[Lars Fred riksson]

On p. 130 in Atkins & De Paula Physical Chemistry 10^th Ed. so-called absolute ion entropies is introduced. The bearing idea is that H⁺ should have a proper value of - 21 J/molK instead of the customarily assigned value 0 J/molK.

In the exercise included "brief illustration 3B.4" they convert conventional entropies for Cl^- and Mg²⁺.

For Cl^- the entropy should change from 57 J/molK to 36 J/molK and for Mg²⁺ it should change from - 128 J/molK to - 149 J/molK.


But wouldn't this method of just adjusting all ion entropies have really far-reaching consequenes...?

1. If just all ion entropies all changed this way, then ΔS°_sol would change for all salts and hence all ΔG°_sol would change accordingly, and hence all K_sp values would have to be recalculated. The latter is in itself unsatisfactory since, in principle, it should be readily measurable for some sparingly soluble salts (with, for example, ion sensitive electrodes).

For example, for NaOH ΔG°_sol would be decreased from - 40 kJ/mol to just - 27 kJ/mol using the Atkins method of absolute entropies. For NaCl it would shift from -9 kJ/mol to + 4 kJ/mol (and hence NaCl should be insoluble!).

2. To keep K_sp and ΔG°_sol stable, all S° for all solid salts would have to change or...

3.  ... all H°_sol are 'recalculated' but that would be very counter-intuitive since ΔH°_sol are readily measurable as the heat released or absorbed when a salt is dissolved (just measure at different molalities and extrapolate to zero molality).



I thought such a modification of customary ion entropies (with H⁺ having 0 J/molK) to 'absolute' ion entropies (with H⁺ having assigned -21 J/molK) should adjust all other values in a different way: All monovalent cations should decrease by 21 J/molK while all monovalent anions would increase by 21 J/molK (and appropriate adjustments for divalent ions of course). For example Cl^- should, this way, have 78 J/mol.  Then all ΔS°_sol would be kept the same, and thus all the three K_sp, ΔG°_sol and ΔH°_sol would be kept stable.

There must be a flaw somewhere, but I can't figure out where it is...

[mjc123]

I think you're both making mistakes. The book seems to say that all ions (apart from H⁺) decrease by 21 J/mol/K, whereas you say that cations should decrease and anions increase. In fact cations should increase and anions decrease. Thus for HCl, -21 + 57 = 0 + 36. For MgCl₂, 114 - 128 = -14 = 72 - x; x = -86 = -128+2*21.

In fact we can only measure cation-anion combinations, which should usually be well-defined. How we split them between cation and anion is problematical; the important thing is to be consistent in what your reference is.

For an example involving different values of enthalpies, see https://www.chemicalforums.com/index.php?topic=81896.msg297925#msg297925

[Lars Fred riksson]

I'm sorry but I can't really see the logic in that "cations should increase and anions decrease", because if H⁺ is down to -21 J/molK and Cl^- is decreased as well, then the total ΔS°_sol (for HCl) would decrease by 42 J/molK.

I think that, in order to keep ΔS°_sol constant, either all anions must decrease and all cations including H⁺, must increase or vice versa.

[mjc123]

Oh, sorry, I was misreading; I was taking H⁺ as changing from -21 to 0. So if it's from 0 to -21, then yes, cations should decrease and anions increase.
For HCl, 0 + 57 = -21 + 78, so the value for Cl^- should be 78.
For MgCl₂, -128 + 2*57 = -14 = x + 2*78; x = -170

[Lars Fred riksson]

Thanks a lot! This seems very reasonable! Hence the zero entropy for H⁺ is merely a standardised convention, albeit a very practical one. However, one that might change in the future. 

But from an educational perspective let's hope it stays as it is since it is rather easy to rationalise all normal potentials ε° by having H⁺/H₂ 'fixed' at 0 V (this would of course change if the -21 J/mol K were to be adopted).