Lecture 21. The Steady State Approximation.
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Lecture 21. The Steady State Approximation.

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Part Number 
21

Number of Parts 
27

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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 noncommercial 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  
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University of California Irvine (UCI)

Release Date 
2012

Language 
English

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Abstract 
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 21. Thermodynamics and Chemical Dynamics  The Steady State Approximation  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 thermochemistry 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: 0:03:36 Svante Arrhenius 0:05:59 Arrhenius Equation 0:10:25 Consecutive Reactions 0:20:23 Steady State Approximation 0:33:58 Irvine Langmuir and the Lightbulb 0:42:20 LindemanHinshelwood Mechanism 0:48:18 Applying the Steady State Approximation

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OK so we posted the results request 6 this morning you guys did well the meeting was a little lower than last rate pretty high phase B
00:24
lower grades OK midterm
00:29
is Friday and we're going to have 1 more quick as a week from Friday with 7 them were done were winding down what we'll do is wearing a review in in detail of what's going to be on the midterm on Wednesday a
00:43
walking through a problem by problem in review that material for you what will not
00:50
be honored for share these 2 topics from Chapter 19 right at the end right polarization Fuller chemistry were not going to get to those 2 topics but I think everything
01:03
else in Chapter 19 will be included if where we're going to get to really get right up
01:09
to section 19 . 8 by the end of a lecture today OK so we're in the final stretch is just 7 lectures including this 1 laughter and we've just got 1 quiz laughter but
01:24
most of the points in this class are still to be decided to twounder .period finally we have 100 .period midterm it was 1 quiz left from this is the core these next 2 weeks would be good weeks to focus on doing well the class because it could make a huge difference to you me so far we've basically decided for most of you what your quiz Graves going to be for the quarter just go 1 quiz laughed a ride and since you can drop to he pretty much you come close to locking in your quiz Grady you can still affected with Chris 7 a little bit and is taking midterm 1 right but would get 300 points and exams slept in the costs and so it's tempting to think that
02:17
were coasting into the summer vacation period but in reality now is the time to do well all right so going certainly do a good job of reviewing this midterm 2 for you on Friday CEO
02:32
exactly what's going to be on
02:37
so what we're gonna do today the talk a little bit about a radius Arrhenius developed a
02:44
phenomenal logical equation but we find very useful in chemistry it's used virtually all the time by people doing all kinds of chemistry and so it's very important to us but it's really phenomenal logical equation hopefully by the end of the
03:00
quarter will understand where it comes from there were going to talk a little bit about consecutive reactions in the steadystate approximation this is a very important this is right in Chapter 19
03:13
and there will definitely be a problem on returned to that involves this topic because it's 1 of my favorite topic ss
03:21
and never talk about the Langmuir Hinshelwood mechanism which is a complicated mechanism for you know molecular reactions that exploits the steadystate approximation the Langmuir Hinshelwood mechanism OK so a
03:40
radius is a Swedish guy and we
03:45
already know he created definition of acids and bases for us that involves Proton donation and
03:52
I hydroxide accepting the
03:56
he but for the purpose of of kinetics he recognize the relationship between temperature in reaction rate he recognized a trend in the scientific
04:07
literature for the temperature dependence of reaction rates that other people haven't noticed and so
04:17
will say more about that in the 2nd but he also discovered the greenhouse effect most people don't appreciate that there's the Arrhenius equation that relates that rate constant for a reaction to the temperature but he also figured out the greenhouse effect in 1896 and this is the paper that he wrote a great deal has been written on the influence of the absorption of the atmosphere upon the decline so he
04:48
understood climate change in
04:52
1896 Tindall particulars .period of enormous importance of this question to him was transferred to a world Trojans it is the mean temperature of the ground in any way influenced by the presence of heat absorbing gasses in the
05:11
atmosphere but the 1st thing
05:14
about this is actually 1948
05:17
yes that 48 but
05:23
but in this paper actually a radius works out the expected temperature
05:29
change for the No 1 concentrations of things like C O 2 in the atmosphere and gets a decent answer for that did the amount of warming that should occur and it's just really amazing that you
05:41
can even make that calculation in 1896 the Carbide on the influence of carbonic acid in the air upon the temperature of the ground
05:54
amazing all right that doesn't really have anything to do with kinetics but this
06:00
equation the right this is the famous Arrhenius equation and so what we have here this CD a year that's something called the activation energy
06:11
we haven't talked about that yet but we will before the end of the quarter In case is the a pre
06:17
exponential factor obviously it's before the exponential right but it's also called the frequency factor it's units have to match those of K oracle what this equation predicts 1st of all this activation energy the summit products some reactants Statement between the product react state there's an energy barrier that has to be surmounted that the top years something called the transition state it's the state of
06:46
the reactants when they're halfway to becoming products right that's the socalled transition statements on higher energy
06:54
state for the system that gets the highest energy state of the system it as it
06:59
progresses from reactants the product you have to get over this he at the very top of the speakers the transition state by definition and so that the height all of this energy barrier here with respect to the reactants state that the activation energy and we're not
07:16
really more about it right now but I just wanted you know where that comes
07:21
but so if you go to the lab and you carry out a measurement of a reaction rate as a function of
07:30
temperature would you notice and everybody in this room already knows this is the rate of most chemical reaction goes up as you should increase the temperature so
07:40
here's what that data might look like this is supposed to be the rate constant on this vertical axis here this is the temperature on this horizontal axis and as we increase the temperature it turns out that we're talking about this reaction right here right the dissociation of N O 2 but the reactionary goes on and and on up and on all right and what our readers noticed is that if you replant this data as Of the rate constant verses and 1 over temperatures these data file almost on a straight line and
08:18
he knows that this was true for all wide variety of different types of reactions reactions that occur in solution reactions that occur in the gas phase this is a very general observation that if you
08:29
recast rate versus temperature data there's a lot of great verses 1 of attempted 80 get a straight line in this equation explains why that would be the case right of
08:42
chemical reactions adhere to this functional form because I
08:46
just take the log of all sides of this equation I get lot equals logged a minus the IEEE over T and so you would expect a plot of like Avis is 1 of a the straight line with the negative slope in the slope is going to be CA overall are and intercepts to be logged a and so but
09:07
this would explain phenomena logically only why the data would adhere to this functional form he didn't explain what this activation energy
09:18
was in detail and he didn't explain what it was in details we have to
09:24
understand those things yet and we're going to talk about something called transition state theory that allows us to understand what these
09:31
parameters are in more detail but suffice it to say this is a phenomenal logical reaction to the equation rather that is very important to us so canister
09:42
constantly bearing the temperature the reaction measuring the reaction rate as a function of temperature calculating an activation energy
09:49
using that equation right there write all kinds of campus
09:54
for all kinds of reactions
09:58
but OK so we're not going to see more about that for now will only pointing out that there
10:07
is this parameterization of them the rate constant with
10:11
temperature from which we can extract some parameters pay any mind as he said at an end he said rather right that
10:19
have relevance in terms the kinetic mechanism but we haven't said what the relevance is yet willing to come back to it OK so
10:28
consecutive reactions are sequences of reactions which prodding raises wins so far many times in chemistry
10:35
what we observe His reaction occurs in the product of the reaction serves as the reactants for following reaction in the product that following accesses reactors for another reactions he hit sequences of reactions occurring right now the single reaction in isolation of others which is what we always talk about and kinetics turns out that some relatively unusual what we often see a cascades of reactions occurred this is an
11:03
example of a a case where there's true reactions that occurred in sequence right we've got this methyl bromide reacting with whatever the heck this thing again right now ethyl ester all right in any intermediate is formed by that reaction that this guy right here which is Esther onto which we've appended but a methyl group and then and hydrolysis occurs right now we end up with this guy all right where this Apple group is small enough I should actually have a plus Apple group here this melodic acid misses the synthesis more water gas and from this medical ethyl ester so the point is it's important to understand consecutive reactions because consecutive
11:57
reactions are sort of the rule not the exception right reactions are usually consecutive there's usually more than 1 thing happening in sequence rather than just having something happening in isolation of other chemical reaction all right because they teach how
12:14
the constitution many reasons yes so what to talk about 1st is the
12:21
simplest consecutive reaction right 1 where we've
12:25
got irreversible conversion of ADB and irreversible conversion of Beta seat with these 2 rate concentrate here no reverse ability in either 1 of these 2 reactions all right the simplest
12:39
possible case of 2 consecutive reactions the minimum number of number of react react some
12:45
products now without going through and deriving these equations are derived for you in Chapter 19 this is equation 19 . 2 7 B. This is equation 19 . 2 7 C this equation here we didn't arise all right this is just the 1st order the reaction of a going to be we derided into greater rate was like 3 times OK so these are just the integrated rate lost for a B and C. for this reaction mechanism right here that's not
13:17
really what we're interested in right as I'm going to show you what we
13:22
wanna find our simpler expressions for these integrated rate right because in general the consecutive reactions that were really care about are going to be much more
13:35
complex than this right and I
13:38
think you'll agree that these equations are already getting pretty complex even for the simplest case where we stripped down the number of reactants and products to the absolute minimum were already getting pretty complex mathematical expressions here imagine if this was a plus B goes to see blood the policy goes to AFP was G was
14:00
and opposed choosing the metrical efficiency not all 1 I think you can see this is going to start to be a nightmare scenario for us so we would like to
14:09
do is look at these complex equations see if there's a way to strip down the complexity but and generate a
14:15
simpler way to think about these reactions that with the steady state approximation does for us but allows us to simplify
14:24
these integrated lots for reactions that consecutive OK so let's 1st of all look at
14:31
what these rigorous equations predicted and see if we can see something generalisable from what they predict that will help us In terms of figuring out what this steady
14:44
approximation of what these equations predicted about the versus time Beasley intermediate here write an intermediate it is not a
14:54
reactant and not a problem right by definition it's something that is formed to try
15:02
and least in the middle of this reactions what we may see in the lab as we put a into a beaker see comes out but the was there transient wing
15:13
but was formed and then it was consumed it was formed
15:16
by this reaction was consumed by this reaction but what we want now is and what is what happens to its concentration is a function of time but let's consider the case 1st work K 1 is faster than K 2 that fast that's a lot right qualitatively what we expect to happen if this fast and this is slow
15:39
these gonna build up right because
15:42
where else Formby rapidly but that's only the dictator see slowly and so what we're going to expect qualitatively is the larger the disparities between K 1 and K 2 in this direction where this is fast and this the slow the higher the
15:59
concentration of B is going to be so I calculated the concentrations of a B and C
16:06
vs time right for the case for cable 1 overcame a 2 is 5 the Member K 1 is faster than K 2 so the ratio between K 1 and K 2 is going to be bigger than 1 right all right so let's say we make it 5 if that's the case in the world where the start off with a equals 1 Moeller OK on this access and this is just a time axis here so you can see a just a case like it would in any
16:35
you know molecular reaction just an exponential decay of a not very interesting
16:40
the look happens to be b increases reaches a peak and then decreases as a function of time so there is a big spike in me as a consequence of the
16:50
fact that the 1 is faster reform and it's slowly reacts to give us
16:57
right we reform be rapidly and then slowly reacts to give us see and you can say here is the concentration of C is a function of time that makes sense now if
17:10
we change this ratio to make it better not make a 1 faster relative to Kato to you see the good bigger here's where was whose word is right the
17:21
concentration of the intermediate builds up more if I make a 1 versus case fast
17:29
and K 1 or K 2 equals 20 bigger yet here's 10 was 20 OK case qualitatively these equations tell us exactly what we expect intuitively we expect as we make a
17:43
1 faster versus K 2 weeks that the build of this intermediate to be more more prominent we expect the peak concentration of the intermediate to go up and up and up as we make that number
17:55
bigger but that's 20 that's 50th think you get the idea now let's look at the other possibilities right if we make a 1 slower than K 2 what's going to happen but we
18:13
slowly Formby be reacts quickly right under those conditions we don't expect the EU to build up very much like we slowly formed the and as formed the reacts faster that's what that limit
18:27
means right there right K 2 is faster than K 1 bite so this is slow this is fast and if we look at it with we make that ratio 1 to 10 in other words K 1 of the key to his 0 . 1 look the forms but it doesn't we never get very much of the Internet leaks away White but the concentration of the never gets very large compare that to the case for K 1 advocate who was 10 potluck hoping
19:02
enormous difference OK and if
19:08
we increases now I made the ratio 1 to 20 in other words . 0 5 we made the K1 even slower compared to take to be gets smaller there's the wet . 1 B would . 0 5 the woods . 0 2 smaller
19:30
yet by so what's interesting about this is if you look at this now it looks like these becoming clause I constant as a function of time all right it's concentrations hardly changing but the concentration is not quite 0 all right it's becoming almost invariant is a function of time that's the key
19:53
thing is that we want a focus on right so there's an assumption that we can use that we can bring to bear on reactions like this that allow us to simplify the mathematics enormously and that's the
20:06
steadystate approximation basically what we're going to do is soon for all of the
20:12
intermediates in the reaction but the time rate of
20:16
change of those intermediate time rate of change of the concentration is going to be
20:21
0 so here are the
20:24
top rate of change in the would be 0 that's the steadystate approximation what is that do for us now it's going to allow us to
20:36
do I simplified equations for the rate at which the product appears mainly that we care about how fast is the product appears a function of time what's the integrated weight loss for the product and that's what we really care about here so what we wanted you supply the steady approximation derive new integrated rail offer the product that is simpler than what it would be if we had to work out all the complex mathematics so when
21:02
all simplified equation that result so for this reaction mechanism right here the time rate of change of the going to be K 1 times because at the rate of these forms be plus the onetimed a and B is consumed by this reactors will be minus K 2 times be so that's the rate would be consumed that's the rate at which abuse formed and what we're saying in a steadystate approximation is that since that time reader changes 0 those 2 things happen equal 1 another the rate at which
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its formed the rate at which it's consumed are going to be equal to 1 another and if that's true
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then indeed saw steady state right in the special case that we're talking about the steady approximation B is going to be able to carry 1 over K 2 times a very
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simple much simpler the whole truth about the reaction the rigorous equation that we talk about on an earlier slide also to
22:02
again in the 2nd we always have to keep 1 thing in mind are right it's tempting to
22:07
mindlessly applied a steady state approximation to everyday reaction mechanism that we come in contact with but it's important to understand that this reaction this assumption
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write the steadystate approximation is
22:21
an approximation and this approximation fails badly 15 1 it is faster than K 2 right if K1 is faster than K 2 we're going to give you build up a B it's concentration is not going to be constant is a function of time not even close right what we've learned by looking back In calculating concentration of B is the steady state approximation can be expected to work when K 2 is faster than K 1 right when that when the intermediate is used up rapidly in subsequent chemical steps but for 1 yes In other words this is the the case with
23:13
K 1 overcame 2 is small K 2 is fast and he won a slow so to reconcile this equation with this equation right here we insist that K 1 be much much less than K 2 right if that ratio approaches 0 0 these 2 results can be reconciled
23:44
with 1 another right this 1 says the tiring change of
23:48
a 0 this 1 says the Thai rate of change in the matches the time rate of change of ages racial by the 1 Kate to write but if K whatever K 2 is their the
24:02
concentration of these are going to be very low at all times right that's really what we're assuming in the approximation we deviate from that assumption the
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steadystate approximation is not going to work very well let me
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show you that both of presented to
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guests just pointed that out of sir some this suggested Expedia method for dealing such reactions becomes disabled so solution yet OK so here's the integrated weight loss for seed all right
24:42
if if this is the concentration of the right then we know statistical the K 2 times b right and so consequently obliges just plugin for me from the steadystate
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approximation solution really Bibi said state should really be beasts of steady state and so when I plugged in for OK to cancel a distinctly onetime that
25:11
Is the differential rate laughter DC for the 1st see the words the CVT is the 1 time so I couldn't solve that despite integrating in the normal way to derive an integrated rail office see and when I worked through the integral I find that the concentration of C is equal to the initial concentration of 8 times won over this yet the term here but it depends on K it doesn't even
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depend on K 2 all right so
25:42
this is new integrated rate subject to the assumption that we are applying the steadystate approximation right so here are the integrated laws that we have from the state approximation this is the 1 that we derive directly by thinking about the steady state of B
25:59
by setting DVD to equal the 0 we derived this
26:04
equation directly and then this 1 has never changed as the firstorder integrated rate laugh or a you know molecular reaction of any kind that
26:13
was always the same same as it is here since that is here this 1 we derived by just making a substitution of the into the differential rate law offices which is what we did on the previous life I submit to you that these equations are a lot simpler than these equations but that degree
26:31
of simplification here is tiny compared to what it normally right because we're talking about the most elemental sequential reaction mechanism possible right now right as you make that bagels to be goes to see if you may as you make that incrementally more complex these
26:50
mathematics get exponentially more complex right so the degree of simplification that you get becomes very significant which is why we use the steadystate
27:02
approximation so much in chemistry to use a lot it's overused How good is it let's look at some data how well that the steady approximation work let's 1st examine a case for we expect it will work well right what cases that K 1 of the key to small right in other words were forming the
27:30
intermediate ends reacting fast right we look at this data
27:35
before the dash lines are the steadystate approximation is solid lines are they full and correct
27:43
answers write for the concentration is a function of time like this is
27:47
just the concentration of these 3 guys as a function of China's before right check this out it's dash lying here almost falls on top of that solid line would get excellent agreement is green date every year by the way is the 1 that we care about malls we wanna know
28:03
what the product is doing is a function of time but the product concentrations were use the steadystate approximation get at that and here we're
28:11
going to do a great job but we got an excellent Of the steadystate approximation to the true answer look at what they're steadystate approximation predicts for the intermediate it's it's killing this right on top of it right and of course is doing a a good job for the reactant as well rights of the steadystate
28:33
approximation works great here the world's great because
28:37
that's much less than 1 now let's make it works right let's make it a little bit bigger now we're not killing quite as well it's a little bit hard to see a still looks great seeing love for pretty good said but not quite as good as it did here is kind of hard to see that there is a difference but it's still
28:59
doing a pretty good job don't you think right now we care mostly
29:03
about this green curve and the dashed line here is almost right on top of that Green Line not quite now you can see a little bit of
29:11
daylight there but not much
29:14
of the steadystate approximation still working pretty well here now what if we make this 10 In other words we're gonna
29:23
start forming the intermediate faster than it gets consumed but this is a case where we expect the steadystate approximation to fail all right and we're going to remember that even tho nobody else does even tho other people use the steadystate approximation indiscriminately we will not do that we will always remember that this is a case where the steadystate approximation
29:50
really should work very well doesn't work very well what am I talking about check this out here is the dash line from the steady approximation for the product here's what the product concentrations really doing that's a pretty big dealt right that doesn't look like if it's that very well at all right in the
30:11
intermediate but terrible
30:19
except except and you're actually not not quite as terrible as you might think but but it's still a distilled a pretty good job I took it's doing a poor job in K 1 over Katie was 10 by making whatever 250 it gets
30:37
downright nasty right look at this year's the dash streamlined here the solid green line there's miles between these 2 curves here right and many
30:52
people will apply the steady approximation without any qualms at all 2
30:59
cases that conform to this problem this he said of of rate constants right here all right so you
31:07
have to be careful that the intermediate is not building up because in that case he doesn't make any sense to apply the steady state approximation
31:17
parts of the steady approximation of what we do
31:21
but if we want to apply the steadystate approximation to the Connecticut Protestant kinetic mechanism my 1st
31:27
sequential reaction 1st of all we right a the process look at the end I'm talking about the process that generates product usually
31:38
Susan what we wanna know the words in this
31:40
case the CDT is K 2 times right that's the rate at which sees formed then what we do His we ask Father intermediates in this weight loss identifying them and then apply the steadystate approximation
31:55
to all of them here we can
32:00
find an intermediate it's right there right and it shows up in the differential rate laughter the formation of product as well perfect
32:11
this is a great candidate for the application of steady state approximation but then what we
32:19
this at the time change for these intermediates 2 0 or in this case DVT is equal to 0 and then we write equations for the creation the intermediate quite reasons although the states the concentration of the intermediate that's what we did here all right so I said at the time rate of change of the intermediate 2 0 and I said what that means for this reaction mechanism is at the rate at which the EU's formed has the equal the rate at which it's consumed by these 2 rates have to be equal 1 another now I just the road for the concentration of B but you saw
32:52
the concentration of those of the intermediate alright and
32:56
inevitably the concentration of the intermediate appears in
33:00
the rate expression for the concentration of the products
33:04
and so the next thing to do is just plug the sand To the differential rate offer the product right substitute suppression the riddle of the product the words DCT K 2 times Beach right now instead of being paid 2 times the it's going to be TK 2 times be steady state and we just plug in what we said is the steadystate concentration abuse K 1 overcame 2 In this case the 2 Katie's cancel and that then becomes art differential rate laughter C and we can integrate that an
33:38
integrated reel off we want to but
33:45
remember this works if and only if the 1 is less than the 2 they say the ready I know it OK now and take a little
34:05
conceptual breakthrough all that information is sinking deeper into work or Texas a retired what Irving
34:15
Langmuir Irving Langmuir was 1 of the 1st Great American chemist end of it we Lewis he invented Lewis .period structures
34:32
Lewis called them Languedoc structures that's not true I just made that is the father of surface
34:39
chemistry revolutionize the light bulb he discovered how to manipulate modern molecular what layers on water who cares what that turns out to be rather interesting to do turns out you revolutionize the light all yeah but the
34:54
incandescent light bulb mean there's been several revolutions yet in the meantime that this is a
35:01
page from and Keisha interested JeanLouis notebook right he actually made Lewis .period structures that's why they call it was .period structures like animal as a notebook or a cocktail napkin but pretty cool and he
35:21
wasn't very mean the see but so
35:28
Langmuir figured out how to make the light bulb work properly lots of people had worked on the light Edison's famous for the light right but he wasn't the first one to make an incandescent light bulb turns the other light bulbs for his his
35:44
work better right when you think about it this is enormously unlikely way to make light right what is this that is a tungsten tungstenfilament that is almost sold almost so
35:57
tiny in diameter need microscope the see and tungsten what we know about Constance tungsten a very stable metal How does it compare to other plant not as stable as planned it's less noble than platinum right right does a react Indiana we buy a reading Wayne wedding ring do you want a tungsten wedding ring it also said he would be impressed by that the
36:43
problem with tungsten is it reacts rapidly Van Exel Thurmond with oxygen
36:51
deformed tungsten and so you know if you're going to choose a metal to make life with you might not choose tungsten in
37:02
effect Edison didn't you Stockton chose carbon
37:09
by the original light bulbs or carbon the only lasted 40 hours because carbon filaments felt like oxygen needed by then a guy
37:20
named here on Webster figured out how to make a really really good carbon filaments at General Electric beckon like 1897 and he made carbon
37:34
filament light bulbs that lasted 100 hours these were the case of carbon filament light bulbs but the only lasted 100 hours and
37:43
100 hours really wasn't good enough I minnows like a couple months at most In your light bulb had to be replaced and at that time these
37:52
were not cheap but until 1906 or labeled a carbon filaments so turns out lying there was not I figured out that we should use tungsten for this development there was another guy the General Electric in 1908 who did it 1st he made
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tungstenfilament why tungsten especially in view of
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this 1 makes tungsten special anybody now Thompson
38:20
turns out is the best at something no he capacity that's a good a like that answer but that's not the correct what problem you going to have when
38:35
think about this and put 100 volts across this
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filamentous that With of a human hair right what probably going to have a film it's going to get hot right melting did you say nothing melting Wells is going to happen
39:07
what happens to solids when you hear them up and get really hot even before they melt but say that it doesn't decomposed somehow His yes that the person you'd expect but a dozen decompose it could still fall apart house but about sublimation what
39:38
sublimation direct transition from a solid of a gas phase right metal sublime right so it turns out Thompson does have the highest melting point of every man in the periodic table all right and it has been extremely low rate of sublimation all right and so the problem with tungsten was that when you turn on the light bulb as soon as you turn on the light while the tungsten Woodstock a sublime quantities glass surfaces here and return is liable black red the daily by the slide Bob
40:15
screwed and it's clear 2 weeks later starting to turn gray 2 weeks after that it's getting darker and so the model like becomes of your light bulbs decays exponentially as
40:26
the inside surfaces of his like all where their act right because what happened is that Thompson would evaporate under the light bulb and then this tungstenfilament this tungsten film would react with trace oxygen
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and water are right and would coat the inside his libel turned black
40:46
Selangor solved that problem right he sold the light bulb
40:52
turns black problem and he's all the time so when he saw the light bulb turns black problem he created
40:58
another problem right this Fellman said last very long and yet has yet to solve that problem too so
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just to make a long story short what he did as he failed the inside is involved with nitrogen and it turns out but the reason these tungsten
41:15
light bulbs worth of work were were
41:17
turning black it's because of this reaction here but the reason that the Thompson was blind under the surface of this glass was
41:26
because it was reacting with trace waters that was inside the light bulb all right and that former the tungsten
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oxide and it's actually the tungsten oxide that's blind on the surface of this glass right now the tungsten directly the tungsten
41:43
oxide actually got sublime metal oxides it turns out to have much higher vapor pressures than Parra metals the metal oxides you wouldn't necessarily expect that so he felt find
41:55
out into the field this whole thing with nitrogen got rid of all the water that not only did the tungstenfilament last longer than that surfaces of his glass and didn't turn black anymore yet a
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patent for that so the way that
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he made light bulbs is the same way the say whether they're made today by the essentially
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solved the incandescent light
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bulb problem of course is completely obsolete today look at me those opposed to rest rest
42:30
your thought process so we can go back to
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thinking about kinetics we got
42:35
8 minutes let me just type but the
42:42
figured out something about how really simple reactions occur so even a reaction that looks like this can be geometric In
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other words not elementary
42:58
even reaction at the symbol of this as this can have multiple steps but
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how is that possible well
43:07
but as an example if there
43:14
is a barrier for the reaction to occur right if in the process of going from a to B. they have to surmount an energetic barrier right it can be necessary for there to be an activation of a that has to occur before the reaction can happen how could
43:32
that happen let's say a is in the gas phase aching collide with itself and if that collision is energetic enough you could generate an excited a that has
43:42
a lot of kinetic energy a lot internal energy that and
43:49
then that activated a could give rise to products right so there's several steps here it reacts with itself together and activated a that's his orange thing then of course they can
44:03
deactivate as well right so there's a bad reaction this is
44:07
just the Midas was so this is just this going back to the messages written all the reaction for a year there were activated a collides with another AM loses its energy
44:17
but it also happened and finally this activated a
44:20
could give rise to be that is the Langmuir Hinshelwood mechanism for you know molecular reactions turns out that
44:31
lots of reactions
44:33
that look as simple as this occur by this mechanism right here all right this activation of them reacted by itself but it's it's
44:44
activating itself passed a worker before the reaction can happen right the Hinshelwood mechanism
44:53
now were a possesses internal wonderful or to give BES said that but why do we I bring this up
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right after the steady approximation
45:06
I think you know the answer we're going to apply the steadystate approximation OK so let's think about what happens to the time rate of change of the intermediate here does everyone agree that the intermediate is a start How do I know a star's new media I don't see a star here but it's not a product and not a reacted and its formed during the reaction and then it's consumed In the course of forming the product business all
45:41
right so the 1st thing we have to be able to do is spot the intermediate in the reaction but can be nontrivial depending on how complex the reaction mechanism OK then what we will
45:54
what we want to do is write a differential rate while forward but with the time change of any looking at this reaction right here I can see a is formed by 8 2nd reaction of a with itself with the recounts the tale 1 inside the right K1 1 times a squared that's the rate at which it is formed now can anyone see the the film's story based camels won a stock as a consequence of this reaction
46:24
what else can happen when a stock can react with a and it can get consumed by this reaction right here right so I have to write a term for that some nifty minus 1 minus sign 1st book is this makes a star smaller not bigger this 1 makes the Questar are bigger and what what is that right it's a star times a withering constantly minus 1 and finally a targets consumed by this reaction right here right inside that K 2 times a star and that's a minus sign to that someone site is a star gets smaller that the miners signed as a started smaller and that the plus side as they started right so
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this is my differential rate about people like that for the intermediate because the next thing I would do the steadystate
47:15
approximation studied equal to 0 so this is just analogous rate Lofa AT is consumed by this reaction formed by this reaction those are the only 2 that matters Ciarlini 2 terms
47:31
why is this minus Q 1 8 squared and not to k 180 squared because there pertains To this reaction right here
47:47
think about that and if the answer does
47:52
arrive but In the short answer is
47:58
you only consuming 1 a in this industry Woodside to ways getting consumed forming 1 his own reality only losing 1 that's why it's of 1 another to OK and the different rail of abuse just as everyone can see that yes yes yeah now what we're going to do with the steadystate approximation said this guy equal the 0 out here is not 0 period
48:31
and can work out what the kinetics of insured reaction OK so what I said this guy with the 0 still agree with that now I'm just rearrange this equation and remove them negative terms to lefthand side in the positives the right hand side and set them equal to 1 another and analysts offer a stark and then applied a star into the expression for DVD tea and
49:04
this is going to give me an integrated rate lockable Lindeman Hinshelwood reaction In a midtable about that on on Wednesday