| Advanced solution in Thermodynamics
| Datasets of Aqueous Substances

5.6. Thermodynamic systems with aqueous Substances

Content
1.Calculation of the Solubility of Substances in water, Example AgNO3
1.1. AgNO3 Solubility in Water
1.2. State Functions of AgNO3[aq]
2.Example Na2SO4
2.1. Na2SO4 Solubility in Water
2.2. State Functions of Na2SO4[aq]
3. Process Modelling Using Datasets of Aqueous Substances,
heat- and mass balance of the desulfuration-process to battery recycling
4. Important notes for calculations using AsTher Applications Equilibrium and Process Calculator
5. Accuracy of the Datasets

5.6.1. Calculation of the solubility of substances in water based on the datasets
The datasets of the aqueous substances, like AgCl[aq], AgNO3[aq], NaCO3[aq], CaCO3[aq] etc.
valid for the sum of the all parts of the substance in the aqueous solution.
AgNO3[aq] contains all parts of the solved AgNO3 in water: AgNO30 , Ag+ and NO3-

mAgNO3[aq] = mAgNO3°+ mAg++ mNO3-

You can calculate also the solubility of a substance in water using the datasets of the aqueous substances.
For the solution equation

AgNO3 (s) = AgNO3[aq]

the equilibrium constant K is defined with

When AgNO3 exists as pure substance in the equilibrium state, then activity is one

At high concentrations we can write activity a nearly equal to mol fraction x

Equilibrium constant K is nearly equal to the mol fraction x of AgNO3[aq]

5.6.1.1. AgNO3 Solubility in Water

In the following graphic, the line shows the solubility of AgNO3 in water [g AgNO3/100 g water] in depend of the temperature,
which is calculated using AsTher Process Calculator for MS Excel und measured values given in different sources

Ref.:
Line AgNO3[aq]: Calculation result from AsTher Thermodynamic Database
[CRC] : CRC Handbook of Chemistry and Physics; CRC Press LLC 2004
[Perry]: Robert H. Perry; Cecil H. Chilton: Chemical Engineers’ Handbook; McGraw Hill, 1973

AgNO3 (s) = AgNO3[aq] (l)

T [ C ] | dH [J/mol] | dS [J/mol K] | dG [J/mol] | K | T dS [J/mol] | dCp [J/mol K]
0 | 22590.3 | 65.06 | 4818.63 | 0.11982 | 17771.6 | -0.00781
10 | 22590.2 | 64.25 | 4397.57 | 0.154437 | 18192.6 | -0.00588
20 | 22590.2 | 63.36 | 4016.11 | 0.192483 | 18574.1 | -0.00395
30 | 22590.1 | 62.4 | 3673.82 | 0.232797 | 18916.3 | -0.00202
40 | 22590.1 | 61.38 | 3370.28 | 0.274046 | 19219.8 | -0.00009
50 | 22590.1 | 60.3 | 3105.11 | 0.314835 | 19485 | 0.00184
60 | 22590.2 | 59.17 | 2877.94 | 0.353808 | 19712.2 | 0.00376
70 | 22590.2 | 58 | 2688.43 | 0.38973 | 19901.8 | 0.00569
80 | 22590.3 | 56.79 | 2536.27 | 0.42156 | 20054 | 0.00762
90 | 22590.4 | 55.54 | 2421.14 | 0.448486 | 20169.2 | 0.00955
100 | 22590.5 | 54.26 | 2342.77 | 0.469951 | 20247.7 | 0.01148

5.6.1.2. State Functions of AgNO3[aq] in AsTher Thermodynamic Database

AgNO3[aq] (l)

T [ C ] | Cp [J/mol C] | H [J/mol] | S [J/mol K] | G [J/mol]
0 | 88.31 | -104067 | 197.751 | -158083
10 | 90.21 | -103174 | 200.15 | -159847
20 | 92.1 | -102263 | 202.423 | -161603
25 | 93.05 | -101800 | 203.516 | -162478
30 | 93.99 | -101332 | 204.583 | -163351
40 | 95.89 | -100383 | 206.64 | -165092
50 | 97.78 | -99415 | 208.605 | -166825
60 | 99.67 | -98427 | 210.486 | -168551
70 | 101.57 | -97421 | 212.29 | -170268
80 | 103.46 | -96396 | 214.023 | -171978
90 | 105.35 | -95352 | 215.691 | -173680

5.6.2.Example Na2SO4

5.6.2.1. Na2SO4 Solubility in Water

Na2SO4[aq] -> Na2SO4 (s)

The solubilty of the Na2SO4 is calculated using datasets in AsTher and shown in the following graphic

Na2SO4[aq] -> Na2SO4 (s)

T [ C ] | dH [J/mol] | dS [J/mol K] | dG [J/mol] | K | T dS [J/mol] | dCp [J/mol C]
0 | -1688 | -49.187 | 11747 | 0.00567015 | -13436 | 0.0697
10 | -1688 | -43.160 | 10533 | 0.01140102 | -12221 | 0.0089
20 | -1688 | -36.821 | 9106 | 0.02385014 | -10794 | -0.0211
25 | -1688 | -33.542 | 8312 | 0.03497209 | -10001 | -0.0246
30 | -1688 | -30.195 | 7465 | 0.05172326 | -9154 | -0.0205
40 | -1683 | -29.398 | 7523 | 0.05561135 | -9206 | 0.0998
50 | -1682 | -29.538 | 7863 | 0.05358249 | -9545 | 0.0236
60 | -1682 | -29.632 | 8189 | 0.05199929 | -9872 | -0.0218
70 | -1683 | -29.678 | 8501 | 0.05080696 | -10184 | -0.0365
80 | -1683 | -29.679 | 8798 | 0.0499632 | -10481 | -0.0205
90 | -1683 | -29.636 | 9079 | 0.0494357 | -10762 | 0.0261
100 | -1682 | -29.550 | 9344 | 0.04920028 | -11027 | 0.1035

5.6.2.2. State Functions of Na2SO4[aq]

State functions of Na2SO4[aq] corresponding to the dataset in AsTher

T [ C ] | Cp [J/mol C] | H [J/mol] | S [J/mol K] | G [J/mol]
0 | 124 | -1392651 | 89.39 | -1417067
10 | 125 | -1391406 | 99.89 | -1419690
25 | 128 | -1389504 | 116.05 | -1424106
20 | 127 | -1390143 | 110.61 | -1422569
30 | 129 | -1388861 | 121.54 | -1425706
40 | 131 | -1387557 | 126.55 | -1427187
50 | 133 | -1386239 | 130.55 | -1428427
60 | 134 | -1384904 | 134.53 | -1429722
70 | 136 | -1383552 | 138.48 | -1431072
80 | 138 | -1382184 | 142.41 | -1432476
90 | 139 | -1380799 | 146.32 | -1433935
100 | 141 | -1379397 | 150.21 | -1435449

5.6.3. Process Modelling using Datasets of Aqueous Substances
Calculation of the heat- and mass balance of the desulfuration-process of the battery recycling

A directly reduction of the battery paste from recycling causes height SO2-concentration in exhausts of the furnaces for lead production.
Sometimes the paste is desulfurised using NaOH before the reductions process to lead production.

In the Desulfuration reactor, PbSO4 and NaOH react at 30-35°C:

PbSO4 (s) + 2 NaOH[aq] -> Na2SO4[aq]+ PbO (s)

NaSO4 is solved in water.

In the Crystallisation reactor, Na2SO4 (s) forms at 5°C:

Na2SO4[aq] -> Na2SO4 (s)

Paste | [kg]
As2O3 (s) | 0.01
BaSO4 (s) | 0.1
CaSO4 (s) | 1
CdO (s) | 0.01
CuSO4 (s) | 0.1
Fe2O3 (s) | 0.1
HgO (s) | 0.0001
PbCl2 (s) | 0.1
PbO (s) | 10
PbO.PbSO4 (s) | 87
PbSO4 (s) | 1
Sb2O3 (s) | 0.1
SiO2 (s) | 0.01
SnO2 (s) | 0.1
TlCl (s) | 0.001
ZnO (s) | 0.01
Sum | 99.64
Sulfur (in): | 5.68
Des. Paste | [kg]
As2O3 (s) | 0.0096
BaSO4 (s) | 0.1
CaSO4 (s) | 0.0093
CdO (s) | 0.01
Cu (s) | 0.04
Fe2O3 (s) | 0.1
Fe3O4 (s) | 4.24E-05
FeO (s) | 0.00015
Hg (l) | 9.26E-05
NaCl (s) | 0.039
Pb (s) | 5.67
PbO (s) | 78.54
Sb2O3 (s) | 0.1
SnO2 (s) | 0.1
TlAsO4 (s) | 0.00143
ZnO (s) | 0.010009
Sum | 84.73
Sulfur (out): | 0.01
Cryst. | [kg]
As2O3 (s) | 3.4163E-05
CaO (s) | 2.5976E-07
Na2S (s) | 0.5
Na2SO4 (s) | 24.2
NaCl (s) | 0.0035
Sum | 24.7
Sulfur (out): | 5.67

5.6.4. Important notes for calculations using AsTher Application Equilibrium or Process Calculator

When you define sometimes liquid phase and solid phase as following

Liquids

(l) | In [kg] | Out [kg] | w% | a | a.c.
H2O | 603.31609 | 603.56581 | 83.534857 | 0.92307476 |
Na2SO4[aq] | 25.30796 | 0.19361783 | 0.02679714 | 3.7543E-05 |
NaCl[aq] | 0.00389118 | 0.00035148 | 4.8646E-05 | 1.6561E-07 |
NaOH[aq] | 105.77432 | 105.74997 | 14.636032 | 0.07283515 |
As2O3[aq] | 2.7464E-05 | 5.9543E-17 | 8.2408E-18 | 8.2938E-21 |
Ca(OH)2[aq] | 13.564981 | 13.021939 | 1.8022654 | 0.00484381 |

Solids

(s) | In [kg] | Out [kg] | w% | a | a.c.
Na2SO4 (s) |  | 24.206453 | 97.980256 | 4.69E-03 | -1
NaCl (s) |  | 0 | 0 | 0 | -1
NaOH (s) |  | 0 | 0 | 0 | -1
As2O3 (s) |  | 0 | 0 | 0 | -1
Ca(OH)2 (s) |  | 0 | 0 | 0 | -1

then you should enter in the column for Activity coefficient (a.c.)
-1 or (1): The formation of the substances is able, when the substance exist as pure substance, not in any mixture of solids.

When only the formation of the pure substances are permitted in calculations, the calculation my be several seconds longer.

When the formation of the substances not possible,
then you can deselect the substance from thermodynamic system or enter for zero Activity coefficient.

When you do not enter any data for activity coefficient,
then the substance is regarded in a solution or mixture, but not as pure substance.

5.6.5. References and Accuracy of the Datasets
The solubility data of the aqueous substances and enthalpy of the solution can not be always verified more than two different data sources.
We can not say, that the datasets were exact the real physical values.
But we can say, that the datasets can enable a process modelling sufficient to process design,
like Calculation of the heat- and mass-balance of the desulfuration-process of the battery recycling

Recommanded Source for thermodynamic data
ANDRA: Sélection de constantes thermodynamiques pour les éléments majeurs, le plomb et le cadmium, Jui"et 2006
Document Public
Centre scientifique et technique - Service Environnement et Procédés:
A comparation many datasets of the compounds of Al, C, Ca, Cd, Cl, K, Mg, N, Na, O, P, Pb, S etc. from different sources
the another known data sources
CODATA
NIST
JANAF
CRC (Handbook Chemistry and. Physic)
Thermochimie5
Perry (Chem. Eng. Handbook)
webserver.dmt.upm.es
intechopen.com
en.wikipedia.org