The Determination of Absolute Values of Entropies of Hydration [ΔSabs0(H+)h]$[\Delta S_{abs}^0{({H^ + })_h}]$ and Aquation [ΔSabs0(H+)aq]$[\Delta S_{abs}^0{({H^ + })_{aq}}]$ and The Thermodynamics of Proton in Solutions
Authors: Bhattacharyya Ranjana , Chandra Lahiri Sujit 
Published: October 2016

Abstract
Absolute entropy value of H+ ion i.e.

Δ

S

aq

0

(

H
+

)
=
−

22.2

J

K

−
1

mol

−
1

$\Delta {\rm{S}}_{{\rm{aq}}}^0({{\rm{H}}^ + }) = - \;22.2{\rm{ }}J{K^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}$

in aqueous solution, a fundamental parameter of importance was determined using a number of extrathermodynamic assumptions of doubtful validity. The value can in no way be regarded to be absolute or correct and needs reassessment. However, no value of the entropy change due to hydration

Δ

S
h
0

(

H
+

)

$\Delta {\rm{S}}_{\rm{h}}^0({{\rm{H}}^ + })$

was available. Absolute values for entropy of hydration

[
Δ

S

abs

0

(

H
+

)

h

]

$[\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}]$

(entropy change for the transfer of H+ ion from gaseous (g) state to H+ ion in aqueous solution) or entropy of aquation

[
Δ

S

abs

0

(

H
+

)

aq

]

$[\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}]$

(entropy change for transfer of H(g) to aqueous

H

ion

+

)

${\rm{H}}_{{\rm{ion}}}^ + )$

of H+ ion can only be calculated if the related absolute values of Gibbs energy or enthalpy changes of H+ ion i.e.

[
Δ

G

abs

0

(

H
+

)

h or aq

$[\Delta {\rm{G}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\text{h or aq}}}}$

and

Δ

H

abs

0

(

H
+

)

h or aq

]

$\Delta {\rm{H}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\text{h or aq}}}}]$

are known. Critical analysis of the methods used for evaluation of thermodynamics of H+ ion was made. Analysis of the methods showed that the methods had limitations due to defective use of Born equation and ionic additivity principle. Reference electrolyte method using TATB (tetraphenyl arsonium tetraphenyl borate, Ph4AsBPh4), Halliwell and Nyburg’s method and Noyes method or modified Noyes method of Lahiri do not give entropy values. Cluster-ion approximation method (used by Coe and co-workers) gives

Δ

H

abs

0

(

H
+

)

h

$\Delta {\rm{H}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$

and

Δ

G

abs

0

(

H
+

)

h

$\Delta {\rm{G}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$

and hence

Δ

S

abs

0

(

H
+

)

h

=
−

153.0

JK

−
1

mol

−
1

.

Δ

S

abs

0

(

H
+

)

aq

$\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}} = - \;153.0{\rm{ J}}{{\rm{K}}^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}.\;\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}$

is obtained by coupling

Δ

S

abs

0

(

H
+

)

h

$\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$

with

Δ

S

abs

0

(

H
+

)

g

$\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{g}}}$

[entropy of gaseous H+ ion calculated using Sackur-Tetrode equation], comes out to be –44.2 JK−1mol−1. However,

Δ

S

abs

0

(

H
+

)

h

$\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$

and

Δ

S

abs

0

(

H
+

)

aq

$\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}$

determined by Lahiri and co-workers are –50.0 JK−1mol−1 and 20.0 JK−1mol−1. The values can be regarded to be accurate and reliable. Some comments on the surface potential of water towards

Δ

G

h or aq

0

(

H
+

)

$\Delta {\rm{G}}_{{\text{h or aq}}}^0({{\rm{H}}^ + })$

and error ranges on the energetics of H+ and other ions are given. No attempt was made to determine entropy of hydration or aquation from theoretical calculations.