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Lecture 14. The Gibbs Energy.


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Title Lecture 14. The Gibbs Energy.
Title of Series Chemistry 131C: Thermodynamics and Chemical Dynamics
Part Number 14
Number of Parts 27
Author Penner, Reginald
License CC Attribution - ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/18947
Publisher University of California Irvine (UCI)
Release Date 2012
Language English

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Subject Area Chemistry
Abstract UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 14. Thermodynamics and Chemical Dynamics -- The Gibbs Energy -- 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: 0:07:14 J. Willard Gibbs 0:12:52 Entropy in Isolated and Unisolated Systems 0:26:04 Helmholtz Energy 0:28:02 Parr Bomb
so I use your mind
we don't boast about our athletic prowess very often but partly because
we don't have a football team but what we do have is probably the best men's volleyball programs in the
country everybody know we sort of flies under the radar we want to national championships in the last 5 years on this campus national NC double 8 championships were we beat every other team in the country that pretty much speaks for the best men's volleyball team collegiate men's volleyball team in the world because let's face it U.S.
dominates in this sport so these guys beat Penn State last nite In tomorrow they're going to beat
USC in London and then we're going to have a 3rd national championship on this campus at
least that's what I'm hoping we they can be very proud we should talk more about these guys smoking on so we have sadly where to
start talking about begins energy today now this is really
a Chapter 16 topic and I'm not sure we'll come back anything else in Chapter 15 I'm going to think about it over the weekend but I'm guessing will probably done with Chapter 15 wouldn't started to lectures OK that material is important but it's sort of abstract to us as chemists because word is the Cardinals cycle fit in in chemistry how does that affect our daily lives as chemists and I can't answer that question but it's a tenuous connection but Gibbs
energy for Khamis that's what the thermodynamics that's where the rubber meets the road in thermodynamics was the Gibbs
energy it's going to allow us to tell whether a chemical reaction happens or not with the red equilibrium were not right this is what thermodynamics is going to do for us as chemists right so we've really been building up to this thing called the Gibbs energy In today's lecture is extremely boring but important right where they have some of those different lots of symbols today all right but what we want do is 1 of figure out where this
gives energy comes from I was really never spelled out for me in the physical chemistry class I had back in 1981 right
it was just years the Gibbs energy use what it does here's why it's important but no 1 ever really delighted but there is a nice derivation of the gives energy so that's what we're going to try and do today know we've only got 25 minutes so we may not get it we're not going to get all the way through this lectures and if we don't we'll just continue it on Monday so don't worry about that but
all of these guys by the way Claudius not an
Austrian sort of a few forms the Germany has that
flight is right there where only 1 of these guys won the Nobel Prize this sounds like a quiz question for next week a
convincing which 1 of these guys who won the Nobel Prize but in no way that they all
did enough to win but only 1 of them wanted so there's really a mystery here why did only 1
guy when the Nobel Prize 1st of all the which guy was it Lewis no gives and Lewis who are good guesses because those guys should a 1 darn thing it was like the least famous guy on this line nerds the Ernst won the Nobel Prize in 1920 right now
anybody know wine and not wine nursed 1 but why these other guys didn't win I mean objectively they did more than nerds and they didn't win it all the answer
is no other way than Noble Prize works you do
something that's really important and then it takes a while there's an induction period while the rest of the world tries to understand what you've done and then once they understand they have to appreciate what you've done and then once the appreciated the gotta get organized and give you the award but not process typically takes 20 years but wanted the Nobel Prizes stock anybody How do you know
that you just memorize that it's an amazing
statistic that when your fingertips that's the answer
for any died in 1896 and the in his Will and final will and testament to the endowed the Nobel Prize in the first one was given 1901 and they don't give it a dead guys in most of these guys were dead right 1901 is here overriding principle Boltzmann Lewis could have won it but by the time everyone understood what they had done and they were dead far-right merits to hung on long enough 2 women
.period whatever all we get is bars
not quite right yet that right there is no good reason why he did did win the Nobel Prize how
it's 1 of those things where everybody wins this award deserves it and then there's another 50 guys to show the 1 who never did this sort of the way this works I think but that's that's the
reason is that the war started here and it takes a while and you know they only got director gather for era you you're right Lucia wonder so this is geared he's our he's our hero in this whole thing is he is the only American were to be talking about pretty much but see and Lewis was American too John Lewis rather but were
not you know we talk about him a lot when you talk about finding Louis . structures at stake right
but we mentioned him at the beginning of a class probably you might not remember this when he got his he got the 1st PhD in engineering in the whole country the very first one that was given a jail I was in 1863 right before are actually right during the civil war right and then I got you know 1 of the sad
realizations you come to fear an experimentalist does all the guys whose names are attached to equations in chemistry are all theoreticians pretty much right so Lewis was a theoretician it's not the people in the lab mixing the chemicals together plotting the data said it's the theoreticians who sit at their desks and with their pencils and figure stuff out he was the
theoreticians like Einstein direct Schrödinger right these guys never get an experiment outside of school right they just look at other
people's experiments and figure them out so he had an appointment
at Yale graduate from Yale he got point there without salary but this was
common at that time if you hadn't proven yourself as a scholar it was not uncommon to get hired by university you teach you do all this work but they wouldn't pay you anything until you started the published which was hard to do on those days now you write a paper it's in your computer in 10 minutes you can submitted to a adjourn electronically right boom it's a link on your the browser opens his of which uploaded to the website it's gone your submitted in those days you know everything had to handwritten manuscripts in triplicate delivered by horseback to the Journal office which was somewhere on the East Coast thing and I mean this process could take years to publish a paper
right it's a lot different than it was in so it wasn't until he got an offer from Hopkins in Baltimore that Yale which is up in New Haven Connecticut said OK well if hopping does not 3 thousand a year will give you 2 thousand and that was enough for him to stay and then right after that he wrote it trading on this equilibrium header of had genius substance this basically spelled out everything that we think about as the money hammocks these days he
spelled out in know these days 1 the state's standard strategies that we all have is academics as you take some body of data that you've got to try to carve it up the smallest publishable unit so whatever you've done get the most papers I take it promoted in this business he
took everything that he had done and put it into 1 300 page paper and posted it's slightly the opposite of what we would do today he's even got a Facebook page but if you write a 300 page paper you too can
have a Facebook page for your paper
so years is buried on the Yale campus because the Yale campus is 1 of the coolest cemeteries that you've ever seen on it it's right on the campus called The Grove Street Cemetery here it is right here's Grove Street this is the Yale campus in New Haven New
Haven isn't dumb except for a Yale right it's you've got this beautiful University in this town that is really not so beautiful anymore getting better I guess
OK so you can anybody who wants to can go and look at the cemetery in the reason you might want to do that is because that gives very buried next to his dad here's map instead the cemetery
has its own site vacancies the name of everybody was buried in the cemetery what they did that's all people from like the 1800's critical
Noah Webster yes that
Webster number 16
argues that gave you go into really really cool Huge grave markers like that so the every New Haven Grove Street Cemetery OK so what we've been doing is learning the underpinnings of thermodynamics that's what
statistical mechanics is right it's the underpinnings of
thermodynamics but as tennis what we really care about is equilibrium we haven't said the word yet until today we have to use the word equilibrium I don't
think you're maybe once or twice
OK so we we need to get to that because we're ready to be done talking about this whole subject area right so let's get to the meat of the issue and then we can put it behind us but now oops Meyer selected schools to be up there so what we're trying to do today is to arrive at gives
function in this would be a whole bunch of symbols but I really think it's worth understanding this so here we go
the system is running so we talk about this already there's Open Systems closed systems and isolated systems everybody remember that isolated systems no matter or energy can change call systems energy only open both energy and matter most of what we said so far pertains to isolated systems because they're easier to
understand a lot but for
isolated systems we've already joyride that the entropy increases half the increase right for any non-reversible process the process reversible put an equal sign underneath this greater than or equal to 0 remember that
OK so from isolated city interviews increases during spontaneous process that's what that means would actually derived this again today if you're neither 1 of these 2 categories and
we virtually always are right for actually doing an experiment were not an isolated system or even an
open system closest right we have to consider both the system and its surroundings in this nominee inequality In other words it's the total entropy of the universe that's gotta get bigger in the universe includes a system that you care about it and everything else OK so
there's 2 terms in this total entropy theirs the system that you care about and everything outside of it because you're systems and communication with the outside world either by exchanging
matter by exchanging energy
OK so if the system is nice lady intrusive the gaps now this is the only thing that matters in terms of
understanding was something is spontaneous or not derived this gives function but the gets function is going to be
derived from that it's all about entropy the rights of you remember nothing else about this lecture you need to
remember that spontaneity of a chemical process is about entropy and the Gibbs energies just away the cops to parameterize In a convenient way the entropy for us that's all we're dealing with the gets function were parameterize in
entropy and convenient way OK so if this is true then I can move back over the right side a minus sign on him right so that has to be true and we're ready said we've got expression for the entropy in terms of the he gets transferred in the temperature and so I can make a substitution for the surroundings might DS here is going to be DQ it's plus the Cukor's is normally a minus sign that connects his miners DQ over tea with DES odds of that minus the assets in plus the 2 over tea surroundings now Q is a conserved quantity in other words if plus you enters the system might accuse removed their surroundings right if Q goes
into the system and had come from its surroundings I of that's a plus for those system at a minus for the surroundings right
but the focus so what we've already beaten into the ground is that DU use the internal energy that it was DW was the cue that means DQ was do you mind as the W and so I can just plug this Sanford DQ in equation right here right do you -minus dw I know that this equation right here we haven't
done anything fancy yet readings very simple but and
all I've done here is assumed that the only work that's being done is pressure volume work OK so that the TV now let's multiply bolstered by surroundings when we do that really get T surroundings on that side we're gonna lose it from no right side and so here we go right all I get is multiplied baby surroundings set out on the left-hand side it's gone from over here write this
doesn't look like our conservation of entropy equations anymore does it
starting the more my book were still talking exclusively about entropy here but we just made substitutions from symbol but this equation is gonna keep coming up we're going to call it the pink equation "quotation mark what we're gonna do
is we're going to
find convenient expressions were DU plug them into the pink equation and we're going we're find finding gives equation find the Gibbs energy rather the Helmholtz energy but that's already due in the
next 10 minutes really
keep coming back to the pink equation now at equilibrium for nicely system bubbled up to survive for isolated systems DVD equals DU equals 0 in other words the internal energy the system doesn't change the volume doesn't change in sulfide if I prevent the volume from changing and prevent do you from changing this term is 0 this term is 0 in in other words DSS of the system is going to have to be greater than equal to 0 for an isolated systems rights of I just take the peak equation I say if my system is isolated this term is 0 and this term is 0 I divide by T. surroundings DS system that a greater than equal to 0 so we derive that
now for an isolated system from this peak
equation which came from
this entropy argument the total entropy of the system and the surroundings has to be greater than equals 0 for any chemical process if it's spontaneous OK
now a minute stopped writing CIS every time I'm talking about the system so if you see a big of a big
letter would not know subscript assume it means the system some dog lovers running so keep using
that both now this is a general 1st for any system moving toward a new equilibrium that what the not equality means but it
means that the system is in flocks towards equilibrium all right now and then explain in detail exactly why we how we how
we think about that OK at equilibrium in the packed the external pressure and the system pressure in the external temperature in the system temperature are equal 1 another the
words the temperature is the same outside and inside the system the pressures the same outside and inside the system and it's intuitively obvious that this would have to be true for talk about equilibrium right OK so all
this means the president yes OK so at equilibrium the pink equation becomes the yellow equation the only thing that's different is the equal sign right so that's what In
equality means that were involving towards equilibrium when we get there we get an equal sign but will
come back to this equation right this is the so-called master equation of fermenting Amex but they think equations
actually more useful will keep coming back to the pink equation we walking continue to mention the yellow equation but but so the
peak equation again it addresses many processes of interest for example employment interfere held constant if the volume and entropy are held constant volume in entropy a I that constant devious 0 if I hold the entropy constant India's 0 and that means that the US to be less than 0 so what does that mean it means that it's you that is minimized as we
evolve from a non equilibrium state to an equilibrium state its view that as in minimized their only entropy and volume were
held constant do we normally hold on volume Constable we do chemistry I
don't know how you would I mean volume yes you can do it but to be difficult all right
so far it's not super UF's useful for us as chemists to use the internal energy as a marker for weather at equilibrium were not because the internal energy is only going to be a minimum when volume intramural constantly careful entropy constant very easily right so we make note of this and we move on In other words a spontaneous process created constant volume in entropy will minimize the internal energy this is true but not terribly useful
but then last week we talked about the
yen felt the maybe that's more useful but the amphibious you plus PV that's just a definition so I take it total derivative of age that's going to be DU players the deeply because plus .period and I can just solve for you and plug it into the peak equation part
that's standard strategy for the next but 6 minutes finding you plugged into the paint equation rearrange these variables got to you what we do .period into the pig equation with the pink equation tells us know what I do I've got this whole thing now that I'm a plug into their there it is OK and the 1st thing that we notice is that these 2 terms will cancel if the pressures are equal and let's just imagine that were approaching the
equilibrium state and the article right they won't necessarily be equal
until that's true but when were close to equilibrium this terminus term cancel hope you'll agree and if pressure and entropy are now held constant but we held volume and entropy constant earlier right now available pressure in be constant that is not more useful to us by the way but if we do that and to be so that goes to 0 pressure so that those 2 0 these guys can't with 1 another so we're left with deep so the ends helping is
the variable that we're going to care about if we can control and maintain
constant the entropy and the pressure notice that a useful thing for us
to knows chemists well it's a useful thing to know but as a practical matter were not going to be constantly doing this and tho is not going to tell us when Red equilibrium most of the time we
can't satisfy this requirement for maintaining the entropy constant OK now temperature actually it is a variable that we frequently hold
constant as camps so we we
considered DTE equal to 0 and DVD equals 0 ahead polls are requirements that we're sometimes to be able to satisfy the laboratory where
we could do an experiment at constant temperature we do an experiment a constant volume right in In principle that's actually going to be quite a useful for us to understand where the red equilibrium under those
conditions so the thermodynamic variable really care about your something called the Helmholtz energy an organ years wider definition for Tamils energy is called a basic will you monies ts that's just
how it defines right that equation does it really mean anything to us or it wasn't we did
derived from any place we just defined Hamilton that's what it is that we it is right that derivative of that equation are ideas do you mind DTS which is minus TDS minus STT Salford EU and what are we going to do plug into the pink
equation is the right answer right
there's the pig equation again we put this guy in 4 D U and there it is right right there OK and now what we're talking about right so that's going to cancel that without thinking too hard yeah we
assume were close to equilibrium in these 2
temperatures are going to be equal to 1 another that's the system temperature that's the surroundings OK and then if we further assume that DTU 0 devious is 0 the fact that it goes away In and the fact that guy goes away OK and so do you the
Helmholtz energy it ends up being the thing that we really care about right at the Hamilton Agee's getting lower that should be spontaneous the Hamilton a G is getting higher that should be non spontaneous for any system that we care about right
so if we're able to maintain temperature volume constant 8 is going to be our goal to variable now the way you do that is is by using 1 of these guys In case you're wondering where is the Powerball
it's universally called even always like 5 companies that make
these things but power makes the best ones Wallace is a stainless steel container into which the glass jacket that goes inside here and these are gas inlets and outlets and you see these 2 tubes right there are pressure although serve over
pressure valves bring the thin aluminum membranes and if if the pressure of the saying
goes about 3 thousand ATM those below right and sounds like a gunshot right when they go off right here you reading something in here this meal goes all the way up the here and when this thing is about to blow up those 2 valves prevent that from happening but when they go off by golly it's spectacular but I
think you'll agree this thing can maintain constant volume the matter what the pressure is doing as long as the pressure stays below 3 thousand 80 m that's you that's how you do constant volume constant
temperature right now most of the time we were not going to use this guide right so we have to still talk about the gives energy but will do that on Monday
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