# CHBE 551 Lecture 20

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04-Jan-2016Category

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### Transcript of CHBE 551 Lecture 20

CHBE 551 Lecture 20 Unimolecular Reactions*

Last Time Transition State TheoryTransition state theory generally gives preexponentials of the correct order of magnitude.Transition state theory is able to relate barriers to the saddle point energy in the potential energy surface;Transition state theory is able to consider isotope effects;Transition state theory is able to make useful prediction in parallel reactions like reactions (7.27) and (7.29).*

Transition State Theory Fails For Unimolecular Reactions*

Table 9.8 The preexponential for a series of unimolecular reactions, as you change the collision partner. Data of Westley[1980].reactionk0 when X = Argonk0 when X = Waterk0 when X = N2NO2 + X OH + H + X1.7 1014 cm6/mole2 sec6.7 1015 cm6/mole2 sec1.57 1015 cm6/mole2 secH2O + X OH + H + X2.1 1015 cm6/mole2 sec3.5 1017 cm6/mole2 sec5.1 1016 cm6/mole2 secHO2 + X O2 + H + X1.5 1015 cm6/mole2 sec3.2 1016 cm6/mole2 sec2 1015 cm6/mole2 secH2 + X H + H + X6.4 1017 cm6/mole2 sec2.6 1015 cm6/mole2 secO2 + X 2O + X1.9 1013 cm6/mole2 sec1.0 1014

Why Does Transition State Theory Fail?Ignores the effect of energy transfer on the rateConsider a stable molecule AB. How can AB A + BIf you start with a stable molecule, it does not have enough energy to react.Need a collision partner so AB can accumulate enough energy to react.Energy accumulation ignored in TST*

Lindeman ApproximationAssume two step processFirst form a hot complex via collission Hot complex reacts

Steady State Approximation Yields

*

Comparison To Data For CH3NC CH3CN*

But Preexponentials For Unimolecular Reactions Too Big*

Table 9.8 The preexponential for a series of unimolecular reactions, as you change the collision partner. Data of Westley[1980].reactionk0 when X = Argonk0 when X = Waterk0 when X = N2NO2 + X OH + H + X1.7 1014 cm6/mole2 sec6.7 1015 cm6/mole2 sec1.57 1015 cm6/mole2 secH2O + X OH + H + X2.1 1015 cm6/mole2 sec3.5 1017 cm6/mole2 sec5.1 1016 cm6/mole2 secHO2 + X O2 + H + X1.5 1015 cm6/mole2 sec3.2 1016 cm6/mole2 sec2 1015 cm6/mole2 secH2 + X H + H + X6.4 1017 cm6/mole2 sec2.6 1015 cm6/mole2 secO2 + X 2O + X1.9 1013 cm6/mole2 sec1.0 1014

Why The Difference?Bimolecular collision lasts ~10-13 secMolecule must be in the right configuration to reactHot unimolecular complex lasts ~10-8 secEven if energy is put in the wrong mode, the reaction still happens

*

RRK ModelAssume correction to TST by

Qualitative, but not quantitative prediction*

RRKM ModelImprovement to RRK model proposed by Rudy Marcus (ex UIUC prof).*

Derive EquationConsider

Excite molecule to above the barrier then molecule falls apartDerive Equation for reverse reaction

At Equilibrium*

Derivation ContinuedFrom Tolman's equ

Pages Of Algebra*

NoteReactants have a fixed energy ~laser energy

Products have a fixed energy too, but since they have translation, the products can have vibrational+ rotation energy between the top of the barrier and E**

Substituting, And Assuming Energy Transfer Fast N(E*) E* is the number of vibrational modes of the reactants with an vibrational energy between E* and E* + E*G+(E*) is the number of vibrational modes of the transition state with a vibrational energy between E and E* independent of whether the mode directly couples to bond scission.

*

Next Separate Vibration and Rotation where GVT is the number of vibrational states at the transition state, with an energy between E and E*. NV(E*) is the number of vibrational states of the reactants with an energy between E* and E* +E ; qR is the rotational partition function for the transition state and qR* is the rotational partition function for the excited products.*

Note*

Qualitative Results*

Gives Good Predictions for Long Lived Excited States*Tunneling

Ignores Quantum Effects*

Details Of Calculation*

Program Beyer_SwinehartC! density of vibrational states by C! Beyer-Swinehart algorithmimplicit noneinteger(2), parameter :: MODES=15integer(2), parameter :: points=5000integer(2):: vibr_freq(MODES) integer(2):: vibr_degen(MODES)integer i, j integer(2):: start_frequency=0real(8) n(0:points)real(8) g(0:points), x, yreal :: energy_scale=2. c!energy_scale equals spacing for energy bins IN cm-1data vibr_freq /111,409,851,1067,1099,1 1295,1527,1589,1618,1625,3123,2 3193,3229,3268,3373/data vibr_degen/ 15*1/do 5 i=1,MODESvibr_freq(i)=vibr_freq(i)/energy_scale 5enddostart_frequency=start_frequency/ energy_scaleC! next initialize arraysdo 2 i=1,pointsn(i)=0g(i)=1 2enddon(0)=1g(0)=1c! count the number of modesdo 10 j=1,MODES do 9 i=vibr_freq(j),points n(i)=n(i)+n(i- vibr_freq(j))*vibr_degen(j) g(i)=g(i)+g(i- vibr_freq(j))*vibr_degen(j) if(mod(i,500).eq.0)write(*,*)i,n(i) 9enddo 10enddon(0)=0.c! next write data in format for microsoft Excel, lotusopen(unit=8,file="statedens.csv",status= "replace",action="write")write(8,101)write(8,102) 101format("'E', 'E','N(E)','G(E)'") 102 format("'cm-1/molecule','kcal/mole','/cm-1','dimensionless'")do 20 I=start_frequency,points,100x=I*energy_scaley=x*2.859e-3n(i)=n(I)/energy_scaleg(i)=g(I)-1.0write(8,100)x,y,n(i),g(i) 20enddo 100format(f9.1,', ',f9.3,', ',e15.7,', ',e15.7)stopend

Does RRKM Always Work?Assumes fast dynamics compared to time molecule stays excited*A comparison of the experimental rate of isomerization of stilbene (C6H5)C=C(C6H5) to the predictions of the RRKM model

Also Fails for Barrierless Reactions*

SummaryUnimolecular reactions have higher rates because configurations that do not immediately lead to products still eventually get to productsRRKM rate enhanced by the number of extra statesClose but not exact still have dynamic effects

*

QueryWhat did you learn new in this lecture?*

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