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Lecture 26. Transition State Theory

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Lecture 26. Transition State Theory
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UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 26. Thermodynamics and Chemical Dynamics -- Transition State Theory -- Instructor: Reginald Penner, Ph.D. Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. Index of Topics: 0:02:54 Where Does the Arrhenius Equation Come From? 0:04:34 Transition State Theory 0:11:16 Activated Complex 0:14:30 Equilibrium Constants from Partition Functions 0:23:25 Calculating the Partition Function 0:26:28 Vibration Along the Reaction Coordinate 0:32:06 The Eyring Equation 0:35:38 Calculating the Pre-Exponential Factor in the Arrhenius Equation 0:39:27 Activities 0:40:26 Debye-Huckel Limiting Law 0:42:02 Thermodynamic Constant 0:47:25 Equation for the Kinetic Salt Effect
transition states inhibition kinetics Bock source man Trihalomethane Computer animation electron Lecture/Conference enzymes Gamma stuff
transition states Computer animation Magnetometer blue enzymes dynamics Bock chemische Reaktion chemical period end man
Nobel spectroscopic subject Meeting/Interview Lecture/Conference damage dynamics chemische Reaktion chemical Calcium hydroxide man
originators physical chemist Kir Tee bioactive collection temperatures rates Reaktionskinetik important chemische Reaktion man
sense transition states Computer animation Meeting/Interview Gamma Ethylen-Vinylacetat-Copolymere man
areas physical chemist transition states Lava Nobel transition states History chip Lewisite chemical man
German electron model chemical structures chemical bond Lewisite chemical man
bond Polyurethane Quantitative mechanism bond rates potential chemical bond quantum chemische Reaktion Lewisite chemical man Lava Computer animation Meeting/Interview Van der Waals Interactions Peroxyacetylnitrat
transition states bond mechanism bond rates concentration meat potential quantum chemische Reaktion cancer Lewisite chemical pressure Lava Computer animation Geschwindigkeitskonstante Lecture/Conference important Generic drug Silver iodide
transition states molecular bond Insulinkomabehandlung transition states Lecture/Conference Gamma complexes form man
transition states bond Insulinkomabehandlung carbon chemische Reaktion man molecule Bindungslänge age Lecture/Conference Gamma chemical structures Brom oxygen
transition states type bond man
transition states bond Lecture/Conference Weak man
transition states Meeting/Interview activities coordination source man
transition states mechanism activities concentration overexpression Alu element Imidacloprid striking equilibrium constant chemische Reaktion death man
Index Index Computer animation Magnetometer concentration standards set standards man
transition states molecular Atenolol Index Geschwindigkeitskonstante Magnetometer Bohr equilibrium constant Mühle man
molecule connection Meeting/Interview Lecture/Conference concentration Peroxyacetylnitrat Alu element equilibrium constant pressure calculations man
areas species Generic drug Peroxyacetylnitrat overexpression standards molar equilibrium constant chemische Reaktion man standards
delta Meeting/Interview Peroxyacetylnitrat freie Enthalpie level case chemische Reaktion man
transition states transition states bioactive Lecture/Conference Insulin equilibrium constant
transition states transition states bioactive spectroscopic Computer animation Generic drug equilibrium constant chemische Reaktion man
transition states type van Computer animation Magnetometer Meeting/Interview carriers kinetics equilibrium constant man
transition states transition states rates coordination carriers grain chemische Reaktion man
transition states molecule Meeting/Interview concentration rates carriers chemische Reaktion man
transition states Geschwindigkeitskonstante rates coordination concentration overexpression equilibrium constant chemische Reaktion man
elementary reactions transition states Insulinkomabehandlung Computer animation rates concentration Bohr Essenz <Lebensmittel> overexpression rate chemische Reaktion man
transition states physical chemist Geschwindigkeitskonstante properties overexpression Bock Hab Coke (fuel) equilibrium constant overexpression man
transition states Geschwindigkeitskonstante Lecture/Conference Meeting/Interview Oceanic trench Bock overexpression man
Heck Reactions Computer animation Brown adipose tissue Bock overexpression
transition states mode bond stretch van man
mode van Meeting/Interview Altbier overexpression man
mode transition states bond organizations level Bohr mode Peroxyacetylnitrat man
transition states level Expansion Lecture/Conference soft mode man
transition states power bond Expansion soft Bohr mode overexpression beweglicher stuff
fall transition states mode molecule Lecture/Conference mode chemische Reaktion man MOFs
mode transition states molecule bond Lecture/Conference Optische Untersuchungen overexpression end processes
optische Aktivität Lecture/Conference Optische Untersuchungen rates Stickstofffixierung overexpression chemische Reaktion stuff
sodium hydride Lecture/Conference overexpression
cake Geschwindigkeitskonstante Gamma overexpression Einzelmolekülspektroskopie equilibrium constant chemische Reaktion Medroxyprogesterone
transition states Geschwindigkeitskonstante age Lecture/Conference rates chemische Reaktion slides stuff end calculations
delta power bioactive collection factors Gamma Insulin variability man
transition states Lecture/Conference coordination Gamma case man
transition states phase power van Computer animation solvents factors Cocaine chemische Reaktion man
water phase rates rate chloride chemische Reaktion Löslichkeit solutions charge chemical man
reactor transition states phase Computer animation solvents media chemische Reaktion complexes solutions charge period man
transition states water Computer animation Atomic absorption spectroscopy rates Tollens chemische Reaktion charge
Gamma activities concentration solutions man
Computer animation ionic strength Gamma activities concentration Iron overexpression solutions charge solutions man
islands van ionic strength charge man
Computer animation Magnetometer activities Optische Untersuchungen concentration charge variety man
Säuren Computer animation formic acid important citric acid NaCl Bock basic solutions man
Arginine Meeting/Interview Optische Untersuchungen salts man
Neutralisation Computer animation species ionic strength activities Iron salts chemische Reaktion solutions charge man
Sulfide Digital elevation model Natrium Computer animation activities NaCl chloride equilibrium constant solutions Löslichkeit man
Lecture/Conference activities NaCl salts solutions man
transition states Dilution Gamma Iron Maskierung <Chemie> chemische Reaktion solutions charge weight end man
transition states Dilution activities kinetics chemische Reaktion slides solutions firm man collection Geschwindigkeitskonstante Lecture/Conference salts derivatives
Computer animation ionic strength rates salts chemische Reaktion gold charge man
reactor transition states rates Iron salts chemische Reaktion solutions charge man
transition states systems Computer animation Meeting/Interview Iron salts chemische Reaktion charge
systems transition states bond Lecture/Conference rates chemische Reaktion charge man
phase Meeting/Interview Optische Untersuchungen Zigarre slides Revenue man
OK her you guys Dillon while 2
more lectures a review the
final for the final on
Friday so all really be doing on Friday but tell you in
some detail it's going to be honored did I mention that the
electronic course evaluations are available and look to see if any of you guys did these the
last 2 days Monday we talked about enzyme kinetics but were not going to say
anything more about that today but as you'll see on Friday that stuff we're going to be on the final so I J and a lot of information into that lecture on Monday all of enzyme kinetics all of enzyme inhibition it's all in there all right some of that stuff is not in your book like the enzyme inhibition stuff OK so you can either find another source just to study that found where you can study it directly from the lecture I think everything that I put in theirs
approximately correct now today I wouldn't talk about transition state period at the
beginning of the quarter this is what we hope the cost would look like we
had this beautiful blue rectangle of reaction dynamics here at the end of the course it we're optimistic that we'll be able to
talk a lot about this maybe from more than 1 lecture what
actually happened it was it fell off the end of the course In all we've got left is a single lecture but you're going to hear about today but that's all
that's left of reaction dynamics could we have just left it out we could have but enough damage has been done to you guys In 1 31 8 all you heard about was quantum mechanics from Professor Ren In 131 Be all you heard was about was that cost could be from Professor Martin and I know you know a lot about 1 mechanics and spectroscopy and that's good but everything else is important to so this
subject is actually very very important to us and so I
tried to pick out the 1 thing that I cannot allow you to leave this class without knowing I've tried to pull the 1 thing odd reaction dynamics that you you got a Nobel right this is the 1 thing this lecture prime mentality basically what we
want understand is where does the Arrhenius equation come from when we measured the temperature dependence of reactions this is the reaction rate
most of the time we find out that it
conforms to this equation right we make a
plot of a lot of the
reaction rate versus 1 over tea would get a straight line we get the activation energy the reaction from that straight line we report
that we think about that that guides a lot of what we do is physical chemists but we have never explained where this equation comes from right in some ways this is the most important equation in chemical kinetics but we haven't talked about what its origin is fundamentally word does this equation comfort so I wouldn't do that to date I can do that in 1 lecture it reminds me
of course this statement is
grammatically incorrect it's a
dangling prepositioned there might 1 my favorite jokes the
Texans Texas student goes to Harvard in In his asks a Harvard
student worry from the Harvard registers welcome from place we do not and our senses of propositions the 2nd OK
where are you from In other words
the sometimes substitute felt that so I would love to spend 10
minutes talking to you about these 2 guys Henry area worked at the
University of Utah for most of his
career 1 of the great American physical chemist of the 20th century Michael Pliny Nobel Prize-winning
physical chemist by both of these guys are responsible for ordinary talk about today
transition state theory
they work it out in the 1930 so here's the short version of the history that matters here way back
in 1916 she analysts the 1st
Great American physical chemist
Morgan to lose .period structure
right there was no quantum mechanics and 1916 was invented until 1924 he came up with a very compelling model for chemical bonding involving pairs of electrons that turned out to be correct and all much of what it predicted the way before the fundamental underpinnings of quantum mechanics were described he figured all add
up he was a genius Heisenberg interact ensuring their discovered quantum mechanics in 1924 but
Germans Hi learned Fred Heiler
in London rather took 1
mechanics applied at the bonding for the 1st time they did the 1st quantitative description of chemical bonding their names are usually last year we hardly even mention sometimes
we talk about London's dispersion forces remember
that Vander walls forces that is the guy Fritz London is together figured that out all right
1929 5 years after quantum mechanics these guys developed a
quantum-mechanical 1 way to think about reaction rates write these guys
figured out a quantum-mechanical later to think about bonding that's
pretty important Michael Pulandian airing figured out how to think about reaction rates quantum-mechanical sp perspective right Oregon
zoomed froze what they taught us today here's the
basic idea it was the ghost of products which is going to talk about this generic reaction today where we strip
down this lecture so that we've taken everything else out it should be 3 weeks worth elections we know
the radar Is that but the rate constant times the concentration of a cancer concentration of meat these can be pressures or concentrations the transition state theory says that this reaction actually occurs through this mechanism write a plus
B are in equilibrium with something called a B double and that reacts in the use of molecular fashion editors products all right transition
state theory basically takes
all of the reactants but some on 1 side of the products but some on the other side and in between it constructs something
called and activated complex or transition state that's why it's called transition state theory this thing here is
the transition state all
right that's an entity that is
intermediate between the reactants and the products if Bonds exist in the products that don't forming the reactants they exist partially in a weak form in the activated complex on the transition state if Bonds are welcome here the partially broken In the
transition state so the transition state has
structural attributions bond lengths and so on better intermediate
between the reactants and the products 1 of the key
points about transition state there is a postulates
that an equilibrium exists between this transition state enemies reactants Rice so here's the picture in terms of
energy that you've seen a million times but what were presented here now the notation applies specifically to transition state theory you've got
reactants that represented here by these 2 molecules this looks like it could be and OH that CH story that's the age 3 b or are apparently right away minors seats 3 art that's the transition state OK and you're the products notice that in this reaction a new bond is formed between this oxygen in this carbon and this bond here between this government and this bromine is broken
OK on the transition state noticed that the transition state what were depicting here is this bond is partially form you see how long it is it's a long time we
bond right and that bond
is partially broken seal along it is it's a long week bond also by that bond is going to be broken in the product state that Bonn doesn't even exist in the reactants states or the
transition state contains all of the bonds that are present in the reactants and in the products all right but the bonds that are involved in the
formation of the products from the reactants are weakened
right see how long that is see along that bond is these are 2 Super weak bonds all right so we can
construct a transition states by thinking about what the products
look like what the reactants look-alike products reactants and then thinking about how the products
are formed from the reactants geometrically how does that happen all right this
shows an attack in a particular geometrical orientation of the OH minus to the home CH 3 R while thinking about this and thinking about this we can construct what this transition state should look like
try using a few simple rules now
it turns out that
transition state and activate complex should not technically be used interchangeably there's a new wants but the the activated
complex actually exists over range of this reaction coordinate whereas the transition state in principle exists only at a particular point in time
we're not going to bother ourselves with that distinction today but there's a fine point there but you should know these are not identical we're
not into interchangeable to say activated complex in transition date but today were
just an EU source 2 terms interchangeably OK With
that as a premise let's see if we can work out what the reaction radiates here's
our mechanisms are transition state theory mechanism for this reaction criticism that his death so we can write an expression for this equilibrium constants but
what is the product over
reactants notice that normalizing being very careful here To write
activities the activities of the transition
state the activity of a the activity of the chasm dividing by the standard concentration in the air OK and so when we're done canceling the C 0 up the next effective Caesar on the numerator that ensures that the equilibrium constant is
dimension as all right now unfortunately I use the
Microsoft Word Equation Editor tried a lot of these equations it does not allow me to write a 0 with a
line through it all right that is the symbol for the standards concentration 1 molar for
example but understand called C
0 right there's another issue see Double X here this double Microsoft Equationator
editor doesn't contain a dying sets what's the diocese's it's that they're
saying the double dagger the double dagger is the same thing
as their dioceses so when I write to pluses unjust indicating the transition state OK so that
refers to the transition state that's the equilibrium constant that involves the transition state that's the read you the molecular reaction rate constant that involves the transition state you see how I'm a right that is that you see the double plus
it's just the diagnosis if you can if anybody knows a work-around for that I would that would help me a lot how do I
write a dioceses and Microsoft equation editor here I cheated at Pope told I put a white square least this on top
but I thought I can do that is 106 lies in his presentation but now
suggest the directors in terms of pressures if we want to all right here's concentrations pressures no different now
if we flash that were talking right now but Chapter 20 if
we find that the chapter 17 it turns out we can
calculate equilibrium constants from partition function all right and recall partition functions are
very important to us because they allow us to make a connection between statistical mechanics thermodynamics partition functions contain information about the actual molecule we can look at a molecule of we know something about its state distribution we can write a partition function all right
what we learned in Chapter 17 what we didn't
have time to talk about in the class this quarter is the fact that you can also use these partition functions to calculate
equilibrium constants if you wanna read more about that it's on page 670 turns out to be a sort of an important thing that we left out here's what's there right here some generic reaction tables the baby balls of Moses leading roles of the here's what the equilibrium constant expression looks like written out in terms of the standard more partition functions for a B C and
all right so if I know I can
calculate these partition functions for all of these guys and I know that so what is this is the standard more petition for em smaller areas species a what's that that other guy number that's not a miss print right it's Our Daughters
number in every single case
that is the difference in 0 . energies between react in some products so if this is your generic reactant here's your vibrational energy levels here a
vibrational energy at levels of the products right that's the ground vibrational energy level that's the ground vibrational energy level that's Delta already 0 but the difference between the
ground the 0 . energies of the reactants in the products
OK so here's our Gibbs free energy as a function of reaction coordinate all right the delta r e 0 is closely related to this green they are of quantity than indicating here all right if this thing was in but ground vibrational energy level and this thing was its ground vibrational energy level both of these guys and both of these guys then this would be dealt are ye 0 Frank because
we're always talking about the 0 . energy and we could say
something about this equilibrium constant we could calculated using this equation right here now in transition state theory
that's not the equilibrium constant we care about what we say in transition state theory is this is an
equilibrium with that's why I don't care about the equilibrium of this with various that's going give me the normal equilibrium constant that I can learn about
Chapter 17 where public transition state theory says it these 2 guys are in
equilibrium with 1 another so what matters is this Delta already 0 here right this thing that we normally call the activation energy it's
the activation energy from the Arrhenius equation all right so we
want a calculated that
imaginary equilibrium constants right because these things may actually be
an equilibrium but this thing is not really observable except using some exotic
spectroscopic nanosecond Akiko 2nd spectroscopy OK
so it a normal equilibrium applied to this generic reaction right here I could calculate the equilibrium constant using this equation so now apply that same thinking to the transition state theory here's the transition state equilibrium we care about the reacts PD give this transition state and so now what I want I want .period that partition function for that guy in the numerator for these guys in the denominator in and that's of goggles number that's just left over from it's next
effective of goggles number because of 2 reactants 1 product who so
I can calculate this equilibrium constant that applies to the
formation of the transition state all right now keep in mind everything we're talking about here is kinetics right were sort of mixing thermodynamics with kinetics they took a thermodynamic
concept equilibrium constant and applied that to transition state OK so you with me so far we've got an equilibrium constant here we can calculate using statistical mechanics to estimated OK that's the 1st thing to
understand but the 2nd thing to understand is that this
rate right here showing grain that's going to be approximately equal to that of the which with with which the
transition state classes over the top of the barrier we've got a barrier
here we've got a transition state this we are moving along this reaction coordinate from reactants to products the frequency with which this thing moves across the top of this barrier that's gonna closely approximated this way but the rate at which products
are formed but that seems to be a statement of the obvious right obviously as you cross over this barrier for reactants the products the frequency that that happens that's the rate reaction
and the it's probably obvious to say that McCain so the reaction rate I can write as this frequency times whatever the concentration of this transition
status White we're going to talk
about this frequency right if the frequency with which if you think about this as being a molecule all right there's a
vibration that has to happen here all right this guy
moves back and forth between these 2 guys I would get a symmetric
vibration of this transition state the frequency that characterizes that mold is the frequency that we care about now your book
includes something called the transmission coefficient were dismissed and that's what that Kappa right there just forget about it it's 1 OK so the rate
of the reaction is given by the special frequency that applies to the reaction coordinate times the concentration of the transition state but we know we can also write the rate in the normal way With the rate constant times they tend to be right it's what we've been saying all
along so we can but the here was
art equilibrium constant expression for the transitions transition state unifies just all a this expression right here I get this and I can plug that into a B there right so I just solve the concentration of the transition state from here OK and applied that to this equation right here and of summer put all of this in the here and so there there's the there's the frequency the special frequency hears all the rest of at but that's the reaction rate
so in essence this is the phenomenal logical rates expression that we would normally right for this reaction
A-plus goes to products we know that the reaction rate Kate time 8 times Beaver is 1 that's elementary reaction right right and what we said is
love that would rate constant is given by this expression right here that frequency times that equilibrium constant divided by this concentration term just to keep the unit's writes the transition
state theory has already and the
important thing is that these 2 parameters here
relate directly to physical parameters of the transition state that we can think about calculating In other words we can calculate this way
constant from fundamental properties of the transition state because we know
enough physical chemistry to do that already OK so
here's arches so we have the key point is we have expressions but equilibrium constant and for this rate constant right here we said That's just equal to the this guy's c 0 times Kerry double dagger divided by the OK and so on let's say that
we actually do want calculate now but the rate constant but said that we actually
won a calculated that right there we have to be able to calculate became double dagger without being able calculate locator Leger which assisted living How are we going to do
that well use the expression for
making a double dagger we know what the partition function of a and B are we know to calculate that a ready we've done that How do we
calculate the partition function of the trenches transition state had we calculate that
partition function is don't In the
that's the same as that that's the same as that 1 way out of it's a little
confusing isn't it what the heck to search that's also became a
sorry that should be capable there that's just became a sorry you're right those that double-decker should be there thank you OK How do we calculate that France's state and how we calculate that partition function it's a
trend transition state for goodness sake but what is it this is the
question that these guys wrestled with women worked out the transition state theory right if we think about the vibrational trip
partition function 1st right it's the vibrational partition function that we really care about here right essentially the transition state undergoing a vibrations all right I hardly
think about that maybe this bond is getting longer this spot is getting shorter all right it's like an
asymmetric stretch of the transition state that's the mold that we care about so if we could calculate the partition function for that vibrational mode
that's critical to understanding what the reactionary is going to be right so here's the generic expression for the vibrational partition function right for some
mode that has a natural frequency or natural energy H New and natural frequency New all right now what can we say about this magic mode that we care about this asymmetric vibration along this axis is that going to be
high-frequency motor low-frequency known what you guys think High Frequency but you have what and so on tell me this is
a weak bonds here right do we bonds have
high frequencies are low frequencies yeah thank you
parts of organ expect this to be a week I wouldn't expect this to be a very low frequency mode call
the soft mold
right here is a picture from Europe chapter that I think is somewhat not intuitive all right here's the transition state up here what what this picture is trying to convey is that the transition state as a very shallow vibrational energy well with varied with vibrational
energy levels are very very close together in energy all right in other words the frequency
you have to go from here To hear that each new is tiny right yes but
the key point is that the frequency that characterizes these transitions in the transition state along this direction right here is very small so that allows us to do simplify this equation we can write this exponential as as a series and we can truncated at
the 1st term and when we do that we just get that
Katie overreach New fight we take this normal expression for the partition function we truncated we write it as a series expansion the exponential we truncated at the 1st term it would just get Katie overreach knew this is a special new This is the frequency that describes
motion over the barrier but whatever that is for whatever the transition state is whatever mold the product bonds are getting formed reacted bonds are getting consumed we can think about that processes involving a single vibration that has a very low frequency in general if that's what they realize conceptually this is not obvious I think everybody in this room would agree none of this stuff and talk about last by bandits is obvious but this was the conceptual leap that Maine OK so I can write the
whole partition function for the transition state as the partition function for this little frequency mode and then the whole rest of the partition function right noticed that there's
going to be a rotational and electronic translational right the partition function contains many other manifolds and other vibrational modes as well for the molecule that are orthogonal write to this special mode but with a role
that fall into this guy over here this is just the partition function for
the Magic mode the corresponds to the reaction this is the rest of
Q all the rest of the partition function for all the other
modes manifolds and so on OK so that's the
petition and I just plugged that in the end here's the partition function that we were wondering about the expression we now have 4 notice that the rest of this partition function
involves things that we can't already calculated because the things "quotation mark not perturbed in the molecule but what's perturbing the transition state is product bonds are getting formed react bonds are getting broken right and we can describe that we can roll that process all
into up into 1 Mauldin has this characteristic frequency here we're going to have to figure out
what that frequency it all right but
all the rest of the stuff we could is rolling in right bonds at
orthogonal to the to the reaction rate we can just calculate the vibrational partition function the rotational partition function all that stuff using the conventional methods that we already know about OK so now
I really rewrite write this in terms of this guy right here look at those Katie rage New now that's right there is the rest of the partition function this skewer the line over here all right and I'm getting close to being able to calculate this guy this is the contribution of along the reaction cordon only yes yes this is all the rest of it yes but OK sorry Our expression for the rate constant becomes less and we're just plugging now this expression in 4 this
equilibrium constant the double-decker on all right so we can
actually when we do that we can cancel this frequency paid
turns out we don't need to know what it is it cancels for God's sake but we don't have to measure it right we get this expression
right here and this is the same as airing equation but we derived it going way too
fast in about 20 minutes but here's the suspect
that it's very important equation now
why is it so important yeah I it we find K using cake
refined that using Mackay he the and all that can OK this could be
confusing me that Bolton's
ensconced story this is the rate constant phenomenal logical rate constant for the route for the reaction is that is the equilibrium constant that we calculate using this
expression right here ,comma right there the whole thing now you might
ask Are you going be called upon on the final exam to calculate all of this stuff no but I have to be able to sleep at nite and so I am going to disclose all of this information to you even tho I don't think it would be fair meeting write a question you
have to calculate all if you look at the end of this lecture when I IPOs this lecture after class it
doesn't that like 120 slides in the last 20 slides are a calculation that allows you to calculate the rate constant for H plus to goes to age 2 was at the very 1st reaction was studied using this equation we can work out exactly what the rate constant is if we had enough time we would do it but we don't so if you're interested In this way theory stuff this transition state there you might want to slow down the those lights were never going to get to him today it doesn't matter it does
matter but OK so here's the airing the equation but I'm just substituting Alpha 4 K double dagger here but and here's the Arrhenius equation you see that parallels the
activation energy is this delta he 0 that we were talking about the difference in the 0 . energies for
reactants some products this
pre exponential factor a that we've never said anything about that's given by this collection of variables right here party over-age times this guy right what's left over from the partition function we
stripped out From the from the normal partition function for the transition state we strip out the part of it that pertains to the vibration along the reaction coordinate
and that's what's left over because remember that that frequency just canceled for us we don't need to know what that's a good thing
because who knows what it is but how would you measure it you have to have some exotic spectroscopic method to do that OK so the Arrhenius
equation is a special case of the Eyring equation right and we can
calculate these things and if you don't believe me go to slide 101
and we go through and we do it laboriously forward a particular reaction we're not going to say more about sadly right
here are creates financial factors you can calculate this 1 actually it is calculated later
in this lecture right we can calculate
the spree exponential factors for the Arrhenius equation knowing transition state theory so it's very powerful
cocaine what we do in the last 15 minutes something very important what we want
applies this ain't thinking to a reaction that occurs in wild OK and the
key point is that we want to think about what the influence of charge is on the reaction rate it's not inconceivable that there could be a question like this on the file for
example to chlorides react with let's give led chloride all of these things can be In solution but let chloride has some solubility in water
very low all right what rate
with this reaction takes but what is the influence of the charge on the reaction rate you might say naively
if the reaction products opposite charged an ecologically attracted 1 another near action greatly accelerated but if you don't think about this too hard even if you think about it harder you might come to that conclusion right negatively charged reactants and possibly charge reactants are going to be politically attracted and following the react really fast that's going to accelerate the reaction rate but that turns out to be exactly wrong it's important to understand why all right it's great once in a while in chemistry when you encounter a concept that is completely counterintuitive at 1st later on hopefully into it all
right so I'm going to make this happen like 12 minutes here's the idea a reactor media products that's the charge on a NBC and that's the charge the key point here is
reacting surcharge so there's
a version of transition state theory but it's not strictly speaking transition state periods of thermodynamic version of it you can
use transition state theory in its normal form to describe reactions and solution because it doesn't account for reactions with solvent all right if it doesn't transition state theory its normal form does not account for the complexities imparted by having the solvent present in the reactions are episode this is a this looks like princesses a theory but strictly speaking it's something that's related to it not exactly the same thing I fighters
notation wouldn't call this math rights on noticed something if we would if we think about
this in terms of transition state theory when it reacts with the
if we form a transition state the transition state will
have a toll charge equal to a plus B right but the toll charge the transition state will be the sum of the charges on
a and B because charges to be conserved here that's a key point OK so the reason water right this is the reaction rate now in terms of this is just that we concentrate their this is a normal phenomenon than logical rate that we were right for this reaction but while OK so
then we have to think back and remember something about activities activities are going to be
the key to understanding how this works right the activity of
some guy in a musical to concentration time some activity coefficient Gamma sub all right that's the activity of air that the activity coefficient the activity coefficient for a neutral is 1 right the activity
coefficient only deviates from 1 is a consequence of colonic interactions with the solution other lines in the solution right if other lines the president solution the activity coefficient will be less than 1 of the more Alliance the lower the activity coefficient and
there's something called the about limiting lot that's the activity coefficient that's the ionic strength the ionic strength it's just given by this expression with this is the concentration of the iron sorry this is the concentration of the iron and this is the charge on the iron for every in in the solution I add up all the lines the solution multiplied by the square of the charge take at times one-half and about the ionic strength but the higher
the ionic strength it's not
and never obvious to me when equation has a allotted and it like this the higher the ionic strength the lower gamma
becomes if I
0 Gamma is 1 this is the ionic strength on this axis this is down on its axis if ionic strength is 0 Gamma 1 are indeed deviates from 1 as the ionic strength goes on and that the size of his deviation here depends on what the charges on the island interest all right because pursues its charge right so that a charge of 1 there's a small deviation charge of right that's the size if it's small you get a little bit bigger deviation of the charge goes up to 4 major Huge deviations bright so
I too many effects have everything to do with charge How many of you
151 From OK so
this is review for all you got good so when we read in good years of
equilibrium constantly right in terms of activities every activities cover sometimes a concentration you guys
all know that and what's more
important is you have intuition about what the influence of lions are on equilibria here's
a partner important piece of intuition that everybody should have in the room especially those of you took my class if you look at some
equilibrium like this are right
formic acid see the gas
citric acid dissociate the Hydro Eli animosity right
if if I don't sodium chloride into the solution wonder what's going to happen to the pH sodium chloride and inert sold sodium chloride has no acidity or basic city of itself all right and yet the pH will change in a predictable way what will How many people think the pH is going to go down this is get more acidic How many people think the
pH is going to go up to give more basic when I had salt get
those hands way up there at
Thank you guys never had 151 from me now if you add
salt to this equilibrium it will always shift to the right it'll always shift to the
right the addition of a nurse salt and equilibrium always shifted the direction of the most ionic state of the equilibrium see others
irons here and there are no alliance here right that's the most ionic stay if I add salt the reaction will shift to the right it's called
assaulting and by now I can
prove that might use the equilibrium constant this reaction here there activity coefficients the activity coefficients for the neutrals are 0 1 rather idea to be cooperative with this guy's 1 can be covered the skies 1 these activity coefficients for the charge species are
less than 1 OK
and they will become lower as I increase the ionic strength solution those guys will get smaller OK
so so what that means is that the equilibrium constant that applies if we think about this activity effects it's going to get
bigger if these guys get smaller that gets bigger that the activity coefficient that applies to me and sodium
chloride to the solution or any other units sold I it's going to get more
acidic what about this guy what happens to the solubility of led sulfide I sodium chloride solutions sodium
chloride doesn't appear this this equilibrium asked why would it
affect this equilibrium and yet it does in a predictable way what's going to happen is that led sulfide more soluble were less soluble when I dump sodium chloride more all
right why because look this side of the equilibrium is lot of alliance decides got no alliance if I add more lines to the solution
equilibrium is favored but the addition of more finance and I can
prove that's true by working out what the new equilibrium constant is that these are the 2 activity coefficients they both gets smaller when I add sodium chloride so equilibrium customers which to shift to the right right every time you see
an equilibrium you can affect its position by adding in a salt or removing an inert salt from the solution that also altered the equilibrium a predictable way OK
what is always have to do with the transition state theory very simple To make a long story short we can work out the
map Boris escape over here because we're almost out of time here's
the bottom line the transition
state has the total charge Of the reactants and alright if the transition state it has a high then the weight of the reactions to be influenced by by the presence of other irons in the solution so that at the end of the
day when we're done during the derivation we get this equation right here which is the equation for the kinetics salt affect what is this big pay right here it's just the collection Of the activity coefficients for the transition state and the reactants OK
they're not is the rate constant that applies for 1 more everything that's
what's gonna 0 1 and that the
actual rate constant at the reactions OK so this is the
most important slide that has to do with the 2nd concept here
part what my plotting here this is the reaction rate for reaction involves a with
some charge pleasant with some charged going on to products
right and this is the ionic strength right so the key point here is we want understand how
salt affects the reaction rate where it's easy to understand how salt affects the reaction equilibrium constant how does it affect the reaction rate the way to think
about that is 80 reacted B and they both have a plus to charge the ball positively chargeable got plus 2 charge the
transition state has a charge plus itself there's an equilibrium between the transition state and the reactants it's going to be favored by the addition of sold the reaction is gonna get accelerated Is that counterintuitive the reaction
rate goes as I add salt To the solution even tho the reactors the products of the same charge they have overcome
Colombian barrier to react because ball positively charged the reaction rate goes up not down check this
out if a two-plus iron reacts with the 2 -minus Ryan you expected to be big
colonic attraction right reaction should go faster it
goes all you have to do so will host
of transition stage position which is absolutely not know there are no 0 that's it not of that question but the answer is no
how bad this everybody see what has
happened so there's an equilibrium Allstate Allstate also this 1 last time that I have any more time but there's an equilibrium between a and B right the reactants and the transition state all right what we just agreed on is that we can decide which side of the equilibrium will be favored when we add salt to an equilibrium the most ionic state of the system is favored OK so if the if the charge on the transition state is higher than the charge only the 1 of the irons because the only way they can be true that the alliance said the charge of the same signed like plus 1 plus 2 plus 2 plus 2 plus 1 plus 1 right then the charge transistors it'll be like 384 and so on the transition state it's favored by the addition of salt
OK in reaction rate goes up looking goes up here to like goes up here also all right if if there is no charge nothing happens and if the charges on the on the reactants are opposite to 1 another than the charge
the transition state law the charge on the alliance the transition state has a law ionic it's it's it's the the least ionic state of the system the reactants are more ionic the transition state and the reaction is slowed
down by the addition of that's
told Lee counterintuitive if you understand that you understand something that most contests even are going to get wrong right you can get right principles charges the reaction slower you can figure out so
on Friday and there's more here yeah it's 0 my goodness riders like 20 more slides
that works through the equal revenue of rights on Friday where work on the final please take the course evaluations right