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@FusRoDah My prior comments were not aware of later edit, involving explicit exposure to air. I do not deny the major CO2 influence. The comments pointed out the fact measured pH rarely fits calculated ones and CO2 absorption creates ionic strength forming ammonium and (hydrogen)carbonate.
@FusRoDah Not really. it is more about being constant than unity. Any parameter being constant enough can be implicitly involved. OTOH, a parameter being about 1, but not constant enough, cannot.
One of reasons is your theoretical pH prediction worked with approximation that molar concentrations are numerically equal to thermodynamic activity. // You did not provide the volume of titrated ammonia solution (not ammonium hydroxide solution, as hydroxide neutralises ammonium).
I assume it would be the formation entropy as the entropy difference for the formal change H+ to H+, Similarly as O2 has formation entropy/enthalpy/Gibbs energy as S/H/G changes conventionally zero, for the change O2 to O2.
Negative rate means the negative net rate of the reaction in forward sense and positive net rate in backward sense. But the rates of forward and backward reactions are never negative.
Additionally, see the Trouton's rule (Delta S_vap = Delta H_vap / T_b is approx 85-88 J/K/mol, useful for most nonpolar solvents, but with deviations for polar solvents with hydrogen bonds.)