Orientation of the colliding molecules, however, is a crucial factor in the reaction of N2O and NO  The fundamental changes that occur during a successful collision are that the N-O bond in N 2 breaks and a new O-N bond is established to the NO molecule  As a result of the collision, the molecules2N and NO2are formed  Transition State Theory o In a theory proposed, special emphasis is placed on a hypothetical species believed to exist in a transitory state that lies between the reactant and the products o This state is called the transition state and the hypothetical species, the activated complex o The activated complex, formed through collisions, either dissociates back into the original reactants or forms product molecules o In a reaction profile, energies are plotted on the vertical axis against a quantity called “progress of reaction” or simply reaction progress on the horizontal axis
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