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Physical Chemistry Thermodynamics and Kinetics Rates Reaction Thermodynamics and kinetics Thermodynamics Physical Chemistry Observe relative stability of states Energy differences Static comparisons of states Lecture 4 Kinetics Introduction to chemical kinetics Observe changes of state over time Several different topics Empirical description of the rate of reaction Determination of experimental parameters Microscopic theories Rates Reaction velocity A chemical reaction is described by an The rates of appearance of products and equation of the type disappearance of reactants are related by 1 stoichiometry of the reaction H() gas O () gas H O ( liquid ) 2222 Define the reaction velocity, v, in terms of Rates: “normalized” rates of appearance of products and disappearance of reactants Rate of change of [H2O]: d[H2O]/dt Rate of change of [H ]: d[H ]/dt 1 di[] 2 2 v Rate of change of [O ]: d[O ]/dt 2 2 i dt Rates related by the overall equation Example of the production of water: 1 oxygen molecule disappears for every 2 dH[]dO []dHO [ ] hydrogen molecules in the above reaction v 222 2 dt dt dt Rate laws Order Describe of how reaction velocity depends on In many situations, one may write the functional parameters such as concentrations, form of the reaction velocity approximately as vkABC [][][]abc temperature, pressure, etc. a, b, c are the orders of reaction under the vfABTP ([react ],[ prod ], , ) conditions examined May be simple or complex Many reaction velocities are more complicated functions than the simple one above Gives insight into the manner in which the Example: Production of HBr over a wide range reaction occurs 12/ [][]HBr22 Reactions do not necessarily occur in the manner vk HBr []HBr indicated by the overall reaction equation 1 k' []Br2 Orders are often determined over a limited range Initial order of reaction Differential method of Determining initial order determining order Calculate approximate derivatives as ratios of Measure initial velocity as a function of the differences for specific concentrations amount of reactants in the mixture Plot approximate derivatives versus concentration Example: OCl- + I- OI- + Cl- [OCl- ] [I-] [OH-] Initial velocity ln(v) k nln(C) 0.0017 0.0017 1.00 1.75 10-4 0.0034 0.0017 1.00 3.50 10-4 0.0017 0.0034 1.00 3.50 10-4 0.0017 0.0017 0.50 3.50 10-4 Concentrations are in mol dm-3. Rate is mol dm-3 sec-1. By comparison, one finds the initial rate Example: Decomposition of di-tert-butyl peroxide equation Line slope = 1.04 1 vinitial k[OCl ][I ][OH ] Order with respect to DTBP is close to 1 under these conditions (and probably is 1) Integrated rate laws - first order in a reactant First-order rate law For simple chemical reactions, integrate the Example: rate laws to determine decomposition of di- how the reactant dA[] v kA[] tert-butyl peroxide dt 1 concentration changes slope -k with time 1 First-order rate law [At ( )] [ A (0 )] exp( kt1 ) Rate constant for Exponential in time this reaction is Linear form is the ln [At ( )] ln [ A (0 )] kt1 determined to be logarithm -1 k1 = 0.0193 min from the slope of the line Reactant or Product? First-order Product What if one can only Example: First-order Rely on conservation of matter measure a product reaction [B(t)] [A(0)] [A(t)] concentration with A B [A(0)] [A(0)]ekt time? Then Sometimes one can kt d[B] d[A] [A(0)] (1 e ) derive an equation for the product dt dt Rearrange to find the linear form concentration with Can solve for the [A(0)] [B(t)] time concentration of B ln( ) kt exactly [A(0)] Integrated rate law – second order in reactant (Case I) Second-order rate law Second-order rate 1 dA[] 2 Example: law may be v kA[] 2 dt 2 integrated Collision-induced decomposition of Linear plot of 11 diacetylene, DA 2 kt2 1/[A(t)] versus t [At ( )] [ A (0 )] Hou and Palmer, Often see reported 1965 rate constant for 1 Linear plot of [DA]-1 kt disappearance of A [()]A 0 eff versus t k = 2 k 7 eff 2 keff = 6.79 x10 Exercise caution in cm3/mol-sec assessing reported rate constants Integrated rate laws for other Second-order rate law reactant orders (Case II) A + B Products Integration gives a Previously considered general form for all Homomolecular v k [A][B] orders (except 1) reaction ( A + A) 2 d[A] d[B] v The power of the 1 If other species dt dt [A(t)] [A] x [B(t)] [B] x function of affected reaction, 0 0 concentration linear they were held dx 1 k [A] x [B] x 1 constant dt 2 0 0 in time is related to 0 [A(t)] [A] order of reaction for Consider second-order ln ln 0 [B] [A] k t [B(t)] [B] 0 0 2 the conditions under heteromolecular 0 which the system is Second order overall . Does not work for observed First order in each [A]0 = [B]0 reactant Determining kinetic Half life parameters Can describe time First order Two conceptual steps dependence in several Find parameter proportional to concentration different ways ln 2 Find appropriate function of time to allow Rate constant, k t1/ 2 evaluation of time course Half life, t , time for one 1/2 k Phase Parameter often measured Parameter needed half of reactant to Gas P, total pressure Pi, partial pressure of disappear Second order reactant Other times that describe Total optical absorption Absorption of a single the amount left 1 component Solution Total conductance Conductance of a single t1/2 component k [A(0)] Total volume Volume change of a eff single component Titration Concentration of a single component Summary Chemical change quantified by the mathematics of chemical kinetics Rate constant and order characterize a reaction Determining rates and velocities Differential method Integrated-rate-law method Results often limited to a particular time scale or situation Initial reaction With some materials in excess.
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