On Chemical Equilibria

[Anonymous No.15577745]

A random question that's bugged me for many years.
In the equilibrium constant of any aqueous solution, if water is involved, the activity of water is always treated as 1. This is by definition. However, it is the case that reactants or products within an aqueous solution can exceed a concentration/activity of 1. That doesn't logically make sense to me - the solvent surrounds all the molecules of reagent and product and it just doesn't seem right that the activity of a reagent can be higher than that of the solvent when both are involved in the reaction.

Say, for instance, the reaction of a 2M solution of Manganese (II) with sodium hypochlorite in hydroxide to yield sodium permanganate, chloride and water. If we remove the spectator ions, the conventional equilibrium constant approximating the activity to the concentration will be of the form K=[Cl-]^5[H2O]^3[MnO4-]^2/[ClO-]^5[OH-]^6[Mn2+]^2 (If i have not been careless)
Apologies for the formatting. The point is that we will conventionally take the activity of water as 1 and then remove it from the equation. But here, this implies that water is less active than Mn2+, the latter of which is orders of magnitudes more sparse within the reaction mixture. It thus makes little intuitive sense why water would be less active than Mn2+ in such a solution. The concentration of H2O is always 55.6 (iirc), and this factor is always ignored. Why?

I did first consider the issue to lie with the approximation of activity to concentration. However, activity coefficients still remain high in concentrations of solutions upwards of 10 molar. Meanwhile, water, despite surrounding literally all the reagent molecules, is arbitrarily capped at 1.

Stackexchange was pretty useless in answering this question. As such I come to /sci/ without much hope, considering this is fucking /sci/. But you guys did manage to solve some difficult math shit, I think some basic pedagogical equilibria chemistry cannot be especially difficult.

Thank you.

[Anonymous No.15577762]

I'm not sure,

a_b = x_b (gamma)_b
(gamma)_b = 1 for ideal
x_b =1 for water (assumed because it's concentration will always be basically infinite compared to the 1-10ish mol/dm3 solute?)
Therefore a=1*1=1 ?

[Anonymous No.15577773]

I'd need you to define some symbols there, if I am to have any hope of understanding you.

[Anonymous No.15577791]

>>15577773
a=activity
x=mole fraction
gamma = activity coefficient

[Anonymous No.15577846]

Ah, I see. I thought about that for a while. I think the formatting had some issues unfortunately, but I do understand what you mean.
Interesting. I think however this only pushes the problem back one step; based on my further research, the activity coefficient of certain ions can exceed 1 (and unfortunately appears quite mathematical in their derivation). Which I mean, makes it still quite odd, as this causes their calculated activity to exceed 1. Physically, there remains little explanation for the answer. I'm looking at it from a most visual standpoint - perhaps solvated particles are special in some way that makes them much more active?

I feel that there may be a concerning issue when it comes to taking the activity of water as 1 when the solution gets relatively concentrated (2M), but searching about an infinitely dilute solution of water in water is somewhat bizarre and unlikely to yield results.

Mathematically, I think that's actually quite a clean explanation for the situation when the mole fraction of water approaches 1. I am more curious about the physical intepretation, which remains quite odd (why can the activity of a solute be much higher than the solvent? I took the data for solute activity from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/Solutions_and_Mixtures/Nonideal_Solutions/Activities_and_their_Effects_on_Equilibria)

Regardless, thanks kind anon.

[Anonymous No.15577872]

>>15577846
Do we know what the physical definition of activity is. As in what it represents.
Or is it another made up thermodynamic concept?
(Looked it up it's effective concentration, so for water could it be again the assumption there's way more water meaning effectively, you can ignore the term. This would break down and not be possible in a reaction with eg ethanol solvent, with a few drops of water and solute. Perhaps either finding literature on something similar to this or idk could shed some light)


I think your best option is to mass email professors working on something similar and hope one gets back to you with a reasonable answer. Best of luck anon

[Anonymous No.15577889]

Indeed, I do think it is a term that can be ignored. It is just that by calculating it as 1, a bizarre conclusion where the solutes are somehow are more active than the solvent arises. After all, water is a 55 M solution of water in itself; it's hard to imagine how a 3M HCl solution would lead to a higher activity of H+ ions within it. My working theory right now is that is has something to do with the nature of how water molecules solvate compounds.

Experimentally, K is related to dG and thus dH, and calorimetric analysis of course shows that there's nothing wrong with the assumption. It is simply the visualisation that seems odd.

I shall probably take the question to a discord. Failing that, I will likely message a friend of mine who is in close contact with a professor. I'll hope to get an answer, and may update /sci/ on it. Thanks for the help. Though of course, perhaps other anons with good insights might stumble on this thread. No high hopes though.