borates kaj thomsen

Thermodynamic Modeling of the Solubility of Alkali and Earth Alkali Borates

Kaj Thomsen, Associate Professor

CERE, Center for Energy Resources Engineering

Department of Chemical and Biochemical Engineering

Technical University of Denmark

24-07-2012 Thermodynamic Modeling of the Solubility of Alkali and Earth Alkali Borates

2 DTU Chemical Engineering, Technical University of Denmark

Importance of borates

• Metabolizing effects – useful for controlling insects and bacteria

• Bleaching effects – useful in laundry detergents

• Buffering effects – widely used for controlling pH

• Dispersing effects – useful in paints, adhesives and cosmetics

• Vitrifying effects – modify the structure of glass, facilitate the production of LCD screens

• Inhibiting effects – forms a coating that protect metals from corrosion

• Flame-Proofing effects – useful as a flame retardant

• Neutron-Absorbing effects – useful in connection with certain hospital equipment and nuclear containment shields

• Micro nutrient for plants

• Glazing on ceramics

• Largest single use worldwide is as an ingredient in fiberglass



Complexity of borates

• The chemical formulae for borates are often written in terms of the amounts of oxides:

Na2O B2O3 H2O Formula 1 Formula 2

1 1 1 Na2O•B2O3•H2O NaBO2•½H2O

1 1 4 Na2O•B2O3•4H2O NaBO2•2H2O

1 1 8 Na2O•B2O3•8H2O NaBO2•4H2O

1 2 Na2O•2B2O3 Na2B4O7

1 2 4 Na2O•2B2O3•4H2O Na2B4O7•4H2O

1 2 10 Na2O•2B2O3•10H2O Na2B4O7•10H2O

1 5 10 Na2O•5B2O3•10H2O NaB5O8•5H2O

2 1 1 2Na2O•B2O3•H2O NaBO2•NaOH

2 5 7 2Na2O•5B2O3•7H2O Na4B10O17•7H2O

2 9 11 2Na2O•9B2O3•11H2O Na4B18O29•11H2O



Complexity of borates

• In this work, all borate species were expressed in terms of:

– H3BO3(aq), Boric acid

– B4O72-, Tetraborate ion

– BO2-, Metaborate ion

• B2O3 is considered to be a dehydrated form of Boric acid:

2H3BO3(aq) ↔ B2O3 + 3H2O

• B5O8- is formed when pH is raised:

5H3BO3(aq) + OH- ↔ B5O8- + 8H2O

• Tetraborate, B4O72- +is formed at slightly higher pH:

4H3BO3(aq) + 2OH- ↔ = B4O72- + 7H2O

• Metaborate, BO2- is formed when pH is increased more:

H3BO3(aq) +OH- ↔ BO2- + 2H2O



Extended UNIQUAC model

• Not a new model but new parameters

– Original parameters were limited in terms of temperature, concentration, and pH

• Thermodynamic model for solutions containing electrolytes

– Debye-Hückel term for electrostatic interactions

– UNIQUAC term for short range interactions

– Soave-Redlich-Kwong term for gas phase fugacities

• The model is used for calculation of

– Speciation equilibrium

– Solid-liquid equilibrium

– Vapor liquid equilibrium

– Liquid-liquid equilibrium

– Thermal properties




• Relative permittivity for pure water is used for all solutions

– The effect of other species on the chemical potentials in the solution is accounted for by interaction parameters

• The hydrogen ion is given fixed parameters, including interaction parameters with all other species

– The hydrogen ion is considered an anchor for the parameters

– The properties of all other species are determined relative to those of the hydrogen ion

• The temperature dependence of chemical potentials is determined by the Gibbs-Helmholtz equation:

0 0

2

/ln at constant pressure

d G RTd K H

dT dT RT



Model parameters and standard state properties • Volume and surface area parameters for each species

– 6 parameters

• A binary interaction parameter for each pair of species

– 26 interaction parameters were used

– 5 of these have linear temperature dependency

• Values of the Gibbs energy of formation for ions is usually found in the NIST tables

• Values not found in the NIST tables were determined during parameter estimation:

– Enthalpy of formation of the tetraborate ion, B4O72-

– Gibbs energy of formation for 22 solid phases

– Enthalpy of formation for 20 solid phases



Determination of parameters

• The adjustable parameters were determined using a modified Marquard routine from Harwell subroutine library and a Nelder-Mead simplex routine

• Parameter determination:

1. Core system consisting of H+, Li+,Na+, K+, Mg2+, Ca2+, OH-, Cl-, HCl, NO3

-, HNO3, SO42-, HSO4

- based on ca. 27000 experimental data points distributed on 23 binary and 87 ternary systems.

2. 3000 experimental data for borates in the above systems except HNO3 were used for

• Determining the 6+26 model parameters for the borate species

• Determining the 43 standard state properties for the various solid phases and the tetraborate ion



Online experimental data bank - free

• Data bank for electrolyte solutions at http://www.cere.dtu.dk/Expertise/

• Over 150,000 experimental data on electronic form

• More than 350 solute species

• Types of data include:

– Activity/osmotic coefficient

– Enthalpy of mixing

– Heat capacity

– Degree of dissociation

– Gas solubility

– Enthalpy of absorption/evaporation

– Density

– Salt solubility (Solid-liquid equilibrium)

– Liquid-liquid equilibrium

– Vapor-liquid equilibrium



-5

15

35

55

75

95

115

0 5 10 15 20 25 30

Tem

peratu

re °

C

Weight percent Na2B4O7

Horn and Van Wagener (1905)

Teeple (1929)

Blasdale and Slansky (1939)

Nies and Hulbert (1967)

Platford (1971)


Na2B4O7·10H2O Borax

Na2B4O7·4H2O Kernite



0%

1%

2%

3%

4%

5%

6%

0% 10% 20% 30% 40%

wt

% H

3B

O3

wt % MgCl2

Extended UNIQUAC

Gode (1969)

H3BO3

MgCl2·6H2O

25°C



0

10

20

30

40

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

mo

l H

2O

/(m

ol

Na

2O

+B

2O

3)

Na2O/(Na2O+B2O3) molar ratio

Extended UNIQUAC

Nies and Hulbert (1967)

Sborgi and Mecacci (1916)

60°C

H3BO3

Sassolite

NaB5O8·5H2O Sborgite

Na2B4O7·10H2O Borax

NaBO2·4H2O NaBO2·½H2O

NaOH·H2O

Na4B10O17·7H2O Excurrite

2Na2O·B2O3·H2O

NaBO2·2H2O



0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1

H2O

/(K

2O

+B

2O

3) m

ol

basis

K2O/(K2O+B2O3) mol basis

Carpeni (1955)

Extended UNIQUAC

45°C H3BO3 KB5O8·4H2O

K2B4O7·4H2O

KBO2·H2O KOH·H2O



0

50

100

150

200

250

300

350

400

450

500

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

H2O

/(M

gO

+B

2O

3 m

ol

ba

sis)

MgO/(MgO+B2O3) mol basis

D'Ans and Behrent (1957)

Extended UNIQUAC

83°C

H3BO3

MgO·3B2O3·7.5H2O

MgB2O4·3H2O



0

500

1000

1500

2000

2500

0 0.2 0.4 0.6 0.8 1

H2O

/(C

aO

+B

2O

3)

mo

l b

asi

s

CaO/(CaO+B2O3) mol basis

Sborgi (1913)

Extended UNIQUAC

30°C

Ca(OH)2

CaB2O4·6H2O

2CaO·3B2O3·13H2O Inyoite

CaO·3B2O3·4H2O H3BO3



0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50

Li 2

B4O

7

LiCl

T= 25.0°C

Extended UNIQUAC modelLepeshkov et al. (1963)Skvortsov et al. (1981)

Li2B4O7·3H2O

LiCl·H2O



0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Li+

C

ation C

harg

e fra

ction

K+

SO42- Anion charge fraction B4O7

2-

T= 14.9°C

Sang et al. (2004)Sang et al. (2006) -metastableZeng et al. (2005)Zeng et al. (2007)Extended UNIQUAC model

Li2SO4·K2SO4

K2SO4

Li2SO4·H2O

K2B4O7·4H2O

Li2B4O7·3H2O



Conclusion

• The complex system of alkali and earth alkali borates could be modeled using a relatively simple model with only a few parameters

• The system was modeled considering only three aqueous species H3BO3(aq), B4O7

2-, BO2-

• Can the modeling be improved by including B5O8- ?

• Most of the model parameters were not temperature dependent

• Many experimental solubility data are conflicting – better solubility data are needed!

• Meta stability is an issue in this system

Thank you very much for your attention



Model implementation

• The model is implemented in a dynamic link library (DLL-file)

– Multi-phase flash algorithm

– The program can be called from programs that have a Visual Basic interface such as Microsoft Excel

– Simulations can be carried out directly in Excel

– The excel sheet can be used as an interface to Aspen Plus®

– The model can be implemented as a user model in Aspen Plus®

borates kaj thomsen

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