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# PhysicalChemistry CHM453

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This 50 page Class Notes was uploaded by Mrs. Kiara Medhurst on Thursday October 29, 2015. The Class Notes belongs to CHM453 at Wright State University taught by PaulSeybold in Fall. Since its upload, it has received 45 views. For similar materials see /class/231123/chm453-wright-state-university in Chemistry at Wright State University.

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Date Created: 10/29/15

PHOTOCHEMISTRY The excited states of molecules are in effect new species with different charge distribu tions and possibly different geometries The FranckCondon principle states that electronic transitions are so fast that the nuclei remain fixed in position during the transition The transition moment for the transition depends on the overlap of the vibrational wave functions of the ground and excited states The principles of photochemistry First principle Grotthus 1843 and Draper 1843 Light must be absorbed to cause photochemical change Second principle Stark and Einstein 19081912 Usually a molecule absorbs a single photon of light in becoming excited Note With intense modern lasers multiphoton processes can easily be observed The Jablonski Diagram Radiative transitions are indicated as solid lines and nonradiative transitions as dashed lines S 39Ic 12 51 i 5 Ici F P 1 ISC so t i v39 Key Abs absorption F fluorescence P phosphorescence IC internal conversion ISC intersystem crossing SternVolmer Quenching of Fluorescence Fluorescence quenching is presumed to occur via diffusion of a quencher Q to the excited molecule F There is a competi tion between fluorescence nonradiative decay and quenching F gt F hv fluorescence k F nonradiative decay km F 0 gt F Q quenching kq In the absence of quencher the fluores cence quantum yield is 130 klkf km and the fluorescence lifetime is To 1kf km 0 With quencher Q i kkf kI1 kqQ and If 1Ikf kn kqQ Taking inverses and multiplying by the unquenched terms ProPf 1 TokqQ tf ltf 1 TokqQ So one plots either Mk1f or moltf vs 0 to get a straight line with slope proportional to kq If To is known you can get kq A SternVolmer plot Quencher concentration 0 Example Quenching of fluoranthrene fluorescence by potassium iodide ie by l39 at several temperatures J Naibar and M Mac J Chem Soc Faraday Proc 87 1523 1991 in methanolethanol solutions rs m Fig l Siem Volmer plan for uoranihene and K as a quencher at 394 K19 308 K x320 K 4 328 K 003 c mol dm Ultrafast Spectroscorav 0 Modern techniques allow laser pulses as short as 5 femtoseconds fs 1015 s o The pumpprobe technique is commonly used pump a powerful laser pulse that starts the reaction probe a weaker delayed pulse that monitors the reaction 0 Note that a pulse can be delayed by moving a greater distance Usually the starting pulse is split by partially mirrored surfaces to give the delayed probe pulse sample delayed pulse Since light travels at 3x10a quot18 a PUISE tfaVeling just an extra 105 m will arrive 33 fs later Ultrafast Studies at CalTech 0 Ahmed Zewail and his coworkers have carried out a number of interesting studies Firstorder reaction Break up cyanogen iodide ICN by pumping at a frequency that shatters the lC bond Watch the molecule come apart over 200 fs Secondorder reaction HI and 002 form a weak complex in a molecular beam Pump into the HI so the H atom is shot at the 002 The reaction H C02 gt HO CO occurs taking about 5 ps Molecular vibrations Study l2 molecules A vibration takes about 300 femtoseconds Molecular rotations Use polarized pulses to follow rotations lasting 600 picoseconds Ultrafast Spectroscopy at the Univ of CalifSan Diego Dou las Ma de s research rou uses a continuous Argon laser to pump a titanium sapphire laser for fluorescence excitation Ar quoteq laser dOUbler a photomultiplier and photoncounting source pulse 4 electronics detector The Tisapphire laser produces 50100 fs pulses at 7 800 nm This is then frequency doubled to 400 nm using a lithium borate crystal This latter light excites the sample The repetition rate is 832 MHz giving about 12 ns between pulses A part of the pulse is picked off to set the time clock Photon Counting for Fluorescence Lifetimes The basic idea is to excite a dye sample with a flash so weak that only rarely will fluorescence photons be emitted Suppose that only 1 in 10000 flashes leads to a detect ed fluorescence photon If there are 83 million flashessec in 200 secs this will give 17x106 detected photons The emitted photons with their times after the exciting flash are recorded on a multi channel analyzer This uses a timeto amplitude converter TAC with 1024 time bins or channels A decay might look like the following This signal can be analyzed on a computer One can use an exponential fit or several exponentials to determine the time decay pattern No of photons time Chemical Timing 0 Work by D Dolson C Parmenter and co workers at Indiana University See Chem Phys Lett Q 360 1981 lntramolecular Vibrational Redistribution If a specific vibration is excited in an isolated molecule the energy will be redistributed to other vibrations of a time of the order of tens of picoseconds IVR This might be studied using ultrafast elec tronics but the technique is difficult Dolson et al used chemical timing to study NE in pfluorotoluene pFT Qg mols Quench the fluorescence of pFT so that only molecules that emit quickly can fluoresce The fluorescence spectrum from the fast emitting pFT molecules found with 02 added shows vibrational structure indicating that IVFl has not yet occurred With no added 02 the pFTmolecules redistribute the vibrenergy before they fluoresce Theories of Reaction Rates There are two maior theories for the determination of reaction rates Collision theory TransitionState theory 0 Both theories attempt to explain the details of the form roughly k Ae39E RT of the rate constant for bimolecular reactions For many reactions of atoms and radicals with small molecules the preexponential factor A is about 1010 1o12 Lmols Collision theom is based on the kinetic theory of gases The basic assumption is that molecules must collide in order to react 0 Transitionstate theom also called absolute reaction rate theory and activated complex theory assumes that the reaction passes through a transition state activated complex in going from reactants to products The Collision Theory of Reaction Rates I Recall that the kinetic theory gives the upression below for the rate of collisions her unit volume between species A and B ZAB d 2 lanNANB from this the rate constant should have the form k 7 dAB 28kBTIIJ12 his is the rate for simple hardsphere collisions Here is hogadro s number dAB is the collision diameter k3 is Boltzmann s constant and p Is the reduced mass of A and B Several different units are commonly used Concentration k in litersmolesecond SI units kln malmols Other kin emsmolecules common in gasphase work But of course things are more complicated than this The reaction rate should depend on the energies of the collisions the relative orientations of the species A and B during the collision These factors can be difficult to take into account L Collision Theory Cont How can we treat the energy dependence Work with the reaction cross section 0 Constant 6 Assume an Use a more value activation energy complicated form energy a Eu energy 9 gt energy a gt Results km 202kTvru l2 W kT c39T12eaokT Note not Arrhenius CTW1EokTe39E kT Note that we assume a MaxwellBoltzmann distribution of velocities e 12uv2 in deriving the expressions for the rate constant 0 Note that the exponential dependence on T is much stronger than the dependence of A on T1quot 50 the exact dependence is hard to detect experimentally 0 Often collision theory gives higher values than observed suggesting steric effects occur Collision Theory cont Some typical bimolecular rate constants Rate Coefficients for SecondOrder GasPhase Reactions According to k Ae EGRT for R in J Kquot mol 1 Reaction Ratc Coef cient mol L39 s l 112 I2 AZHI 1X 101 Ie IevoooRr QHI H I7 11 6X lolne ls4000mn 2N0Z gt2NO 02 45 X 1098 112500RT ZNOCI 2NO l C12 9 X 109e 1000RT NO Cl2 gt NOC Cl L7 X 1096 51000027 II i39C3 gtNO2 02 8X1088 10500ckn CH3IHI CH4 12 16x lone monoclmn ZCZF4 a yCIO C4F8 6396 X 1076 108OOOIRT ZCZH4 gt cyclo C4H8 71X 1076 1580001RT Unusual applications of collision theory Zooplankton predatorprey behavior Rotifer mating behavior Statistical Mechanics We start with severeiguestions What is tatistical Mechanics about m and by whom was it developed What mathematical tools do we need 0 What do we need to know about statistics to work with this material 0 What is a normal distribution Whoor whatis Maxwell s demon o What is the Boltzmann distribution law and how can it be derived What is a MaxwellBoltgmann distribution of molecular speeds What is a gartition function and what s it good for How is statistical mechanics used to calculate reaction rates Wh is this subject called sadistical mechanics The Early Historical Development of Statistics 0 Roman numerals I V IX were hard to work with There was no zero 0 The earliest known work using Arabic arithmetic was by alKhowarizmi ca 825 30 He used Hindu numbers including the zero The term algorithm comes from his name In 1202 Leonardo Pisano Fibonacci published Liber abaci the Book of Calcula tions introducing the advantages of the HinduArabic numbering system to the West G Cardano introduced the modern notion of probability in 1545 o In 1654 the Chavalier de M r challenged Biaise Pascal to solve a puzzle regarding a game of chance Pascal and Pierre Fermat 39 worked together to develop the theory of probability Girolamo Cardano 15011576 Italian Physician and Mathematician In 1545 he published his great book Ars Magna The Great Art describing solutions to quadratic and cubic equations and introducing the square roots of negative numbers later called imaginary numbers 0 His book Liber de Ludo Aleae Book on Games A R T13 M A G NE of Chance was the first SIVE DB REGVLIS A BRAICIS Libtmus Qui ctoa39us open dc 39 cu aquod serious attempt to l a describe the statistics of probability He was the first to define probability as the ratio of favorable outcomes to the total number of out comes Blaise Pascal 16231662 3 French physicist mathematician and theologian A child prodigy he published a book on the geometry of conic sections at the age of 16 with many original discoveries Pascal s triangle gives binomial coefficients 1 3 3 1 1 4 6 4 1 1 5 1O 10 5 1 0 In 1654 after a nearly fatal accident he turned completely to religious writing He is noted for his Divine gamble Basic Statistics The basicguestion is What is the probability of a certain thing happening 0 We need to determine how many ways the thing can occur and compare this with the total number of possible outcomes The classic situation is that there are i objects taken n at a timeeg one might draw five cards n 5 from a deck of 52 cards N 52 or throw a die N 6 three times n3 0 Questions to ask 1 Are the events n independent 2 Is the order of the events important 0 How can we determine the total number of possible outcomes Independent events Wm Nn N choicesmevents Example Choosing a number between 0 and 999 Wm 10x10x10 1000 Dependent events Exampledrawing cards from a deck wtot NN1N2 Nn1 N Nn For 5 cards Wtot 31187x108 Statistics cont In many cases the order is not important eg in drawing cards How do we correct for this How many ways can the five cards n 5 be arranged 540321 120 n differentorders first card So the number of different hands order not important is W N 52 2598960 Nnn 475 0 Probability P Number of desired outcomes Total number of outcomes Ex Flush in hearts all hearts after drawing 5 cards P P1P2P3P4P5 wall heartswtotal ix12xuxmxg 13111135 13x47 52 5150 49 48 5211525 8x52 495x10394 z 5 chances in 10000 13135 5 z 1287 52525 5 2600000 More Statistics Examples Royal straight flush AKQJ10 all in the same suite There are four suites clubs hearts spades diamonds so there are just four such hands So P 42598960 one chance in 649740 Qoin tossing A man named Kerrich was interned in Denmark during World War II He tossed a coin 10000 times and got 5067 heads and 4933 tails Sex ratios at birth France 18001802 Laplace 110312 boys and 105287 girls ie 512 boys England in 1956 514 boys in different regions it ranged from 512 to 517 In rural districts of Dorset it ranged from 38 to 59 effect of small sample sizes The probability of having the same birthday The question What is the probability that two or more people in a group will have the same birthday Approach First calculate the probability PNo that there are no matches Then determine the probability of a match as PYES 1 PNO PNO 1 364365363l365362l365 Thus with just one person PNo is 1 For two people PNo 364365 since there are 365 days in the year and only one posible day that matches the first birthday Add a third person and there are 363 days that don t match and so on Result Calculation shows that the probability of a match changes from just under 50 to just over 50 in going from 22 PYES 0476 to 23 people PYES 0507 in the group With 40 people PYES 89 Twochoice Problems and Binomial Coefficients We often face twochoicngroblemsnflipping coins heads or tails a box divided into two equal parts left or right etc The possible outcomes can be understood in terms of the binomial coefficients which are the coefficients that appear in the expan sion of x yquot For example x y4 x4 4x3y 6x2y2 4xy3 y4 The binomial coefficients are 1 4 6 4 and 1 0 If you flip a coin 4 times there are 24 16 possible outcomes The binomia coefficients tell you how many outcomes cogespond to each specific result If x heads y tails one all heads four 3h1 t six 2h2t four 3t1 h one all tails The probability of 2h2t is therefore P2 616 0375 etc Pascal s Triangle Can Help Consider a box with two equal sides llow will n molecules divide b etween the two sides 39 Again the binomial left right coefficients tell the results Use Pascal s triangle to get them 1 molecules M 1 1 1 212 1 2 1 2 234 1 313 1 3 238 1 4 6 4 1 4 2416 151010 51 5 2532 1 615201561 6 2664 1 7 2135 35 2171 7 27128 1 8285670 56 2881 8 23256 Thus 8 molecules have 256 different micro scopic ways to divide themselves between the two sides 70 of these have 44 P44 70256 g Binomial Coefficients Consider tossing a coin n times and observing the numbers of heads h and tails t 0 The order is not important but we would like to predict the expected number of heads and tails The total number of different ordered outcomes in 5 throws is 25 32 Only one of these is no heads ttttt So the the probability of no heads is 132 0 There are five different ways to throw one head so the probability for this is 5x132 By the same reasoning there are 10 ways to throw 2 heads 10 ways for 3 heads 5 ways for 4 heads and just one way for 5 heads 0 In general there are n ways to arrange n objects so the number of different ways of finding x successes in n trials is n x n x o The probability of x successes in n trials is Px n PxQnx xnx The Normal Distribution The binomial coefficients approach a normal distribution in the limit of a large number of trials or objects Also called a Gaussian distribution or bellshaped curve For a random variable x with an averaqe mean value m and standard deviation 6 the probability distribution fx is fx 1lo27texpxm2l202 I I Probability Density Function of the Normal Distribution For a normal distribution 683 of the results fall within is of the mean 954 within iZG and 997 within i 30 Chemical Kinetics Thermodvnamics can describe the final equilibrium position but not how fast this situation will be achieved 0 Chemical kinetics is the science of the rates and mechanisms of chemical reactions 0 For a general reaction aAbB gtcCdD the rate is defined as 1dA1 1dB 1dC 1dD adt b clt c dt d dt The rate law for a reaction expresses the dependence of the rate on the concentrations of the reactants What does the reaction rate depend on The rate of a chemical reaction depends on five features of the reaction 1 The nature of the reactants For example ionic reactions may be very fast breaking strong bonds may cause a slow reaction 2 The effective concentration of reactants 3 The temperature Most reactions go faster at higher temperature 4 The presence of a catalyst Usually a catalyst speeds up a reaction A good example enzymes 5 The phase of the reaction Solid liquid and gas phase reactions occur Rate law expreSSions For some reactions the rate law can be expressed in the simple form rate k AmBn where k kT is the quotrate constantquot for the reaction The exponents m and n are the orders of the reaction with respect to reactant A and B respectively The overall order of the reaction is m n 0 It is important to understand that the rate law expression comes from experiment It is not necessarily related to the stoichio metric expression for the reaction 0 Note that kWill vary with temperature The units of k will depend on the order of the reaction Many reactions cannot be described by the simple rate law expression above The rate law expression can help us to decide upon the mechanism of the reaction First Qrder reactions The rate law expression for a firstorder reaction is A kA dt 0 Examples include nuclear decays some isomerizations and some decompositions 0 To integrate the rate law expression we rearrange it quotAI k dt A Thus idAA k idt Integration from A10 to A and 0 to t yields IniAi mm kt So that A Aloekt Cabin14 Dating First proposed by the American chemist Willard Libby Univ of Chicago in the 1950s Awarded the Nobel Prize in Chemistry 1960 Cosmic rays striking nitrogen atoms in the Earth s atmosphere cause the reaction 14N n gt14C H The 14C becomes incorporated into C02 which in turn is taken up by living plants 0 The 14C decays by firstorder kinetics 14C gt 14N e with a halflife of 5730 yr 0 So long as the plants are alive a steady state of 14C incorporation and decay is main tained but upon death uptake of HC ceases The E of an artifact can be estimated by measuring the relative amount of 14C in the sample Good for moo50000 yr Carbon has several isotopes with the following abundances and halflives Lotone Abundance Halflife Decay carbon9 01265 5 3 20c carbon10 192 5 3 carbon11 2038 min 3 carbon12 9889 stable carbon13 111 stable carbon14 ppm 5730 y 339 carbon15 2449 s 3 carbon16 075 s B Since x xoekt we can calculate the age from the ratio xxo The halflife is given by 39 t12 In 2k so k ln2t12 05935730 y 121x1O4ly Thus t nxlx0k Consider a sample that exhibits 63 of the 14C radioactivity of a fresh sample Then t Eln063l121x103y 3820 y Other Dating Technigmes Uranium238 has a halflife of 45x109 years 238U decays through several intermediates to form lead206 206Pb Assume that rocks start with only 238U and no 206Pb Then measure the ratio of 238UZO in Analysis of this gives the age of the rock your assumption is correct Note that normal lead is lead208 which will be present if other processes caused lead in the rocks Potassiumar on datin of rocks When 4 K decays to 40Ar in rocks the 40Ar is trapped Potassium40 has a halflife of 125x109 years Assuming all the 40Ar detected comes from 40K decay one can date a rock sample Some other methods Thermoluminescence fission track dating amino acid racemization etc FirstOrder decay The halflife is the time it takes for one half of the initial material to disappear It is given by t12 A10 A f Al2 l Al4 l l A8 O N 0 t12 2 12 3 12 t To derive the t12 formula plug in A 05A0 and solve for t 0 For a firstorder decay the halflife is independent of the starting time o The most useful way to plot the data for this case is nA vs t nA nA nA0 kt slope k Catalysts Term due to Jons Jacob Berzelius in 1836 He examined the following studies Added at speeds the conversion of starch to sugar Kirchoff 1812 Decomposition of H202 to 02 increases in the presence of metals such as Ag Au Pt and Mn Thenard 1818 Oxidation of alcohol to acetic acid is speeded up by finely divided platinum Reactlon H2 and 02 gt H20 is increased by Pt Sulfuric acid speeds up the conversion of alcohol to ether 0 In Chinese Tsoo Mei marriage broker Definition A catalyst speeds up the rate of a chemical reaction without being consumed or produced But it obviously enters into the reaction in some way 0 Great Economic Importance of Catalysts 1939 data U 5 catalyst sales 19 billion world sales 5 billion total value of fuels and chemicals produced with catalysts was 891 billion 17 of US GDP Petrole fn industry cracking and refining Auto emission controls catalytic converters Polymerizations making plastics Chemicals production Enzymes Great Events in Catalysis 1850 Ludwig F Wilhelmy 18121864 measured the rate of hydrolysis or inversion of cane sugar in acid solution by polarization He found dZdt kZA where A acid This was the first math formulation of a rate 1909 Fritz Haber employed an iron catalyst to sythesize ammonia from nitrogen gas and hydrogen gas fixing nitrogen Tested more than 1000 materials before settling on iron During World war l this allowed Germany to continue the war and produce explosives after imports of saltpeter from Chile were cut off It revolutionized agriculture by making fertilizer cheaply Haber won the Nobel Prize in 1919 Haber a German patriot was forced to leave Germany in 1933 by the antiJewish policies of the Nazis 1913 Michaelis and Menten describe enzyme mechanism 39 19181922 lrving Langmuir at General Electric Co studied solid surface catalysis eg 2C0 02 gt 2C0 rate k02lCO Catal sts cont 0 Two main types of catalysts Homogeneous in a single phase Heterogeneous two phases at interface the chemical industry pursues research on heterogeneous catalysis with great vigor protecting successful catalysts with blankets of patents and cloaks of secrecyquot W C GardinerI Rates amp Mechs of Chem Reactions 0 A catalyst speeds up the rate of a reaction but does not change the equilibrium position 0 A common picture is that a catalyst lowers the activation barrier for the reaction by providing a new path Substances that slow down reactions are called inhibitors Poisons are contaminants that destroy catalystic activity Auto Catalytic Converters 0 First used in US cars in 1975 0 Technical problems Exhaust gas contains N2 H20 02 C02 802 and traces of lead and phosphorous Temp may be gt 600 C Gas contact time is just 100400 ms Engines and fuels need to be adjusted to fit w converters Early catalytic converters removed hydrocarbons and carbon monoxide Platinum and palladium are placed on beads with a large surface area to catalyze CnHquot1 02 gt H20 CO CG 02 gt co2 Less than 01 oz of platinum spread over about 150000 beads per converter In 1981 stricter standards caused rhodium to be added to reduce NOX Also Ce oxide Lead eg as in tetraethyl lead poisons the catalysts therefore lead was removed from gasoline Reactions in Solution How do reactions in solution differ from those in the gas phase Reaction intermediates F 39quot8quotf The cage effect Encounters vs collisions Diffusioncontrolled reactions Solvent influence dielectric effect Effect of ionic strength Reactions in Solution I The presence of a solvent can greatly influence a reaction Reaction intermediates may be different Gas phase reaction intermediates are often free radicals but in solution ions are often present as intermediates The solvent may slow down diffusion of both reactants and products 0 The cage effect refers to the influence of surrounding solvent molecules on reactions It can speed up or slow down reactions reactants once they reach each other and are caught in a solvent cage cannot escape each other encounters vs colllsions products once they form cannot easily escape and may recombine Ultrafast studies of the cage effect Zewail and coworkers studied the dissocia tion of I2 in molecular beams using femto second pump probe techniques Nature m 427 1993 They excited two different states of l2 excitation at 614 nm breaks I2 up very rapidly 2 250 fs and the l atoms move apart with high speed but excitation at 510 nm dissociates l2 more slowly 2 15000 fs via an intermediate state They added 40150 argon atoms to form solvent clusters around the la molecules At 614 nm the separating l atoms bounced off the walls of the argon solvent cage and recombined to lg Energy was lost through collisions with the solvent and the I returned to its ground state At 510 nm the argon atoms had time to adjust and the excited I dissociated to form free I atoms Recent experiments by others on l239 show that 6 Ar atoms are enough to form a cage and cause recombination of the l2quot Science June 97 Svante August Arrhenius 18591927 0 Child prodigytaught himself to read at age 3 PhD thesis at Uppsala University on electrolyte solutions It was not well received Copies sent to some leading workers includng Ostwald Ostwald saw the value of the idea Arrhenius joined with Ostwald and van t Hoff to further develop the idea of ionic solutions In 1887 Arrhenius suggested that electrolytes dissociate to form ions in solution Publ in Z phys Chemie In 1889 he published his classic study of the 39 effect of temperature on reaction rate In effect he concluded that kT A expCT Won the Nobel Prize in Chemistry in 1903 He had ideas on many other subjects including the greenhouse effect and the theory that life came to the Earth via spores from space Tengerature Degndence of Reaction Rates 0 Reaction rates depend on temperature in a number of different ways any 5 cl Temperature gt Reaction rate gt Arrhenius considered eight sets of data from the scienti c literature to show that for many reactions kT A eAEkT I Here A is the preexponential factor and AE is the energy of activation for the reaction 0 The normal way to plot data for a reaction thus would be to plot lnk vs 1T to get a straight line The negative slope gives the activation energy and the yintercept gives lnA Ink TABLE 151 Rate Constant as a Function of Temperature for the Reaction in Ethanol CH3 CszOH CH30C2H5 H 2 C k2 mol L 1 0 560 X 10 5 6 118 12 245 18 488 24 100 30 208 SOURCE From W Hecht and M Conrad Z Phys Chem 3450 1889 396 l l 7 FIGURE 153 The Arrhenius plot of Eq 157 8 for the data of Table 151 The straight line is represented by In k 9840T 2622 or n k 9 81800RT In 24 x 10quot W Thus E 81800 and A 24 X 10quot molL squot 0 I I I 00033 00034 00035 00036 00037 IT Kquot Reaction Mechanisms An pigmenng reaction is a molecular event a reaction that takes place on the molecular scale These reactions may be unimolecular bimolecular termolecular rare For an elementary reaction the stoichio metric equation and the rate law expression agree For example for A B gt C Rate k AB bimolecular Generally macroscopic reactions involve several elementary steps Thus the stoicio metric equation and the experimentally determined rate law expression do not agree 0 A ction mechjanism is a set of elementary reactions proposed to be responsible for the observed overall reaction The mechanism must be consistent with the observed rate law expression Elementary Reactions An elementary reaction is a molecular event a reaction that takes place on the molecular level 0 Because these are molecular events the rate laws for elementarv reactions obey the stoiciometries of the reactions Recall that for overall chemical reactions which may involve a number of elementary reactions the rate law forms are determined by experiment Example For a bimolecular elementary reaction A B gt products the rate law would be rate V kzA1B1 Kineticists refer to the molecularity 9L elementary reactions unimolecular a single molecule reacts bimolecular two molecules collide termolecuar three molecules interact Bimolecular reactions are by far the most common Reaction Mechanism Example 0 Consider the reaction 2H2 a N2 0 This does not take place by a collision of two NO and two H2 molecules a very unlikely event 0 The observed rate law is Rate kH2N02 thirdorder overall 0 One proposed mechanism 1 H2 2N0 gt N20 H20 slow 2 H2 N20 N2 H20 fast Reaction 1 would be the ratedetermining step thus setting the rate law It is a rare 3molecule collision Another proposed mechanism 1 2N0 gt N202 2 N202 H2 gt N20 H20 slow N20 H2 gt N2 H20 Reaction 2 is the ratelimiting step From reaction 1 N202 is proportional to N02 39 AnotheLexampJe Consider the reaction H24 21c1 a 12 2Hc1 The observed rate law is Rate k H21c1 A possible mechanism is 1 H2 ICl gt HI HCl slow 2 HI ICl a HCl I2 fast Again the ratelimiting step here 1 sets the rate law expression Consecutive reactions Consider the reaction sequence A gt B gt C Depending on the relative rates for the two steps the concentrations of the three species might change as shown below l ollllll 09 Concentration changesforthe sequential reaction A gt B gt C 08 07 06 C 05 04 03 Concentration 02 01 0 L l 10 20 30 40 50 60 7O 15 0 For a sequence of reactions such as A gt B gt C gt D the slowest step in the sequence is the ratelimiting step The reaction can t go faster than its slowest step 0 Many nuclear decays follow sequences such as the above Q 235U gt 239Np gt 239Pu The first halflife is 235 min the second 235 days Competing Reactions 0 One frequently encounters competing reactions B o The total decay rate constant for A is the sum of the two decay constants k k1 k2 The concentration of A decays exponentially as A Aoe39k The rates compete so the path with the higher rate constant is more productive The relative yields are g k1 A Q k2k1 k2 kz kw The concentrations of both B and C rise as ki 1e39k but the one with g the larger ki dominates 39 time Kinetic Control and Thermodynamic Control Consider the reversible39situation with two competing reactions K C Initially the path from A with the highest ki will dominate kinetic control but eventually at equilibrium the path with the higher equilibrium constant K kilki will dominate thermodynamic control Example Suppose the relative rates are k1 10 k1 001 K1 100 k 01 k2 00005 K2 200 Initially B will be formed at 10 times the rate of C but in the long run since C is the more stable product twice as much C as B will form

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