Talk:Chemical potential

message: Chemical potentials are not a per-system phenomenon. One system can have multiple chemical potentials. For instance, in a non-equilibrium system, at any location, the chemical potentials of different species are not guaranteed to be the same. Furthermore, even in an equilibrium system (such as one in a steady state steady flow condition), the chemical potential would be different at different locations. Finally, the change in energy is not just a change in Gibbs free energy, it is a change in all the energy potentials of the system including internal energy (excepting energy potentials that are not functions of the chemical potential). ChrisChiasson (talk) 03:35, 20 November 2007 (UTC)
replies: text: OK, I over-simplified. Under the "precise definition" section (Chemical_potential#Precise_definition) it does state that "the chemical potential is the partial derivative of the Gibbs free energy with respect to number of particles" "under conditions of constant temperature and pressure" (typical laboratory conditions). I do think that a simpler introductory sentence would be helpful for general readers than the existing introduction -- without compromising accuracy. --Ben Best (talk) 07:40, 20 November 2007 (UTC)
replies: text: Hi. I find the introductory section to be rather poorly worded. I, for one, did not understand it. Perhaps we should update it Paskari (talk) 13:42, 7 October 2009 (UTC)

text: I concur with Paskari.  The introduction should begin with a definition, not a history.  --BBUCommander (talk) 21:40, 6 February 2012 (UTC)

text: I've moved the cited definition into the first sentence. It's still not the best definition, but it's better than just stating the origin of the term, I think.Forbes72 (talk) 01:44, 28 February 2012 (UTC)
thread_title: on the simplified introductory sentence

message: 1) Chemical Potential is a noun, it should not be described as a verb, such as "change". Velocity is a noun and defined as the change in position with time. ......
So the article is fine.
2) Constituent: an artifact that is one of the individual parts of which a composite entity is made up; especially a part that can be separated from or attached to a system
A particle is added to a group of particles.  The energy required defines the chemical potential.  I ommited the word "constituent particle" because the additional particle need not be "one of the individual [particles] of which the [group of particles]" is added to.  A chemical potential is still defined if I take a particle that is not a member of the group of particles and add it to the group of particles.
3) Point 1) above is not right. Change can be a noun as well as a verb. E.g., if I change (v.) x to x+1, then the change (n.) in x is 1.
4) The fundamental concept of the chemical potential (1st sentence of the article) as being the change in energy on adding a particle, is often (in many books and papers) taken literally to mean a finite difference F(N+1)-F(N), where N=number of particles and F is either the internal energy or the Helmholtz free energy (the difference is taken at constant entropy and volume in the former case, at constant temperature and volume for the latter). That this can be essentially incorrect for finite systems (even for some very large finite systems) has been discussed recently (see The Chemical Potential, by T. A. Kaplan, J. Stat. Phys. 122, 1237 (2006)).--Tomkaplan 19:16, 3 January 2007 (UTC)
thread_title: Random comments

message: I believe this article should eventually be split into 2 articles and then have a disambiguation page.
Theoretical chemists use the term "chemical potential" to refer to the electronic chemical potential.
All other chemists use the term "chemical potential" to refer to the thermodynamic chemical potential.
It seems totally obvious to me, but this confuses nearly all chemists (because the electronic chemical potential is rarely discussed in undergraduate course work - and even in graduate course work).
For the time being, what is written might suffice; however, if/when more content is added to describe the electronic chemical potential more accurately and completely (including the principle of chemical potential equalization arising from density functional theory - here refering to the electronic chemical potential), the amount of content and the mixing of the terminology on the same page may prove far too confusing. --anon
:I broke it up into sections and added a description of the electronic chemical potential.  It seems to work fine, in my opinion.  I don't think splitting it up into several pages is necessary. I need to include some references, but I am awfully tired right now. --anon 06:00, 2 December 2005 (UTC)
replies: text: I think its a bad idea to split up the article. In physics, more precisely statistical physics, the chemical potential is usually defined as a rather abstract lagrange multiplier connected to the avarage number of particles. Thermodynamic and electronic chemical potentials, used in chemistry, are rather special cases of the more general concept of chemical potential!  —Preceding unsigned comment added by 82.211.200.170 (talk) 20:32, 15 January 2009 (UTC)
replies: text: As seen in this article, the physicist's definition of chemical potential is applicable to the interaction of any system of particles. It is so general it is being applied to nucleus physics and I suspect we will soon hear of the chemical potential of a galaxie. The article is on chemical potential. The article should focus on all the definitions of chemical potential that are used to calculate, measure, or predict chemical reactions (and the physical changes of phase, etc. which influence the course of chemical reactions.) Of course the article should include any underlying physical principles and especially clarifying examples thereof, but they should be put in subsidiary sections, not in the principal section. BTW, I give the idea of electronic chemical potential to my Advanced Organic Chemistry students (undergraduates also) because it is so tied in with the concepts of electronegativity, HOMO, LUMO, etc. that they use to describe the potential for an organic reaction to take place. I also use chemical potential in my course on organic photovoltaics, with much more physical theory. I also told both not to spend too much time wading this article (as of this date). There are much clearer sources. But, bravo to those who are trying to make this article clearer. Laburke (talk) 16:52, 13 September 2011 (UTC)
replies: text: The term chemical potential is used in chemistry with a very specialized definition.  In physics, the exact same term is used for a more general idea which can be specialized into the chemist's definition.  While I agree it would be preferable for chemical to refer to chemistry, the current usage in the literature suggests it does not.  Since this is an encyclopedia, the current usage should be used.  Thus splitting the article would be akin to original research as it would imply an attempt to adopt a new language not commonly used.  My suggestion for resolving this dilemma is to mention in the introductory paragraph that chemical potential is used in both a broad and specific sense.  The initial definition should use the broad sense, and then the specific use in chemistry should be given to introduce the specific sense.  That way any point of confusion is headed off immediately, especially for readers new to the subject who are likely to run into this dual-usage fairly quickly.  Thoughts? --BBUCommander (talk) 19:34, 5 February 2013 (UTC)
thread_title:  Should this article be split? 

message: I think that the section titled relativistic chemical potential should either be clarified by an expert or removed.  It is totally unclear to me what the relativistic chemical potential is.  It is stated as being related to symmetries and charges, but some sort of definition (preferably an equation) seems necessary (I mean, there's all sorts of things related to symmetries and charges, so it is quite a vague description).  
I don't do any relativistic-stuff, but I am fairly well-versed in atomic physics, in general, and if it's not clear to me I highly doubt it's clear to anyone other than the original author.  I'm going let it sit for a day-or-so, and then just remove it unless there is any discussion or changes.  DrF 03:43, 24 May 2006 (UTC)
replies: text: Added Expert request tag.  I'll let this section sit a little while longer before I delete it.  DrF 04:20, 26 May 2006 (UTC)
replies: text: This reads about right I clean it a bit and add a ref link for those who want to read more.--Sadi Carnot 15:12, 25 July 2006 (UTC)
thread_title:  Relativistic chemical potential? 

message: A curve would be a clearer illustration than the 2D plot.
Chemical formulæ are not all correctly subscripted.
Refers to non-existent "web-links".
—DIV (128.250.80.15 (talk) 04:36, 1 April 2008 (UTC)
thread_title:  Suggestions 

message: I think the example figure needs to be expanded( such as how the particles flow downhill, in more detail). Or it is too dry to give any useful information. At this stage it does not help people to understand the concept of chemical potential.  —Preceding unsigned comment added by 128.61.29.249 (talk) 18:20, 27 September 2008 (UTC)
thread_title:  The example figure 

message: # The opening paragraph has a Gibbs quotation prominently displayed.  If it's a direct quotation then it needs a reference.  My temptation is to remove that quotation until a citation can be added to show that it really comes from Gibbs.  It should be possible to track the quotation down.
# The example figure is, well, I'm not sure what it is.  The x and y axes appear to refer to chemical potential with, I assume, typical units of something like energy per mole.  However, the text says "Particles will tend to move from regions of ..." and I'm not sure what that movement means at all with reference to the figure's axes and units.  Again my tendency is just to delete the figure completely.  A previous entry on this page suggested that a curve might be clearer.  I agree, particularly since this will be the first example the reader meets.
I'm not a regular contributor to this article, and don't have time right now to become one.  I trust that my comments will be taken in the helpful spirit in which they are intended. - Astrochemist (talk) 23:54, 17 December 2008 (UTC)
thread_title:  Two items 

message: I think the article is misleading when it separates "electronic chemical potential" from "thermodynamic chemical potential". Any mobile species in local equilibrium has a chemical potential. When the species is, say, a hydrogen ion or a water molecule, the article calls it a "thermodynamic chemical potential". When the species is an electron, the article calls it an "electronic chemical potential", as if that was totally different. It's not different at all, it's the exact same definition, just electrons instead of protons, neutrons, or whatever. Would anyone object to me rewriting on that basis? :-) --Steve (talk) 07:49, 29 March 2009 (UTC)
thread_title:  False distinction? 

message: The units used for chemical potential should be discussed in the article. This seems like an important missing detail. Thanks!  David Hollman (Talk) 21:40, 1 September 2010 (UTC)
replies: text: Done. PAR (talk) 23:24, 2 September 2010 (UTC)
replies: text: Wow, awesome, cheers! David Hollman (Talk) 11:58, 3 September 2010 (UTC)
thread_title:  Units 

message: :::I would like to have an explanation for the (approximate) logarithmic dependence of the intrinsic chemical potential on concentration. Is it only for the Boltzman distribution of particle energies? --Rainald62 (talk) 23:24, 3 May 2012 (UTC)
replies: text: See E.T.Jaynes, 1957. --Rainald62 (talk) 21:30, 4 March 2018 (UTC)
thread_title:  Explanation 

message: I have done a major revision, principally to clarify the thermodynamics and to give chemical potential its chemical context. This was based mainly on Atkins, Physical Chemistry. The ordering of some material has been changed. For example, history was moved from the lead-in to the history section.
The questions regarding electrochemistry are still to be resolved (see above). Atkins, Sections 7.5-7.9 devotes 15 pages to electrode potentials, but there is no mention of the internal/external issue, nor is there any reference to chemical potentials on those pages; the whole treatment is in terms of the free energy and reaction quotient. Petergans (talk) 09:08, 5 May 2012 (UTC)
replies: text: The first two sentences still seem problematic to me.  The energy released in a chemical reaction is more properly the internal energy or enthalpy, right?  Also, why is chemical potential assigned as "potential" energy.  In reality, some of the Gibbs energy is "kinetic" (molecules moving) and some is "potential" (e.g. intermolecular forces).  Finally, the second sentence would seem to be confusing at minimum with a key property about the chemical potential, which is that the chemical potential of a substance in the a phase is equal to the chemical potential of the substance in another phase if the phases are in equilibrium.  What exactly is changing during a phase transition?Stieltjes (talk) 17:43, 29 August 2012 (UTC)
replies: text: The energy released in a chemical reaction is free energy not enthalpy. In fact a reaction may be endothermic, ΔH=<0, and still occur spontaneously because of the entropy contribution. Some of the free energy released can indeed be turned into kinetic energy, for example in an explosive decomposition, which is why the term "potential" is apt.Petergans (talk) 07:49, 30 August 2012 (UTC)
thread_title:  Major revision 

message: All:
I'm not qualified to edit this article, but have a small request for those who are working on it.  It would be helpful for those not versed in the field if the terms in at least the important equations (e.g. the first one in the "Thermodynamic Definitions" section) were defined.  The article on Helmholtz Free Energy for example, does a good job of this.
It also might be helpful to make the reference to "Gibbs energy" an inline link to that article.
Thanks to all for your effort!
Ma-Ma-Max Headroom (talk) 18:05, 10 September 2012 (UTC)
thread_title:  Request: define variables in equations 

message: The statement "The definitions given above are mathematically equivalent" appears to me to be meaningless. The three possible definitions
:\mu_i=\left(\frac{\partial G}{\partial N_i}\right)_{T,P,N_{j\neq i}}
:\mu_i = \left(\frac{\partial H}{\partial N_i} \right)_{S,P, N_{j \ne i}}.
: \mu_i = \left(\frac{\partial U}{\partial N_i} \right)_{S,V, N_{j \ne i}}
correspond to three different ways of defining partial molar free energy. There is no way in which the three definitions can be considered to be "equivalent" as there is no way in which Gibbs free energy (G), Helmholtz free energy (H) and internal energy (U) are equivalent. 
The second and third definitions are of little practical value because they apply at constant entropy (S), a condition which is virtually impossible to achieve in practice; I have included them for the sake of completeness because they can be found in texts on thermodynamics. Petergans (talk) 09:33, 13 May 2015 (UTC)
replies: text: The thermodynamic potentials are all related by Legendre transformations, a fact so well known that there is even a Wikipedia section on it . Xxanthippe (talk) 03:48, 20 May 2015 (UTC)
replies: text: This is very misleading. Although there is a mathematical relationship, the definitions are not "equivalent" because they relate to different physical quantities.Petergans (talk) 08:28, 20 May 2015 (UTC)
replies: text: They are equivalent in the sense that they are all equal to each other. Do you have a better term to use? PAR (talk) 21:10, 20 May 2015 (UTC)
thread_title:  Definitions 

message: I am now translating this page into Chinese. I notice something not understandable to me. In the section of "Chemical Potential in Ideal vs. Non-Ideal Solutions", there is a function:
𝜇𝑖=𝜇𝑖0(𝑇,𝑃)+𝑅𝑇𝑙𝑛(𝑥𝑖)
Here it seems that 𝑥𝑖 is the amount of certain species. However, if the amount is zero, then this logarithm diverges. Is this well? 
Besides, is there any special name for the term 𝜇𝑖0(𝑇,𝑃)? It looks like the chemical potential when 𝑙𝑛(𝑥𝑖)=0.  — Preceding unsigned comment added by Swenly (talk • contribs) 18:58, 30 April 2018 (UTC)
replies: text: Hi Swenly, Consider the asbolute ideal chemical potential  \mu_i^\text{ideal} = kT \ln(\lambda_i^3 c_i)  (this you get also via the difference quotient \mu=(F(N)-F(N-1))/1. For the concentration c_i=0 the ideal chemical potential approaches -\infty kT. However consider that the free energy of such a system goes like F(N,V,T)=TS-pV+\sum_i \mu_i N_i  This means that the free energy contriubtuion of the chemical potentials is given by  \sum_i \underbrace{c_i V}_{N_i} \underbrace{kT ln(c \lambda_i^3)}_{\mu_i} which goes to zero and does not diverge in the limit (all) c_i to zero.--Biggerj1 (talk) 11:41, 3 May 2018 (UTC)
thread_title:  About the function in the section of "Chemical Potential in Ideal vs. Non-Ideal Solutions" 

message: Recommend changing the confusing wording of this statement in the article:
"Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero."
- to -
"Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. If the chemical potential of a region is higher than the chemical potential of the photons in or entering that region (chemical potential greater than zero), photons would spontaneously disappear from that region until the chemical potential went back to zero; likewise, if the chemical potential of a region was less than zero, photons would spontaneously appear until the chemical potential went back to zero."
Or similar such language to explicate that it's a comparison between the chemical potential of the region, and the chemical potential of the photons.
71.135.39.238 (talk) 07:29, 9 June 2021 (UTC)
thread_title:  Chemical potential 

message: Hello, I submitted a section about the chemical potential of Van der Waals gases by showing how the chemical potential of Van der Waals gas depends on the Van der Waals constants a and b as well as on the entropy, and how these dependencies can be explained. The submitted section was deleted by user Xxanthippe. The plots, in my opinion help to understand the basic dependencies of the chemical potential from the constants of a pure gas.  — Preceding unsigned comment added by E-gabrielyan (talk • contribs) 04:07, 4 July 2022 (UTC)
replies: text: The opinions of individual editors are not enough for inclusion in Wikipedia. Original research WP:OR is not acceptable. Reliable sources WP:RS are needed to obtain consensus of other editors. Xxanthippe (talk) 04:28, 4 July 2022 (UTC)
replies: text: I was committed to provide a high quality and useful contribution. The section which I added was removed while I was inserting the references into the text. The entire section was removed within only minutes from the submission, completely, without specific requests, and without discussion. Not having seen any interest and transparency, all desire to invest time into the improvement of articles vanished. E-gabrielyan (talk) 06:52, 4 July 2022 (UTC)
replies: text: See my comment on your talk page. Xxanthippe (talk) 08:06, 4 July 2022 (UTC)
thread_title: The chemical potential of Van der Waals gases

message: Hi Xxanthippe, the punctuations are not part of the equation and I think the formulas look much cleaner without such punctuation or at least not in the same font style as the equation. Without punctuation is how textbooks normally show these too. What do you think? I was looking for MOS on this, but tried visual first.  Ramos1990 (talk) 00:55, 5 February 2024 (UTC)
thread_title:  Equations