Is it pK=-8 or pK=-6.3?
From the current definition of pH and from the electroneutrality is measured and calculated the value of K=10^8:
If we measure pH and if we know the total amount of chloride in solution tCl with low ionic strength then the calculation is quite simple b(H+)=10^(-pH)=b(Cl-), so K=10^(-pH) * b(Cl-)/(tCl-b(Cl-)) = 10^(-2pH) /(tCl - 10^(-pH)), where b is molality.
However from the free Gibbs energy of the reaction is the value around K=10^6.3, where the tabulated value of free Gibbs energy of formation of Cl- in water is dfG(Cl-) in J.mol-1 and the tabulated value of free Gibbs energy of formation of HCl in water is dfG(HCl) in J.mol-1. The calculation is
K=exp(-drG/(R*T)) = exp(- (dfG(Cl-) - dfG(HCl))/(R*T) ) as described in UIPAC.
Can be this huge difference described by activity coefficients of H+ and Cl- also in the situation if the ionic strength of the solution is very small?
The value of drG for reaction HCl + H2O = H3O(+) + Cl(-) is almost the same as drG for HCl = H(+) + Cl(-), because dfG(H+(aq)) si almost the same as dfG(H3O+(aq)) - dfG(H2O(l)).
Strong acids such as this are more than 99% dissociated even at concentrations as large as 10 M. This suggests a Ka~infinity . The pka given in the literature is -7.0 see Perrin, D. D. (1969) Dissociation constants of inorganic acids and bases in aqueous solution. Butterworths, London, 1969. I think the difficulties you are encountering in making estimates may be due to the fact that many of the definitions are accurate only for dilute if not infinitely dilute solutions? As for pH measurements , if you are not using a SHE then all sorts of nasty things may be happening at the electrode junction giving significant errors in the potential measured. Good luck!
From a chemist's point of view, H+ (or in OH-) are very reactive species, so it might matter if they are present in solutions even at low concentrations. So it seems reasonable to calculate these concentrations using the pK concept.
On the other hand, it does't matter much whether 99.9% or 99.99% of a strong acid is dissociated. So, practically speaking, there is no difference between pK=-8 or pK=-6.3, neither in terms of chemistry nor in terms of thermodynamics.
My purpose of this question is to somehow experimentaly prove the serious bag in definition of pH by UIPAC using wrong assumption for molality standard state m°, which I am currently writting about (see my very first draft attached). The idea of this kind of proof is based on examination of very acidic solution, where the calculation of [H+] (hydronium ion concentration) must be inserted to electroneutrality equation of the solution (see my next question about H+ concentration). However, without the validated values of pK (both - dependent and independent of m° selection) is this proof useless.
https://www.researchgate.net/post/What_is_the_concentration_of_hydronium_ions_H3O_or_free_unbound_protons_H_as_an_equivalent_of_pH74_in_water_solution
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