Lecture 17. Finding Equilibrium

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Lecture 17. Finding Equilibrium
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UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 17. Thermodynamics and Chemical Dynamics -- Finding Equilibrium -- 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: 0:00:58 Free Energy of an Individual Species 0:07:16 Chemical Potential 0:10:18 Why is G Bowed? 0:24:58 Three Types of Reactions
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OK I was already talking
about equilibrium I would have a little bit more to say about new
because new is important and I'm attack about the Boland and talk about the equilibrium constant this is Chapter 17 material we've already
totalled through chapter 16 leaving out lots of stops along the
way not ideal solutions we don't have time to talk about them they're very important partners of
lots of other stuff there as well for were already in Chapter 17 out of new
individual react some products contribute to energy there could be a whole slew of reactants years there could be a whole slew of products all right how do we a tribute to the G for reaction to individual reactants and products as chemist this is obviously a plane importante think we talk about this thought experiment right here we have 2 isotopes of hydrogen into different faults separated by a valve initially close then we open it and when we open it we can describe the change in the free energy on the left side in terms of what's happening with component wondered what happened with component to In this case component 1 age 2 and component to his D OK so we can write 2 equations for the left side to equations for the right hand side to request to right here is the left-hand side here's the right hand side here's component 1 hears component to the same thing over here on the right-hand side component 1 in component to and then if we consider that
anything that leaves the right-hand side as they entered the left-hand side and ending that leaves the left-hand side as they enter the
right hand side we can write a 2nd pair of equation these 2 guys part and what this says In only talking about component 1 here let's say hydrogen the partial derivative of the free energy on the left side and the partial derivative energy the right side souls 2 things but I have to be
equal to 1 another at equilibrium and the same thing as to
be true worth in terms of component to rights of this could be for hydrogen this could be for deuterium these partial derivatives have to be satisfied he's
a qualities that involve these
partial derivatives white so these are a so-called partial molar quantities whenever you take the a partial derivative of a thermodynamic state function with respect to the number of
malls of something it's called a partial molar
quantity Moeller because you're taking the partial derivative With respect to the number of OK the chemical potential as a special case of a partial molar quantity that involves the Gibbs energies but the gives energy the partially Gibbs energy with respect to component wine or component to work upon 3 would be the chemical potential component 1 component to work component 3 new describes how GE is affected by changes in the amount of 1 component right it is in effect the G out of a particular component it is the Gibbs energy of a single component right why didn't they just call it the gives
energy of component once I don't know it would have been a lot easier because that's what it is but it's just a Gibbs energy of component 1 hydrogen or
deuterium now it's not obvious to me when I look at this partial derivative that looks a lot more complicated than just the Gibbs energy component why why did they write it this way this really is the gives energy of component 1 or
do other people have a problem saying that because I know
I always have so the way I like to think about it it is shown here right here's a system that contains 3 different components and the total for this system think about it as just being a balance and there's a scale here we call this the gene meter we know the free energy excuse me the Gibbs energy is an extensive quantity don't we all right and so this is a beautiful analogy for that were awaiting these components like a genie this is an extensive this is going be an extensive quantity isn't just it's just like men OK and so what we said is the partial derivative of with respect to and here we're gonna pay attention to and below right now we're trying to think about the chemical potential of blow here by a constant green orange Chianti by the way to think about that derivative is that if you remove a little bit of below or add to it I do not a blow here we subtracted a unit of blue this partial derivative is just this difference and what we're left with is the block that used to be here that's the
chemical potential of the blue for me it's a lot easier to think about it this way right now it's clear that
yes this is just the chemical potential of the right now it's not the comic chemical potential of the blue always it's chemical potential blow exactly when the composition of the system is as I'm showing in here there's green near there's warned cheered as a bunch of other below here by the chemical potential is talking about a specific to the rest of the stuff being there to the chemical
potential could be different if
there was a different amounts of stuff here right it would be as old as balance could be different this arrow could point in different directions even for a single blow Bob block if the rest of these guys maybe if there's only 3 green guys are 6 or disguise the chemical potential to change a little bit but we're always talking about the chemical potential this pure component that worked out whatever it is
that we're talking about this case is the the blue
box just make anymore since I don't does for me OK so what we need to know about the chemical potential its extensive just like G it's got units of energy from all just
like G it's pressure dependence is the
same as J and so the temperature dependent OK so I can't
consider partial derivative of the chemical potential many component with respect to its partial pressure is a sequel to the role of all of that component and by integrate that I'm going to get an equation that looks just like the equation every right for J except
now it pertains to a single component and the same thing with the
entropy but how does it depend on concentrations what is the chemical potential depend on
concentration we haven't talked about that even with
respect to GE well here's the equation right the chemical potential some species aid is given by the standard chemical potential that applies under defined
standard state conditions which in the case of the gas would be pressure 1 baht attempted to 98 . 1 6 degrees Kelvin right in
the case of a soluble in a solution of the standard state is an activity of 1 we have activity is right so it's equal to this new 0 which is chemical potential for that you cannot pure compounds in its standard state plus RT log of the activity of a What's that well to
beg the question and not answered the activity-based a
sequel to the activity coefficient of 8 times its concentration now I'm told with the
activity coefficient right that the
activity coefficient that's the concentration so now we have a relationship between the chemical potential in the concentration of a we all know the concentration is the concentration could be a pressure I could still be an activity
coefficients the rights of gas
phase it's a pressure the partial pressure of course and if it's in the liquid phase of the concentration and is set to become efficient it turns out can vary vary between 0 1 1 1 talk more about that later on but it's sort of a distraction for now so we're not
going to talk about it right now for work for our purposes were just going to the quake for the time
being the activity with the concentration were just gonna pretend for the time being that this activity coefficient is always OK that's an assumption it's an incorrect assumption most of the time will talk about activity coefficients later OK so we can relate the chemical potential to the concentration to an equation that looks just like this OK now we already extended use minimized on approach to equilibrium we ready talk about this equilibrium is at the bottom of this curve but we didn't talk about why this is shape because it's not
intuitive there won't be any
of if this is the Gibbs energy the Reagans gimmicks Gibbs energy the products why doesn't the Gibbs energy of every intermediate mixture of reactions and products polymers -dash line here it's the simplest solution to this problem is
and if that were the case there would never be any equilibrium where there because there would never be any curvature displaying no
matter where you put this died and where you put this . you're always going to have a straight line and it's
never going to have a minimum where you would expect to find equilibrium is
there right so the fact that there's a ball out of his curve is sort of essential to chemical systems work the chemical systems have equilibrium we need to
understand that this is
not what happens focus
so it's too simple calculation
about 0 2 on the left side and 2 on the right side half a mile of each but not open the valve this reaction cord is the mole fractions and 2 but when I open the valve and . 2 5 moldable of 0 2 . 2 5 older than after everything comes the equilibrium OK so I'm the
mole fraction simple moles eventused . 2 5 over the toll number balls as . 5 and so 25 Aug . 5 is . 5 in the lower right here on this diagram now what we're right here after all the mixing is
happen OK so let's calculate
Jabal budgies just equal to the number of moles of and 2 times the chemical potential eventually number of all the to accept Beijing's not in there that should be 0 2 and the chemical potential boat too it's all 0 to an end
to here OK and so what the
chemical potential eventually what is given by that because we're talking about a gas that's the partial pressure event to this is the This is 1 bar we can just sort of ignored your book usually does Scott 1 OK and
this is that analogous term for 0 2 but we multiplied by the number of moles yes this is the chemical potential eventual 1 board to 98 . 1 6 degrees Kelvin and that's 1 yes yearbook his rights it gets rid of the P 0 2 scores of 1 don't be confused by that OK so since P is the same on both sides will discolor people I equilibrium the total pressure on the
2 sides of the same what is called the
prime OK so after all being involved we're have people I'm over 2 nitrogen people I'm over 2 for oxygen because half the oxygen is going to go until the last ball valve let the ball happy oxidants going to go into that you know what I mean happened I
didn't get a goal all right so the pressure is going to go down actor too right
now this is all about overnight the name of the game the energy on my initiative this is the time to let the kind of thing that I so you know what the the ones or if you are in the last 2 years where later in life the a little flat on his back is in the jewel of this going on that's not a lot there also lot only why is that a lot of history the museum relates to the euro after all 0 not that of the Standard real world In view of organization look at last year the not prior right this year and all right you get what you want to where is the history but the question is what do you know you have in the region the responsible there is no change in 3 of the New because of me you know it's not a natural In the whole thing about to get here we will opponents I want it is there was right was his 1st this year on the little all right in the US that is 1 of the things that I do that all this year you know what he was there in the American people the debt don't you In the so this and while I was eating into the air it is not immediately it is is not a Jean is part of a group right university of the 1st thing he did on the Net this is what all of this is all black and my where is the hero what about all the things we live longer than you might hear from you through life and human beings may also by the end this for June I'm very strong in the history of the world In then the In this is the most you what their call the the end of the year if you like it because of the way a lawyer this could be a problem and there are a lot of information you the question is of the the results of the summit of the system the where soldiers as well as some of these roads you know you like the asked about the terrorist the In the area it is a small hole in the euro but what is the use time she also ran her the aim of the meeting the reaction you they made so of that all ,comma really where this has Ontario so my wife and I want you to hear roles the reaction to people on a the whole being on of this for the past 2 years it the lot the pays 1 you're part of Europe all at once and for all 1 more I promise you wanted to OK so you don't know what the so he is looking leader of this In so I think this here "quotation mark earlier this year in the office of the Chief of the history of the year it turns out not to be in the interior of the world OK so you know what you hear about this whole thing is that you you get all these years you're going to those are the greater the heroes in all they know that follow the reaction is it's not good so far I remember him on the other side of the the road rail by some right it well you would thing think that will be the head of the state on
OK here we have a reaction from D N A would be a
negative quantity would because a would be getting smaller b would be getting bigger so that would be positive that would be negative insult in order for this to be equal to this I have to have a minus sign there because that's going to be positive by definition everyone that OK
so these 2 things are equal 1 another and so if that's the case I can factor out this what is that factor that out and about this expression right here in some other words this Gibbs reaction energy right now is just going to be proportional to the difference in the chemical potential so Delta g of art should be dealt R of GE of course is just the difference between a chemical potentials it's just that right when I take D G D come I get that done OK so it's obvious from this part state anyway that gives reaction energy changes continuously monotonic lay with the progress of the reaction of the extent of the reaction therefore the composition reaction mixture yes this is a smooth and continuous function OK so that means that there's 3 types of reactions reactions that are extra on it X served on Inc were dealt argues lessons 0 ended on were dealt RG is greater than 0 and equilibrium word equals 0 and if you don't know what this word means as always Wikipedia can help you means the releasing energy in the form of war if it's an excerpt reactions they can release energy in the form of work you can do work
right if Delta genius Delta
Delta RG is less than 0 or if you want Delta are due to be greater than 0 you
gotta put work into the system to make that happen OK
but we still Miller anything more about where equilibrium is located in terms of the extent of the reactions to get let's assume a beer ideal gasses then you'll recall from lectures 17 isn't this
lecture 17 but this may be
ideal gasses then you Valencia 16 yes that's right right so said the difference in the free gives energy between some initial state some final status is given by the Centergrove where that's the molar volume and we can convert that we know if a talk about an ideal gas in charge here is the expression as a function of pressure OK and we can define a standard Moeller Gibbs free energy as 1 that applies at a pressure of 1 bar and 298 . 1 6 degrees Kelvin that's what that is right there OK and so if a beer gasses we can make the chemical potentials in this form for example because this is just the chemical potential of a single species and the fall exactly this form I can write this equation right here by analogy to that 1 this is the standard chemical potential which once again applies at 1 bond to 98 . 1 6 degrees Kelvin OK so that begins reaction energy we said is the difference between these 2 chemical potentials and so fire right next to equation like this for a another 1 4 B I can't take the difference there's the B-1 there's the anyone when I take the difference yes I really at that I've got Mubi 0 minus the way 0 that's that on the nite the P 0 the anti-cancer lemon ended with PB over PA and then yes is the standard Gibbs reaction
energy that applies at 1 born to 98 .
1 6 degrees Kelvin OK and we have a name for them like this quotient between the partial pressure being a partial pressure of a it's called the reaction quotient it's something that you heard about general
chemistry lo those many years
ago right recalled accused the reaction cautioned OK so for every value of the extended the reaction across Florida likes Virginia versus some erection diagram we can calculate the gives reaction energy from the gives wrecking new-product reactions species present at that extended the reaction yes and so finally had equilibrium the reaction cautions demise but so when this is 0 at the bottom of that well but we've got a horizontal line tangent to the curve we can call this right the reaction quotient is in Q anymore here excuse all right under the special case were that's 0 we can call a reaction quotient case Carrick equilibrium right and these are then equilibrium values for these 2 partial pressures it sounds From there 2nd move this kind of a left-hand side about minus 30 like take so there's a relationship between the free energy of the reaction the
standard free energy of the reaction standard because this
is a 0 and the equilibrium constant for example but say that the delta G the reaction is 0 but if Delta G is 0 White himself 10 a you 0 exponential zeros 1 yes right In my extent of the E in my my equilibrium constant the reaction it is 1 all right which is going to be correspond to equal partial pressures the BNA right because the equilibrium constant is the partial pressure be divided by the partial pressure of OK here's the reaction the standards reaction free energy difference between a and B it's 0 0 all right equilibrium constants like the militant in symmetrical curve isn't yes it on the other hand if this standard gives reaction energy is less than 0 In other words the final gives energy minus the initial gives energy His as shown here like this is less than 0 now the curve is gonna look like that now equilibrium is gonna be over here all right and that means that's to greater than 1 that has to be greater than 1 what
is that mean for the equilibrium constant well if we look at the equilibrium constant here's the equilibrium constant refresher for generic reaction a moles of vapors the moles of egos as he a C and the mulls at the can right that equilibrium constant Hermès illegal activities of each reaction products feces yes it's just the activity of taking to the sea power time the activity of the the the power and so on products over reactants right with writers in terms of activity coefficients in concentrations yes these activities and the the concentrations of these are activity coefficients and so what this means is that you've got a product rich mixture thank you got more product than you do reactant because you're on the right hand side a 1 and if the opposite is true if you're going up hill from a to B. you're going to end up with an equilibrium constants that has the opposite it's reactant rich part will come back to
this on Monday have a good weekend


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