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Lec. 15. One Midterm Problem, Free Energy & Equilibrium

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Lec. 15. One Midterm Problem, Free Energy & Equilibrium
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UCI Chem 1B General Chemistry (Spring 2012) Lec 15. General Chemistry -- One Midterm Problem, Free Energy and Equilibirum -- Instructor: A.J. Shaka. Ph.D. Description: UCI Chem 1B is the second quarter of General Chemistry and covers the following topics: properties of gases, liquids, solids; changes of state; properties of solutions; stoichiometry; thermochemistry; and thermodynamics.
power AdoMet calculations
case solutions gold Knot Tanning solutions Calcium hydroxide water van Computer animation Ideal Ideal calculations
Computer animation Optische Untersuchungen temperatures Wasserscheide Stoffmenge pressure stuff
Computer animation function Optische Untersuchungen temperatures Pitch (resin) Stoffmenge case end man
sense Primärer Sektor complications valine case Computer animation function Optische Untersuchungen Oceans report Stream bed Ideal calculations
sense type flame freie Enthalpie chemische Reaktion case pressure end systems water conditions Tee flow Computer animation match temperatures low temperatures entropy chemist stuff
sense drug Gases factors burnings burning chemical molecule firing age electron temperatures Sieden Stream bed mineralischer Seltenerdmineralien Gases chemische Reaktion complexes chemical Tanning Thorium water Wasserstoff conditions Computer animation Optische Untersuchungen materials oxygen chemist atom
sense type chemical element biosynthesis molecular nitrogen biosynthesis balance carbon chemische Reaktion pressure Knot Wasserstoff Wasserstoff Computer animation temperatures stone standards low temperatures Carbon dioxide basic ammonia processes
type biosynthesis Electronegativity pressure Tanning systems Computer animation yield Optische Untersuchungen materials temperatures low temperatures ammonia spontaneously
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power nitrogen Haber-Bosch biosynthesis rates chemische Reaktion abundant Wasserstoff flow Computer animation yield temperatures Iron rate low temperatures scale ammonia
flame areas nitrogen biosynthesis Haber-Bosch Colamin Carbon Monoxide oven Nicotinsäure food source man membrane water firm Wasserstoff Computer animation age Methane Coca natural gas oxygen atom ammonia
Index type chemical element Index chemical element nitrogen freie Enthalpie Hausmannit chemische Reaktion atoms pressure end firm death conditions Computer animation temperatures compounds standards fertilizer ammonia standards
delta biosynthesis Hausmannit solutions pressure Knot solutions chemical Computer animation yield Optische Untersuchungen temperatures molar standards molar Ideal AdoMet Ideal ammonia standards
Substituted case Humifizierung chemical age temperatures molar derivatives Ideal TPD standards chemical formulae set Gases freie Enthalpie Gletscherzunge Cadmium sulfide chemische Reaktion pressure Knot end Tee Computer animation Gamma molar AdoMet Ideal
Digital elevation model Seltenerdmineralien Computer animation function rates Gases standards pressure mineralischer AdoMet standards
chemical formulae chemical element chemical element Computer animation function Gases compounds molar chemische Reaktion man end
Index power delta power chemische Reaktion case pressure Knot syndrome Computer animation function standards derivatives Mole Fractions standards
reactor chemical formulae delta power concentration Gases chemische Reaktion pressure chemical conditions Computer animation firing important overexpression standards
sense Wasserscheide case solutions chemical Käse Clenbuterol temperatures important storage standards areas Holes concentration Gases chemische Reaktion Electronegativity solutions pressure water Computer animation metabolic pathway function Optische Untersuchungen Wasserstand standards molar overexpression stuff host
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chemical formulae delta Computer animation Gases temperatures molar freie Enthalpie standards chemische Reaktion Knot standards
chemical formulae delta type left drug oil chemische Reaktion Tanning chemical Computer animation age yield Feinchemikalie Gasoline Optische Untersuchungen important materials Kunststoffe Gasoline standards barrel fertilizer stuff
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I think on the exam I saw people counting Digital With their fingers to determine the power of that's crazy put your calculator on scientific notation and never take it off scientific notation unless you're going to become account leave it on that and let the calculated the figure can't digits is very prone to error to get the wrong power of 10 new commitments they it's way off it's a small mistake accounting but it's way off in terms of the answer OK we had
a problem to do in which we we had Vander Wal Stassen and it's still solvent for VAT like on the 1st midterm we had the anti and we were asked to estimate how many moles all of gas were in there and of course we can get our 1st estimate from the ideal gas equation but we don't expect that sold center will scarcely question because the whole point of the vendor well-staffed equation is that takes into account the attraction and repulsion and because the Constance a and B have been obtained by looking at the actual performance of staff it's going to be more accurate the ideal gas equation the price we pay as a and B are different for every material OK so let's have a look at this problem and make sure we all know how to get estimate for lack of a better term to 2 digits the value of an you could actually solve but solving equations symbolically is usually far far too much water if you only want 1 answer if you want to keep changing he vehemently and figuring out over and over yes it's probably worth the the time to sit on the and solve things a can equals some gigantic with that of spreadsheet commands plot watch a lot but if you just getting 1 value it's way way too much work and the other thing about it is that symbolically solving things is also prone to error you can make a slip-up and it could be
that the number of calculators strolls in the exact solutions is about 10 or 20 times the number of calculators strokes to just get the answers in that case it's going to be far faster just give the answer OK here's our equation
the foreign I didn't example for we have a fixed the value of the number of moles and the pressure and we were trying to get the we had a and B of course and the temperature we could take the same approach here but it's no good if when you get asked both sides change because when both sides change it's hard to figure out what's going on it's like a target that keeps moving around it's much easier to you target that still than issue that an animal that's running around much harder to get and so to get rid of this I want to somehow set this up so that 1 side doesn't change on the other side has that's the idea and I can do that anyway I want but the simplest way that I can see the doing here is to divide both sides by an and since it is not I'm OK doing whatever I take equation and I divide both sides of the equation by anything I make note the margin whatever ideas divided by better not later turned out to be 0 or that I have made a real mess up sometimes that does happen you forget answers 0 but you've solved the wrong equation it will divide by an on both sides of this the central goal and whether 1 over and out here and we've got a bunch of stuff that depends on him and we've got arch eh an arty well Wozzeck constantly was specified so that means
that we now get this nice equations to
Salford it's a fixed target we can home in on it quickly so let's put in the number on the exam at least in 1 version we have . 7 leaders for the volume of 50 . 5 degrees C for the temperature which we immediately convert to Celtic to atmospheres 20 . 4 for pay and the appropriate units and . 1 3 8 leaders from all 4 bh we just put on every single number that we've got into this side and then we end up with a strictly numerical equations to Seoul which
is this following equation on the
left-hand side we have won over and times quantity to plus 41 . 6 3 2 6 5 and squared times . 7 -minus . 1 3 and equals 24 of 26 . 5 5 7 9 1 I tend to put a lot of pitches because I want to make sure that I'm not inadvertently getting up were result because I rounded the target off and usually it's OK but I'm in habit of writing down a lot of digits just to make sure it's OK and then putting in our guest now we only need entered 2 digits it's not too bad we have a guest for an if we don't have a guest but in some guests and I just don't put an end equals 0 that's a bad idea too small my 1st guest in this case since we know P B and C. we just get I guess that it's probably pretty close to ideal let's say and so I'm going to guess the number of moles this can be Over and once I have that then I up this function and if I a calculated that will set up a function so that's 1 keystroke I use that feature of the
calculus because I'm in to beginning this function over and over and over it's going to be much more efficient OK let's have a look Our 1st guess
if we take TV Over is . 0 5 2 7 mold and because it has won over leading when I increase and it's going to make the functions small but I don't need to know that in the events in other words if I have a complicated equation lots of things with some variable X equal to I'd take a guess and I sector decrease and I see how in the hell and I'll figure out whether I should go up and down if I make a if I don't make a table that I might get lost and that's why I always like to make a table when I'm doing this because I found out with experience that it's quick I said what I'm going to guess for an what I'm going to get to the function and I usually divided by the units so that I just write a number that I have a target value which is part time at sea and then I have a comment in case the phone rings or something happens and I have to go back to I like to have common off I go back to it weeks later and I have to redo it again for a report the comments tell me what I was thinking at the time so I guess the ideal gas value . 0 5 to moles and I find that function comes out to the number 29 . 0 6 4 2 what I want again is 26 and so the function is to bed when I say too big I'm referring to the value that I got not the guests for in think just the function .period now it since it's too big that means that and is probably too small and 1 good way to do it as a wallflower How too big and too small it came out to be 29 over 26 about so therefore if I increased and by about 29 over 26 but it might be pretty close it turns out that's a little bit too big and with some experience I say Well I'm not going to go all the way to the see the minor sense where the the other thing and I by like then Dec 29 over 26 to get about 1 0 5 7 I guess about halfway and this was just pretty lucky I got . 0 5 5 I tried I increased it and yes it went down 26 . 6 1 4 6 I want 26 . 5 5 7 9 2 this is just blind luck this is what I really did and it's just luck but it's that close but it is quite close and I only need 2 digits if I were in a rash I'd say I've villages . 5 5 as my 2 digits 5 . 5 times that in the months to but since I have a little bit of time I'm going to bump it up a little bit to see if I can lower this down and I just tried putting another digit here because I saw 1 when I went up 103 it it went down by 3 I'm just going to bump it up just a little bit and I tried . 5 5 1 and now I get 26 . 5 1 0 2 I want 26 . 5 5 7 9 so I'm just below here's what I've got you when I guess . 0 5 5 I'm a little bit of time when I guess . 0 5 5 1 I'm a little bit low therefore the answer is between . 0 5 5 1 . 0 5 5 1 while I only to digits I'm done I quit it's between these 2 if there were between . 0 5 5 and . 0 5 5 4 4 9 it would still be . 0 5 5 so I'm done but can be that fast if you practice a little bit or it can be like a game of hide and seek where you punch wrong buttons 1 time and you get down to answer for and then you kind of get lost a mixed up that can happen you can just make a mistake on the calculator and then 1 of these values you get is way off but if it's not behaving stopped for a 2nd try that again to make sure that you didn't punch wrong but then your home in on it has to keep a it has
to to make sense because these equations or not that complicated some equations can be tricky because they have a lot of wiggles and and they may come down near the answer go up and then really hit the answer those kinds of equations can be very tricky for anybody to solve including a computer then you may have to grasp the whole thing and look at it and try to cement on where you where you need to OK so that's the comment on that type of problem now let's get back to to the free energy where we
left off we had a summary and near here is the summary we considered exit there make actions reactions disorder the system and ultimate reactions reactions that awarded the system and we came to the following conclusion if the reactions XO Thurman so don't into the environment and disorders the environment and in addition if a disorders the system because the entropy of the system increases for example by making a lot of again then such a reaction is always spontaneous at all temperatures those kinds reactions are considered winners they always were you always get a high yield of products if on the other hand yet x 0 Thurmond disorders the environment but the system waters for example life-size freezing good in that case it's spontaneous at low temperatures low enough temperature if its end of the match and the system becomes more disordered then I can overcome the end of the match part of it by making minus the Delta take a negative and that means making tea BA since Delta as is positive and that means that this kind of reaction will be spontaneous at high temperatures and then we have some we get stuck with the end of the month was for making it more orders and such a reaction is not spontaneous that doesn't mean we can't do it that means that in order to do that reaction we have to couple that with some other reactions we run into different beaker that's highly favorable so the overall putting everything together the whole 9 yards is favorable that's what chemists oftentimes reactions on favorable we put on energy we beat on we put pressure on it we make it happen anyhow but it needs it's going to cost more To do that on somebody's going to be paying for that whereas the top 1 I just makes and Schmitz this stuff up and it just go 1st I think I don't have to do anything and the way we figure this out in every case a constant temperature and pressure is we just look at Delta G and we say Delta chief or whatever change were were writing whether it's a phase transition or chemical reaction or a nuclear reaction or anything Delta GE has to be negative and so either Delta H is negative this thing's negative or both are aware that some of them is negative and that's how we come to the east conditions on planned the reactions can occur yes just because the reaction is spontaneous however that doesn't mean it's going to happen facts it is spontaneous for us to burst in the flame we
write down all the materials were made out of what's oxygen and we work out delta G it's been a huge and negative but we still live a rather a long time because the reactions Our slow on the other hand if we keep a person up enough they get caught in a burning building then they will land on fire and they will burn and that reaction and its saddening to quickly and that's extremely dangerous OK now I
gasses always have higher and solids and liquids that just makes sense because they're far far more disorder so we have a chemical reaction of any kind that produces a gas or if it produces more malls of gas that uses then we can predict that reaction will have positive dealt passed without doing anything else just without knowing anything will assume it has positive Delta S and therefore any reaction that produces a gas will become more and more favorable higher and higher temperatures because the miners T Delta last terms will will take over and finally no matter how Windows amid the reaction here's how how positive Delta ages if we hit it high enough the minus the Delta last term becomes bigger negative if the reaction is producing gasses and the bed that term takes over and that's why if we eat up molecules enough they'll break apart because when they break apart we take let's as 1 wall of material as a gas and we converted to several moles by making them all Adam and that will be favorable at high enough temperatures sometimes temperature is very high but it means you can eventually break things apart by beating them up and finally you can actually boil the electrons themselves off the Adams you can meet them up they become much more disordered and they sail off and now we have kind of a sea of ions that's a very very high temperature the material is called a flattened the study of for plasma physics because there's not that much chemistry that can occur In a plasma in the traditional sense that a chemist talks about making complex molecule molecules like drugs or materials and we can do this as it stands now we can actually by brute force we can run water backwards so we can take a nuclear reactor and we can heat water itself out so hot that we can normalize it busted apart in the page to 102 we need a lot of muscle to do that but you've got a factor of 10 million in the nuclear reaction so you've got the muscle and you can make hydrogen that way if you
want to and it works hydrogen is extremely useful because you can use it in lots of other reactions and as we saw it might be useful 1 day as a fuel because it is very very green in the sense that it doesn't produce any carbon dioxide because it doesn't have any carbon OK let's take a look at at them at the ammonia synthesis which is a
very very central reaction to our well-being as will go into here in a 2nd the synthesis of ammonia From hydrogen and nitrogen is is an excellent thermal process good Delta which is negative we aren't dead yet and we know that because we'll see if we make ammonia from elemental molecular hydrogen and molecular nitrogen were making it out of the elements if we make it out of the elements in the standard state Delta of formation we can look up at 298 . 1 5 Calvin is minus 45 . 9 killer jewels for more and of course that's from all of ammonia so therefore the ballots reaction we have to right has fractions and we write down formally possible of molecular nitrogen plus 3 halves of a mole of molecular hydrogen and we get 1 of ammonia NH 3 well let's look at this and what we can ascertain so based on what we know and the reaction that should we carry out this reaction and high temperature for low temperature and then looking at it further should we carry out the reactions at high pressure for low pressure here's what we know there's a half a mall again last year and 3 have small gas here and therefore there's 2 malls aghast on this side there is 1 more Lagasse on this side but there's more malls of gas in the reactants than the products it was it's axle Thurman it's
dumping heat into the environment but it's becoming more ordered because we're producing fewer moles of gas then we start out with that should tell us what to but here's what I said we've
got more moles of gas for the reactants and products so Delta test is negative Delta H is also negative and therefore minus t Delta as is possible because dealt as his negative T is always positive therefore I don't want that the Delta asked to be too big I in fact want to make the reaction spontaneous by keeping the small if I heated up too much what I do is I break the ammonia backup into the starting materials and fact felt there might dynamically we should use low temperature rather than high temperature and with respect to pressure will come back to this in a little bit there more moles of gas for the reactor and for the product and so if we apply pressure today will literally squeezes the reactants into the product because the system will try to contract as we squeeze on gets smaller it's not hard to try to get bigger when we squeeze on it and try to get smaller and by squeezing on it we can try to force the formation of ammonia and therefore what we would predict just from this analysis is that we should use low temperature and high pressure In order to get the best yield of ammonia make sure that
the reaction is spontaneous and organ and have more products than reactants at equilibrium no in fact ammonia
synthesized by the harbor process I'll show you what that is in the 2nd In practice high temperatures review really hot 450 soldiers in his heart is wearing off and people are not in the habit of wanting to have stuff up for a fall because it requires a ton of money the stuff up fear requires even more money it turns out to cool stuff down if you talk to a chemical engineer and you say I've got a process and it involves heating stuff up like crazy and then we get the product they will be that please the 1 0 how much energy is going to be paying for hiring and reduce the heat but they won't say in honor of a non-starter but if you say Well I've got a cool the stuff down very very cold that's also extremely expensive today because not that pump the heat out of everything To keep it cold and they're much less comfortable with that for for most industrial processes so most industrial processes and try to keep stuff up it's too simpler then there are the giant refrigerator and all the maintenance and everything else the cool stuff down the question is why on earth do they in fact eat this stuff up across a ton of money and it should give a low low-yield and the answer is they aren't in the business of getting the best
deal there are in the business of getting something done before they go out of business and that means they have to get the reaction to run quickly enough they don't want to be in the position of waiting for somebody like me today I'm unstable but you have to to wait too too long and so if you try to make money on the dying and I learned a long time because I'm genetically stable you don't make much money and if you're trying to make ammonia and you put it at low temperatures and the nitrogen and hydrogen sit there and stare at you for hours and hours and hours and say Come on come on a new product I note eventually you have to give me the product eventually too long if so to get the reaction to the at a reasonable rate were forced to heated up and this is why catalyst it would be extremely important for this reaction in fact a lot of research been and put all kinds of catalyst for this kind of reaction there some really really good ones the problem is we run this reaction is such a huge scale hundreds of millions of tons of ammonia but we cannot afford to to use a catalyst that uses something like Latin because it's just too expensive they have enough catalysts to be able run the reaction so we have to use something that's abundant and what they typically uses specially treated iron To get
material to the form but if we could find something cheap allowed let's say this reaction to run at 200 Celsius over 100 Celsius we went all the way around we get much more ammonia yield and it would cost much less money because we would never be he'd everything up to such an enormous temperatures
why are we worried about ammonia and the region were worried about ammonia is that
we like to eat and if we stop producing ammonia then we will surely stars the way it's done this is analysts the no particular plan just generic I have to get the hydrogen 1st in the wake of the hydrogen is written by Cameron ,comma I bring in methane and water and I heated up like crazy and I get carbon monoxide and age this is what being at the English is used for natural gas in fact that's what they called water against it had a lot of problems because carbon monoxide is poisonous so if you're yes flame went off the actually flooded the kitchen with carbon monoxide and that was the way a lot of people committed suicide you read accounts Nour Sylvia Plath stuck her head and other Americans tend to think he stuck his head in the oven on Friday ahead of blue yourself up or something but you didn't have to do anything like that he stuck his head in the oven and closed space and the carbon monoxide filled so it was nothing so violent that and then we landed area which has the oxygen and nitrogen and down we go here with nitrogen hydrogen and CEO and then we heated up to 500 Celsius and we get C O 2 the C O 2 goes off eventually and we end up finally over here with nitrogen and hydrogen which we then he like crazy and compressed like crazy 243 100 PSI 300 by and then we produce ammonia and then vote the way we get to run in Sweden and cooler and the ammonia condenses out eventually as a liquid which we take away and then we recycle the hydrogen and nitrogen that didn't react and round and round and round we go and we have to keep putting a lot of energy because we have to keep compressing it and then we have to keep it and then we have
to cool than we drain off the ammonia but in the end we get what we want we produce ammonia at a reasonable rate and although some money and then gets put into usually artificial fertilizer sometimes they just simply use ammonia in the Midwest you can find places where they have they the ship divots in the ground that apply of creates and they haven't yet and they just sticking ammonia HSH and you know what the anywhere around when they're doing that because the harmonious very very powerful smell and you won't like why do we have to do this well here's here's the reason 1 out of 2 of the nitrogen atoms in your body and my body came from this 1 was done by Ken if you rely on organic farming you really going to be half as big for the gonna be half as many people OK let's go back to the standard free energy the standard free
energy of formation is just like the standard mentality of formation it's whatever the value of Delta G when we make a compound from the elements in their standard states at 1 atmosphere were sometimes updated to 1 bar but will just assume 1 atmosphere the closed pressure and the quoted temperature and the "quotation mark temperatures usually "quotation mark room-temperature 25 degrees Celsius which is a bit warm actually for room-temperature that's the standard and we reserve the special symbol Delta G With a subscript deaths to mean formation and was superscript 0 2 mean the standard state just like Hess's loss we can figure out the standard change in free energy for any reaction if we have the standard free energy of formation of the product and we have a standard free energy of formation of all the reactants there we just take products minus reactants and we get a number and if that number is negative then that means that standard conditions it's favorable for the reaction to go to the right
for an ideal gas the standards state is 1 atmosphere pressure and the quoted temperature which is usually to 98 . 1 5 Calvin if we have an eye on in solution Our standard state is going to be 1 molar concentration and in more advanced courses you have to make corrections for not ideal behavior but freshman chemistry we ignore all those we wait until you decide major in chemistry and then we say all its way way more complicated that it was the 1st to provide then it's too late to buy already taken Oregon but for an ideal gas we know the molar volume that's the overran his arty over the In the standard state than the standard pressure the molar volume is just Artie over the Standard and then if we know delta G standard we can figure out delta G at some of the pressure the reason I want to do this is to eventually show you why it is that when we apply pressure to the ammonia synthesis we're going to get much higher yield we probably won't get to that today but I want to lay the
groundwork for that will
remember the definition of she is H minus the S H and asked state functions he is obviously dependent on the state and nothing else so G is a state functions and if we do it per mole I tend to like to put a little subscript and which means cheaper mold of material saying thanks H per mole and ask for more if I want to make a small change in free energy I can do it by just putting the magic little D in front of things and taking the derivative as I say I got said before if you don't like using just the Jeep and TEDx those doesn't matter the Axel go away at the end small change in the Imola free energy is equal to a small change in h Moeller minus the S a small change in a smaller just DH mall a small change in a product bring out minus sign it the DS smaller plus a smaller DT that's just the rule for taking the derivative of a product of 2 things and now I can look at this and I can't say Wait a minute I know what H was we invented age because we didn't like the internal energy we said we want to know that he needed constant pressure not the heated constant volume because we don't do chemical reactions that constant volume and so forth H I'm gonna substitute you plus the smaller and this part here I'm just going to keep the same now I've got this thing and then I can take the derivative of that that's the plus PDB Class -minus TDS minus STT and it looks like this is getting more and more complicated so I said here this looks like a match but the mass fortunately is going to get simple because we're going to use the 1st law and 2nd law them and the 1st loss as that basically he must work is the internal energy so for a small change in you do you this DQ smaller lusty W. Moeller it's always true and it's also true if I do a reversible because reversible is just a special case on the other and if I do a reversible even reason I like that is what I do irreversibly I can say the reversible he upon the temperature is the change in Anteby or DQ reversible Muller is equal to CDs Muller and then finally if we don't allow any kind of work except pressure volume work in other words were were running the reactions and we are definitely not doing any kind of electric chemistry or something else where we're taking office :colon the only kind of work were allowing his pressure volume expansion then the reversible work remember is when the external pressure is equal to the internal pressure which is just he and there's a minus sign because as the gas expands its internal energy goes down so workers negative if we then insert those guys PDB and TDS In up here and 2 you we then get the following which is this big long there the DU and
then there was the PDB that cost and EDP and TDS nasty and what I now notices that I can get rid of this tedious would that tedious because they're the same and I see that to PDB isn't so I go a I get rid of that 1 now there is this 1 now they're gone "quotation mark now it's starting to look like something that means now for a small change in free energy it's equal to the molar volume times a small change in pressure -minus the molar entropy once a small change in temperature and now find willing to fix the temperature but say at standard then NTT is 0 because I fixed the temperature so tea is a constant there is no change in tea we finally get this simple formula that the change is small change in Mohler free energy it equal to the molar volume times the and for an ideal gasses we know the molar volume as we know the ideal gas equation now we have a little equation here at the agency is Artie upon the I'm steeply and that's nice possesses that separated equations and so this formula letters figure of finite change From he standard some of the pressure he and let us figure out how she is going to change so let's do that
you don't have to know how the liberals were but the goal of the just acts and once you have an upper limit on the lower limit you just the fact that so the inability G From the standard to some other value g it's just the top miners GE ball on the interval as the integral besides party upon the he is 6 hours fix those constants that come out the interval of the over the years the natural law and I think the natural log at top -minus the law and I usually write that 1 fractions by knowing how logs were you subtract logs you can do it 1 term by dividing and so I end up with this the equation here she at some of the pressure minus G at the standard rate is equal to party times the natural log P at the other pressure divided by P at the standard pressure usually bad I write this so that everything I want is on the right hand side I write the gives Muller gives function at some of the pressure is equal to the mall gives function of the standard pressure Saadi log P over the standard and if I've got a bunch of gasses and this
equation applies to each get the suppose
we have some reaction like that will get back to a monument the Lester I've got a walls of the compound which is aghast plus the moles of compound Bigby which is aghast you see most of compound being C plus the malls compound the dealers oppose these are all gasses ABC indeed the little ones the numbers and the other ones they're going to be molecular formula for something so they could be elements like the on that suggests and in the end the reaction then we just for each 1 of us we just use this formula get this big man and we say Gee we would know what the gives function as the standard state and now we have to use the partial pressure of because only the partial pressure of any changes the Muller gives function of air it doesn't care about the other ones because they are not and the partial pressure B changes the function of B and so forth 1st eh indeed they're all separate the 2 have nothing to do with each other you treat them all separately and there are minding their own business my bank account depends on how much I got checking how much I gotten savings but not on somebody else's bank account who's not me on the way to think about OK if we want to figure out the changing we're going to take G of the year got multiplied by the numbers as we always do that subtract G of the reactants multiplied by by the numbers and that should tell us what we need and since we have a formula effigy of the of the reactants and the products we can much all this together and and get
what we want we get the following we 1st write
down what we mean the Times the Muller gives function of C plus the times function apologized for using little the heroes a number 1 slightly earlier in this lecture I used it to mean the derivatives and then a hero and then be subtracted some of them and I know that these things break apart into 2 terms each and I'm gonna write them separately see times the standard becomes a standard for D -minus state suspended for a post the times the standard function for B and then I had these other 4 term plus the Times Artie Long PC over the standard the DRT log PDO or the standard minus the some of the reactants K and B the same thing and this is just down an exercise bookkeeping we want simplify what this means the 1st line is what we're just coming called delta G standard for the reactions In the 2nd line we're going to see how the simplified that of 1st we agree what delta G standard means for the reaction it means the difference in the standard gives functions multiplied by the story geometric coefficients that's what it means and for the other we like to make it a little
bit simpler and the way we do that is we just follow are usual trick for logs in this case we leave the RTC we could put CRT up here if we want but we leave the RT that's common to all the reactants and products instead we put the sea I'm here In the exponent of as here because the natural log of something to a power is the power plant's natural log on to something outside the natural works and if I want to use Dalton's love partial pressures I can say Gee the partial pressure of sea In this equation is equal to the mole fraction of C times the total pressure and I have to divide by the stand of pressure and noticed that we can't have any units here so whatever the units of the standard pressure are that's 1 atmosphere that all the pressures have to be atmosphere because I cannot take the log of something With unit and I switched X C because I was getting carpal tunnel syndrome From switching back and forth in this clunky program From symbol 2 non symbol fonts and for a while I should use the nice car for the mole fractions if I were doing that had would been dead and my arm in a sling and so I just decided to use for the mole fractions close enough all right now let's and let's condensed them all those 4 terms with Lotty log P and that this form and if we put it
all together we get this
thing we get delta G for the reaction His delta G standard plus party natural laws and then we have the ratio of the partial pressures of the products raced to their powers divided by the ratio of the partial pressures of the reactor raced to their power that chemistry work this way actually took people of very very long time to work out fire was equilibrium behaved like this it now seems pretty obvious to us to us but it was actually a total mystery for a long time until this kind of law was discovered we usually write this like this as we have a ratio quotient we write as Capital and we call that the reaction quotient and all of this is the ratio of the products raised to various powers divided by the ratio of the reactants raced to the various power and that lets us then finally get a very nice formula which is very very very important that's delta G for a reaction and some other conditions is equal to delta G Standard Plus RT log he but the this is just what I said the definition Of the reaction quotient all these things here for gasses are going to turn out to be basically measures of concentration pressures of gasses tell you what the concentration of the gasses but pressures of gasses agreed easy to measure because I just have a pressure so I usually like to express concentrations of gasses In terms of pressures and not in terms of moles per liter for a gas I don't like that so much because the gaskets everywhere it can be a little bit harder to figure out what the volume is not a lot right away the gas because it doesn't weigh that much but I can measure the pressure easily With the pressure gage
if we have solutions tho then instead of measuring the concentration of a solution by pressure which would make any sense we we just use a standard concentration 1 Moeller as the standard and then we measure all the concentrations in mall or malaria moles per liter and that we can do for solutions and here itself doesn't have any unit all the units and you are divided out by whatever the standard stages and I have to know what the standard stages to know what the numbers mean but as I said for gasses often will express the concentration is pressure partial pressure we can also use small area if we like and freshman chemistry books seem to have a B and their bonnet about converting back and forth between Haiti and Casey I don't think it's that important at equilibrium whenever the thing settles down and it's made all the reactants it's going to make Our all products is going to make Excuse me and used up all the reactants it's gonna use the reason why the reaction is because the gets function for the reactants and products is the same the way to a imagine a chemical reactions is to imagine having a bunch of popular with poses you poor water somewhere and if this 1 is lower and most of the water falls out of this tank and fills up this 1 if they're connected by a vote of their connected by a host because there's no pathway then it's going to take a long time that the panel but if we have a catalyst and as a great big holes and we pour stuff and once higher than the other all the reactions are gonna run downhill melted cheese negative and make profit but sometimes the bottom of the reactants is not higher than the top of the products in that case and then have a little bit and stuff like the catcher left behind in this it's not all going to go most of the world In fact for any reaction in 1 phase In theory not all that can go although in practice sometimes the concentration we predict is so small that it might as well be 0 but this is just a very important point In constant temperature and pressure things
run down the hill in any way they can until the gives functionaries equalize the gets function is like the water level for chemical reaction it's what tells you how it's going to work and that's why we want to to figure out what it is so we can prediction where were going to get a lot of products are a little products and or or whatever we're trying to do OK usually we
want to get the deal we want to know what we always want to know what yield products we can and how much of the reactants will be left because if they're too much reactants left over that's a purification headed sometimes I could be making a very useful medicines Out of poison it often happens that this exactly what you're doing if the yield of the reaction is extremely high I don't have to worry too much about the reactants that are left over but a coating of tablets and stuff but if the yield is not so great and I have 1 per cent of the original sloppy toxin left over it's a big headache now I have to do something to purify it whenever I have to purify things it cost money a lot of it sometime depending how here I need to get it but like to try to run reactions that are so-called quantitative they give essentially 100 per cent yield oftentimes we can't do that b equilibrium value of Q is so important that we give it a special symbol call the equilibrium constants Hugh itself just depends on whatever the concentrations are but Hewitt equilibrium so OK take the concentration of C equilibrium constellation deity equilibrium not divided by the concentration of a constellation of when all the smoke it's clear that some number and that number we call Casey if we express in for concentration in malaria if a gasses To keep them separate where express it in terms of partial pressures and then the cost and escaped with he for pressure and for us it doesn't really matter we just have to keep them straight but the boat equilibrium constants that's the most important thing the
equilibrium constants that means that they don't change there are constant once we know the cost and we know how much we're going to get and here's the formula that advocates the if everything's
aghast we just use the partial pressures and we remove the units by dividing by the standard state let's say 1 atmosphere and 3 3 lines just means I'm telling you it's not just equal its I'm telling you what to do it's defining what it is then so this is defining what the simple kicking me here's the important point if we know the standard free energy which we can get by just leafing through tables are looking them up online then we also know the equilibrium concept because Ed equilibrium Delta G is 0 so instead of delta G here the reaction to the equilibrium there is no change in Gee that's why it's all settled down the delta G is 0 they settled and that means I can substitute in 0 and at equilibrium is OK but I will put a subscript so it can be either 1 but delta G itself is 0 delta G standard is not 0 because Delta G standard refers to the temperature quoted in the table and everything in their standard state I want more well at equilibrium is not going to be 1 molar we hope it's all going to be products for example since this is 0 we know that this this is Artie land and that means if we look at Delta G standard we know today because we have a formula for it we certainly know what our Antioch and that's really the most important thing about looking at free
energy is what we look at free energy we can predict if we're going to get more product the reactants and we can predict exactly how much which is important this
is a very very very I should put for important formula delta G standard physical the minus party natural log K because now while the table but were putting me to sleep when I was a student I just couldn't see the point of all these tables tables Tables Table Delta age of formation Dalton formation this matter what was the point of it suddenly they become very interesting because now all I have to do it's it's Duck Soup I just look up the delta G a formation of everything all the In the reaction when I subtract the products finds a stocky magical coefficients -minus reactants times historic metrical traditions and now I know delta G standard for that reaction magic I know How much yield of products and then again without doing anything else and that's for any reaction I write down I know what the theoretical yield can be usually I'm going to get less than that because might prompt mind reactants 100 per cent pure I can't wait long enough for equilibrium a long long long but I know what I can possibly get in if what I can't possibly get is not good enough then as is usual I have to do something else usually what we want is a high-yield like about 100 per cent of something this much more valuable than when I start I'd like to be able to take a barrel of oil
and turn it all into gasoline because gasoline is worth a lot more then a barrel of oil but I can't get 100 per cent yield of gasoline because of the way the reactants work and so I have to use the left over to pave the road and do other stuff and you can be assured that every part of every barrel of oil is used up the sad thing is that most of it is eventually just burned In fact we need all the fossil fuels not to burn up but we need them to be able to make like drugs like fertilizer like plastic like all the fine chemical industry we need to have them around because all those materials come from these things so if we just take every single barrel that we can pump out and and burned that's good for energy but then the C O 2 is far less useful then the actual oil was in the 1st place when it comes to synthesize and other chemicals because delta G 4 C O 2 going back to what we want get is possible and that means get to go back we've got put energy and when we get the energy from we just burned everything up that could be a big problem in the future OK let's do 1 more problem
we probably won't have time to do the whole thing let's start To let's go back to our our however synthesis of ammonia and now I've looked up the free energy of formation of ammonia because table was interesting I started leafing through it rapidly and minus 60 . 6 killer jewels from all what's the equilibrium constant in terms of partial pressures cake at 298 Kelvin at 598 . 1 5 Calvin at 798 . 1 5 just do the 1st temperature today will do the other 2 starting on Thursday well 1st of all if I see is state function if advising Delta something I write the reaction whenever I see Delta aged delta G anything I say what's the reaction before I do anything and the reaction is to make 1 mole of ammonia which means I need these fractional coefficients again and the quoted free energy refers to exactly this reaction because this happens to be the at at free energy of formation because I'm using nitrogen and hydrogen and therefore 298 Kelvin I can take delta G is minus Artie log and I can say here's is minus delta G over hot blockade and then I can take the exponential functions both sides blockade goes away the exponential gives me this I get rid of the killer jewels by writing 16 thousand 600 jewels I put in are in jewels not . 0 8 I put in a temperature and I get some positive number and 298 the equilibrium constant is 730
that means this is the winter idea gangbusters of ammonia and only a few per cent Of the reactants left and I will see what happens at a higher temperature next time