Talk:Equilibrium constant

message: 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)
thread_title:  Untitled 

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

text: 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)

text: \ \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)

text: This is, of course, completely true: however, don't forget that the numerical value of K (and of ΔG°) depends on the form in which you write the reaction equation. Physchim62 (talk) 16:41, 26 April 2008 (UTC)
replies: text: 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)
replies: text: 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)
replies: text: 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)
thread_title:  units 

message: 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)
thread_title:  Merge with Chemical equilibrium 

message: 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)
thread_title:  Poor applications section 

message: 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)
replies: text: 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)

text: 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)
thread_title:  Effect of temperature 

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

message: 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)
replies: text: This is clearly wrong. The pressure dependence is illustrated in the section equilibrium constant#Pressure dependence. Petergans (talk) 10:15, 1 August 2009 (UTC)
replies: text: 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)
thread_title:  Dependencies 

message: The article really needs a definition of the term in simpler layman's terms.  Please.  BriEnBest (talk) 03:03, 5 October 2010 (UTC)
replies: text: I agree. Nicolas Perrault (what did I screw up again?) 21:26, 9 January 2014 (UTC)
replies: text: 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)
thread_title:  Laymen's terms 

message: 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)
replies: text: 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)

text: 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)
thread_title:  Needs significant revision 

message: 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)
thread_title: Microconstants

message: 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)
thread_title:  Curly brackets 

message: 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)
replies: text: 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  () which was created for use in thermodynamics, but it may also appear in other articles. Petergans (talk) 08:10, 2 June 2013 (UTC)
replies: text: 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)
thread_title:  Symbol not visible in Internet Explorer 

message: 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)
replies: text: 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)
thread_title:  This article is an embarrassment to wikipedia 

message: 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)
replies: text: 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)
thread_title:  Cumulative micro-constant equation error? 

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

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thread_title:  External links modified 

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thread_title:  External links modified 

message: 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)
replies: text: 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.  --Jayron32 12:18, 30 November 2017 (UTC)
replies: text: 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)
thread_title:  Ionic strength effects and dimensionality 

message: # \Delta G^\ominus = -RT lnK this requires that K be a pure number (no dimension)
#K=Q_{eq}\Gamma = concentration quotient  × quotient of activity coefficients (at equilibrium).
#The dimension of \Gamma must be reciprocal of the dimension of Q_{eq}. 
#If \Gamma is assumed to have a numerical value of 1 then Ln K = Ln Q_{eq} numerically.
 
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)
thread_title:  Thermodynamics of equilibrium (continued from recent edit, above) 

message: 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)
thread_title: Second major reversion

message: , 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)
replies: text: 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)
replies: text: 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)
replies: text:  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)
thread_title:  Equilibrium constant and pressure 

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

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