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deltaH
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Quote: Originally posted by woelen  | | Quote: | | [...]the slowest step causes all others to be assumed to be at equilibrium.[...] |
This cannot be true, because if this indeed were the case, then every chemical reaction would behave like a first order system (only one differential
equation, all other equations being algebraic, because all other steps are in equilibrium).
...[]
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Ok, I'll give this a shot and probably make a total ass of myself... I hated chemical kinetics, nevertheless, here goes my attempt at refuting this
 I thought the best way to illustrate my point concisely is by a 'simple'
example (turned out not to be simple at all, but it's as concise as I could make it).
Consider the hypothetical reaction with the same form as yours:
a + b + c => d + e
Let us say that this consist of the set of elementary reaction steps where rxn 1 is rate limiting (thus others being in eqbm.):
(1) a + b => f
(2) f + c <=> g
(3) g <=> d + e
Note: Specie 'f' and 'g' are therefore 'reactive intermediates'. I am not saying your equation works like this, this is simply made up for
illustrative purposes and to keep things as simple as possible.
We can write rate equations for each:
r1 = dCf/dt = kf1.Ca.Cb – kb1.Cf
r2 = dCg/dt = kf2.Cf.Cc – kb2.Cg = 0: K2.Cf.Cc – Cg = 0 by using K2 = kf2/kb2
r3 = dCg/dt = kb3.Cd.Ce – kf3.Cg = 0: Cd.Ce – K3.Cg = 0 by using K3 = kf3/kb3
Eliminating for the transient specie ‘g’: Cd.Ce – K2.K3.Cf.Cc = 0
Rearranging: Cd.Ce/(K2.K3.Cc) = Cf
Using this in r1 to eliminate the transient specie ‘f’:
d[Cd.Ce/(K2.K3.Cc)]/dt = kf1.Ca.Cb – kb1[Cd.Ce/(K2.K3.Cc)]
The rest of the maths is simply tedious (chain rule differentiation, pulling out constants and grouping constants to make new constants), but my point
is you don't land up with a first order equation.
What is incorrect here please?
[Edited on 11-11-2013 by deltaH]
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watson.fawkes
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| Quote: Originally posted by deltaH | I'll [...] probably make a total ass of myself... I hated chemical kinetics, nevertheless, here goes my attempt at refuting this
[...]
What is incorrect here please? |
You have certainly succeeded at your originally stated goal.
Incorrect? This is in the not-even-wrong category. "First-order" means something different in chemical kinetics than it does with respect to
differential equations. woelen's statement is perfectly meaningful because it refers to a first order chemical reaction, not to a first-order
differential equation.
This link and this link should help.
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deltaH
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watson.fawkes, you need to understand the meaning of the insult before you can use it effectively. The 'not even wrong' category
refers to statements that are not falsifiable. For example, a statement such as "invisible gnomes adept at hiding all traces of themselves frolic in
my garden at night" is clearly not falsifiable, so that would indeed be in the category of 'not even wrong'.
However, I have provided a mathematical derivation which certainly can be falsified if incorrect, but you have not done so.
Implying that I do not understand the difference between the order of a rate law and the order of a differential equation does not change the order of
the derived rate law.
This is a classical strawmanning strategy.
The fact remains that my derived rate law is not first order because the power of concentration terms are not one and so I have demonstrated by
exception that woelen's assertion, that setting all fast steps to be in equilibrium results in the reduction of the rate law to first
order, to be incorrect.
Well, that is at least what I tried to do 
[Edited on 12-11-2013 by deltaH]
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woelen
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Please, no quarreling in this thread, I don't like that at all!
@deltaH: Your equations assume equilibrium, but my equations all are about far from equilibrium situations, except the NH3OH(+)<-->NH2OH+H(+)
equilibrium. Algebraic constraints also come from reactions which are very fast compared to other ones. Such reactions simply can be propagated to
their final products and the rate at which these final products appear are algebraic expressions of the concentration of intermediate products.
@blogfast25: I myself also have the feeling that the 4-particle reaction is not the best description of the reaction between bromate, bromide and
hydrogen ion. So, I actually agree with you and deltaH. But I see no better explanation. And observed kinetics also is according to this model, so for
the time being, I use this at least as a mathematical model, describing the kinetics quite well, realizing that although this mathematical model does
describe the reaction quite well, it probably is not a true reflection of the underlying physics. Most likely, the system has more state variables,
but the other equations are very stiff (have much smaller time scales) so that the observed behavior within the accuracy of the measurements is like
the equation I presented in earlier posts.
Even now, while I still have no complete describing model, I learned already quite a few new things about chemical kinetics. It is a highly
descriptive branch of science, which heavily relies on macroscopic observations and for which it is amazingly difficult to elucidate all intermediate
steps. The real mechanisms behind the transfer of atoms between reactants is a fascinating and largely unknown area of science.
@PHILOU Zrealone: I have done some more experiments with KClO3, but it really does not show any interesting reaction. I even provoked the goddess of
chemistry a little, but she did not bite this time  :
I (carefully) tried boiling a fairly concentrated solution of (NH2OH)2SO4 with KClO3. No visible reaction. To that I added a little 2M H2SO4, while
still hot. Still no visible reaction. Finally, I added a little NaCl. When this is done, there is some slow production of gas, but nothing
interesting. Most likely the chloride with chlorate at low pH slowly gives some Cl2 and/or ClO2 which immediately react with hydroxylamine to give N2
and/or N2O.
[Edited on 12-11-13 by woelen]
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Marvin
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| Quote: Originally posted by woelen | | Quote: | | [...]the slowest step causes all others to be assumed to be at equilibrium.[...] |
This cannot be true, because if this indeed were the case, then every chemical reaction would behave like a first order system (only one differential
equation, all other equations being algebraic, because all other steps are in equilibrium).
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Actually it does make sense, all the other reactions have time to get close to equilibrium. It doesn't mean the equilibrium point doesn't change
throughout the reaction. If the products of the reaction affect the equilibrium, or catalyse the rate determining step then the reaction overall
will be high order dynamically. I think the general feeling is that during the induction phase of this reaction the pH drops, leading to increased
concentration of the species involved in the rate determining step. It's an Autocatalytic reaction.
I'm not. If nothing else, a third body is often needed just to take away the energy. Any reaction that happens on human time scales must be pretty
unlikely on the molecular level.
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watson.fawkes
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Excuse me. I managed to have
forgotten that you live in a Humpty-Dumpty land where everything you say means exactly what you choose it to mean, neither more nor less.
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watson.fawkes
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| Quote: Originally posted by woelen | | Algebraic constraints also come from reactions which are very fast compared to other ones. Such reactions simply can be propagated to their final
products and the rate at which these final products appear are algebraic expressions of the concentration of intermediate products.
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Just because a reaction is fast doesn't mean it generates a constraint. As above, this is a question of
topology of the equation. For a fast reaction to generate a constraint, that means that every solution of the original equation has to lie near the
solution set defined by the constraint. This may be a property of specific equations, but it is not a property of these systems in general.
Indeed, with regard to the original reaction, the "instant" phase change is evidence of a very fast rate constant somewhere in the system. If you were
to convert that immediately into a constraint, you'll end up with a class of candidate functions for solutions that do not contain that rapid phase
change behavior.
What I am seeing here is that you have two very fast rate constants in the system, one for a reaction that goes forward in some sense, and another
that goes in reverse. The rate constant for the reverse reaction is faster than for the forward one. The combination of these two looks like nothing
is happening for a while, until some input of the reverse reaction is exhausted, and suddenly the forward reaction proceeds without inhibition.
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morganism
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Are you doing this experiment at a window ?
It is possible that this could be a nanoparticle creation/reaction.
Lots of studies of water purification with nanoparticles are happening for developing countries.
I may have posted some up here.
They have found that nanoparticles absorb energy, creating a vapor bubble around themselves, preventing heat from escaping. this can lead to vigorous
boiling, but havn't heard of anything this rigorous from that model yet...
Sunlight is enough to run these reactions, don't know if a halide would.
[Edited on 14-11-2013 by morganism]
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blogfast25
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Like where precisely?
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woelen
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I made quite some progress. I derived a set of equations, which wonderfully captures the observed behavior. Initial addition of bromide ion shortens
the induction period, but the reaction remains sharp and sudden. Initial addition of H(+) ions also shortens the induction period, but the reaction
also becomes more like a normal runaway. This behavior occurs in reality, and the equations also capture that behavior.
The model has 5 state variables (concentration of bromate, bromine, bromide, hydrogen ion and hydroxylammonium ion).
I also made a few more movies. One movie with sound, so that you can hear the POP sound and a movie with mixed liquids instead of added solid to
liquid. The mixed liquids actually seem more impressive than solid added to liquid. Most of the liquid simply evaporates immediately after start of
the reaction.
More will follow tomorrow or the day after tomorrow. I also want to write a webpage about these phenomena.
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Mailinmypocket
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Came across a somewhat similar experiment, albeit not as violent or complex. Thought I would share it here in case there is interest
http://www.versuchschemie.de/topic,17874,-chemischer+Geysir....
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woelen
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I finally have finished the webpage about this experiment. It has a lot of pictures, a few videos and a mathematical model of the reaction dynamics,
which explains the observed behavior quite well:
http://woelen.homescience.net/science/chem/exps/hydroxylamin...
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Your link from versuchschemie is quite interesting as well. Something I certainly will try myself. This reaction, however, is not nearly as violent as
the one I have (re)discovered. I also want to warn people not to scale up my reaction to the size of the reaction, described on versuchschemie! That
would almost certainly lead to really nasty accidents!
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blogfast25
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It's an interesting one. It seems to be autocatalytic (on superficial inspection)
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woelen
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I tried a few other similar reactions.
- The one on versuchschemie.de (Na2S2O5 with solid KClO3): It works as described. The reaction becomes faster and faster over time and ends with a
climax in which the liquid becomes boiling hot.
- N2H4.2HCl with solid NaBrO3: This gives a violent, but not explosive, reaction at once. No induction time at all.
- N2H4.2HCl with a drop of 30% hydrazine added and then addition of solid NaBrO3: No reaction occurs at all, not even after ten minutes. When a drop
of 30% HCl is added, then there is slow increase of reaction speed and a runaway occurs.
- (NH3OH)2.H2SO4 with solid NaBrO3: There is an induction period, followed by a small explosion (POP sound), which is only slightly less violent than
with NH3OH.HCl. This most likely is due to the somewhat lower solubility of the sulfate salt, so that the concentration of the solution is somewhat
lower.
It appears that NH3OH(+) ion has some specific property which the other reductors do not have: N2H6(2+) immediately seems to react quickly with
bromate, while NH3OH(+) only reacts slowly with bromate.
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woelen
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After 5 years I revisited this reaction again. I now have a camera which can make movies with 1000 frames per second at good resolution. The movies
are really really stunning.
Have a look at these two videos:
http://www.homescience.net/chem/exps/hydroxylamine_bromate/N...
http://www.homescience.net/chem/exps/hydroxylamine_bromate/N...
Five years ago I already made a webpage about this very special reaction. The videos are not yet in the webpage, I will add links to them soon. The
webpage is the following:
http://woelen.homescience.net/science/chem/exps/hydroxylamin...
I am still struggling with finding good video editing software. I now had to reduce the resolution and bitrate a lot to make videos of acceptable
dowbload size (still appr. 15 MByte), but this reduces the quality a lot. The videos are fairly small (360x640), the originals from the camera are
1080x1920, but the original files are almost 1 GByte, not suitable for web publishing at all. I think, however, that the videos, I have uploaded, show
the stunning effect of the reaction sufficiently well.
Each video covers appr. 2.5 seconds of real time. The start of the reaction already is very fast on these super slow motion videos, in reality it is
in the milliseconds time scale.
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Waffles SS
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Woelen,
I get excited when i read your posts.
That is great,
How you find out this reaction mechanism?you spent a lot of time for providing dynamics of this reaction on your website.
after 5 year you are still interested to this reaction and want to complete information about it.You are really talented chemist.
[Edited on 24-10-2018 by Waffles SS]
Chemistry = Chem + is + Try
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woelen
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In the derivation of the equations I used a few papers. They can be downloaded on my webpage (there are links in the webpage to these papers). By
combining the equations of the papers I come to a complete set, which can be simulated with a numerical method.
I expect to revisit more reactions on my website. With the new camera I can make new recordings and some reactions may exhibit interesting phenomena
when recorded at high speed.
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wg48
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| Quote: Originally posted by woelen | In the derivation of the equations I used a few papers. They can be downloaded on my webpage (there are links in the webpage to these papers). By
combining the equations of the papers I come to a complete set, which can be simulated with a numerical method.
I expect to revisit more reactions on my website. With the new camera I can make new recordings and some reactions may exhibit interesting phenomena
when recorded at high speed. |
FANTASTIC job on the experiments, simulation and web report woelen.
Borosilicate glass:
Good temperature resistance and good thermal shock resistance but finite.
For normal, standard service typically 200-230°C, for short-term (minutes) service max 400°C
Maximum thermal shock resistance is 160°C
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