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