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Offline Mitch

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Re:Canonical chemistry
« Reply #15 on: September 16, 2004, 07:08:37 PM »
Don't worry we understand how slow it is for the chemical community to accept new ideas. It is even harder to grow a community around such ideas. It's taking us a while to develop and grow a chemical community in our little niche of chemical education. We can still offer you webspace for your articles(ad free). We can even give you a @chemicalforums.com e-mail address if you feel the yahoo address isn't professional enough. Just let us know how we can help.

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P.S. Remember we also own www.citizenchemist.com and are comitted to helping non PhDs publish their own articles on Chemistry here. Although they're probably not as mathematically rigorous as your's would be.
« Last Edit: September 16, 2004, 07:13:09 PM by Mitch »
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Offline Juan R.

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About mathematical difficulties
« Reply #16 on: September 20, 2004, 08:19:50 AM »

Hi Mitch,

Thanks by your enthusiastic comments! As said, I do not post comments about “bureaucracy”. I will send the reply to your personal mail.

Let me a comment; you said, “Although they're probably not as mathematically rigorous as your's would be.” This and my previous comments about canonical chemistry could introduce a distorted image of the new discipline.

The revolutionary canonical chemistry is a hierarchical theory. I.e. there are different levels of molecular description, from simple (at level of thermodynamics or “macroscopic” chemical kinetics) to the most advanced. The most advanced level that I have developed is a quantum formulation at level of Prigogine Liouvillian extension of quantum theory, for example, but generalized with relativistic corrections. In principle, one can work at the most adequate level for each specific situation, using many details for simple processes but few details for complex ones, for instance. This is a very “democratic” theory!

Now, I am working in the extension to full (general) relativity. This is very difficult for me. Note that the extension generalizes the usual approaches to quantum gravity, including the most recent or “radical” ones. Special relativity works only with flat spacetime. Now, as a first step, I am developing a formulation of chemistry in curved space-times. It would be useful in cosmo- and astrochemistry.

Fortunately, very basic ideas of canonical chemistry can be discussed at an elementary level, for example, Chang course in general chemistry. Of this manner, all people (scientist or no) that can understand that book can understand the basis of canonical chemistry.

For example, the “rate coefficients” for generalized chemical processes are key elements in the theory of canonical chemistry. At the simplest mathematical level, the coefficients are only numbers, somewhat as the constant rates k of chemical kinetics are. At the Liouvillian non-relativistic level, the full mathematical expression for the coefficients is so complex and mathematically demanding that one needs an entire page for writing them. Compare it with the simplistic Schrödinger equation H phy = E phy!

At the relativistic level, things are still more complex. I am sorry to say this but one cannot use the standard relativistic quantum chemical literature.

To be precise, one can choose in canonical chemistry the level of math compatible with both the problem that one is working and personal feelings. I know that some organic chemist hate math. This would be a problem in quantum chemistry (formulated in a clear physics’ way) but it is not a problem in canonical chemistry, because one can use a symbolic formalism in the style of the “mechanistic approach” or organic synthesis and discuss many things in a qualitative fashion. Undoubted, math becomes necessary for doing explicit calculations, but this is also true for the current organic theory.

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Offline Juan R.

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A simple experiment
« Reply #17 on: September 20, 2004, 08:22:23 AM »

Chemistry is more than the study of “stinking liquids in a flask”. Canonical chemistry recovers the viewpoints of alchemists or the general view of ancient chemists as Lavoisier. In fact, Lavoisier studied the vital processes of animals (e.g. his manuscript “Sur la respiration des animaux”) thanks to his chemical theory of gases and combustion. Now, that is seen as belonging only to biology...

With the aim of illustrating those things that are not teaching in current (“20th century”) courses of chemistry, let me introduce a simple elementary example.

Take the following chemical scheme

A + F ==> 2 A

P + A ==> 2 P

Look at a manual on physical chemistry or chemical kinetics, write the rate expression for d[A]/dt and post it in this forum.


Juan R.

Note: this is more interesting if this is done by a student of first courses of chemistry. Mitch, you cannot participate here.   ;-)

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Offline Donaldson Tan

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Re:A simple experiment
« Reply #18 on: September 21, 2004, 01:26:37 PM »
A + F ==> 2 A
P + A ==> 2 P

Which of the two equations is the rate-determining step?

The 2nd equation looks wierd, because one P can removed from both the left and right hand side. It appears that either the 2nd equation is more than meets the eye or P converts A to another P magically
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Re:Canonical chemistry
« Reply #19 on: September 21, 2004, 02:10:46 PM »
With kinetics you can sometimes get away with turning your brain off. The d[A]/dt will equal the formation of [A] in equation 1 minus the loss of A in equation 2. Although the fact that your using A to make A is throwing me off right now, I'll have to look at it closer when I have some more time.
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Re:Canonical chemistry
« Reply #20 on: September 21, 2004, 02:42:47 PM »
These are of course general expressions, but I would venture to rationalize a scenario where F is an isomer of A, and F uses A as a catalyst to rearrange to produce A.

Or as predator-prey, where A eats F and produces an offspring: A + A   lol,
« Last Edit: September 21, 2004, 03:01:30 PM by Demotivator »

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Re:Canonical chemistry
« Reply #21 on: September 21, 2004, 04:26:18 PM »
I was sleepy and still is sleepy, as it's 4am here now..

Rearranging Juan's reaction equation, we've:
(1) A + F => 2A
(2) A + P => 2P

Assuming both (1) and (2) occurs at the same rate and they are valid equations, then d[A]/dt would remain 0 until all F are used up. Then d[A]/dt begin to decrease.
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

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Re:Canonical chemistry
« Reply #22 on: September 21, 2004, 09:55:15 PM »
my head hurts :P

Offline Juan R.

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Re: Simple experiment
« Reply #23 on: September 23, 2004, 08:27:22 AM »

Thanks by your comments. There are numerous replies and due to a lack of time, my answer will be unified.

1)  A + F ==> 2 A

2)  P + A ==> 2 P

For writing the rate of a chemical (e.g. d[A]/dt), it is unnecessary to know, a priori, which is the rate-determining step (if there is any!). The rate-determining step (if any) introduces simplifications on a generic chemical equation.

Above equations are of generic kind

A + B ==> 2 B

Of course, the stoichiometric equation is A + B = 2 B or simplifying both sides A = B. However, B (product) participates also as reactant in the molecular mechanism. This equation is known as quadratic autocatalysis. See an introduction to autocatalysis on section 26.7 of [Atkins].

The total rate for A is

d[A]/dt = k1 [A] [F] - k2 [P] [A]

where k1 and k2 are the constants of reactions 1) and 2) respectively.

In principle, the above scheme was though for many of yours as chemical reactions between chemicals A, P, and F. However, note that I said not that they were. In fact, effectively I could say that A and P are animals, and F is food. In fact, you can see that I inspired in the Lotka-Volterra mechanism, what is a classical on mathematical ecology (Lotka was a American chemist and Volterra was a Italian mathematician). Reactions 1) and 2) are reactions a) and b) (with other letters for species) of the section 26.8(a) of [Atkins]. In mathematical ecology, the Lotka-Volterra mechanism is a simple mechanism of Predator-Prey interactions. In the above example, A is a prey and P is the predator.

Rearrange the total rate and defining R = k1 [F] - k2 [P], the rate looks as

d[A]/dt = R [A]

This is the first principle of population dynamics. According to Berryman (a professor of Entomology and Natural Resource Sciences), this principle is truly general in that it applies to all populations and, in fact, to all self-replicating entities. Note that this principle is postulated without discussion in usual literature. Now, we derive it (somewhat as a “theorem”) from a simple chemical mechanism and using the laws of chemical kinetics.

Next, we could analyze the above rate law and study the different regimes, for example what succeed if k2 is zero, if k1 is zero, if R is zero, if at glaciations [F] -> 0, etc, and our discussion would be parallel to the ecological discussion of real ecosystems working below the first principle. E.g. if R = 0, Berryman says that the birth rate is equal to the death rate. This is precisely the idea that we discover when one observes that 1) is birth of A and 2) is his death.

I put this simple example for showing that chemistry can be thought as a general science beyond the usual thinking of 20th century chemists. The advantage of physicists thinking is that they see physics as a general science. They apply physics to all from particles and molecules to biology (biophysics), universe (cosmology), economy (econophysics), etc. My research shows that chemistry (canonical) is more general and advanced that usual physics. Chemistry can be used as a model of how Nature works (ecology, physics, biology, vehicular traffic, etc.). In the language of canonical chemistry, I use the concept of “generalized chemical equation” and “generalized chemical systems” for describing those systems that usually one does not consider chemical ones but that work as traditional chemical systems perfectly.

In fact, the separation between “chemical systems” and “non-chemical systems” is somewhat artificial in the formalism of canonical chemistry (by this reason I talk about generalized chemical systems). To ignore the contribution of chemistry to the understanding of other sciences would be like if one defines organic chemistry as “the chemistry of organic compounds without nitrogen atoms”. In nature, there is not an artificial splitting on disciplines. I think that this potential of chemistry and chemical laws would be utilized, somewhat as Lavoisier studied animal respiration or Boyle the “physical” behavior of a gas. Note that precisely physicists have enlarged their own field of applications (now physicists work even in the synthesis of materials as polymers!) since the study of celestial bodies, whereas chemists (specially in the 20th century) have self-restricted their own field. In fact, this has been the main criticism of many young chemists as Michael Ward: “Things like polymers and surfactants were picked up by chemical engineers and material scientists, but that’s changing now and chemistry is trying to get them back” [Adam]. One of my objectives is that chemistry goes back to the fascinating 19th century status.

This experiment was directly based in chemical kinetics (chemical kinetics can be derived from canonical chemistry). In the next experiment, I will introduce other example more close to the formalism of canonical chemistry.

Literature:

Atkins, P. W. Physical Chemistry (Sixth Ed.); Oxford University Press: Oxford, 1998, pags. 808-809.

Adam, David. What’s in a name. Nature 2001, 411, 408–409.
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Offline Juan R.

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Second experiment
« Reply #24 on: September 25, 2004, 07:47:14 AM »
Please, if you have time, you could try to find if the following processes are physical or chemical ones:

- Heat transport between two bodies (e.g. metals).

- Industrial synthesis of ammonia, N2 + 3H2 ===> 2NH3.

- Ammonia inversion, :NH3 <===> 3HN:

You could introduce your own ideas, criteria, reasons, etc. On the other hand, if you prefer, you could cite to some author of your own choosing.

If there are many heterogeneous replies, the discussion will be more instructive for all us. I acknowledge in advance your replies. I will post my own reply and personal beliefs the next Friday.

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Re:Canonical chemistry
« Reply #25 on: September 25, 2004, 09:40:29 PM »
I don't think they are chemical or physical. I believe they are biological, deriving behavior from a canonical psychology!

Heat transport is an example of "the grass being greener on the other side" impulse. It is the need to migrate to unoccupied realms.
Ammonia synthesis stems from the need to achieve stability through union with another.
Ammonia inversion is an example of entities (most notably politicians) flip flopping as they cannot decide between two plausible arguments.
 8)

ssssss

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Re:Canonical chemistry
« Reply #26 on: September 26, 2004, 09:02:46 AM »
I really want to Join your Discussion but i dont have time right now,i goota go.But someday i will be with you.

Offline Juan R.

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Chemical processes (I)
« Reply #27 on: October 01, 2004, 07:16:28 AM »
Thanks by your interest.

What is the difference between physical and chemical processes? One can define scientific terms according to two methodologies: descriptive and systematic. In a descriptive approach, one simply lists the different physical and chemical processes. However, in a systematic approach, we define and use a definition for cataloging the processes of natural word. Nevertheless, let me introduce a bit of history and “marketing” first.

Whereas physicists were more interested in mechanical aspects of matter, alchemists were interested in all properties of matter. Ablation, coloration, dissolution, or evaporation, between other were (al-)chemical processes for a 16th century alchemist. Antoine Lavoisier (1743–1794) is often considered the father of modern chemistry. In his Tableau des substances simples, Lavoisier considered the calorique (heat) and the lumière (light) simple substances participating in a chemical process in the same way that oxygen, hydrogen, zinc, or mercury participates in other processes.

However, the modern tendency of chemistry has been towards an increasing use of the terms “physical” and “physics” instead of “chemical” and “chemistry”. Many physical chemists have guided this wrong philosophy. Two physical chemists wrote the following shocking words: “all subjects treated under chemistry tend to be subject, as time goes on, to treatments at the more advanced degree of sophistication attained under the aspect of the science we call physics.” What a beautiful piece of chemical “marketing”, perhaps focused to 15-years old students and policymakers! Again, chemistry is underestimated and seen as a cuisine. Attitude like this are the true basis of the current unpleasant status of chemistry.

Actually there is no systematic definition of chemical or physical processes (or properties), and authors use their own criteria according to specific preparation, knowledge, and personal views.

For example, Cram and Hammond’s book on organic chemistry distinguishes chemical processes from other formal processes by the use of “double” or “single” arrows respectively. They symbolize ammonia inversion with a double arrow as in a chemical reaction. However, they state that solubility of a compound is a physical property (i.e. dissolution is a physical process). But what is a chemical reaction? According to Cram and Hammond (CM) chemical reaction is a event in which two molecules collide in such a way as to break one or more of their bonds and make news bond and hence new molecules. Then is ammonia inversion a chemical reaction? Moreover, if participate only atoms in a process, then it appears that is not a chemical reaction, i.e., the redox reaction, Zn + Cu2+  =  Zn2+ + Cu, would be a physical process according to above (CM) definition.

According to general chemistry by Chang (C), a chemical reaction is when new substances arise from a process, but as he does not define “substance” then chemical reactions remain undefined. Moreover, Chang opines that by heating a block of ice we do not change water, only its “appearance” and thus is a physical process. I imagine that the ammonia inversion would be a physical process for Chang. It is interesting remark that Chang considers that redox reactions are chemical reactions (note that this is contrary to CH).

Physical chemists McQuarrie and Rock (MR) state that all chemical reactions can be assigned to one of two classes: reactions in which electrons are transferred from one reactant to another and reactions in which electrons are not transferred. This is similar to (C) but different of (CH). Whereas, in a well-known Spanish manual on physical chemistry, the author, Diaz-Peña (DP), states that electrochemistry is outside of “pure” chemistry. For example, the standard electrochemical reaction Mn4+ + e- ===> Mn3+ is named an electrode reaction, because it is formed of two steps

(1) Mn3+ + e- ===> Mn2+

(2) Mn2+ + Mn4+ ===> 2 Mn3+

The first step is named an electron transfer process and the second a chemical reaction, and thus the global reaction (1+2) is considered not a chemical reaction by (DP). Others chemists opine that redox reactions are non-chemical processes because none bond is formed or broken, then I ask they what is a chemical bond and I do not receive systematic reply.

Many chemists state that heat transport is a physical process. However, Karen Timberlake (KT) says, in her manual on chemistry, that evolution or absorption of heat is a chemical change if is not associated with changes of state. (?)

Many inorganic chemists will say you that ammonia inversion is not a chemical reaction but, recently, two theoreticians have claimed that it is a chemical process, because computed how bonds are broken and formed. Philosopher of chemistry Joachim Schummer (JS) opines that the solubility in a certain liquid is an example of chemical property in direct contraposition with (CH) own ideas.

That is, there exits an enormous confusion in theoretical chemistry and this is transferred to current chemical education. Compare by yourself the above criteria and definitions. You will see that there is not unique definition of chemical process or property. Moreover, Demotivator (a Staff member of chemicalforums) has claimed:

Quote
I don't think they are chemical or physical. I believe they are biological, deriving behavior from a canonical psychology

I could critique many of the definitions above stated from different views: philosophical, educative, historical, theoretical, experimental, etc. For instance, Chang talks about “physical” processes in water when water changes just its “appearance” in his celebrated manual on general chemistry. However, he fails to define rigorously what water is...

What is water? In a first instance, water “is” H2O and then in processes like

H2O(solid)  ===>  H2O(liquid)

or

H2O(liquid)  ===>  H2O(gas)

Water “substance” remains “unchanged” according to Chang. However, in a more detailed observation, one observes only internal interactions (chemical bonds) in the gas phase molecule, whereas there is also hydrogen bonding in both ice and liquid water systems. That is, there are extra bonds in condensed phases and the atomic “array” is not the same.

From a quantum view, the wave function of the phase gas molecule of H2O is not defined in an ice cluster (H2O)n formed by n “water” molecules, indicating that the molecular system is not the same as its quantum state is not the same. However, there is more.

In a more accurate level of description, one discovers that Chang calls “pure” water is really a mixture and aggregations of H2O, H3O+, and OH- species, and that the concentration of all three components varies with temperature. We can measure the changes in the chemical composition of water with temperature. That is, when one studies the process with more molecular detail, then appears that the initial Chang distinction between “physical” and “chemical” processes is somewhat arbitrary.

Due to the current divergence of criteria, I could introduce my own definition of chemical reactions according to my own beliefs but inspired in traditional points of view of ancient chemists. For example, nobody would say to me (once an inorganic chemist did) that, “traditionally heat transport is a physical process” because tradition was changed in 19th and specially 20th century chemistry. However, I prefer talk about generalized chemical reactions with the aim of facilitating the adaptation of “archaic” chemists to the new canonical ideas. I can say that heat transport is a generalized chemical process whereas ammonia synthesis is a standard chemical reaction. Both are chemical processes in a generalized theory.
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Offline Juan R.

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Canonical chemistry processes
« Reply #28 on: October 01, 2004, 07:22:16 AM »
Why have the 20th century chemists separated “chemical” from “physical” phenomena ignoring ancient chemical views? I think that was a problem of stoichiometry. For example, Prigogine (Nobel Prize for chemistry) was known for his successful application of his chemical theory not only to usual chemical systems but also to sociological, biological, and physical systems. He applied satisfactorily his theory of dissipative structures to diverse systems as the Big bang or vehicular traffic in cities. In fact, his theory of Big bang was revolutionary as instead of a beginning of time it claimed for a phase transition from a pre-universe. It is very remarkable that the most advanced cosmological models based in string theory use his basic ideas.

However, the own Prigogine recognized that the analogy with chemical reactions was “formal”. For example, he said that order-disorder transformation in an Au-Cu alloy could be characterized as a chemical reaction but one has not well-defined stoichiometric coefficients.

Some similar happens for the above water transformations. According to Prigogine and others, the concepts of chemical kinetics can be applied to (liquid) ===> (solid) transformations. In fact, the usual form of computing enthalpy changes for “physical” processes in thermochemistry (including phase changes) is applying the definition of enthalpy of reaction: i.e. enthalpy of products minus the enthalpy of reactants (see, for example, the P. A. Rock manual on chemical thermodynamics for illustrations).

Then if one can compute many things as if the physical process is a chemical one, why could we not achieve a unified theory based in chemical ideas?

Canonical chemistry begins saying that a system of interest for chemists can be described by a vector n. Vector n include all the necessary for describing completely the system of interest.

Description of matter is hierarchical. This is point usually omitted in chemical education. There are different levels of molecular descriptions from the most simple to the most sophisticated. In a first analysis, gas phase water is formed by molecules of H2O, but are those molecules indistinguishable? Response is negative, in a more detailed analysis, we can split the “concept” of H2O in a sum of different H2O(w) where w symbolizes the electronic state, e.g. H2O(1) symbolizes molecules of “water” in state 1. Our flask with simple water will be formed by a determined composition of “specie” [H2O(w)]. This splitting is necessary (is usual in molecular dynamics) because the molecular properties (geometry, frequencies of vibration, bond energies, etc.) are different. Are all molecules of kind H2O(w) equals? Again, the response is negative, and we can incorporate additional molecular details, for example rotation or vibration, nuclear state, isotopes, etc. For example is not the same o-H2 that p-H2 and the diference is only in the nuclear spin of hydrogen atoms. For many studies, the difference is insignificant, and one talks just about H2 but spectroscopic data is different for both and one can detect each “specie” separately. That is, in canonical chemistry one use the level of molecular detail needed for the concrete study that one is doing in each instant. If you are an analytical chemist and you are measuring the concentration of CO2 you work with one single specie CO2, if you are a theoretician computing kinetics constants for interstellar clouds you can split the total concentration of CO2 in molecular species. Let me continue with canonical theory.

The following step in canonical chemistry is to write the generalized chemical process

(n+) <===> (n-)

This is an important point of canonical chemistry. The failure of Lavoisier’s view was to consider that stoichiometry was only restricted to atomic or molecular quantities. As said in this forum, 20th century biologist and physicists had minds more open. This is also true for ecologists. Ecologists use the term stoichometry in a broad sense in the so-called stoichometry ecology.

By this restriction of chemical theory, Prigogine could not apply completely his chemical ideas to other systems as the Au-Cu alloy. Prigogine, Kondepudi, and others chemists could derive formulae for phase equilibriums using the same criteria that one applies to chemical reactions, when they defined the chemical affinity for the “reaction” gas = liquid, but they cannot apply all the theory of chemistry to the change of state. For example, we can compute the condition of equilibrium doing affinity = 0, or using the equality of chemical potentials what is “equivalent” (affinity is a more modern and successful approach but unfortunately many chemical thermodynamics textbooks do not use), however we could not apply the equations of chemical kinetics for deriving the heat transport before equilibrium is achieved. In canonical chemistry, it is possible because Lavoisier’s restriction is overlooked!

The thirst step is to write the basic rate equation of canonical chemistry. I do not write here. It appears in my research and educative articles (canonical chemistry web site is becoming soon).

One of the simplest descriptions of two metal solids (A and B) is using macroscopic quantities at the discrete level of molecular description. The vector is n = (UA, UB) being U the internal energy. There are several heat transport mechanisms, one simple is the direct molecular transport.

(eA+, eB+) <===> (eA-, eB-)

the es are molecular amounts of energy necessaries for the process (see below the description of a typical chemical reaction). The simplest mechanism is one does not “concerted”

(e, 0) <===> (0, e)

Introducing this mechanism into canonical rate equation, one derives the thermodynamic description of heat transport. However, as stated above, we can introduce more details. The next level of description is the continuum or “hydrodynamic” level of molecular description. At this level, one introduces a field description of thermal quantities as that of TIP formulation of thermodynamics. Using a mechanism like

(e, e, 0) <===> (0, 0, 2e)

and working out the canonical equation one derives the Fourier law of heat transport. Note that Fourier law is usually postulated in physical chemistry books alluding to phenomenology. We derive using molecular mechanisms and a rate equation directly inspired in the law of mass action.

Heat transport is a generalized chemical process in canonical chemistry because is a change in the generalized composition, vector n, of the system of interest. Of this form, one obtains a unified formalism of matter processes. Of this form chemistry, far from be a closed discipline, is generalized and turn into the most fundamental discipline at the beginning of this century.

In principle, “all” could be derived of the same form, using always the same systematic theory. Of this form, all physical chemistry and many of physics are rederived and improved from a single rate equation; an equation more exact and powerful.

I think that this formalism is easiest for chemist that the usual physical formalism, because is based in the chemical point of view of “chemicals” and “reactions”.

If you are a organic or inorganic chemist you do not need to think in term of mechanisms and reactions and after change the “chip” when take a course in physical chemistry. All of physical chemistry is rewriting and improved at a high level in a full chemical fashion.

It is necessary only a few of practice for adapt to the new stoichiometric formalism. For example if the vector of state is n = (A, B, C, D) being the composition of different chemicals, and you are interested in the chemical reaction

A + B <===> C + D

In canonical chemistry one writes (see the last vector n)

(A+, B+, C+, D+) <===> (A-, B-, C-, D-)

or

(1, 1, 0, 0) <===> (0, 0, 1, 1)

and using the canonical rate one obtains exactly the laws of chemical kinetics. However, the canonical theory is more mathematical, elegant (the 0s that appear in the mechanism contain a significant information about quantum correlations and probabilities), and exact. In fact, canonical chemistry is the more exact theory that I known.

Working at the Liouvillian canonical level, one obtain a basic equation that generalize Schrödinger based quantum mechanics and one can obtain, for example, the basic master equation used in quantum optics when one write the adequate generalized chemical reaction (n+) <===> (n-). That is from the generalization of chemical kinetics provided by canonical chemistry and the adequate mechanism one derives the basic equation used in advanced quantum optics. In fact, this chemical theory can improve and correct some errors of quantum optics literature. By this and other reasons you will that quantum version of canonical chemistry is much more sophisticated that quantum chemistry.

This chemical theory is unified. If you dominate the basic assumptions of canonical chemistry that I cited above, then you can study practically every process. Current chemical education and research oblige to one to learn different disciplines, for example, thermodynamics is completely different of chemical thermodynamics and this later of quantum chemistry. If study quantum chemistry you will know nothing about quantum optics and Lax equation. If you learn that of quantum optics, you know nothing about the semigroup theory developed by mathematical physicists. If you learn the latter, you will know nothing catalysis in heterogeneous surfaces and if you are a specialist in those themes, you will know nothing about ratio-dependent ecological models. If you are an expert in the recent MTE ecological theory, you will know nothing about scattering amplitudes in electron-positron reactions of particle physics, and even if you are an expert in the topic (as Feynmann was or Weinberg is) you will know nothing about reaction dynamics. Etc.

In canonical chemistry, there is only a single theory, a single notation, a single rate equation, etc. E.g. if I show you what is the condition of equilibrium in an ecological system, the condition of equilibrium is the same in particle physics, brane theory, chemical reactions, ion transport in biological membranes, thermal equilibrium, mass diffusion in a vessel, etc.

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Offline Juan R.

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Doubts about canonical processes
« Reply #29 on: October 07, 2004, 05:40:14 AM »
Hi!

I would like to receive a lot of questions, comments, criticism, etc. about the last two posts, especially about the post on canonical chemistry processes and the basic formalism and ideas exposed.

Juan R.

The first canonical scientist.

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