[Borek]

an electrode pH-meter shows pH = -1 for a solution of NaCl in 6 N HCl; which is wrong (pH < 0 )

Wrong why?

And from the very beginning the question was not about pH, but about Na⁺/sulfonate association. More or less I read the initial post as "is it possible to estimate stability constant for Sulfonate/Na⁺ knowing stability constant for Sulfonate/H⁺?". The latter is just Ka^-1.

[pgk]

Because pH = -1 is translated to [H+] = 10 N for a solution of 6 N HCl; or else, the protons concentration is higher than the concentration of the monovalent acid that is not true.

[Borek]

pH is not -log of concentration but of activity. For 0.01 M HCl measured pH is already not 2, but around 2.05.

[Lucek]

@ OP, I don't see how at pH 5.5 that the naphthalene sulfonate can be low in concentration compared to protons.

pH was controlled by use of HCl

for some reason when only HCl is present than Naphthalene Sulfonate is protonated and we results in naphthalene + SO3 , whereas when I add NaCl to the mixture the Naphthalene Sulfonate remains stable. I am trying to understand the mechanism behind this phenomena. I can image few options... but it might be unrealistic:

1) the Na⁺ is attracted to Naphthalene Sulfonate (to the sulfonate itself) and this attraction protect the naphthalene backbone from the H⁺ attack which would appear if no NaCl

2) maybe the ionic strength controls the stability? as H⁺ activity decreased by increasing salt concentration

3) Solvation ?

I calculate that pH wont change much even if we heat the solution up to 300C

[Borek]

for some reason when only HCl is present than Naphthalene Sulfonate is protonated and we results in naphthalene + SO3

You mean it decomposes? How do you determine that?

Looks like you asked about secondary things completely derailing the thread from the very beginning

[pgk]

Correct!
Thus:
An electrode pH-meter shows pH = -1 for a solution of NaCl in 6 N HCl; which is wrong (pH < 0 ) because pH = -1 is translated to protons activity = 10 N for a solution of 6 N HCl; or else, the protons activity is higher than the concentration of the monovalent acid that is not true.

[pgk]

Naphthalenesufonic acids and HCl are strong acids and therefore, their salts are in equilibrium:
ArSO3Na  +  HCl  ← →  ArSO3H  +  NaCl 
Thus:
1). Addition of NaCl forces the equilibrium to the left.
2). Heat forces the equilibrium to the right because HCl is a gas.
Conclusion: Better results can be obtained by slow addition of aqueous HCl in presence of NaCl at low temperatures, e.g. cold water bath that may contains a few pieces of ice.

[Borek]

Correct!
Thus:
An electrode pH-meter shows pH = -1 for a solution of NaCl in 6 N HCl; which is wrong (pH < 0 ) because pH = -1 is translated to protons activity = 10 N for a solution of 6 N HCl; or else, the protons activity is higher than the concentration of the monovalent acid that is not true.

Sorry to say that, but it looks like you have no idea what you are talking about. Activity coefficients for high ionic strength solutions are higher than 1, so it is perfectly OK for activity of H⁺ to be higher than the concentration in 6N solution. See for example http://www.umich.edu/~chem241/lecture11final.pdf

2). Heat forces the equilibrium to the right because HCl is a gas.

You would need very high concentrations of HCl for that to matter, we are talking pH 5.5 solution. Stop posting nonsense, you are not helping.

[pgk]

Dear Administrator,
Thank you for your kind compliments!
But please, permit a few remarks:
1). In the provided reference, it is clearly stated that …”So if solubility increases with ionic strength---meaning that concentrations increase---then activity coefficients decrease as you increase ionic strength!!”……
2). In the provided reference, it is also stated that …”Debye-Huckel equation valid from μ =0 --> 0.1 M; beyond, not  very accurate at predicting activity coefficient!”
3). Moreover, it is stated therein that …” the smaller the hydrated radius--more effect of μ on activity coeff. (decrease)”…..
4). The cited schema refers to the increase of NaClO4 concentration and change of activity coefficient; but not to the increase of acid (HClO4) concentration, neither to the proton activity coefficient. Besides, ClO4- is a very bulky anion and consequently, it might not be a typical example for general conclusions.
5). By ending, HCl solubilization in water is highly exothermic and thus, fast addition of small amounts of concentrated HCl can significantly increase the HCl partial pressure and significantly decrease its Henry's constant, even at room temperature.
Sincerely yours

PS: Thinking twice, stopping posting does not sound a bad idea.