Half-Life of ReactionsDeriving Rate Law from the Rate-Determining StepRate Law Derived from Mechanism with Slow First Elementary StepRate Law Derived from Mechanism with Slow Second Elementary Step:Rate = k2Keq[NO]2[O2] = k[NO2]2[O2]; (where k = k2Keq)Correlating Reaction Mechanism with Rate LawHomogeneous CatalysisHeterogeneous CatalysisCHAPTER 12 - CHEMICAL KINETICSChapter Summary:- The expressions of rate of reaction and types of rates;- Stoichiometric relationships between the rates of appearance or disappearance of components in a given reaction; - Determination of rate orders and rate law using the kinetic data of a reaction;- The graphical method to determine a first-order and second-order reaction.- The meaning and calculation half-life of a first order reaction;- Determination of the activation energy, Ea, either graphically or from rate constants at different temperatures.- Derive rate law from reaction mechanism.- The role of catalystChemical Kinetics is the study of reaction rates; that is, how fast a given reaction does proceeds. It is ameasure of the change of the concentration of reactants (or products) as a function of time.Reaction rates provide information regarding how fast a chemical process occurs as well as the mechanism bywhich a reaction occurs at molecular level.12.1 Reaction Rates The rate of reaction is a measure of the change in concentration of reactants or products over time. Rate can be measured at the beginning of the reaction, which is called the initial rate, at any point in time while the reaction is in progress, called instantaneous rate, or over an interval of time, which is the average rate.In the initial rate the change in concentration of a reactant or product as a function of time is measuredwithin minutes (or seconds) the reaction starts. Determination of the dependence of initial rate to theconcentrations of reactants allows one to derive the rate law for the reaction. A rate law is a mathematicalequation that shows the dependence of reaction rate to the molar concentrations of reactants at constanttemperature.The instantaneous rate is calculated from the slope of a tangent drawn at any points on the graph ofconcentrations versus time. The slope of tangent taken at the initial point of the graph is assumed to be equalto its initial rate.The average rate of reaction is obtained by dividing the change in concentration of a reactant or productthat occurs over a longer period of time by the time interval that the change occurs. For example, consider thefollowing reaction at 300oC:2 NO2(g) - 2 NO(g) + O2(g)If in the first 150 seconds, the concentration of NO2 has decreased from 0.0100 mol/L to 0.0055 mol/L, theaverage rate for the disappearance of NO2 for first 150 s under this condition is, t][NO-2 = s 150mol/L) 0.0100 - mol/L (0.0055- = s 150mol/L 0.0045 = 3.0 x 10-5 mol/(L.s) Suppose that in the next 150 seconds the concentration of NO2 decreases from 0.0055 mol/L to 0.0038 mol/L. The average rate during the second 150 s period is t][NO-2 = s 150mol/L) 0.0055 - mol/L (0.0038- = s 150mol/L 0.0017 = 1.1 x 10-5 mol/(L.s)1The average rate is the mean of several instantaneous rates taken over a period of time. Note that instantaneous rates of a reaction decreases as time progresses as the concentrations of reactantsdecrease. Then the average rate taken over a longer period would have a smaller value compared to thosetaken over a shorter period after the reaction begins. How is the rate of reaction measured?The rate of reaction may be determined by measuring the rate of disappearance (decrease in concentration) of one of the reactants or the rate of formation (increase in concentration) of a product. For example, in the reaction:2 NO2(g) - 2 NO(g) + O2(g)Various expression of rate can be derived, such asRate1 = t][NO-2; Rate2 = t[NO]; or Rate3 = t][O2The stoichiometric relationships between the different rates are as follows: t][NO-2 = t[NO] = t][O22That is, in this reaction the rate of appearance of NO is the same as the rate of disappearance of NO2, but double the rate of appearance of O2.Exercise-1:1. For the reaction: 2N2O5(g) - 4NO(g) + O2(g) (a) write the rate expression in terms of (i) the disappearance of N2O5; (ii) the formation of NO; (iii) theformation of O2. (b) What are the stoichiometric relationships of the various rates for this reaction?2. For the reaction: 5 Br-(aq) + BrO3-(aq) + 6 H+(aq) - 3 Br2(aq) + 3 H2O(l);(a) write the expressions of rates in terms of (i) the disappearance of Br-; (ii) the disappearance of BrO3-,and (iii) the formation of Br2. (b) What are the stoichiometric relationships of the various rates for thisreaction?___________________________________________________________________________12.2 Rate LawsConsider a general reaction: A + B - CThe rate law is expressed as, Rate = k[A]x[B]y, where k is the rate constant; x and y are the rate orders with respect to individual reactants. The rate orders x and y are not related to the reaction coefficients. Their values must be experimentally determined from a set ofkinetic data. For example, the rate law for reaction: 2 N2O5(g) - 4 NO(g) + O2(g), is Rate = k[N2O5]That is, the rate of the decomposition of N2O5 is first order with respect to [N2O5], which means that the ratewill double if [N2O5] is doubled; it will triple if [N2O5] is tripled.2For the reaction: 2 NO2(g) - 2NO(g) + O2(g), the rate law is Rate = k[NO2]2. That is, the rate of the decomposition of NO2 is second order with respect to [NO2]. Therefore, the rate willquadruple if [NO2] is doubled.The reaction: 2 HI(g) - H2(g) + I2(g) is found to be a zero order reaction in the presence of gold catalyst. For this reaction, the rate is independent of [HI].12.3 Determination of the Rate LawMethod of Initial RatesFor many chemical reactions, the expression of rate law contains only the concentrations of reactants,while the concentrations of products do not appear. However, for some reactions that are reversible, theconcentration of products may be part of the rate law. To simplify the rate law and avoid the complication thatmight be contributed by products in reversible reactions, the measurement of rate for rate law determination isnormally done at the moment the reactants are mixed. At this point, we can also assume that the effect ofproduct concentration is