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