Talk:Equilibrium constant

Untitled
Kc and Kp are also dimensionless, as they are defined properly using activities of the reactants and products which are dimensionless too.

For simple calculations for Kp, dividing by the standard pressure of 1 bar for each component in the ratio brought to any power will always yield a dimensionless result.

Daniel0ng 13:43, 21 April 2007 (UTC) Daniel.

Isn't it K=[(C^n)(D^p)]/[(A^k)(B^m)] ?

I do not know who wrote this but I agree about that. I'm going to correct. Ange Blanc

units
see section on "Needs significant revision" below — Preceding unsigned comment added by 128.175.195.228 (talk) 16:11, 6 July 2011 (UTC)

can any one write something about the units of the reaction constant and how they are generated?

If you learned anything about equilibrium, you should know that equilibrium constants don't have units. No offense meant, but thats the one thing my teacher seemed to think was important about equilibrium, so I guess I have it deeply ingrained. Kr5t 02:41, 29 March 2006 (UTC)


 * I've been taught otherwise. Equilibrium constants can have units; in fact, they only don't if the equilibrium reaction in question involves the same number of moles on both sides (e.g. A+B->C+D has a Kc with no units, but A+B->4C involves a Kc with units). The units of Kc can be worked out simply by the relevant equation: for instance, in the reaction expressed as A+B->4C, Kc = [C]^4 / [A][B], and therefore its units are mol^2•dm^-6. - (Anonymous), 17 May 2006

Im sorry but anonymous above is actually incorrect. The equilibrium constant is always dimensionless because you devide each term by the standard state, effectively "cancelling the unit." I would refer you to "Atkin's Physical Chemistry", by Peter Atkins (Professor of Physical Chemistry at the University of Oxford) which i believe is the standard text for 1st year chemistry undergradutes. - (Markus), 28 July 2006

I agree with Anonymous, it is exactly what I was taught too. To get the units correctly you must write the units as if writing the normal reduced-over-oxidized equation... If none are squared (or cubed, whatever) then K is dimensionless. If one of the reduced is squared, the overall unit is mol/L3. If one of the oxidised is squared, the unit is (mol/L3)-1. —Preceding unsigned comment added by 195.158.102.80 (talk) 16:32, 26 April 2008 (UTC)


 * An equilibrium constant can be expressed as being dimensionless (Ko, or simply K): however, it is more usually referred to in terms of Kc or Kp, both of which can have dimensions . This approach avoids having to use activity coefficients or fugacities, which are essential for the dimensionless approach (read Atkins more carefully!) Physchim62 (talk) 13:40, 28 July 2006 (UTC)

-- I agree. Each concentration should be divided by standard concentration, in the same units as the concentration. if the concentrations are in mols/liter (say), and the standard conc is 1 mol/liter, then the division has no numerical consequences, but it DOES get rid of the units. However,if the concentrations happen to be in molecules per cubic Angstrom, if you're a molecular simulation person :), then the standard concentration of 1 mol/liter needs to be included explicitly and its numerical value is something like 1 molecule/1660 cubic angstroms. So this WILL change the numerical value of K (compared to omitting it), and it will, again, get rid of the units.   I think this issue is worth getting right in so widely used a widely-used reference site as Wikipedia! (Unsigned)

Let's be absolutely clear about this. The expression
 * $$\ \Delta G^{std} = -RT \ln K $$

requires that K be a (dimensionless) number because only numbers have logarithms. K can be written as the product of a concentration quotient and an activity coefficient quotient. The two quotients have reciprocal dimensions. If the latter quotient is assumed to have a value of unity the numerical value of the concentration quotient is the same as the equilibrium constant. The device of dividing each concentration by a unit concentration works because the corresponding activity coefficient can be multiplied by the same unit concentration, leaving the activity coefficient quotient with a value of one and a K value which is is unchanged.Petergans 22:24, 24 April 2007 (UTC)
 * This is, of course, completely true: however, don't forget that the numerical value of K (and of &Delta;G°) depends on the form in which you write the reaction equation. Physchim62 (talk) 16:41, 26 April 2008 (UTC)


 * Perhaps it should be added that in biochemistry it is not unknown for a "binding constant" to be written as though it had units. For example, the binding constant for a host-guest complex, HG, can be written as $$K=\frac{[HG]}{[H][G]}$$ so that apparently K has the dimension M-1 when concentrations are molar. Perhaps this is done to indicate the scale of measurements. Is this the source of the confusion above? Petergans (talk) 20:27, 26 April 2008 (UTC)


 * Two important points. First, all concentrations are expressed as Ci/Ci0, where Ci0 = 1 mole (not simply Ci). Therefore, K is a dimensionless quantity. (see Alberty, R.A. 1983. Physical chemistry, 6th ed. Wiley, New York, or Gilson, M.K., Given, J.A., Bush, B.L., and McCammon, J.A. 1997. The statistical-thermodynamic basis for computation of binding affinities: A critical review. Biophys. J. 72: 1047-1069). Second, all concentrations are molar concentrations, not mole fractions or anything else (see Holtzer, A. 1995. The cratic correction and related fallacies. Biopolymers 35: 595-602, for example.Biophys (talk) 03:01, 22 July 2009 (UTC)
 * This is mental gymnastics. The real issue is that a thermodynamic equilibrium constant is a quotient of activities, which are dimensionless, so K is also dimensionless. Therefore the the standard state is defined such that the activity quotient can be taken as having a value of unity. This consideration applies whatever concentration scale is used.Petergans (talk) 07:38, 22 July 2009 (UTC)

Merge with Chemical equilibrium
This really oughtta merge with Chemical equilibrium, and with solubility equilibrium, and with an added section about solubility product constant, one of t he more special equilibrium constants since it doesn't involve the reactants. —The preceding unsigned comment was added by Daniel0ng (talk • contribs).


 * Let's discuss about a merge over at Talk:Chemical equilibrium. --HappyCamper 16:46, 24 April 2007 (UTC)

Graph
The graph in this article is useful however it is slightly misleading. As a student we mostly study Gibb's free energy (and its relation to the Equilibrium constant) with spontaneous reactions of which this graph represents none. It would be nice to show the lower side of this curve too in order to allow for a better perception of the concept.

Poor applications section
A perfectly sensible tidy up of this section I made was reverted. I've re-inserted the cleaned up wording of this section but left the dubious examples:

For example, in the Haber process for the formation of ammonia, the value of K is around 30 at pressures and temperatures standard for the process. In an equilibrium between two conformers with energy difference 0, the equilibrium constant is 1 and both conformers are present in a 1:1 ratio. When the energy difference increases to 1 kcal/mol, the equilibrium constant at 25 °C becomes around 5 and the concentration of the more stable conformer gets 85%.

Not only is this poorly worded but they are random examples which add nothing i.e. detract from article. Left for discussion.

Similarly the Derivation section is muddled and: When the equilibrium constant is close to unity and the reaction rates very fast for instance in conformational analysis of molecules, other methods are required for the determination of rate constants for instance by complete lineshape analysis in NMR spectroscopy. is just bizarre.

What was the scientific reason for reverting this deletion?

84.92.241.186 18:10, 30 April 2007 (UTC)


 * Please consider getting a user account. You have bluntly deleted two sections from this article and I did not have any seconds thoughts reverting your edits as a whole. It is considered vandalism. Also get some manners: my edits in general are not considered dubious, muddled or bizarre (you must be English). I am always prepared to discuss controversial sections. Simple add a Fact tag and its up to me to provide an explanation and a reference.  The first statement that you find dubious is from March or from Vogel so no problem there. The second statement simply explains that the equilibrium can establish itself slow or fast and that special techniques are required when they are fast. V8rik 19:53, 30 April 2007 (UTC)


 * I'm trying not (but failing?) to get sucked into the potentially bottomless pit that is Wikipedia - hence the lack of account. But I take the point that a drive-by edit by an anon user will arouse suspicions (despite WP:AGF).  I'm happy to discuss my take on things off-site (nospamATphodgkin.plus.com) but in short: there's nothing wrong with the 1st statement but it is equivalent to "the Haber process is run under conditions that make the Haber process favourable" (gosh!).  As for the 2nd statement, I'm afraid the explanation leaves me even more confused and I teach all this stuff!  Any way, I've found that the parallel Chemical equilibrium article is more to my tastes, so I'm a bit calmer about things (although still not convinced that Wikipedia will work for this stuff). 84.92.241.186 21:27, 30 April 2007 (UTC) (Random chemistry professor)


 * Thanks for your reply. The image giving free energy vs equilibrium constant is my adaptation of a table in carey/Sundberg Advanced Organic Chemistry Part A Sec. Ed. p 144. The first statement gives an idea how to interpret the image. I have thus far neglected to include the ref but I will solve that. I like the Carey / Sundberg table because it tries to relate different quantities. Also Wiki chemistry should not be about explaining chemistry to chemists but to the general public and these sort of details will specifically help these readers. I understand a brand new chemical equilibrium article is about to float so much is happening but also notice the merge discussion on its talk page. Yes I do too believe Wiki will eventually fail but for other reasons V8rik 20:56, 1 May 2007 (UTC)

Effect of temperature
This addition is unsatisfactory for various reasons.

1. To quote from chemical equilibrium

"The effect of changing temperature on an equilibrium constant is given by the van’t Hoff equation
 * $$\frac {d\ln K} {dT} = \frac{{\Delta H_m}^{\Theta}} {RT^2}$$

Thus, for exothermic reactions, (ΔH is negative) K decreases with temperature, but for endothermic reactions (ΔH is positive) K increases with temperature. An alternative formulation is
 * $$\frac {d\ln K} {d(1/T)} = -\frac{{\Delta H_m}^{\Theta}} {R}$$"

This is much clearer and more informative. A corollary is that K for an athermic reaction (ΔHo=0, ΔSo positive) is independent of temperature. In this context it should also be stated that ΔHo is itself a function of T (depends on heat capacity), so the the second equation gives an only approximately linear relationsip of log K with 1/T.

2. " The related Nernst equation in electrochemistry gives the difference in electrode potential as a function of redox concentrations.

When molecules on each side of the equilibrium are able to further react in secondary reactions the final product ratio is determined according to the Curtin-Hammett principle."

These statements are irrelvant to temperature change and should be removed.

3. The graph is all wrong as it puports to show free energy as a function of K, but it should be K as a function of T as that's what this section is about. Also the axis labelling is faulty and the caption "More stable isomer" is incomprehensible without the original context. A better graph would be of log K as a function of 1/T (straight line) for various values of ΔHo, such as -20, -10, 0, 10, 20 kJ mol-1 for example.

Petergans 09:04, 15 June 2007 (UTC)

Hi Petergans, I just reintroduced the whole section because like I stated before, I was opposed to its deletion. The title is new and as it appears now creates more confusion. I think that both the Nernst equation and the Curtin-Hammett principle are integral part of equilibrium and should be incorporated either in chemical equilibrium or equilibrium constant. Suggestions please where exactly it should go. The plot is there simply to give an idea what sort of energies are involved in equililibria between two isomers. I will redo the plot and I am open to suggestions (reversing the axes is okay with me.) I disagree with the faulty axis labeling, exactly what is wrong? V8rik 20:17, 15 June 2007 (UTC)


 * 1) I agree with the idea that there should be a section on the effect of temperature changes, but the current content is vague and lacking basic material.
 * 2) The Nernst equation is not currently included in chemical equilibrium but is referenced in the See also list. I suggest you put a question on that discussion page to the effect : should there be a section on redox equilibria? My own view is that it's rather complicated, particularly in relation to redox electrodes, and best left as a reference. It certainly does not belong where it is at present.
 * 3) The Curtin-Hammett principle is about kinetics and as such has no place in a discussion about equilibria. The first sentence in that article is wrong in this sense: the equilibrium product ratio does not depend on transition state energies, but on the free energy difference between the two products.
 * 4) When there are two independent variables on an axis it is customary to show them on opposite sides of the plot, like top and bottom for the x-axis. Labelling on the y-axis is confusing as it seems like one quantity is subtracted from another. In any case kJ mol-1 would be sufficient on its own. Note that the notation kJ/mol is deprecated by IUPAC since the plot is of numbers, that is, of ΔG/kJ mol-1 vs K; number=quantity/unit.

Petergans 08:31, 16 June 2007 (UTC)


 * The reference to Nernst equation should never have been deleted in the first place. A reference is sufficient, no need to duplicate information
 * Your Chinese wall between kinetics and thermodynamics is artificial and without merit. Check out Free-energy relationships to see how interrelated they are.
 * I am not convinced about you criticism regarding the plot. V8rik 20:50, 16 June 2007 (UTC)

You are mistaken. It is not a Chinese wall. Let me put it this way: does the activation energy for a reaction have any bearing on equilibria? Of course it does not. It follows from this that kinetics has no bearing on the composition of a mixture at equilibrium. Petergans 09:58, 17 June 2007 (UTC)


 * Free-energy relationships are empirical and often inadequate. Actually, kinetics is a deeper level of looking at things than equilibrium thermodynamics. The latter is much more easier and used more often, but it can be derived if there is a complete knowledge of the former, in the same way that thermodynamics can be derived from Statistical mechanics. The chemical potentials of all equilibrium (and non-equilibrium) species can be calculated from a complete knowledge of the potential energy surfaces, so it is not entirely correct to say activation energy does not have any bearing on equilibrium composition (the very concept of activation energy is itself dubious, as it ignores entropy considerations which can often dominate reactions, particularly biochemical ones). The inter-relation between kinetics (or in a broader sense non-equilibrium thermodynamics) and equilibrium thermodynamics is quite complex, and the differences are great enough to require emphasis. I agree that purely kinetic phenomena should be kept out of this article. However it is often superficial to strictly avoid all references to kinetics or mechanisms when discussing equilibrium. Loom91 08:36, 18 June 2007 (UTC)


 * It is important to emphasize that no kinetics are introduced in this article, kinetics are used where needed. I also want to point out that it is important to first explain things in a simple way with focus on educational value and then discuss the finer points. You cannot outright dismiss Free-energy relationships (please point me to literature). This whole discussion reminds me of an earlier discussion about where a bunch of chemical engineers where about to scrap the entire Rate equation article with the argument that systems in real life are not closed. That really does not help wikipedia V8rik 19:40, 18 June 2007 (UTC)

I think this argument can be very easily resolved. Chemical equilibrium has a lot of stuff about Gibbs energy, so Free-energy relationships can be referenced in the See also section of that article. That is where the reference belongs, not in the body of the article, as they are somewhat peripheral and add nothing of substance to the topic. Petergans 08:05, 19 June 2007 (UTC)


 * I am not going to settle with the see also section. I am against it for the reason that a lot of links are presented without any context at all to the article. I will not insist in having Free-energy relationships included at all and I think that with both oscillating reactions and Curtin-Hammett statement in just two lines in a section of chemical equilibrium already overwhelmed with links, their presence is very modest. V8rik 19:18, 19 June 2007 (UTC)


 * I support including oscillating reactions, but Curtin-Hammett principle has little relation to equilibrium. I think it's way off the topic. Loom91 20:58, 19 June 2007 (UTC)

Nomenclature
Please follow standard nomenclature. See e.g.. —DIV (128.250.80.15 (talk) 08:54, 16 March 2008 (UTC))

Dependencies
The introduction of this article says, that "All equilibrium constants depend on temperature and pressure (or volume)." This is not correct since all equilibrium constants are only dependent on temperature, which follows directly from the definition of the standard Gibbs energy. Though the equilibrium composition of the mixture may vary with pressure, the constant does not, because standard Gibbs energies are defined for one single pressure. -- 92.193.57.25 (talk) 21:13, 31 July 2009 (UTC)
 * This is clearly wrong. The pressure dependence is illustrated in the section equilibrium constant. Petergans (talk) 10:15, 1 August 2009 (UTC)
 * I modified the link indicated by user Petergans in order to reach the section.--85.121.32.27 (talk) 12:11, 15 January 2018 (UTC)

Time dependence
This section does not belong here. Equilibrium constants by definition do not have any time dependence.

A case can be made for mentioning the relationship between equilibrium constants and rate constants, but this is not the way to do it. The relationship is simple only for elementary reactions. In general the relationship is very complex and can only be derived by splitting every reaction into elementary components. This is neither practicable nor informative.

A clear distinction needs to be made between equilibrium and kinetics. Chemical equilibrium results from the free energy being at its minimum value. The kinetics regarding the equilibrium state must always allow this state to exist, regardless of what reactions might be taking place. In other words, the forward and backward reaction rates must be equal as a result of equilibrium, not a factor that determines it.Petergans (talk) 13:27, 28 March 2010 (UTC)


 * in your incorrect scheme equililibria establish themselves at infinite speed. You are blocking any effort to present a balanced article and to that problem there is unfortunately no solution, a basic Wikipedia weakness V8rik (talk) 22:28, 4 April 2010 (UTC)


 * I'm sorry that you feel like this. I, too, would prefer to reach a rational resolution to the issue. The point that I am making is that the speed at which equilibrium is reached starting from an arbitrary composition has no bearing on the equilibrium composition. To illustrate this, consider the reaction of dissolved carbon dioxide with water.
 * CO2(aq) + H2O HCO3- + H+
 * the composition at equilibrium is the same whether the reaction occurs naturally, which is a slow reaction, or is catalyzed by carbonic anhydrase, which is a fast reaction. The mechanisms of the two processes are different and forward and backward reaction rates are different in the two cases, but the end result is the same.


 * Everyone accepts that the equilibrium state is a dynamic state. However, since the kinetics of chemical equilibrium is mechanism-specific, kinetics cannot be used in a general exposition. Thermodynamics, on the other hand, is not mechanism-specific and can be used in a general exposition. I deplore the fact that the lead-in to chemical equilibrium no longer contains any mention of thermodynamics, but I am not going to touch that article again.


 * May I suggest that you look at the new article equilibrium chemistry which I have written. There you will see a much broader picture. Of course kinetics play a part in all the processes discussed. For example, in column chromatography the elution rate should be slow enough to allow equilibria to be reached, otherwise resolution is degraded. Kinetics also come into phase equilibria. I had prepared an article containing both phase and chemical equilibria. The draft is in my sandbox. At this time I don't propose to publish the part on phase equilibria.


 * There is a simple relation between equilibrium and rate constants in a few cases, one being ester hydrolysis, but in general the relation is not simple. I'm no expert on kinetics. Can a general expression for a rate constant in terms of the rate constants for contributing elementary reactions be derived? If so, perhaps the place for a general exposition of the role of kinetics is in dynamic equilibrium? Petergans (talk) 08:00, 5 April 2010 (UTC)
 * dynamic equilibrium has now been revised in this sense. Petergans (talk) 12:32, 13 April 2010 (UTC)
 * issue resolved V8rik (talk) 21:33, 13 April 2010 (UTC)

Laymen's terms
The article really needs a definition of the term in simpler layman's terms. Please. BriEnBest (talk) 03:03, 5 October 2010 (UTC)
 * I agree. Nicolas Perrault (what did I screw up again?) 21:26, 9 January 2014 (UTC)
 * I agree also, so I have added a short opening paragraph before the defining equation, and related the equilibrium constant K to the reaction quotient Q. Dirac66 (talk) 23:17, 18 January 2014 (UTC)

Needs significant revision
There is much confusion throughout the discussion of this topic (i.e., see units). Ultimately, the article is misleading in the definition of the equilibrium constant (I could change this, but I do not know how to use the wiki math syntax). It rightfully defines the equilibrium constant as the activity product (where each activity is raised to the power of the stoichiometric coefficient), but is incorrect in defining it as the concentration quotient. While this is often how general chemistry is taught, it is inaccurate when the total stoichiometric coefficient in is not zero.

With regard to some of the discussions on units. Yes, you do divide by the standard state (i.e., fugacity standard state), but there seems to be confusion of how equilibrium is 'practically' calculated in the gas versus the liquid phase (a very important distinction).

The activity is the fugacity in the mixture divided by the fugacity of the pure component at the temperature of the system at 1 bar (standard state). This definition is not that useful, so we make approximations...

Gas phase:

Fugacity of the standard state is the same as the ideal gas pressure.

If the pressures are sufficiently low (or high temp) the mixture is treated as an ideal gas and thus you get that K is simply (P/P0)ν times the product of the mole fractions raised to each component's stoichiometric coefficient(Π xiνi).

Liquid phase:

Assuming an ideal solution (such that activity coefficient is 1), then K is simply the product of the mole fractions raised to each component's stoichiometric coefficient (Π xiνi). NOTE: Not concentration!!! Thus K is unitless. — Preceding unsigned comment added by 128.175.195.228 (talk) 16:09, 6 July 2011 (UTC)


 * The last comment is without foundation. A thermodynamic equilibrium constant is a quotient of activitities, which are dimensionless quantities. Since activity=concentration*activity coefficient, the dimension of the activity coefficient is inverse concentration, a specific dimension for each concentration scale. Thermodynamic equilibrium constants must be dimensionless because of the logarithmic relation with the standard free energy change. They have different numerical values according to the concentration scale chosen. In practice, where activity coefficients are generally not known, the quotient of activity coefficients may be assumed to be equal to one; under this assumption an equilibrium constant is a quotient of concentrations. Petergans (talk) 10:11, 8 July 2011 (UTC)


 * Agreed. As said directly in the comment, activities are dimensionless. You can use virtually any unit of concentration (eg. mole fraction, molarity, etc) to determine the activity because you must always divide by the standard state. Thus, if your standard state is unit mole fraction, then you divide by 1. If your standard state is molarity, than you divide by 1 M. As it turns out, virtually every chemist utilizes a standard state of 1 molar. It is perfectly reasonable to use the concentration quotient to APPROXIMATE the equilibrium constant for ideal solutions. (Typically the idea of ideality is ignored when teaching general chemistry.) Sirsparksalot (talk) 13:50, 26 April 2012 (UTC)

Ionic Strength Comment
I want to see what people think about the comment-

"It is common practice to determine equilibrium constants in a medium of high ionic strength. In those circumstances the quotient of activity coefficients is effectively constant and the equilibrium constant is taken to be a concentration quotient."

Am I confusing myself or is this statement incorrect? When ionic strength is high, solutions deviate substantially from the ideal, which means that the activity coefficient is far from unity and, consequently, quite important to include. Only when solutions are ideal (typically dilute, with low ionic strength) can we assume an activity coefficient of unity, which allows us to use the concentration quotient.

I would like to remove this statement. Any thoughts? Sirsparksalot (talk) 13:38, 26 April 2012 (UTC)
 * This statement surprises me also, but it seems to be supported by discussion at ionic strength and especially Determination of equilibrium constants. Apparently if the activity coefficients are constant they can be corrected for somehow. So rather than removing the statement, I think it needs clarification and a brief explanation of the correction.
 * Also I searched the revision history and this statement was inserted by Petergans on 16 May 2007, so I will leave a note on his talk page asking for further explanation. Dirac66 (talk) 17:43, 26 April 2012 (UTC)

The answer to this apparent paradox lies in the relative concentrations of the "medium" and the "analyte". A typical medium is 0.1M NaNO3, whereas the analyte concentration is of the order of 0.005M or less. The quantities at issue are the activity coefficients of the ions derived from the analyte; those of the medium ions (e.g. Na+ and NO3-) are irrelevant. Take the analyte to be a simple acid, of formula HA. The activity coefficients of H+ and A- depend on the total ionic strength which remains nearly constant at 0.1 M through the titration of the acid with base. The "thermodynamic" equilibrium constant defined as
 * $$K^0=\frac{ \{HA\} } { \{H^+\} \{A^-\} } = \frac{[HA]}{[H^+][A^-]} \frac{\gamma_{HA}}{\gamma_{H^+}\gamma_{A^-}}$$

where {} signifies activity, $$\gamma$$ is an activity coefficient and [] signifies concentration. As the activity coefficients of all species involved in the equilibrium can be assumed to be effectively constant, the quotient of activity coefficients can also be assumed to be constant. It follows that the equilibrium constant, K, calculated as a concentration quotient in a particular medium is related to the "thermodynamic" constant by
 * $$K^0=K\frac{\gamma_{HA}}{\gamma_{H^+}\gamma_{A^-}}$$

The value of the quotient of activity constants is a function of ionic strength. The thermodynamic constant may be obtained by measuring K at different ionic strengths and extrapolating to zero ionic strength. See, for example, Acid dissociation constant

None of this is controversial. The method has been in use since at least the 1950s. Petergans (talk) 19:34, 26 April 2012 (UTC)
 * OK, the above explanation is pretty clear (except that your "activity constants" should be "activity coefficients"). So the statement in question should be retained, but could perhaps be improved. I will think about wording which is clearer than what we have now but briefer than what is in Acid dissociation constant, with a link to that article for more detail. And we can quote the book by Rossotti and Rossotti as a source here also. Dirac66 (talk) 02:24, 27 April 2012 (UTC)
 * Rossotti and Rossotti (I have a personal copy!), chapter 2 "Activity and concentration quotients". Section 2-1 "Control of activity coefficients", 2-1-A ", "Composition of the ionic medium", 2-1-B "Limitations of the constant ionic-medium method" I've tweaked the text aabove a little. Please note that the treatment above, and in the rest of this article, relates to association constants, the linked article refers to dissociation constants. Petergans (talk) 09:18, 27 April 2012 (UTC)
 * OK thanks. I have added a few lines to the text which are intended as a summary of your comment above. I didn't distinguish association and dissociation constants though, as I think the intro to this article applies to equilibrium constants in general, and the paragraph we are discussing applies to any ionic reaction at least.
 * Also perhaps since you have a copy of Rossotti and Rossotti, you could add the page for the general definition of K which someone has requested at the beginning of the article. Dirac66 (talk) 22:52, 28 April 2012 (UTC)
 * Excellent summary! I have added the page number. BTW I am currently working on a computer program to determine thermodynamic constants directly from a set of titrations at various ionic strengths by assuming log βc is a polynomial function of ionic strength. This is an adaptation of the program BSTAC which has been already published. I feel that this is too technical to go in this article. Petergans (talk) 08:05, 29 April 2012 (UTC)
 * Perhaps this last topic would be better suited to Determination of equilibrium constants which is more technical. Dirac66 (talk) 12:15, 29 April 2012 (UTC)

Microconstants
Should one not rather move the paragraph on microconstants to the article on Acid dissociation constant? Microconstants of acid-base reactions are quite an issue, but hardly in other contexts, just eventually with oxygen binding with hemoglobin. Or should one even make a separate article on microconstants? — Preceding unsigned comment added by Bubblerock2 (talk • contribs) 15:49, 27 May 2012 (UTC)

Equilibrium constant and dimensions
In the table on page 58 of the 2nd printing of the 3rd edition of the IUPAC Green Book there is one nice, pretty dimensionless equilibrium constant that theoreticians, physicists, and statistical mechanics folks like and then there are these three naughty, mean, and nasty equilibrium constants with SI units that those uncouth applied scientists actually use in the real world. But who cares about how equilibrium constants are used in the real world? All that really matters is that the vast majority of science-types on Wikipedia are happy, and those science-types are theoreticians because applied science folks are too busy doing useful things to make major contributions here. Shame on those IUPAC writers! Why don't they pay attention to Wikipedia consensus like they should? Obviously they are missing something very important, huh? Flying Jazz (talk) 01:49, 16 August 2012 (UTC)


 * Great tirade! Now, perhaps you real-worlder can explain to this "theoretician" how to take the logarithm of an equilibrium constant with a value of K = 100 litres per mole, a typical real-world stability constant for the formation of an adduct of formula AB . Is it possible to take the logarithm of a quantity? Of course it is not possible to do so, but we happily write log K = 2. How come? There are two separate issues here, the scale of measurement and the thermodynamic definition. Numerical values depend the scale of measurement, such as moles per litre or partial pressure. The thermodynamic definition, in terms of activities, always gives a dimensionless quantity. So, the key to understanding the paradox is the relationship between, say, concentration and activity. In the real world this relationship is given in the small print, but it can have a significant impact on equilibrium constant values. Petergans (talk) 19:19, 17 August 2012 (UTC)


 * Thanks! I don't consider myself to be strictly a real-worlder. I'd prefer to think of myself as helping to develop an encyclopedia for everyone. Six years ago Physchim wrote on this talk page that an equilibrium constant can be expressed as being dimensionless (Ko or K) or it can be referred to in terms of Kc or Kp which can have dimensions. I agree with him. There is only one issue here: a general purpose encyclopedia should reflect the complex reality of how scientific concepts are actually used in the real world. To address your questions, no person should ever use units with an equilibrium constant in thermodynamics where the log will be taken. That does not change the fact that in the real world, many people do use units with equilibrium constants in non-thermodynamic situations, and it seems like IUPAC says at the moment that this is an OK thing to do. It's also certainly true that many people in the real world never use units with equilibrium constants in any situation, even when they're expressed as Kc or Kp. That's what I was taught about equilibrium constants, that they never have dimensions, and I learned about why. Other people really can be taught something different without being wrong. Some people are taught different things at different times during their chemical education. Even your usage of the phrase "thermodynamic definition" indicates that you seem to be conceding the fact that there is an alternate non-thermodynamic definition that you don't think should be mentioned in the article. Why not? If there is some "small print" in the IUPAC green book that I've missed then please point it out. It's easy to find multiple conflicting recommendations on-line and in textbooks. Different and conflicting opinions about usage don't indicate a paradox, and a good encyclopedia article would reflect this reality. Flying Jazz (talk) 12:05, 18 August 2012 (UTC)

The idea of two definitions is unacceptable. So why does one see things like "K = 100 litres per mole" in the literature, particularly in biochemistry, where it appears to be the norm? I think that this has to do with the scale of measurement. A biochemical constant may be written as "x litres per millimole". In biochemistry this makes sense because millimolar is a more useful concentration scale than molar. It means that the dimension tag is not the dimension of the equilibrium constant but an indication of the concentration scale used in deriving the equilibrium constant value. It is needed because values on the molar and millimolar scales differ by a numerical factor (1000 for simple adduct formation). Stating the concentration scale is an indirect way of establishing the nature of the thermodynamic standard state on which the equilibrium constant value depends. Petergans (talk) 10:53, 21 August 2012 (UTC)


 * I would probably enjoy engaging you in a conversation about the usage of K in biochemistry and in other contexts over a cold beverage. We could also discuss the differences in strictness between the concepts of "usage" and "definition" at that time. Or we could have that chat on my usertalk page or yours. On this talk page, I'd prefer your opinion about page 58 of the IUPAC Green Book. Do you find what's written on that page to be unacceptable? Do you believe it will be altered in a subsequent printing or edition of the Green Book? Why do you think it's there in the current edition? Can an established and recognized convention be unacceptable? Can it be wrong? Would you prefer that a general purpose encyclopedia ignore an IUPAC statement clearly saying, "These quantities are generally not dimensionless" when referring to equilibrium constants? Why do you have this preference against an acceptable IUPAC convention? I'm hoping for answers that involve the sociology of science and of how it's taught and used because those seem to be the relevant issues for this discussion. Flying Jazz (talk) 11:21, 1 September 2012 (UTC)

Green book, p58, note (18) "This quantity [ thermodynamic equilibrium constant ] is equal to Q in equilibrium, when the affinity is zero. It is dimensionless and its value depends on the choice of standard state, which must be specified..." This is exactly equivalent to what I have been saying. Lower down there is
 * "Concentration basis ... Kc ...$$(mol m^{-3})^{\Sigma \nu_B}$$"

Moles per cubic metre?? Nobody uses those units. This does not give me confidence in this section of the Green book. What is "concentration basis" supposed to mean? My interpretation is that the thermodynamic equilibrium constant is dimensionless, but a quotient of concentrations will have dimensions. When I see dimensions after a symbol K, I assume this refers to the "concentration basis" on which the quotient of equilibrium concentrations was calculated. Petergans (talk) 18:53, 1 September 2012 (UTC)


 * Unfortunately, you were unable or unwilling to answer my questions, but I am beginning to understand more about what does and does not give you confidence. I'd like to encourage you to not lose confidence in an organization like IUPAC when it uses terms or units that may confuse you. If you broaden your scope of thought or read more attentively then common sense explanations may begin to appear. For example, in my 1984 copy of Perry's Chemical Engineering Handbook, moles per cubic meter are given as the SI-derived unit of molar concentration. In the Wikipedia entry on Molar concentration, the SI unit is given as moles per cubic meter. And in the IUPAC table we've been discussing, moles per cubic meter is involved in an entry under a column titled "SI unit." A common sense explanation would be that you did not see the "SI unit" heading on that column or that you may not fully understand SI base units or that you are choosing to ignore the existence of that column heading and pretending instead, for some reason, that the column heading says "commonly used units". Of course, with Perry's Chemical Engineering handbook, another Wikipedia article, the IUPAC Green Book, and my own knowledge all telling me the same thing about SI units, I hope you forgive me when I write that your unwarranted lack of confidence decreases the confidence that I have in your interpretations and judgements. As for the remainder of your post, if you don't answer my questions, why should I answer yours? Please have another go at it. Wikipedia Projects have many editors on them who will pay attention to an IUPAC statement like "These quantities are generally not dimensionless" regardless of whether or not you chose to ignore it. Flying Jazz (talk) 03:32, 3 September 2012 (UTC)
 * This is another case of a clash between real world and ideal world. It is true that I know nothing about the practises in chemical engineering. All I can say is that in chemistry no-one uses the "SI unit" mol m-3. Is not mol dm-3, the commonly used unit for concentration, also an SI unit? I don't want to continue this discussion. We seem to be at cross-purposes as I thought I had answered your questions. Petergans (talk) 08:17, 4 September 2012 (UTC)
 * Moles per cubic decimeter is based on an SI unit with a prefix. It is commonly used (although, of course, moles per liter are used most often where I live) in both chemical engineering and in chemistry. Moles per cubic meter is based on SI units without prefixes, like other entries in the IUPAC Green Book which is where I have attempted to focus this discussion. I agree that further discussion between two people about what is written on page 58 of the IUPAC Green Book is not possible when one of the people is unwilling or unable to address specific questions about what is written on that page regarding units on Equilibrium Constants. But thank you for trying. Flying Jazz (talk) 14:46, 4 September 2012 (UTC)

A third opinion based on history
The above discussion has become rather heated. In my opinion, each of you is partly right, and the relation between the two points of view is an important point which should be clarified for Wikipedia readers. I think the two ways of representing equilibrium constants (with and without units) goes back to the double origin of the concept in the 19th century. First there was the Law of mass action of Guldberg and Waage, in which equilibrium constants were derived from the equality of forward and backward rates which were the products of concentrations (in solution) which have units. In this (historically first) kinetic-based theory there was no ln K so the presence of units caused no problem. The only problem of course is that the argument of Guldberg and Waage is invalid because their assumed rate laws are very often false.

Gibbs then developed a correct theory of chemical equilibrium from thermodynamics for ideal systems, and Lewis generalized it to nonideal systems. But the thermodynamic method is based on ΔG° = -RT ln K, and ln K is only defined for a K without units. So K was redefined to eliminate the units, by dividing each c by a standard-state value c° = 1 mol/L, and each p by a standard-state value p° = 1 atm. This is equivalent to defining K as a ratio of thermodynamic activities, or their approximate values for ideal systems.

So yes, I believe there really are different definitions of K which should be indicated by different symbols. The IUPAC Green Book presents a notation which is fairly common: K or K° for the dimensionless thermodynamic constant, and Kp, Kc or Km for the practical constants with units. The advantage of the practical constants is that they force the user to use the right units; the thermodynamic constant implicitly requires the user to choose the correct standard state.

So what should the Wikipedia article say? Since both methods (with and without units) are still used in many books and papers today, I think WP:NPOV requires that we mention both. And since many readers may also wonder which way is "correct", I think we should explain the relationship between the two with an example in which the number of moles on each side is different. Dirac66 (talk) 23:59, 4 September 2012 (UTC)
 * This is a fair summary of the historical position. I have no problem with Kc having units. The problem is that the symbol K is in general use where Kc would be more correct. I propose is to add a new section to this article, based on the first two paragraphs above. It's partly historical and partly about units, so what would you suggest for the section title? We have also to deal with the fact that most published data, including the NIST database, give values for log Kc. This is justifiable in terms of a medium of high ionic strength being part of the definition of the standard state, but it's a pretty technical argument Petergans (talk) 09:39, 5 September 2012 (UTC)
 * The historical part is already included at Chemical equilibrium (where I have just added the word Historical to the section title), so in this article I would focus on the units. I suggest the title Definitions and Units, with Definitions plural. We can mention that Kc is from the ideas of Guldberg and Waage and K from thermodynamics, but refer to the Chemical equilibrium article for more details on the history.
 * As for the varying symbols in the literature, we can just say that IUPAC recommends that K refer to the thermodynamic constant and that Kc or Kp be used for the others which have units, but that many authors do use K for constants without units. Wikipedia cannot impose the IUPAC convention on the world; Wikipedia can only report the true situation.
 * Finally I think the ionic strength argument is only one of several reasons why people use K for Kc. The most common reason is probably simplicity - if you are writing a paper and all your equilibrium constants are Kc and you are ignoring non-ideality, it is simpler just to call them all K and assume your readers will understand. Dirac66 (talk) 13:57, 5 September 2012 (UTC)
 * The technical argument is given at Acid dissociation constant. This is not a case of ignoring non-ideality, but of defining conditions in which the quotient of activity coefficients, Γ, can be assumed to be constant. In practice this means that all individual activity coefficients are constant, so the system is "ideal". For me the key point of all this as that log K can only refer to a dimensionless K value. So, log Kc is only possible when it is divided by Γ which has a unit which is the reciprocal of the the unit for Kc. In effect taking the logarithm of Kc implies Γ=1. This is not just an academic point. There are areas of interest in the real world where activity is important, such marine chemistry and pharmaceutical chemistry.
 * There is another quibble concerning the qualifier "thermodynamic" for an equilibrium constant. Some people use it to refer to the (extrapolated) zero ionic strength value, others, including the green book, use it for a value based on activities. Petergans (talk) 10:22, 6 September 2012 (UTC)
 * Yes, these points are important but only for ionic reactions (and to some extent for reactions of polar molecules in solution). So I think it would be pedagogically better to divide the discussion of Definitions and units in two. First a section of points which are true for all reactions, with a simple gas-phase example (K vs. Kp) such as N2O4 = 2 NO2 or 2 NH3 = N2 + 3 H2. Then a subsection with a title such as Ionic reactions in solution, starting with a sentence saying that in this case the effect of ionic strength should also be considered. Dirac66 (talk) 15:00, 6 September 2012 (UTC)

Draft revision and comments
I have prepared a draft at User:Petergans/sandbox. It still needs tweaking, but at this stage all comments will be welcome. Petergans (talk) 10:02, 9 September 2012 (UTC)
 * I think this is much improved over the current intro, and explains the role of both activity coefficients and units. I think though that the treatment of units can still be made clearer, in dealing with the third factor in the equation for K0 (which includes the standard concentrations), and also in comparing the two ways to deal with units in problems.
 * Since we are discussing units here, I would write "By convention the standard concentrations have a value of 1 mol/dm3 (or 1 atm)". Then we can say that the third factor has a numerical value of 1, multiplied by some combination of standard concentration (or pressure) units. And point out that Kc is properly dimensionless because it is equal to the product of the first and third factors. The draft says that the equilibrium expression is a product of two components, which is confusing since the next equation apparently has three factors.


 * Also we can add that there are two ways of dealing with this units factor.
 * For calculations of thermodynamic properties which involve ln Ko, Ko (or Kc if activity coefficients are neglected) must be unitless so that the 3rd (units) factor must be included.
 * However for calculations of equilibrium concentrations (or pressures) from their initial values and the equilibrium constant, Kc (or Kp) is often quoted with units, which is equivalent to ignoring the units factor. This procedure does not cause any error because these calculations do not involve ln K.Dirac66 (talk) 17:02, 9 September 2012 (UTC)

Good points! Have a look at the revised draft. I suggest we put it in as main section 4 of equilibrium constant, with the deivation from Gibbs energy as a second sub-section, after units. Petergans (talk) 10:58, 10 September 2012 (UTC)
 * Much better and I only have one more important correction to suggest. I disagree with calling the first factor a reaction quotient and Qc, since this phrase and the symbol Q normally refer to a value either at equilibrium or not, as in the equation ΔG = ΔG° + RT ln Q. which is not (and I think should not be) in this article. So Q doesn't really belong in this article at all; it needs to be a K with some descriptive subscript.
 * A minor point is that (1) we seem now to have mixed several concentration units = M, mol/dm3, mol/kg etc. Perhaps minimize unnecessary mixing.
 * As for the placement of this new section in the article, I have no strong opinion as interested readers can always find it from the Table of Contents. The only thing is that some of your sandbox text corresponds to the current introduction, so I presume you will eliminate the duplication.
 * After dealing with the above, I think the new section is ready to be inserted in the article. Dirac66 (talk) 21:46, 10 September 2012 (UTC)
 * I have been re-thinking the notation. Your Qc (the first factor with units, at equilibrium) is referred to as Kc in many books (e.g. Petrucci et al., General Chemistry 8th edn 2002, p.629), so I think we should conform to that usage. This means we have to rename your dimensionless Kc (= Kθ/Γ), perhaps as Kθid (= ideal value of Kθ, without the activity coefficients). Dirac66 (talk) 00:11, 11 September 2012 (UTC)

Now done. I decided to retain Q in the form QE for the reaction quotient at equilibrium - change it if you can think of something better. I've replaced the derivation section by something which I hope is clearer. You'll see other minor changes, including a simplified lead. Please check for typos which may have slid under the spell-checker. Petergans (talk) 15:32, 11 September 2012 (UTC)
 * I think that QE is acceptable since it is clear that E is for equilibrium, and also the symbol QE is not used for any other quantity in this article.
 * However I still have a problem with using the symbol Kc for the dimensionless quantity Kθ/Γ. Elsewhere in the article Kc is a ratio of concentrations with units, as in the IUPAC Green book and many chemistry texts. This ratio is in fact the special case of QE where all the generalized concentrations are in fact concentrations and not pressures or mole fractions. So the article now uses the same symbol with two meanings, which is always confusing.
 * I propose therefore to refer to the dimensionless Kθ/Γ as Kθid rather than Kc. For the Definitions section we can keep QE as more general than Kc, and point out that Kc (as used elsewhere) is a special case. Dirac66 (talk) 18:46, 15 September 2012 (UTC)

I've replaced Kc by K in the units section. This corresponds to general usage; the subscipt c rarely appears in published papers. As for text books, it will be impossible to cohere with all of them as there is no generally agreed convention. Indeed we have the ludicrous position that the Green Book appears to offer two definitions of the same thing! The general rule when quoting an equilibrium constant value in publications is to state the expression used in its derivation (D.G. Tuck, Pure and Applied Chemistry, 61 (1989) 1161 (http://dx.doi.org/10.1351/pac198961061161) Petergans (talk) 19:43, 15 September 2012 (UTC)
 * After reflection I think the notation is now ok, except that I have added a brief mention of the units problem in the intro section. This will serve to guide the reader who is confused by the apparent dimensional inconsistency between K and Kc, and point to the section which explains it. Of course other readers who understand the units (or don't care) will just skip this brief mention. Dirac66 (talk) 02:10, 23 September 2012 (UTC)

Curly brackets
Re yesterday's edit summaries by 96.29.169.125 and Petergans. I think 96.29.169.125's point was not to remove the { } from the article, but rather that the name curly brackets is slang and should be replaced by the name braces which is more formal. However the punctuation article Bracket (see section Braces or curly brackets) accepts both with a slight preference for curly brackets in contexts where confusion is possible. Dirac66 (talk) 15:26, 28 February 2013 (UTC)

Symbol not visible in Internet Explorer
The superscript in K⊖ and p⊖ does not appear with Internet Explorer (8.0) which shows it as just an empty square, at least in the text. It is all right in the Latex formulas with Explorer, as well as for both text and formulas with Mozilla Firefox. In order to have an article which is legible to everyone, could we change K⊖ and p⊖ to K0 and p0, at least in the text? Or some other symbol? Dirac66 (talk) 19:05, 1 June 2013 (UTC)
 * I'm using IE8 and the symbol is shown correctly. Where does it come from?. Is it in a font being used by WP that is not installed on your PC? I will replace it by [[File:StrikeO.png]] ( [[File:StrikeO.png]] ) which was created for use in thermodynamics, but it may also appear in other articles. Petergans (talk) 08:10, 2 June 2013 (UTC)
 * OK, all symbols are visible now, thank you. Perhaps I do need to learn how to install the font as you suggest, but presumably some other readers will have the same problem and I think it is best to use a symbol visible to all if possible. If I come across the same problem in another article I will know how to fix it next time. Dirac66 (talk) 11:15, 2 June 2013 (UTC)

This article is an embarrassment to wikipedia
Imagine if the lede of an article about chocolate-chip cookies was a list of the chemicals, and the article body was the properties of the atomic elements in those delicious cookies.

That's what this article is. I'm a relatively educated layman (okay, an extremely educated one), but other than the fact that it involves thermodynamics, I have no clue as to what the equilibrium constant is.

This is a great example of the difference between a "real" encyclopedia and this playtoy, make-believe one.
 * The nontechnical articles are poorly-written and often inaccurate.
 * Technical ones are accurate but written for other geeks who already know what the term means and only want details.
 * If expert opinion—even universal expert opinion—differs from popular opinion, the experts are harassed and deliberately chased away.
 * Any subject with even vaguely political import is grossly tilted in whatever direction the American admin clique is biased (e.g., middle east stuff).
 * If admin prejudice is split (e.g., abortion), the article content bounces around in edit wars.
 * Jimmy Wales doesn't give a damm about any of this as long as he can make 20 grand an hour for speaking to college groupies.

The only subjects that get serious, through, appropriate, stable, exhaustive entries here are ones popular with dimwits, like "Dancing With the Stars", automobile models, and Kim Kardassian.

Now fix the lede so it is intelligible to someone other than students of physical chemistry. 67.162.165.126 (talk) 03:07, 24 June 2013 (UTC)


 * Your second bullet point, technical articles "are accurate but written for other geeks who already know what the term means and only want details," is the relevant one for this article. But the situation is even worse than that. People who already know what the terms mean and want details would turn to a textbook, not a Wikipedia article. Articles like this one are a classic example of not writing for the intended audience, which in our case is the general population. This article looks like it was written to make the writers feel smart. Of course, an article like this one should begin with the concept of an equilibrium constant as a ratio of concentrations in a reaction, Kc, just as it's taught in an early high school or late middle school chemistry courses long before students have learned about thermodynamics, chemical activities, or even how to take logarithms. The general population knows what "concentrated" and "dilute" mean because we can smell, taste, and see the concept every day. Going from that sensual knowledge to a ratio of concentrations is a short jump. One or two real-world examples that are relevant to the general population could be given. The equilibrium constants for hemoglobin interacting with carbon monoxide versus oxygen come to mind as a pedagogically-useful-if-overly-simple explanation for the toxicity of carbon monoxide. Then the article would proceed to Kp (a ratio of partial pressures), just as most high school curricula worldwide proceed there. And finally, the article would clearly state that everything that had previously been written had used assumptions that are not present in the real world, and then we'd drone on with the upper-level undergraduate material about fugacities, activity coefficients, and the intimate relationship of everything to thermodynamics. A well-written article doing things this way would be a work of beauty that would last for about five days before a 20 year old engineering major or physics major would rewrite the entire first half of the article because they want to feel smart by informing the world that what they learned in high school wasn't right. Then there would be a moderate edit war in slow motion with the inevitable results that the article would go back to looking pretty much the way it does now. So why bother? Flying Jazz (talk) 06:00, 22 October 2013 (UTC)

Cumulative micro-constant equation error?
The following statements are inconsistent:
 * K1 = k11 + k12

In the same way,
 * K2 = k21 + k22

Lastly, the cumulative constant is
 * β2 = K1K2 = k11k21 = k12k22

It seems like the last = should be a +, since it's the sum over 2 pathways. I'll not 'fix' it, in case I'm wrong. 173.25.54.191 (talk) 02:37, 27 September 2013 (UTC)
 * No, it's not the sum of the two pathways. The overall constant is independent of pathway, so its value is the same for both pathways. Petergans (talk) 08:37, 27 September 2013 (UTC)

Assessment comment
Substituted at 14:34, 29 April 2016 (UTC)

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Isotope effects
The addition of this section is welcome, but I have a concern. Deuteration constants are presumably measured using D2O as solvent. Comparison of stability constant values obtained with H2O and D2O as solvents is not quite as straightforward as it might seem because the standard states of the reactants are different. To ignore the differences in standard states is to make an approximation. In general, stability constant values obtained in different solvents cannot be compared directly to each other. In this case it can be said, without approximation, that 50% dissociation of a monobasic acid occurs at pH = pK(H) in H2O solutions or at pD = pK(D) in D2O solutions. Petergans (talk) 09:20, 31 May 2017 (UTC)
 * Yes, the DA acid dissociation constants are measured in D2O, which is indicated in the chemical equation DA + D2O ⇌ ... We could explain this citing Laidler, who says that H attached to O or N exchanges rapidly with an ionizing solvent, so that if ROD (his example) were dissolved in H2O the ROD would rapidly exchange and become ROH. Meaningful experiments therefore require ROD [or RCOOD] to be dissolved in D2O. He admits that this "gives rise to some difficulties of interpretation" of solvent effects, an approximation if you like.
 * He also adds that the simple explanation which I have summarized "is useful for remembering the direction of the isotope effect", but neglects numerous solvent interactions. So yes, it is approximate. If you want to go further, he cites a more detailed treatment including solvent interactions by Bunton and Shiner here (which I have not yet read).
 * And I agree that it would be useful to add the interpretation of pK(H) and pK(D) as the pH and pD for 50% dissociation in H2O and D2O respectively. Dirac66 (talk) 00:30, 1 June 2017 (UTC)

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Recent edits(text transferred back from User_talk:Alsosaid1987)
Earlier communications at User talk:Petergans

The first line of the lead has a link to the article reaction quotient. Also, the first section of the article gives a full explanation. Therefore there is no need to include a detailed description of reaction quotient in the lead. Perhaps there should also be a link in the main text, section Basic definitions and properties " reaction quotient Qt (a function of time...)"? I shall revert your edit unless you give a convincing reason to keep it. If you have one, please post it to my talk page. Petergans (talk) 10:57, 19 November 2017 (UTC)
 * I have reverted a long list of changes because at least one of them contained a fundamental; error of chemistry. It is wrong to assert that equilibrium is never achieved. The reason for this is that chemical equilibrium is a dynamic process Dynamic equilibrium, not a one-way process. Therefore it will be achieved in a finite time. Mostly, after a change in composition, equilibrium is reached in 1-30 minutes. However, there are some chemical systems that are extremely slow to come to equilibrium; an equilibrium constant cannot be measured for such systems, so they are out of the scope of this article.
 * Please note that I am an expert in this field (retired from Leeds University). I understand that you are acting in good faith,trying to make the article easier for a non-chemist to understand. However, this cannot mean "dumbing down" at the expense of scientific accuracy. I had to revert all of your edits in order to return to a version I know to be error-free. If you wish to make further edits, may I suggest that you make them in your sandbox and let me know when they are ready to be posted.


 * You may find it helpful to look at Equilibrium chemistry which I created. This article contains useful background material. Petergans (talk) 14:51, 20 November 2017 (UTC)


 * I notice a very interesting aspect in the above comments re the speed of reaching equilibrium. This leads to the question how can that be expressed in formulae!--82.137.13.12 (talk) 13:33, 22 November 2017 (UTC)


 * Actually, it's quite straightforward, just a bunch of algebraic manipulation: Consider A<->B with forward and backward rate constants k and k'. And let x=[A]_0-[A]. Then we can write the differential rate law as dx/dt=k([A]_0-x)-k'([B]_0+x). It's not hard to show from there that the integrated rate law is ln((k[A]_0-k'[B]_0)/(k[A]_0-k'[B]_0-(k+k')x))=(k+k')t. Now let x_eq=[A]_0-[A]_eq. At equilibrium dx/dt=0, so the differential rate law gives k[A]_0-k'[B]_0=(k+k')x_eq. Substituting into the integrated rate law gives our final result: [A]-[A]_eq=([A]_0-[A]_eq)e^(-(k+k')t), as I asserted earlier on Petergans's talk page. Alsosaid1987 (talk) 16:46, 22 November 2017 (UTC)

From K. Denbeigh, "The Principles of Chemical Equilibrium", Cambridge Univerity Press, 4th edition (1981) page 292. "The condition of equilibrium for the generalized chemical reaction ΣνiMi = 0 was shown in §4.4 to be Σνiμi = 0"

I cannot find any reference to cite which states that this condition cannot be reached in a finite time. In terms of kinetics, equilibrium is established when forward and backward reactions proceed at the same rate. It is fundamentally wrong to assert that equilibrium conditions can never be achieved in a finite time. The explanation for the apparent inconsistency with chemical rate equations is that those equations apply at the level of macroscopic concentrations, whereas equilibrium in solution is established at the microscopic level of atoms, ions and molecules.Petergans (talk) 16:45, 23 November 2017 (UTC)

Source for equilibrium never actually being achieved: http://nzic.org.nz/chemed-nz/issue-archive/ChemEdNZFeb09_Hoor.pdf. This was an article published in Chemistry Education in New Zealand: ChemEd NZ by Marten J. ten Hoor (J.W. Frisolaan 40, 9602 GJ Hoogezand, Nederland), with critical comment from Jim Pearce (Victoria University of Wellington, New Zealand), written by noted academics in the field. The equation derived in the one that I presented in your talk page.

Again given my eduational background (Harvard undergrad, UC Berkeley PhD, and MIT postdoc), I am certainly qualified to correct this error.Alsosaid1987 (talk) 22:32, 29 November 2017 (UTC)

I do not have time to keep arguing with you about this. That equilibrium is approached asymptotically is a well known fact, just as even the most exergonic reaction (e.g., burning octane) is technically an equilibrium process, although K exceeds 10^100. I wish to show proper deference to your years of expertise. However, I am particularly concerned when your equations are dimensionally incorrect, do not conform to IUPAC guidelines, or both. Chemistry and mathematics are separate disciplines, of course (and I know I can seem pedantic in my notation) but mathematical equations in chemistry need to follow the laws of mathematics.Alsosaid1987 (talk) 23:03, 29 November 2017 (UTC)
 * Equilibrium is not approached asymptotically. Both forward and backward reactions occur in discreet steps at the molecular level. This means that equilibrium can be attained in a finite time.
 * The laws of chemical kinetics are based on concentrations varying continuously at the macroscopic level. Otherwise the derivatives dc/dt (reaction rates) would be meaningless. Petergans (talk) 10:46, 30 November 2017 (UTC)
 * The preceding comment seems to suggest that individual molecules (discrete steps) are important in thermodynamics but not in kinetics. Textbook sources generally neglect the existence of individual molecules for both thermodynamics and kinetics when considering macroscopic systems, because their effects are negligible and treating them rigorously would greatly complicate the theory. So I think this article should say that the approach to equilibrium is usually considered to be asymptotic in macroscopic systems, and that the effects of the existence of individual molecules can be ignored. Asymptotic approach implies that the number of molecules of a given reactant at very long times is predicted to be fractional(!), but replacing this theory by a series of discontinuous steps would merely complicate the theory without changing anything important. At least this is implicitly assumed in textbooks. Dirac66 (talk) 14:54, 30 November 2017 (UTC)
 * It is also implicit in text books that equilibrium is attained in a finite time. The point that I am making is that this is possible because changes at the atomic level are integral, not continuous, changes. This means that the laws of chemical kinetics are not valid at the level of atoms and molecules (c.f. statistical mechanics). Please note that there is no discussion in Rossotti & Rossotti,The Determination of Stability ConstantsMcGraw-Hill, 1961, of anything to do with kinetics, apart from chapter 14 which is concerned with kinetic methods for determining stability constants, following the Guldberg and Waage approach. Petergans (talk) 00:20, 1 December 2017 (UTC)

Ionic strength effects and dimensionality
''If concentrations are measured in mol dm–3, the numerical value of Kc is approximately equal to the thermodynamic equilibrium constant K° and is often used as a surrogate in calculations. However, Kc has units of concentration raised to some power[5][7] while K° is dimensionless.''

This statement is misleading. The illustration at the right (below in the article) shows that variation of ionic strength has a significant effect on the equilibrium constant value. The effect is larger the higher the electrical charges on the ions.

The value of Kc tends to the value of Ko asymptotically as the concentrations of the reactants tend to zero.

Equilibrium constants are usually determined using a medium of high ionic strength in order to minimize the effects of changing concentrations of reactants on activity coefficient values. The statement regarding dimensions is highly misleading. Equilibrium constants are intrinsically dimensionless. This is also true if the values have been obtained under the assumption that the quotient of activity coefficients is equal to 1. A unit of dimension is often cited in reports on biochemical system. This is to distinguish values which are based on the use of concentration scales of molar, millimolar or micromolar. It does not mean that K has a dimension.Petergans (talk) 19:05, 26 November 2017 (UTC)

I'm willing to let slide your assertion that reaction reach equilibrium in a "finite" time. I still believe you are incorrect. There is no fundamental distinction between "macroscopic" and "microscopic" events, and rates and equilibria are fundamentally linked by mass action. That is a minor quibble. However, your assertion that Kc is unitless flies in the face of the IUPAC Green Book definition of this constant. Therefore, I have restored the previous comments regarding dimensionality. Alsosaid1987 (talk) 21:22, 29 November 2017 (UTC)
 * Here is the Green Book definition of the equilibrium constant. At no time does it say it has any units.  It is a dimensionless quantity.  -- Jayron 32 12:18, 30 November 2017 (UTC)


 * For the last time, I am not talking about K, but K_c. Please check the Green book definition of K_c not K.  pg. 73 of https://www.iupac.org/fileadmin/user_upload/publications/e-resources/ONLINE-IUPAC-GB3-2ndPrinting-Online-Sep2012.pdf

Of course, K does not have units. I have given up trying to correct the errors on this page. It is not simply worth my time. It's easy to make a statement of not finding something when only making a cursory look through a 270 odd page document.

BTW, your citation is the IUPAC Gold Book, which explicitly states that equilibrium constants can be defined by concentrations, pressures, etc. as well as by activities. The version of the equilibrium constants to be used in thermodynamic equations needs to be dimensionless, and that is K^\ominus, defined by activities. Thus, the gold and green books are entirely consistent.

Alsosaid1987 (talk) 06:40, 25 December 2017 (UTC)

Given the whole host of wrong equations and inaccurate statements, I should have reverted your edits. Instead, I am giving you the benefit of the doubt, and the courtesy of fixing your errors, given your years of experience in the field. However, in the future, please edit more carefully -- there is no excuse to saying "Delta G^\circ=-RT\log_10 K".Alsosaid1987 (talk) 22:24, 29 November 2017 (UTC)

Thermodynamics of equilibrium (continued from recent edit, above)
In Wikipedia the term equilibrium constant must be distinguished from the term concentration quotient at equilibrium. The reason for this is that the individual values of $$\Gamma$$ and $$Q_{eq}$$ are concentration-dependent, whereas the product, $$K$$, is concentration-independent. It may be noted that these terms are used interchangeably in some publications concerning equilibria in biochemical systems, where there is an unstated assumption that the numerical value of $$\Gamma$$ can be taken to be 1. Petergans (talk) 22:20, 11 December 2017 (UTC)
 * 1) $$ \Delta G^\ominus = -RT lnK$$ this requires that K be a pure number (no dimension)
 * 2) $$K=Q_{eq}\Gamma$$ = concentration quotient × quotient of activity coefficients (at equilibrium).
 * 3) The dimension of $$\Gamma$$ must be reciprocal of the dimension of $$Q_{eq}$$.
 * 4) If $$\Gamma$$ is assumed to have a numerical value of 1 then $$Ln K = Ln Q_{eq}$$ numerically.

In this context I mention a research article in The Journal of Chemical Physics by author Milton Manes: http://adsabs.harvard.edu/abs/1950JChPh..18.1355M .--82.137.12.90 (talk) 12:50, 10 December 2017 (UTC)

Second major reversion
The places marked as inconsistent are inconsistent (dimensionally) speaking (since activity coefficients gamma are unitless and cannot change (unitless) activity to concentration without applying a factor of the standard concentration of 1 mol/L). I am going to let others fix these.Alsosaid1987 (talk) 10:24, 25 December 2017 (UTC)

I hate for this to have to be an ad hominem attack, but unfortunately, Petergans, you are taking advantage of the fact that as a retiree, you have more time to make Wikipedia edits than many others, myself included, who have busy professional careers and do not have time to participate in an edit war with you. However, you have committed a basic logical fallacy of equating absence of evidence with evidence of absence. Suffice it to say, very few, if any textbooks, need to mention a fact about equilibration that can be deduced from equations of elementary kinetics. That is why this is mentioned in the Chem Ed NZ article, an article meant to dispel the confusion of beginners.

I am still surprised that given your background, making mathematically and dimensionally incorrect statements does not seem to bother you.Alsosaid1987 (talk) 10:17, 25 December 2017 (UTC)

For the final time. I am talking about principles and not practicalities. If the half life of a process is on the order of 10^-5 seconds, then for all practical purposes one sees equilibrium after about a millisecond, but that does not alter the mathematical truth that an exponential function never reaches zero. And why do you dismiss this Chem Ed. NZ article as a legitimate source again? These authors are no less academic chemists than you and I.

In summary, I give up; I don't have time to fix this every time you revert it. I will simply tell my students to disregard some of the dimensionally inconsistent nonsense you write on this page.Alsosaid1987 (talk) 06:46, 25 December 2017 (UTC)

I have now checked both the article Chem. Ed. NZ and Atkins and Beran, "General Chemistry"§ and in no place is there support for the statement (in the Chem. Ed. NZ article) that "a value of 10-5 s-1 seems typical". This statement is pure conjecture.

It is common knowledge that acid-base reactions in solution are very fast. For example, in a titration of acetic acid (a weak acid) this sodium hydroxide (strong base) the reaction is effectively instantaneous as the indicator changes color "immediately" after a drop of titrant is added at the equivalence point. I have checked the following sources to see if there is any indication that equilibrium in acid,base or complexation reactions, cannot be reached in a finite time. There is none.
 * Atkins "Physical Chemistry"
 * Denbeigh, "The Principles of Chemical Equilibrium"
 * Wright, "An Introduction to Aqueous Electrolyte Solutions"
 * Burgess,"Metal ions in Solution"
 * Beck, "Chemistry of Complex Equilibria"
 * Baes&Mesmer, "The Hydrolysis of Cations"
 * Rossotti&Rossotti, "The Determination of Stability Constants"

It is true that some reactions can be slow. For example titrations of a metal ion with EDTA may take some time to reach equilibrium ("Vogel's Textbook of Quantitative Chemical Analysis"; Skoog, West, Holler, Crouch "Fundamentals of Analytical Chemistry") There is no evidence that equilibrium cannot be reached in finite time, except with certain extremely inert macrocyclic complexes; those cases are irrelevant in the context of this article.

Previous notes 2. "In the simple case "$$\mathrm{A}\rightleftharpoons\mathrm{B}$$, with forward and reverse rate constants k and k ', approach of equilibrium is exponential: the integrated rate law is given by $$[\mathrm{A}]_t-[\mathrm{A}] = ([\mathrm{A}]_0-[\mathrm{A}])\exp(-(k+k')t)$$, where $$[\mathrm{A}]$$ is the equilibrium concentration of A, and $$[\mathrm{A}]_t$$ is the concentration of A at time t." This too specific for an article of general nature. In any case the expression $$K^\ominus=\frac{k}{k'}$$ must be applied with care as k and k' must have the same dimensionality for the ratio to be a pure number.

Previous note 6 "Some texts, such as Atkins and de Paula, Physical Chemistry (10th ed., Oxford University Press, 2014) define Kc as a unitless quantity, contrary to IUPAC conventions" is wrong. The IUPAC convention is not contrary to the laws of thermodynamics. It refers to published values of concentration quotients.

Previous note 7. See previous note 2 above.

Previous note 8 The question of dimensionality is discussed thoroughly in the section equilibrium constant.

The approach of Guldberg and Waage is discussed in detail in the article Law of mass action. A link to that article already exists.

In the light of these facts I will again revert the article to the status quo ante, apart from a modified version of the section. Any future edits relating kinetics to equilibrium constants must be backed up by verifiable citations, in accordance with Wikipedia policy.Petergans (talk) 12:12, 16 December 2017 (UTC)

§ Atkins & Beran, Chapter 13, "Chemical equilibrium" is framed entirely in terms of the law of mass action. There is no mention of Gibbs free energy and the examples given in the text relate almost entirely to gas-phase reactions. This book is therefore not suitable as a general reference in the context of this article. Petergans (talk) 09:00, 17 December 2017 (UTC)

Factual errors
The following are marked dubious in the article. I hope my fellow Wikipedians can fix these.

Gibbs energy change is minimum should be Gibbs energy change of reaction is zero (or gibbs energy is minimum)

For correct dimensionality of K_c, see pg. 73 of https://www.iupac.org/fileadmin/user_upload/publications/e-resources/ONLINE-IUPAC-GB3-2ndPrinting-Online-Sep2012.pdf

The reaction quotient at equilibrium is the equilibrium constant, it is not some magical version of the equilibrium constant "with units"

Alsosaid1987 (talk) 10:37, 25 December 2017 (UTC)


 * I have corrected $$\Delta G$$ = minimum which was clearly an error, and added the symbol $$\Delta G$$ to distinguish it from $$\Delta G^\ominus$$ further down. Dirac66 (talk) 12:42, 25 December 2017 (UTC)


 * As for units, the problem in the article starts with the dimensionally incorrect equation
 * $$K^\ominus= \frac

= \frac{{{[\mathrm{R}]}}^\rho ^\sigma ... } {{{[\mathrm{A}]}}^\alpha ^\beta ...} \times \Gamma$$


 * Since Γ is unitless, this would imply that activity and concentration have the same units which is wrong. The dimensionally correct relation is found in the article Thermodynamic activity as:
 * $$a_i = \gamma_{c,i} \frac{c_i}{c^{\ominus}}\,$$
 * The factor $$c^{\ominus}$$ = 1 mol/L is necessary to get the units right, although it is often omitted in textbooks at all levels, and Wikipedia should point this out for readers. Dirac66 (talk) 15:14, 25 December 2017 (UTC)


 * We must find a way to define an equilibrium constant that has no dimension in order that it can be related to Gibbs free energy. One way that it can be done, for reactions in solution, is to express each term in the defining expression as being a quotient of concentration divided by the corresponding standard concentration which, by definition, has a numerical value of 1. For practical reasons this is inconvenient for a general treatment of equilibrium constants. The process of splitting the equilibrium constant expression into a product of two quotients is more convenient. The two components can be given units which are the reciprocal of each other. Then for any given system the quotient of activity coefficient can be set numerically equal to 1. This is equivalent to specifying the standard state. So, when a equilibrium constant is determined using a medium of high ionic strength, that medium effectively defines the standard state. Using this convention, the equilibrium constant, calculated as a concentration quotient, is a function of ionic strength, as illustrated. Behind the thermodynamics is the fact that all general-purpose computer programs which are used for the calculation of stability constant values, going back to Letagrop (ca. 1960) work with numerical values of concentrations. It is therefore implicit, when using one of these computer programs, that the quotient of activity coefficients is assumed to have a numerical value of 1.Petergans (talk) 20:04, 25 December 2017(UTC)


 * I am not familiar with giving the two components (does this mean the two factors Kc and Kγ?) reciprocal units. For your example of the ionization of acetic acid in the presence of NaNO3, do you mean that Kc has units M (if solvent water is ignored) and Kγ has units M-1? How is this reconciled with the Debye–Hückel equation which estimates $$\ln(\gamma_i)$$ and therefore requires each $$\gamma_i$$ to be a pure number so that it has a logarithm?
 * The nonideal ionic equilibrium calculations I remember (long ago, I admit) used unitless Kc (as functions of c/c0) and unitless activity coefficients so that this problem did not arise. Also, elementary calculations which assume ideality often ascribe units to Kc but then the activity coefficients are ignored and of course the answers are quite approximate. Dirac66 (talk) 03:20, 26 December 2017 (UTC)

Definition:$$ K^\ominus= \frac{{{[\mathrm{R}]}}^\rho ^\sigma ... } {{{[\mathrm{A}]}}^\alpha ^\beta ...} \times \frac$$

This definition splits the equilibrium constant into a quotient of concentrations multiplied by a quotient of activity factors. The two quotients have dimensions which are the reciprocal of each other, so the product is dimensionless. The quotient of activity factors may be set to be numerically equal to 1. The effect of this is to redefine the standard state and it allows the equilibrium constant to be specified and calculated as a concentration quotient. The use of concentration quotients is virtually universal with published stability constant values.

The issue was settled more than a half century ago; c.f. J. Bjerrum, Metal Ammine Formation in Aqueous Solutions,Haase and Son, Copenhagen,(1941). Rossotti & Rossotti The Determination of Stability constants(1961), Chapter 2 "Activity and Concentration Quotients" gives a detailed account of historical attempts to control the effects of activity variation in determining the values of stability constants. The use of a medium of high ionic strength relative to reactant concentrations helps to ensure that the quotient of activity coefficients (Γ, above) is effectively constant over the range of experimental conditions, such as pH, used in the determination. Obviously a different convention is used in relation to the Debye–Hückel equation. This would matter only if the Debye–Hückel equation was used to model the variation of stability constant values with ionic strength. In practice this does not happen. Rather, theories like SIT theory and Pitzer equations, with empirical parameters, are used. to extrapolate measured concentration quotient values to zero ionic strength; use of the parameters allows values to be calculated at any ionic strength. Petergans (talk) 11:43, 26 December 2017 (UTC)
 * Yes, a different convention. There seem to be perhaps three different conventions for the units of activity coefficients and concentrations which need straightening out. Let's simplify and consider the units for one species at a time.


 * 1) The most logical way of writing the relation is $$a_i = \gamma_{c,i} \frac{c_i}{c^{\ominus}}\,$$, with unitless activity (since $$ln \gamma$$ is related to chemical potential) and concentration as mol/L (or mol/kg etc). However this is unpopular because of all the c0 factors which are "all equal to one".
 * 2) The method I have seen most used is to write a product of two unitless factors: $$a_i = \gamma_{c,i}c_i$$, where $$c_i$$ is really $$\frac{c_i}{c^{\ominus}}$$. This avoids dealing with units completely, and has the advantage that $$\gamma_{c,i} = 1$$ corresponds to ideal behaviour.
 * 3) The third method which you seem to be describing is to associate the $$c^{\ominus}$$ factor with the activity coefficient. That is, if I have understood correctly, $$a_i = \gamma_{c,i}c_i$$, where $$\gamma_{c,i}$$ is really $$\frac{\gamma_{c,i}}{c^{\ominus}}$$. This would lead to the equilibrium constant expression which you have described. If this method is standard usage in the stability constant literature (with which I am not familiar), then I suppose Wikipedia should include it. However I think it would be clearest for readers to mention all 3 methods as possible alternatives, with sources if possible. Dirac66 (talk) 00:56, 27 December 2017 (UTC)


 * P.S. re Debye-Hückel: The SIT theory and Pitzer equations are effectively refinements of Debye-Hückel. They still calculate $$\ln(\gamma_i)$$, albeit with improved equations, so the problem with units will be the same as for the original Debye-Hückel equation. Dirac66 (talk) 01:05, 27 December 2017 (UTC)


 * Atkins, Physical Chemistry. 8th. edn. p 208 states "use $$a_j = \gamma_j x_j$$ or $$a_j = \gamma _j b_j/b^{standard}$$", which seems to imply that both conventions are acceptable. In the context of stability constants it does not matter which convention is used as the value of the quotient of activity factors is set, arbitrarily, to 1 so that the equilibrium constant can be calculated as a quotient of the numerical values of concentrations. I suggest that the original text should be reinstated, and a footnote added regarding the alternative thermodynamic definitions. Incidentally, when concentrations and activity coefficients are expressed in terms of mol fractions, the issue of dimensionality does not arise in the theoretical framework as mol fractions are pure numbers. Petergans (talk) 13:29, 27 December 2017 (UTC)


 * This change does sound like an improvement in that it would recognize alternative conventions. It is probably best that you be the one to initiate the modification since you have the clearest idea of what should be changed exactly. Dirac66 (talk) 01:45, 28 December 2017 (UTC)

Re the third method mentioned above involving the ratio activity coefficient - concentration, I have seen some source(s) saying that molarity- and molality-corresponding activity coefficients can have the dimension inverse to concentrations instead of being divided by standard concentrations.--109.166.131.41 (talk) 16:20, 15 July 2019 (UTC)

Temperature dependence or Enthalpy and Entropy
Re yesterday's change from a Temperature dependence section to an Enthalpy and Entropy section, summarized as Re-written and renamed - the old version had become garbled. I think that not only has the section has been rewritten, but it has been switched from solving one problem to solving another problem which is the inverse of the first. To be complete as befits an encyclopedia, both problems should be described, possibly in consecutive subsections.

The first problem is Temperature dependence, i.e. how to find K(T2) from K(T1) given ΔH(T) from calorimetry, as well as the simplest approximation with ΔH constant. This will be of interest to some readers and so should be covered.

The second problem is the inverse of the first, i.e. how to determine ΔH(T) (and ΔS(T)) from K(T). It can be mentioned that this is an alternative to calorimetric methods.Dirac66 (talk) 03:00, 5 January 2018 (UTC)
 * An interesting comment. The reason for leaving out details of the first is that I am not aware of any instances in the literature where this has been done. Some reasons for this are as follows. i) It is easier to measure the equilibrium constants at different temperatures. ii) Calorimeters are are available only to a small minority of researchers. iii) I am not aware of any practical applications where a calculated ΔH value is used; the main use is theoretical, helping to understand the equilibrium process. With industrial gas-phase reactions, such as SO3 synthesis, it is the variation of K with temperature and pressure that is important.Petergans (talk) 10:15, 5 January 2018 (UTC)
 * It is true that calorimetry is not a usual technique for reactions with a conveniently measurable K. It is more often used for reactions with K too large to measure, such as combustion, which are admittedly not the subject of this article.
 * The first sentence of the section should therefore not refer to determining K and ΔH experimentally which suggests calorimetry. Instead I would start with If the equilibrium constant K for a reaction has been determined experimentally at several temperatures, then ΔH and ΔS for the reaction are easily derived using the van't Hoff equation. This is what I called the second problem above, but I would now put it first since it is more fundamental. And I agree there is no reason to mention calorimetry yet.
 * Then as a second point (which I called the first problem above), we can restore the mention of find K(T2) from K(T1) given ΔH. This calculation is probably not often found in current research papers because it is too simple, but it is a textbook-level application which will be of interest to some readers. Dirac66 (talk) 21:29, 6 January 2018 (UTC)
 * Atkins does provide an example on p. 214 (8th. Edn.) so I will amend the text along the lines you have suggested. Petergans (talk) 10:46, 7 January 2018 (UTC)
 * OK, the section is better now I think. I will just reinsert T-dependence at the end of the section title, so that it will appear in the Table of contents. Dirac66 (talk) 22:38, 7 January 2018 (UTC)

Equilibrium constant and pressure
, do you have any comment to my edit summary? "Undoing last three edits. No reference before or after though. But the equillibrium constant depends on the activity, and the activity depends on the chemical potential, and chemical potential depends of the number of particles which is related to the pressure. No expert, just followed the definition here on WP". Oftentimes, the equilibrium constant is defined with conentrations (and not activity) to make it simple. Therefore, the article "The pressure dependence of the equilibrium constant is usually weak [...]] and thats why its normally omitted. (btw. I remember my teacher saying in the firest lecture "Everything you have learned so far - is wrong" Christian75 (talk) 13:41, 16 April 2019 (UTC)
 * There appears to be confusion between the effect of pressure on the composition of a reaction mixture and the pressure-dependence of an equilibrium constant. This section is now pretty much incomprehensible. Petergans (talk) 19:37, 16 April 2019 (UTC)
 * I agree. Perhaps we should point out this distinction at the beginning of the section in words such as: At normal or lower pressures the equilibrium constant is essentially independent of pressure, and only the composition of a reaction mixture varies. However at high pressure (hundreds or thousands of atmospheres), the equilibrium constant itself varies because ...Dirac66 (talk) 20:05, 16 April 2019 (UTC)
 * I've just reverted a set of misguided edits. Of course the value of an equilibrium constant will vary with pressure. Equilibrium constant values for solutions are determined in conditions where the quotient of activity coefficents is assumed to be a constant with respect to varying concentrations of the species involved. A similar consideration applies to gaseous mixtures. The issue here concerns departures from ideality. In effect these are dealt with by re-defining the standard states for each set of conditions, which is equivalent to setting the quotient of activity coefficients to a value of one. Petergans (talk) 21:41, 18 April 2021 (UTC)

Chemistry
Equilibrium constant and dynamic and static equilibrium 119.160.69.157 (talk) 18:50, 16 July 2022 (UTC)

Chemistry
Equilibrium 39.44.225.8 (talk) 16:18, 19 October 2022 (UTC)

A question about a link.
In the section entitled "Association and dissociation constants", on the third line there are two links. The first one says "acid association constant". When you hover over it a small window appears with the definition of "acid association constant" as I would have expected. The second one says "base association constant". When you hover over it a small window appears with a repeat of the definition of "acid association constant" as I would not have expected. Is this correct? 2603:6080:5F05:7400:1973:3B3F:A301:99C9 (talk) 20:53, 25 December 2022 (UTC)


 * It is almost correct. The point is that in some cases a link is used to explain a term which does not correspond exactly to a real article on Wikipedia, so we point the link to a related article which explains the term which is to be explained.


 * In your first example the term to explain is actually "acid DISsociation constant", and we do have an article with that name so the link just points there.


 * However in your second example, we need to explain the related term "base association constant" which does not correspond to its own article, because we cannot have articles on every possible term. Instead it is explained in the section "Bases and basicity" of the same article Acid dissociation constant, so the link should point there.


 * At the moment the source code for the sentence which includes these links reads "For bases, the base association constant, pKb is used." The second part (after the |) is the term in the article text to be defined by the link, and the first part (before the |) should link that term to a section "Bases" of the article "Acid dissociation constant". However the section name has been changed to "Bases and basicity" (in August 2013 according to the edit summary of that article), so I will now correct the link from this article so that the link can find the intended section. Dirac66 (talk) 02:48, 26 December 2022 (UTC)


 * Done. Note that clicking on the corrected link now leads to the correct section of the targeted article, rather than to the top of the article as the previous edit because it couldn't find a section named just "Bases".Dirac66 (talk) 02:59, 26 December 2022 (UTC)