THERMOCHEMICAL DATA FROM SOLUBILITIES
Statement
Deduce the standard thermochemical data of solution of oxygen in water from its solubility data.
Calcular los datos termoquímicos del proceso de disolución del dióxido de carbono en agua, a partir
de su curva de solubilidad.
Solution
We start from the following data, extracted from the tabulation in Solubility data for aqueous
solutions, although the whole solubility curve for oxygen in water from 0 ºC to 100 ºC is readily
available too.
Table 1. Gas solubility data in liquids and solids. The quotient ci,liq/ci,gas or ci,sol/ci,gas is presented, i.e.
the so-called Ostwald solubility coefficient, Kcc (in mol/m3 of solute in solution, per mol/m3 of
solute in its pure phase); other forms of Henry law constant are also in common use, as
Kp=KccRuT/Mi (in kg/m3 of solute in solution, per unit partial-pressure of solute in its pure
phase; e.g. for CO2 at 273, Kcc=1.8 implies Kp=KccRuT/Mi=1.8·8.3·273/0.044=0.93
(kg/m3)/bar).
Mixture
O2(g) in H2O(l)
at 273 K at 288 K
0.044
0.036
at 298 K
at 323 K
0.032 (=23 ppm_mol/bar=1.3 (mol/m3)/bar)
0.025
Applying the general thermochemical relation:
ln
K cp (T )  g r (T )
K cc (T )
0.032
kJ




g
(
T
)

R
T
ln
 8.3  298·ln 3
 16.4
r
u






5
c p
RuT
c RuT p
10  8.3  298 10
mol
where the standard values used are c=1 mol/L, T=298 K, p=1 bar=105 Pa. The comparison with the
value of gr tabulated in Thermochemical data of solutes (extracted below), is perfect.
Table 2. Standard thermochemical data for some solutes, either pure at 298 K and 100 kPa, or in
infinitely dilute aqueous solution at 298 K, 100 kPa and extrapolated to 1 mol/L, including in
the latter case the standard electrochemical data for the reduction reaction.
Solute
hf 
gf 
s
Reaction of formation
(state)
kJ/mol kJ/mol J/(mol K)
-11.7
16.4
111
O2(aq)
O2(g)=O2(aq)
0
0
205
O2(g)
O2(g)=O2(g)
Applying now van't Hoff's thermochemical relation:
d ln
K cc
K 2cc
K cp
0.025
d
ln
ln
ln



cc
c
R
T
p
K
c  p  hr
0.053  11.0 kJ
u
1

 hr   Ru
  Ru
 8.3
1
1
1 1
1
1
Ru
mol
d
d


T
T
T2 T1
323 273
which compares not too bad with the hr value in Thermochemical data of solutes (11.0 against 11.7
kJ/mol), perhaps due to the discretization on the slope (we had computed the mean slope at 273 K and
323 K instead of the slope at the middle; a better curve-fitting gives hr=11.6 kJ/mol, perfectly
correcting the mismatch).
We can check for consistency in the tabulated Thermochemical data of solutes by means of the general
equation:
O2 ( g ) O2 ( aq )


g r  hr  T  sr 
 hr  g r  T   saq
 sgas
  16400  298 111  205  11.6
i.e. all tabulated data are coherent (11.6 against 11.7).
Comments
A graph of solubilities for several gases:
Fig. 1. Solubility curves for some gases in water at 100 kPa.
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kJ
mol  K