Lecture 18. Equilibrium in action.


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Lecture 18. Equilibrium in action.
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Lecture 18. Equilibrium In Action.
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Penner, Reginald
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UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 18. Thermodynamics and Chemical Dynamics -- Equilibrium In Action -- 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: 0:01:45 Chemical Potential of Species 0:07:39 Extent of Reaction 0:11:35 Standard Molar Gibbs 0:39:58 Henry Louis Le Chatelier 0:42:35 Haber-Bosch Process 0:45:48 Le Chatelier's Principle
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OK so "quotation mark I want better
than quest for 1 pretty well in fact so that sort of an A-minus right there and we only have to wear these things left 1 Friday and then a
week from Friday we have the mid-term too and there's 1 more after midterm June and were done with these quizzes some principle of you already have and a on these quizzes you don't need to take quizzes 6 and 7 because
you can drop to quizzes all right so you only need to take them if you
want to improve your quiz and some of you will want to buy it OK so
what we're going to do today is we're going to talk just briefly about some of the things that we talked about on Friday and then we're going to do some examples we're in the middle of
Chapter 17 we're trying to close out this thermodynamics stuff we should be done with it by the end of a lecture on Wednesday In the morning start talking about kinetics OK
so we've been talking about the chemical potential following is a partial derivative of the Gibbs energy with respect to 1 of the components of the malls of that number number of moles of 1 of the components that serves as the reactant or product in reaction that we're talking about at constant temperature and pressure where we hold the number of moles of all the other components constant all right so you describe Seldon Gibbs energy is affected by changes in the amount of 1 component that's what we've been saying it is in effect the gives energy of a singled out of a single component and the way I like
to think about that because I find this equation to be confusing it is if you have a bunch of different components and you've got some total Gibbs energy that we can think of is just being the mass of all of these elements
of these components blue
Green or all right if we were to remove 1 unit of the blow and that way again that difference is tantamount to taking that partial derivative with respect to the while holding green and orange constant and I think you can see intuitively when you look at it this way that what you're going to end up with is the weight of this unit of blue consequently this is telling us right this is in effect the Gibbs energy of a single component if you think
about it that way right but so what
we know about that chemical potential is that its extensive it's got units of energy from all just like she it's pressure dependence on its temperature dependence mimics that of
the Gibbs energy the
concentration dependence is something that we haven't talked about the gives energy right for the chemical potential here's what looks like for some component a right a step ,comma the standard state for a alright and Artie log and that is the activity of in the activity is just the concentration multiplied by a factor called the activity coefficient which we haven't talked about yet but for the time being were just going to assume that this activity coefficient is 1 so this activity closely approximates the concentration this is true this is rigorously true and alignment of dialup eh where is the
concentration of a is very low then its activity will equal its concentration OK and will set say about the activity later OK so be
we have this thing called the chemical potential now with this chemical potential we can begin to understand why I G is involved in other words why we can't just connect the gives energy of reactants and gives energy products with a straight line it seems
logical that you could do that isn't there Gibbs energy of these
intermediate state just the linear combination of the reactor product concentrations and if that's true when we get a straight line a disconnect these 2 things and if that's true there really wouldn't be an equilibrium would there because there being no way for there to be an equilibrium there be no
doubt no bowling the
Boeing is essential in order
for there to be equally but in so what
we showed is that if we calculate the Jedi when the when where how we we have converted hold 2 inches In other words we have vessels of boat to interweave
allowed and until equilibrium is
obtained right we what we calculate is -minus 1717 Jules right even tho the free energy of formation the gives energy of formation of 0 2 and eventually far below
0 right and so if they have
mixtures of these 2 things were just a linear combination of 0 1 0 we were just haberdasher lying here but that's not what we see right
there's this Boeing Of the gives energy that occurs as we mix these 2 components in the reason that happens is because the entropy of mixing is positive all right
and so if we take the Delta s that equals Delta G except that it's right selected would be a plus what I think of pretty guests plus 17 17 jewels here minus 17 17 jewels because the delta
H of mixing is 0 4 ideal guests yeah we know Delta is Delta H minus
2 Delta S. don't we OK so this positive entropy of mixing is the source of Boeing in all kinds
of chemical reactions but it's a general feature of chemical reactions this Boeing occurs and
consequently because there's going on minimum introduced by this Boeing that's where the equilibrium state is so this when I say the parliamentary mixing is the reason for equilibrium you
get what I'm talking about OK the
last thing that we talked about on Friday was this thing called the extent of reaction or the progress of the reaction a callable thanks the that this funky symbol here which is called 5 I think
so right I'm not very good with
requests I'm just to refer to it as the because it looks like any pride if the Fidelity is 0 . 1 malls as this reaction here progresses from a to B. they basically get smaller by minors .period 1 B is going to get bigger by that amount and so we can recast or Gibbs energy versus reaction progress plot instead of having a reaction coordinate here we can call it the extent of reaction but and what
we pointed out is that the slope of this plot any
value of this be but that all it is the reaction gives energy I see this
Delta here we don't say that we just call it the reaction Gibbs energy but when you say the reaction gives energy you're right
that Delta sub all OK
so the reaction gives energy is just the chemical potential sort of a value would with respect to the instead of the number moles right it looks like the chemical potential except we substituted III for right now we Collison reaction gives energy industry possibilities they can be less than 0 0 or greater than 0 OK so under conditions of constituted threatened so we understand that a change in the gives energy is given by this expression the chemical potential of 8 times the change in its number of malls plus the chemical potential would be times the change in its number of malls right and everyone exchange fought and where we can recast this expression in terms of the extended reactions OK and to do that we have to recognize that DNA is going to be negative because getting smaller right in the extent of the reactions always positive right so we have introduced a minus sign here in order to convert from malls To the extent of reactions OK once we've done that we can write this expression and so the reaction Gibbs energy is just a difference in the chemical potential right DGA the the jury the that divided by that is just that right there the difference in the chemical potentials so there are 3 possibilities as we proceed from a to B. all right initially the reaction is going to be it gives up the reaction gives energy is going to be less than 0 in other words the slope is going to be less than 0 with as we proceed from here to here and then we get down here it's going to be exactly 0 at equilibrium and then we go further it's going to be greater than 0 we have these funny words that describe them OK now we haven't said where equilibrium is with respect to the extent of reaction to get their let's assume that India ideal gasses than you would cover much of 16 that we can take the difference between the molar gives energy of the final state initial state that's just equal to this animal right here in for an ideal gas because that's just over we get RT log P final over P. initial and so we can then define Imola a standard Muller Gibbs energy in all free as 1 that applies at 1 298 . 1 6 degrees Kelvin mccain's Sorenstam instead of thinking about an initial state of final stable Aqaba 1 of these 2 guys
into a standard state that we reference Our Gibbs energy against all the time by that standard state is
characterized by by pressure 1 body temperature to 98 . 1 6 degrees Kelvin right it's that guy with the move them over to the right side now going to call him G
superscript 0 at the standards law gives
energy the OK and so they beer gasses would you rate the chemical potentials in this form by parallel this form now we're just talking about that gives
energy of a single component a it's a if we
look at this difference here I can substitute this expression infer a and then write an analogous expression to it for B I get this guy all right and non-medical like this these 2 news together and call that the
reaction standard reaction Gibbs energy Standard
reaction gives energy OK and the please zeros cancel we just end up with PB over PA that this quotient here is in general gonna be called the reaction cost OK so now for every value of the extent of reaction across the horizontal axis of our G extend reaction diagram wooden calculate the reaction gives energy from them let me up
Gibbs energy of formation right after there the
product reaction species so we can look up these Gibbs energies of formation for the reactants in the product that allows us to calculate what the reaction Gibbs energy at equilibrium the reaction courses given by a special name so in other words at equilibrium where this guy is 0 0 OK we have this we're going to call the reaction quotient case instead of 2 word we call it 2 here right that guy's equal the queue but when this is equal to 0 lower at equilibrium now a college K only applies when you're equilibrium so you have to be
talking about equilibrium concentrations are pressures but every reacted in Prague OK
and so that being the case we can just move the sky over to the left hand side or move out over the left hand side put a minus sign in front of it now we have a relationship between the standard reaction Gibbs energy and the equilibrium constant this is an important
equation OK what is it me
well let's say that the standard reaction gives energy is 0 right in other words the reaction of the
product Gibbs energies are the same all right if that's the
case of output 0 win for this guy all right I give 0 over RTI get the EXP of 0 that's just 1 but what that means the Colombian Constance just 1 in other words if we look at the diagram like this 1 were plotting the gives energy as a function of here too
but we're going end up with an equilibrium constant that is here right at the bottom of this well symmetrically located between a and B and this curve is also perfectly
symmetrical on the other
hand what if this standard gives reaction energy is negative minus sign here and if that thing is also whatever minus minus is a plus right in
EXP of any positive is going to be greater than 1 right right and if it's greater than wine right here is that case right Standard gives standard reaction gives energy is positive sorry native negative negative right final minus initial and so now a curve is going to be skew all right here's someone right on according to the greater
than 1 run the right-hand side
of 1 were over here also qualitatively
equilibrium constants can be greater than 1 What is that but what does that tell us about the equilibrium state more than then that
right so we can be a little bit more specific about that if we have some generic reaction this is just a review from Kam 1 the aim the baby will moles of and moles of equilibrium condoms given by this expression Britain everything in terms of activity right these are the products species these are the reactants PCs and I've taken in every case the activity To this dotcom metrical to the power of the documentary efficient
Everybody remember how to write these things
right and these because these are activities each activity for example the activity of C is its activity coefficient times its concentration and 4 died and 4 8 and 4 B. we the analogous expressions you
know what I told you earlier for the time being as Sunnis
Gamez are all 1 so this whole thing is going to go away isn't it this is going to be
1 OK and that's our
equilibrium constant expression written out in terms of concentrations that's the activity of a that the activity coefficient for it at the concentration of a you get the OK so
what this tells us is that we're going to have a product which states these are product concentrations these are reacting concentrations if Kerry is greater than 1 we got more of this than this that's what this is telling us we have a product rich
state 1st system
conversely if the standard reaction Gibbs energy is greater than 0 in other words be that here it is down here that's the positive Standard Gibbs energy now the curves can skewed the other way case going to be less than 1 OK I'm to be reacted rich by virtue the
same thinking OK so this
picture is self-consistent we can think about in terms of K G Standard Gibbs reaction energy any of those things let's do an
example CEO
hydrogen a methanol right are mixed together at 5 degrees K with these concentrations partial pressure of CEOs tend bar H 2 1 bar Methanol 0 . 1 baht we pass this over a catalyst this mixture right to question asked his Kenmore methanol be form can we adjust the
reaction conditions to form more methanol or we maxed out OK were given the
standard reaction gives energy 21 . 2 1 killer jewels from all
I know the 1st thing to say is a catalyst was outwardly
how does that affect our calculation what's the
catalyst doing what's the role of a catalyst to anybody know speed up the reaction it's exactly
right it's going to accelerate the reactions can accelerate the approach to equilibrium but it does nothing to alter the position of the equilibrium In other words inserting the catalyst doesn't change where we're going to end up In terms of the mix of
products reactants right it's not going to do that by definition OK so
here's what picture looks like we're told the reaction Standard reaction Gibbs energies 21 . 2 intelligence from all here's what that looks like right Rock Hill compared to where we're starting it's a
positive number right so what we
expect while we expect Haiti is going to less than 1 right not denominated this axis in terms of the reaction quotient right the reaction quotient is 0 1 with starting the reaction because the partial pressure of these guys would be
0 at this point but that's not where we are in this problem this problem over here somewhere right but hypothetically if we were here the reaction quota would be 0 here the reaction portion would be infinite witness because we don't know None of that only products no reactants OK so were here that none of this reaction caution would be infinite OK so how do you approach this problem forcing you have to do is write bounce chemical reactions the plus 2 hydrogen is gives methanol then you write an expression for the reaction quotient and calculated the reaction quotient for where you are right now the reaction portion for the conditions that you're given that the woman talking about there are an infinite number of reaction quotients right all different numbers these are all different reactions cautions that vary between 0 and infinity right so what we wanna calculate is the reaction cautioned that corresponds to the initial conditions that were given I should called it something special but I didn't discover the reaction caution it's a partial pressure methanol divided by the partial pressure of CO multiplied by partial pressure of hydrogen squared because as a from the hydrogen OK I put my numbers and I get 0 . 0 1 reaction quotients an
equilibrium constants are always dimension less OK reaction quotients and equilibrium constants are always dimension less I'll show you why in a moment OK so now
we can calculate case just the ecstasy of minus standard reaction gives energy divided by RTE we were given this and the problem it's 21 . 2 1 killer jewels from all such 21 thousand 210 jewels from all I can calculate k sure enough it's less than 1 OK then I
compare you this is where I am now this is work a wants me to be she was bigger than case what does that mean or not equilibrium that's the 1st thing to say because if were to be at equilibrium to have people care right it's bigger what
is mean that it's bigger it's so on the
product side of equilibrium because remember what Q is skewers products over
reactants right In the case of
queues bigger than up more products With respect to react and then we will have an equilibrium so we're on the right hand side compared to worry equilibrium in right we're here and here's where equilibrium by qualitatively where . 0 1 equilibrium is in here McCain and so we can immediately start to make predictions
about what's going to happen camp just look at this diagram OK
but let's just do a couple of the thanks let's calculates the reaction gives energy for this progress of reaction all right the reaction Gibbs energies equal to the standard reaction divinity was over Q We calculated Q already was that was . 0 1 that the temperature that's all are that there were standard reaction gives energy I can calculate now the reaction gives energy at the cue that we care about . 0 1 and that's number I get 2 . 0 6 killer jewels from all but the fact that it's positive it means
that the slope is positive right means the slope is
positive it means that we're here right that's quite positive right we're ready concluded that we were here we know where she was 0 . 0 1 all right and so what this means of course is that at this makes reacted of reacting product pressures the reaction is not the reaction toward methanol is not spontaneous in fact we're going to go back in the other direction right methanol is going to be consumed organ make seal on hydrogen that's not what we wanted to do right so that we were
asked I can we make more methanol under these conditions now you can't you're going to go
backwards there is consumed methanol and make these 2 reactants but now what if I increased the concentration the reactants and increase his concentration and I can just recalculate now the queues . 0 0 1 instead of . 0
1 gotten smaller but I can
recalculate the reaction Gibbs energy but I do that now I'm getting a negative number but the reaction gives energies the slope remember the slope of the green curve myself that's negative that tells us that when we went from being on the right hand side to being
on the left-hand side but I'm
right here -minus value means the reactors now spontaneous and we can make more methanol we were here under these conditions and now we've moved already here under these conditions right here right and now the slope is negative it was positive before so now we will make a little more methanol we're going to go from here down here it's not going to be a huge amount but we should make a little more methanol under these
conditions by adding more what
I had Morris CEO or more each 2 1 all 10 1 I just changed you get a different you because the hydrogen partial pressure squared
OK so we can make predictions In
everything is self-consistent that his self consistent with that is something that the way this thing right here right now all makes sense it's a little intricate but
it all fits together like a puzzle consider the following
reaction and you will fall reacts you molecularly in other words by itself to give to NO to To you the
molecular reactions calculate Delta James
are that should be dealt RJ our should be over there a 290 calculate equilibrium constant calculate equilibrium told pressure of system consisting of 1 eventual form 1 liter at 298 . 1 5 degrees Kelvin the new all 3 things
very similar to a problem that you're going to have on mid-term to but because it rolls together a lot of things doesn't OK that are should be right there it's called the reaction Standard reaction gives energy right now were not given that here for goodness sake but fortunately you've got your book and there's a table of
Gibbs energies of formations in the back your books and just open up the table calculate this OK
so this standard reaction gives energy without that are is actually underneath right there is 2 times that because that's the product 2 times the N O 2 but the standard gives for of energy of formation for the N O 2 minus the standard Gibbs energy of formation of the actual for that's going to give us that Standard reaction Gibbs energy I'm really working hard not to wrap these words around my throat today but I look that up on the back your book I look that up in the back your book and I just plug here and what I guess that is that number right there that's the standard reaction Gibbs energy whatever actually right the rights of thermodynamic uphill that's what we mean when we say Immokalee uphill that's a positive number
OK this from avidly
upheld we expect KP less than 1
right because if I think about where the products the reactants are green curve is going to be skewed towards react inside encased in a less than 1 that's my Chemical intuition kicking and I look at that number and I
know he's going to be less than 1 right we want to develop this chemical
intuition that maybe we haven't had calculated at
this temperature which is calculated that the standard reaction Gibbs energy not just rearranges equation can calculate kid pretty easy for me to do it just plug in a number that I just calculated there it is right there I can calculate everything else folks that's my equilibrium constant sure enough it's less than 1 that reassures me that I might not have made a mistake I
knew it was going to be less than 1 before I calculated OK
what else calculate the total equilibrium told pressure of a system consisting of 1 mall eventual foreign 1 leaders at 298 . 1 5 degrees Kelvin member gee camp
we're doing these problems you have to build 2 problems like this again it's the 2nd time it had
to do this probably maybe like it the 1st time I hope you like it better this time I like his problem myself 1
molar there's no malls this here's the change why minus X is the number of moles they're going to be consumed as the reaction proceeds from left to right plus 2 acts because there's 2 here are right so the told everyone minor Thaksin plus 2 acts
remember this OK here's our
equilibrium constant expression water that he 0 come from I know I've got products over reactants so got the partial pressure than to worlds Square over the partial pressure eventual floor but then again extra repeat here where that come from we need to just talk
about this 1 time and then we never need to talk about it again hopefully every 1 of these
pressures is really the partial pressure divided by the pressures that
characterizes the standard state every 1 of these pressures every attenuator pressured equilibrium constant expressions that anybody ever tell you this Angie camp now where gets left out and you just told that equilibrium constants are always going to be dimension less ah but the reason the dimension less is because
this is not the partial pressure of N N O 2 it's the partial pressure of NO to all Burpee 0 right and so if you work out the algebra if you write piano to Over P. 0 squared and P will form over please 0 all right you end up with an extra factor appease 0 the denominator that makes this expression dimension you see that peace
squared the numerator peace squared and the denominator and all the units and the conference right so it's not magical but equilibrium
constant expressions have no units it's because every pressure or every concentration that you input into an equilibrium constant expression is really a ratio between the concentration of the thing that you're talking about and the concentration or perhaps pressure of the standard state OK Nigel see in a
2nd it becomes important that you not forget about this piece 0 right and you can always in search the right number P 0 just by looking at the expression if you leave out the peace zeros in your right the expression the same way that you would Ng Kam you can go back and look at it and go on I can see there's going to have to be extra factors appease 0 reader in the numerator or the denominator to balance the units you can stick a man
after without thinking about him too hard that's the pressure correspond
to the standard states won by OK so now understand the substitutions from the ideal gas equation I haven't forgot Mikey 0 on the square is just like that squared right there and then applied for this and this can apply again from my expression generated right here in Seoul in the numerator I got to act squared and denominator one-liners acts right there yes that's from there and that's from their right OK and then
now look at this cluster of variables here I've got our to you over the multiplied by P 0 p 0 1 bomb the 1 liter 2 years to 98 . 1 5 degrees Kelvin and are in units of leader Boris recover from all which is not a factor that
I can remember right that's
arguments of leader Boris recover from all all of these units but this thing is not equal to 1 it's equal to 24 . 7 8 9 so you've got a divided your equilibrium constant by that fact did it the right answers like the P 0 is important it without that P 0 you're not going to get a dimension was quantity in this peak rectangle here it's not going to be dimension his see Bart leaders canceled leaders most Candlewood malls take Kansas OK OK so now
I can solve a acts in the normal way across multiply generate acquired radical equation use a quadratic formula this city
parenthetically will always be negative in these problems c will always be negative that's important
because that means that this operation underneath this square root sign here is always going to be an addition it's OK if you remember that it's somewhat helpful to keep hands fly across
the keys of your calculator because you've done as a billion times right and it's always a
plus OK here's what you get of course is also negative wrote that you neglect this is plus or minus OK so that is the ax and now we can calculate finally what these 2 but the number of all they're going to be the final number balls up for both of these 2 chemical species 1 minus X 2 x here's the final number malls but we were asked for the final number we rest for the final pressure the final pressures just as some of the mall's times are geography right this is to
species without Adam To
get the toll number malls aghast and archaea reduces told pressure which is that number right there this is just
taking you back to G. camp right but that step is important we do need to remember how to do these problems
OK so French guy you know how
this can be important in the future
the American English shot that's a name that you know from GE if a chemical system in equilibrium experiences a changing concentration temperature volume or partial pressure than equilibrium just counteract impose change a new equilibrium is established that's what he's famous for he did win a Nobel Prize he just missed out on that at the end of his career he wrote I let the discovery of ammonia synthesis slipped through my hands was the greatest blunder of my scientific career nobody could figure this reaction out In the early 1900 s everybody was working on it analyst shot a even had the right catalyst
anybody know what the right catalyst is Silver works but that's not the catalyst that was actually used it was fired the reason shortly a didn't understand this reaction is this is 1 of the rare exceptions to that was shot the UAE's principle that
doesn't follow his principal he was thinking about his principal and this reaction doesn't follow a lie that's the extra credit
question that's the extra credit question for mid-term too so if you know the answer In between now and then you can try and figure it out when you say it again why is
this reaction which is catalyzed by
Irish not follow the shot liaise principle 1
sentence but it's not a long drawn-out thing there are no equations I want to just tell me who solve this problem but what it turns out
there's 2 guys for harbor and coral blush and Fritz harbor figured out that the chemistry 1st and won the Nobel Prize in 1989 for doing and then Carl Bosch commercialized the process In those 2 guys are 2 of the most
influential not scientists not the
most influential scientists they the most influential
people of the 20th century because they figured this out according Nature magazine a magazine about scientists right right here's 1 my plotting here this is the population Of the world in units of billions right and this is the year right and here is what the population of the world wars was doing any here's when I Haber botched process was invented the early part 19 early 1900 but here's what happened to the population of the world this could never have happened without that but that's why the most influential people 20th century what some
poured about this reaction
fertilizer all right you need to fix nitrogen you have 2 seperate nitrogen from its super-strong triple bond In order to
make proteins because proteins have amino acids in them they don't have triple bonds right half of the protein in your body I was prepared
synthetically by this reaction half of that half of every protein in your body came from this reaction right here the phenomenal
that's called impact right that's a huge impact on your life where did that fix nitrogen come from before the 1920 you can't see it here but these are cows right that's a person's and this is a mountain of exactly
what you think it is right on most
of the world Siegel guano I was on the coast of Chilean Peru and
Bolivia it is a long coastline on the west coast of South America where there are mountains of
seabird guano but at and that is where all of fix nitrogen came from in the world all right at this time in the early 1920 s there were wars spot over it right toward the Pacific read about it but it was 5 over bird guano but it was a
super important commodities skull Saul people soul Peter Wright potassium nitrate right critical component in the manufacture of explosives in gunpowder to right so
very important strategically In the early or late 1800's early 19 hundreds all right I think very interesting OK so much on a what did get the principal right there are reactions there are that run counter to what
his principal predicts right almost all cases of reactions the dollar shot principle have something to do with catalysts catalyst mess up the principal right so that's
part of a clue but if you wanna get the extra credit problem right you have to
think about the catalyst why doesn't the catalyst allowance was shot least principle to be obeyed for the boss process what is the catalyst due to prevent that from happening it's about the catalyst OK with surely
principal cities because intervene position this equilibrium to shift to the left because the ship on reduction of the another words if you increase the total pressure of a reaction vessel a contains the mixture of these gasses you increase the toll pressure you expect equilibrium to ship and look to the because the pressure of the
system will be reduced if you do that right if I
increased the pressure on this reaction the vessel we expect equilibrium to shift to the left because here we got 2 walls of N O 2 and only 1 ball into a sold the pressure of the system will go down if equilibrium shifts from right to left that's what will shut use
principal predicts and that's what happens most of the time if there's no catalyst involved
can we determine the relationship between acts in key total for this reaction and verify the prediction of what shortly the work it
out right in detail and the
one-minute that we have left we don't really have time to do this but let me just click through the slides very quickly and showing this is what we did a minute ago we have to calculate the mole fraction of each of these 2 components there are about
100 refuses to this or that you are I saw was the 1 Wednesday


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