00:05
are you guys the OK so
00:14
"quotation mark Friday it's mainly
00:19
going to focus on the stuff that
00:20
we've done in the last 2 lectures including today and that turns out
00:26
to be stuff that's in these 2 sections mainly in our Chapter 16 all right where the jump around a little bit
00:37
because we're trying to condense this material into the smallest number of lectures possible without throwing out too much stuff that's important were really only been partially successful we are thrown out stuff that's important constantly but we've got to talk about kinetics and chemical dynamics and so we get leave some stuff out and so it feels like and jumping around and skipping stuff as we go forward I am a lot of stuff is getting left behind OK I truly apologize for that if we had 15 weeks we would still probably not have enough time to do everything OK self if you look
01:30
back at the last 2 lectures by you'll do a pretty good job I think of into the problems increased life and
01:36
polar questions right out of the last couple lectures so
01:41
already today's review some of the key concepts from Monday where talk about this thing called the chemical potential for the 1st time
01:52
and I am really not happy with how I explain this a Morgan on this for the last 2 days I still like the way this is getting explained you're the victims
02:07
always talk about the gives doom equation were going to explain the ball also
02:13
it what I mean by that in a minute
02:17
OK and that sort of be the end of Chapter 16 were leaving out a whole bunch of stuff In Chapter 16
02:26
that's really important OK but we're just gonna leave it out so it's
02:34
mainly sections 16 3 and 16 4 OK so when the call this lecture the chemical potential but we're really not doing such a good job
02:48
of explaining this concept I'm afraid so the 1st time I
02:54
put this table of I think was last Friday we were trying to show that these state functions the internal energy the and the the Helmholtz energy that gives energy can be used to tell us whether a chemical processes spontaneous or not when a chemical process is governed by these constraints constant temperature pressure constant temperature and volume constant pressure and
03:23
entropy all right and what we
03:26
concluded is that you know we can we can derive all of these things for these constraints but this guy right here in this guy right here answer .period
03:38
super useful to us because in the laboratory we can't control the entropy these
03:46
2 guys are more useful to us because we can carry out experiments under conditions of constant temperature in volume we can constrain the volume using 1 of these fancy par bonds OK and we can do an experiment in here and that's not a difficult thing to do so as chemist the Helmholtz energy tends to be
04:09
a useful thermodynamic marker for us but even more
04:15
useful it is the gives energy because the gives energy assumes constant temperature and pressure and constant pressure isn't enormously convenient for us
04:25
because we live in constant pressure and so if we do an experiment that opened to
04:30
the atmosphere the pressure will stay constant automatically OK we
04:36
watched chemistry occur at a particular temperature we can predict whether it's spontaneous or not based on the Gibbs energy 2
04:43
calculations that pertain to Chemistry under these OK so what does the P and C with QTL constant Western 0 mean if it means in typically we're going to have a profile for the Gibbs
05:05
energy that looks like that's qualitatively of course right the position of these 2
05:11
endpoints is going to be higher or lower the depth of this well is going to be higher or lower but qualitatively it's gonna look
05:19
like this so we sort of want try and understand the qualitative features of this plot that's sort of what the selectors supposed to be about today
05:29
OK so we've got reactants side pure reactants pure products and in the middle we have a mixture of reactants and products and there's a preferred mixture write a preferred a number of products compared to reactants right and if you have any other mixture react in some products along the screen curve they will spontaneously involved in the direction of this of these blue whereabouts
05:56
because the gives energy gets smaller in that direction and the Gibbs energy tells us what direction things a spontaneous and so things are we
06:06
rolled downhill in this direction until you get here you roll downhill in this direction until you get here and at that point is no further change in the system Murad equilibrium and its derivative write the change in the Gibbs energy with this reaction coordinate here Britain is equal to 0 at that point OK so the Gibbs
06:31
energy is especially we're paying more attention to it we want to think about how it varies with temperature Howard varies with questions we want to be able to calculate how the gives energy varies with temperature and pressure we've got this the
06:46
qualities that we define weeks ago the Gibbs energy is equal to the NFL B-minus temperature times the entropy from this equation is apparent by just take a derivative of G with respect to tea in this equation I get my necessity immediately and that's the temperature dependence of the gives the constant pressure .period but it's minus the entropy so immediately we can conclude since we know that the entropy is always positive g decreases with increasing temperature the gives energy goes down with increasing temperature and that's hard we don't expect energies to go down with increasing temperature energies always seem to go up with temperature but this is an
07:32
exception to that rule 1 of the things that makes this a little counterintuitive and the rate
07:38
of change of GE with the size of this differential here where is the greatest resistance having high S right and that's
07:49
gasses now this 1st
07:54
statement you know I say it like it's a foregone conclusion that we all understand that the interviews positive but we haven't really explicitly said but the 3rd law from an anemic says the 3rd locker money namics the 1st
08:09
love or money nemesis conservation of energy sector of the money namics is the direction spontaneity increases entropy in system and the surroundings combined right so the 1st laws about energy the 2nd laws about inch and the spontaneity of a process and the 3rd loss simply
08:28
says that the entropy of a perfect crystal at absolute 0 is 0 In other words if you make the system cold enough so that it can only occupy 1 state the atoms are locked into the positions defined
08:45
by a crystalline lattice break the interview that system is 0 by definition that took the 3rd laughter running an excessive now we know all way give
08:58
postulated that but we can also derided using just to see the statistical mechanics member equals W In W's wine no words there is only
09:11
1 thermally accessible state for the system right and that at a temperature that slow enough that's always going to be a crystalline state where all the atoms are occupying positions of the crystal why a
09:29
lot 1 is 0 the rights the interview 0 once you get down to a temperature where there are no more
09:37
excited states of the system that are accessible formerly you've only got the ground state that and so the interview that ground state 0 we received
09:47
this but at now he said OK so we said that the temperature dependence of the Gibbs energy it's just minus the interview sulfur gasses the entropy is large and this is a minor steps right UK and so we got a large negative slope here for liquids we've got a negative slope that is not quite as large as 4 gasses and for solids we have a negative slope that is even less larger than it is for liquids OK so qualitatively This is what we expect gives energy to do as a function of temperature
10:28
completely counterintuitive because it's going down now we can
10:41
also think about the temperature dependence of this quotient that gives energy divided by the temperature
10:51
the the reason people do that is because is a compact mathematical form for what the temperature dependence all
10:59
right and so if we take the derivative of this quotient now we have to use the courts to rule to do that and we walked through these this algebra .period on Monday all right but we get down to use here so what are we doing we've got 1 of times Sverdrup Levangie with respect to the energy times derivative of tea with respect and after we do all the algebra we made some substitutions we get this equation right fears the derivative Of this quotient with respect to temperature is is given by miners stage over tea squared and that's a very simple mathematical form it ends up being useful to us right it allows us to make a measurement of H derive information about energy
11:52
from that bright in the laboratory that turns out to be a convenient way to make this measurement so this equation
12:04
isn't important once called the gives Helmholtz equation :colon so there's really 2 equations that pertain to the temperature dependence of the gives energy there's DGT tea which is just minor assessed and there's a gives Helmholtz equation 2 equations that talk about the temperature dependence of G but this can also be dealt G and Delta H gives Hamilton equation also works in that form we don't need to know the
12:37
absolute Gibbs energy the absolute and so what about
12:45
pressure well if we start with this expression for that for DG Elie said the 0 we wanna know what happens how GE depends on the pressure at constant temperature so we get rid of this term we just had the jeep was the deeply and we can integrate that from some additional pressure to some final pressure and this is the whole story In terms of the
13:11
temperature dependence of pressure dependence right this is the only
13:16
thing that we need to know are right and the question is how do we evaluate this integral it depends on whether the molar volume or the volume
13:25
is constant is a function of pressure or not right its claws like constant as a punch pressure for liquids and solids because they're virtually in compressible so it takes enormous pressures to change the volume
13:38
of liquid or solid and sell under those conditions we can get a really good idea of how the free energy is going to change the Gibbs energy by just moving his via out front we know what the molar volume of liquid the solid is and we can just treat this as a Delta temperature but we move the molar volume of front these are now Muller quantities we just attached an end to everything OK and if it's a liquid or solid this is going to give us an excellent approximation to what gives energy changes that were looking at as a function of pressure really simple but if we're talking about again last week in just make a substitution for the smaller volume from the ideal gas equation move the RTL front we've got logged the affable PI and that's the equation that we're going to use right so we can calculate the change in the gives function just by substituting initial pressure in the final part into this equation pretty OK so
14:51
there's hardly any change in the Gibbs energy for liquids and solids as a function of pressure that's what this plot is supposed to show you see flat these lines are the Gibbs energy is not changing but for gasses there's a pronounced In creeks In the Gibbs energies he increased the pressure and that the equation for that purple lying there is right there where we can calculate but the gives energy as a function of that final pressure if we know what the initial pressure is "quotation mark it now yes so this is what I just
15:38
said the temperature dependence of the
15:42
gives function there's really 2 equations that we wanna know about 1 is just the simple derivative of the gives function with temperature that's minus the entropy if we evaluate that derivative the constant pressure and then there's the give samples equation but the temperature dependence of the gives the if the pressure dependence of the gives function is always given by the discernible right here and we just evaluate the integral differently if a talk
16:09
about liquids and solids now we might in detail what the volume dependence of a liquid or solid it's right there good equations that describe that
16:19
if we know that we can just substitute those equations for this vehemently that insiders derivative Leavitt inside the integral rather and evaluate the integral and get the exact
16:31
change Gibbs energy but the rest
16:34
of the time if we don't know what the change in the volume is for a liquid or solid we can use this simple equation to tell us Holly Gibbs energy changes and for gasses this guy skies right pretty simple equations but OK now isn't Francis transition however briefly the Chapter 16 was catalyst to making issues the 1st day do we
17:06
haven't really said anything about her how individual chemical species contributed G but we said we said the Gibbs energy is very important that allows us to predict the spontaneity of a reaction under conditions of constant temperature pressure but we haven't said How individual chemical species factory into the gets function but we have
17:31
explained how to do that's 100 individual reaction products pieces contribute to the gets function can we calculate the gets function and DG from their concentration and the 2nd thing is doesn't matter matter in other words we haven't said much about open systems in an open
17:51
system not only energy can be exchanged but matter can be exchanged right so when the matter fluxes in and out of the system how does that affect the Gibbs functions we haven't said anything about that but OK so
18:07
hot individual reacted products pieces contribute to GE we know we have here reactants here pure products here How does this work and and how was due affected by transfers of matter in another system work talking specifically about open systems now write this problem only exists with open systems there are no exchanges of matter possible here or certainly here right we haven't said anything about this
18:39
stuff how is that always the Gibbs energy affected by matter fluxes so let's do an
18:55
experiment and before we do this experiment just admit I think pedagogically what I'm about to do is completely useless what we're trying to do here is derived the chemical potential all right and if you don't like this derivation I don't believe I like all right and you don't need to know it but I'm going to show what you anyway for purposes of completeness it makes me feel better what's I don't know if tradition is the right word discovered a better explanation for the chemical potential the 1 about to show you but this is what this is what you're
19:42
going to get 2 balls 1
19:47
contains hydrogen 1 contains deuterium and these are just 2 isotopes of the same element for goodness sake will call this 1 container 1 this 1 container to this process that we're about to do this valve is now closed write a process that will bottom used in the current conditions of constant temperature and pressure but for that to be true the pressure these 2 things in these 2 Bob has to be identical since Jews accidents variable what does that mean what's an extensive
20:28
variable what's an example of an intensive variable yes temperature by this temperature additives and and we invited a solution at room temperature and another solution at room temperature and mix them together do I get a solution that's 600 degrees Kelvin no temperatures
21:13
not an extensive variable Mass extensive variable all right and begins energy is an extensive variable in other words I can't think about the Gibbs energy container 1 gives energy container to the total Gibbs energy between container 1 container to is the sound that's not true of the temperature is it OK so it's an extensive variable that means I can write the toll Gibbs energy in terms of the gives energy of container 1 gives energy of container to but yeah this G 1 represents the Gibbs energy of all the deed to an age and container 1 and this G 2 the OK we
22:03
understand the temperature and pressure dependencies of GE already but which also expect concentration dependence so the gives energy continue 1 once I opened his mouth fields open them and these 2 gasses can next I have to consider moles of age 2 and moles of to this
22:27
notation is confusing
22:30
and 1 refers to aged 2 and 2 1st D 2 I need to fix this and likewise the free energy in the 2nd container also contains contributions from these 2 gasses right we can expect to be a function of the 2 guests we are real about 2 isotopes will spontaneously makes that means that the total Gibbs energy
22:56
must be going down because if a spontaneous process we know that the gives energy is a market for that process gives energy will the minimize friends spontaneous process that will go down OK so we know
23:11
what we open the valve 2 isotopes will spontaneously Matty DG's the sum of H 2 in detail right so these are expressions for can't the left side and the right side of the last ball and the right ball container 1 container to In the last fall How much is the free energy change what it's going and In 1 flows out an end to flows in all right there's going to be the rate of change per unit of change in the number of older 1 multiplied by the number of moles of anyone that flows in and then there's going to be the change this is the rate of change of the Gibbs energy with the number of balls event to multiplied by the total number of Moldovan too but
24:06
close in around OK we've got an
24:10
expression it's down here for the right hand side that's analogous rightly considers the change in the number of moles of 1 and the change of number bowls of 2 hydrogen and deuterium hydrogen and deuterium now the other equation that we can write is simply that there is a relationship between India and wanted minus In other words if
24:40
hydrogen flows from ball 1 the ball to all right wouldn't have mine is the hydrogen from ball 1 and plus the hydrogen involved 2 are we all right so there's a mathematical relationship between d and 1 involved 1 Indian 1 involved too right they have to be weak related to in this
25:07
equation right here all right so for Coppola 1 D and 1 E was minus D N 1 for component to Indiana two-week was minus the into intuitively
25:17
obvious that they have that would have to be true but if I now
25:20
combine these equations with these equations I these equations right here what are the odds are right this is everything pertaining to component 1 everything comes pertaining to hydrogen and this is everything pertaining to deuterium right here I've
25:45
taken here's a hydrogen
25:48
term and here's of deuterium terms are right and here's a term for DG 1 DG to buy added these 2 things together and every organize these 2 terms so that I've got only hydrogen terms in that 1st thing and show it to you again these are only hydrogen terms and is only deuterium terms I've just
26:12
done little algebra if you sit down a piece of paper you'll see this is actually pretty straightforward to do this right this equation I
26:24
submit to you as counterintuitive
26:27
visitors is important 1
26:33
the meeting emission didn't have his contempt of so we know
26:39
that we open smell these 2 guesses are going to make them when they start mixing DG equals 0 rights when equilibrium but how can
26:50
DG equals 0 look at this thing right when his Diegidio equal to 0 well there's only 2 ways that can happen but 1 way is if Indiana 1 Indian to Arbil 0 in other words nobody ever open the valve about stayed close
27:07
there's no change in the number of moles flowing between these 2 balls right all the hydrogen stays 1 side all the due during stays on the other side and under those conditions you're equilibrium with the valve closed nobody ever opened the valve that's not the case that we care about we want open the valves like the other
27:30
possibility is that this difference and this difference are both 0 but if that's 0 and then 0 I think you'll agree that DG will equals 0 so that has people that and then as the people that no that's the thing
27:59
although it's not obvious that it would be
28:07
so what we just said the fantastical that as people that this these 2 things have to be able to monitor 1 another in these 2 things have to be equal 1 another what is this right this is the rate of change the gives energy With respect to the malls of hydrogen In on the left in the
28:32
last fall and this is the
28:35
analogous thing about my right that derivative of the gets function with respect to hydrogen I have to be
28:44
the same on the 2 sides by the directive of the Gibbs energy with respect to take this component hydrogen and the same thing that the
28:52
true for deuterium but before right equilibrium all right so this thing is somehow important it's a partial molar quantity that's what we call it right that's what it's so if we take the derivative of many from anemic function with respect to the number of malls is called a partial molar quantities of partial derivatives all this thermodynamic functions the gets function with respect to the number of walls of some components that a partial molar quantity years right from obviously apart from or quantity I'm not telling you anything if I if I tell you that all right but if it's an important enough to be that we give it a special name we call it the chemical potential so instead of saying the partial derivative of the gets function with respect to hydrogen a constant temperature pressure and all the other components in the system but we just right news of 1 all right and would have to be true that in order to be equilibrium is that the chemical potential hydrogen on the left side and the right side of that ball after the people 1
30:10
another otherwise this equality will not be satisfied and we will not be at equilibrium you feel enlightened now about the chemical potential no that's why I think this is probably not terribly useful to do so we
30:34
just demonstrated that the spontaneous mixing of hydrogen and Turin will continue until the chemical potential the isotope indicator 1 is equal to the chemical potential that isotopic container to it's this thing this chemical potential that has to
30:51
the same on both sides before aid equilibrium write
30:56
uniform chemical potential of each component of all the component system is a requirement of equilibrium in other words you
31:09
could think about this rule as being in equilibrium and you could ask yourself up you know in this room where the water well there's water everywhere the waters in these polyester fibers on this chair in his water inside this plastic that makes up the back here chair believe it or not there's water in the plastic between the polymer fibers and there's water
31:33
in the area that we're grieving and there's water in those acoustic tiles right if equilibrium in this room the chemical potential the water in those tiles in
31:45
this polyester in Internet plastic and in the area have all been equal the chemical potential the water everywhere in this genius system it has to be equal to 1 another otherwise were not an equilibrium with the water the water if the chemical potential the water is higher these polyester fibers in both polyester fibers will be out gassing water because DG will go down if that's the case right
32:14
so if you've got ahead of a genius chemical system that has different phases different chemical compounds in it where if it said equilibrium the chemical potential of each component has to be the same everywhere and that had a real genius system that's a very important thing to understand right the chemical potential is the thing it has to be the same everywhere in
32:40
this heterogenous Chemical Systems just an example of that so book chose this
32:46
diagram this is meant to represent 2 phases but let's say fight and 1 liquid water and gas use water right it turns out but if you're equilibrium by the chemical potential of water at the end I is exactly the same as the key chemical potential of
33:11
water in liquid water right at equilibrium that has to
33:16
be true not only that but the chemical potential over here in the liquid water has to be the same as the key chemical potential over here in the chemical potential here in the ice has to be the same as the chemical potential here the chemical potential
33:28
is the same everywhere even the these different faces here
33:33
liquid and solid yes it will mean that shows in the end it in the
33:44
system it was the kind of person well In that example were maintaining temperature and pressure constant so is it independent of the kinetic energy no
34:07
because the chemicals the kinetic energy the temperature is
34:11
a marker of the kinetic energy and we know that for again asked the gives functions is not independent of the temperature right the Bloomberg some no the chemical potential also depends on the temperature in exactly the same way that the gives function does yeah write to yes OK so we use the gives
34:55
function here we express the chemical potential terms the gets function it turns out that there is you could equally well it's it expresses chemical potential in terms of the end Helmholtz energy or the internal energy I think can be defined with respect to any of those parameters if you satisfy conditions of constant volume in temperature interview pressure and so on and so forth the other because a number of moles of the other components of the system other than I are also held constant when you evaluate this partial derivative OK now Fox personalities work it's we encounter this expression for the Gibbs energy before all right but it turns out to generalize this for open systems we have to include the possibility of fluxes of material in and out of the system and that's what this term right here does what is this this is the sum of the chemical potential time times the change in the number of malls of whatever component it is that's leaving
36:20
or being added to the system that's added that the
36:23
summation of subtracted that's it's a subtraction but we multiple we add rather the chemical potential times the number of moles for each species of being added and subtracted from the system that is an additional term in terms of understanding what the gives energy it's right so we simply can't act we just use the
36:50
chemical potential to add
36:53
the Gibbs energy for each chemical component that we're talking about part of wider chemical potential so convenient under these conditions of constant temperature pressure this equation becomes the temperature and pressure are constant then the change in the Gibbs energies just given by these fluxes of material in and out of the system right now "quotation mark so we said can we calculate g and DG from the concentrations of individual chemical species that were doing here OK end can we compensate for the addition subtraction of arterial from the system in terms of understanding what happens to GE yes we just include the Strom right here and we can figure out which is
37:54
getting larger or smaller based on whether adding or
37:56
subtracting material from the system if we know what the chemical potential look yes yes yes yes spoke now if this equation is true we know an equilibrium DG is equal to 0 but in DG is equal to 0 then this thing has to be equal to 0 alright bad equilibrium and so on it seems intuitively obvious that would have to be the case but that's given its own name that's called gives doom equation White sold this year equality has to be satisfied at equilibrium "quotation mark the other words
38:43
things can move around in a system in equilibrium
38:48
but this is the quality has to be satisfied in other words this summation cannot change its credit equal to 0 this equation just as the chemical potential summed over all the walls of products reactants is a conserved quantity equilibrium yes that's all it said so renewed example of what that means for example if you have a getting converted into be let's say this is my summarization reaction the gives to equation said that equilibrium that plus as the equals 0 because the summation contains 2 terms only 2 chemical species a and B. right and so this equality has to be satisfied right so a mixture of methanol waters prepared the mole fraction of water of 0 . 4 ethanol water mixture if a small change in mixture composition results in an increase in the chemical potential battle by 0 . 3 5 jewels from all I don't know how that would be accomplished hypothetically if if you could increase the chemical potential that by 0 . 3 5 jewels from all by how much will the chemical potential melodic change but we change the chemical potential of 1 component of this two-component systems how will the chemical potential of the other component respond right we know this
40:23
is a gives due on problem because right equilibrium this say
40:29
that anywhere mission moreover Swanson should say the mixture of ethanol water and equilibrium OK so rarely use the gives due equation the two-component system so that 2 components we got an ethanol component in water component we just solved for the change in the chemical potential water right any of these derivatives are small 1st assumption to make is that they are small right then we can just treat this as the change in the chemical potential the water that's the change the chemical potentially ethanol were told about it right now we need to know the small fracture these these 2 malls all right what I've written here is the mole fraction everybody understand what the mole fraction is it's the moles of
41:35
component 1 divided by the total moles of all the components of the system and so on this
41:39
case that would be the mole fraction of ethanol right that's not the fraction of the number of moles of ethanol but the mole fraction is just the number of all of Bethnal divided by the total moles in the systems we usually call that acts of ethanol right and I think we you can see that if I take the the quotient of 2 more fractions of the total number of malls will cancel might just get moles that all divided by most water OK and so this 0 . 6 over point for you that's just these 2 mole fractions that's the change in the chemical potential the ethanol and so I can calculate what the chemical potential the water's going it's going to go down by minus 0 . 5 3 jewels from all that's just the jig gives equation very simple OK so once we understand about the chemical potential that the equilibrium is determined by the system looking for the upstart he at the end of the day the finally change the man
43:17
pages which was it is place
43:21
for of the on the other at the the I know there changing with just 1 win in the U.S. and 1 of the things we have where the 1st is on you what do you're right
44:08
this should be a new idea this is
44:12
yet you I'm sorry that is something
44:15
new the and this should be a new idea yes we're write doing
44:19
something that is less than half of the year
44:29
but also in yes right so you can actually recast this equation in either of 2 forms striking Bermudian trendy new Arkansas how you when use it depends on the information they were given yet so what are the consequences of the chemical potential is In understanding this diagram right here right so once again this is the Gibbs energy on this axis and this is the temperature on this axis were talking about 3 phases of particular component let's say what OK and this the slope of these lines is going to be dictated by these derivatives and other words the slope of the slightest bit of minus the entropy for vapor phase water this is minus the entropy of liquid water and this is minus the entropy of solid ice yeah In principle the system can choose 3 different Gibbs energies at any temperature that you choose on its axis right except where there's a phase transition are that the system can choose any 1 of 3 energy that always chooses the lowest of these 3 energies it minimizes the chemical
46:01
potential OK the chemical
46:05
potential 0 liquid water is actually equal to its gives energy are right and it's lowest for the solid at temperature that HBO is below the melting point of isolated 252 253 degrees Kelvin were 20 degrees below the melting point of ice water chooses the solid state and the reason is that the chemical potential the solid is less than the chemical potential liquid or the gas that's why
46:37
From a thermodynamic standpoint Water is ice
46:40
at temperatures below 273 degrees Kelvin all right if we go up 173 the chemical potential of liquid water and ice are equal to 1 another and at that point if we stay in the solid-state the chemical potential life will be higher than that in water right and that's the economically unfavorable with the system can evolve toward a new equilibrium by melting the ice to form water a case of the system now follows this new equilibrium line which is the liquid phase line and so if we keep the system up to 3 30 degrees Kelvin that's above the melting point of ice for tracking now the liquid phase of the system stays in liquid phase because everywhere along this line it is the minimum Gibbs energy that's possible for the why would we arrive at the boiling point of water 373 . 1 6 degrees Kelvin the chemical potentials of liquid and gas phase water are equal 1 another In only
47:54
at that point can you have the coexistence of these 2 phases right Stephen
47:59
liquid water in this case liquid and solid rights but this phase coexistence can only happen at equilibrium at this phase transition temperature and if you go still higher temperatures above the boiling point only gas phase waters possible at for example 390 degrees Kelvin and so the way the system evolves as shown by this red line because the red line indicates the minimal chemical potential the water
48:28
each 1 of these temperatures but
48:35
at this phase transitions the chemical potential of 2 phases are equal 1 another and in principle they can coexist in the chemical
48:41
potentials across the face boundary for steam at the boiling point in the liquid in the gas phase is exactly the same by definition it has to be the same thing is true
48:53
for liquid water the chemical potential the water in the liquid and solid at that point at 273 . 1 6 degrees Kelvin yeah the
49:04
chemical potentials the same in the ice and in the water
49:10
that's when you can have coexistence of those 2 faces yes for distracting the lowest chemical potential for the system as we track along this red line OK finally I want to talk about this right recalled is ball so I think this plot it is actually very counterintuitive right widely say that love if you've got reactants here and he got products here right the shortest distance between 2 points is a straight line if this is the Gibbs energy the products this is give begins Gibbs energy of the reactants why would the Gibbs energy of the mixture of the reactants for the products ever be less than this In other words if this is the gives energy products this is the givers that Gibbs energy the reactants why wouldn't the Gibbs energy of some mixture the reactants the products just lie somewhere along this international that
50:20
is an intuitively obvious that that should be the case Of course otherwise there would be
50:25
no equilibrium in chemistry because equilibrium is defined as the G equals 0 alright right and there is no minimum in this plot it's a straight line and so the reaction would just Goldman but now or if products had a higher G function than reactors there would be no reaction but there's been no equilibrium possible you would either be fully in the product state of Colima reactants state and if they had exactly the same gives energy you'd have sort of a pseudo
51:00
equilibrium where you could have any composition but no composition would be preferred so
51:12
let's go back to this equation here this experiment
51:16
rather we've got oxygen and
51:19
nitrogen we don't have a bowl of each the valve is closed now we opened the valve right here we had entering what will come back
51:35
to this 1 Friday thank you