Reaktoro 
A unified framework for modeling chemically reactive systems
Reaktoro::DebyeHuckelParams Class Reference

Detailed Description

A class used to define the parameters in the Debye–Hückel activity model for aqueous mixtures.

An instance of this class can be used to control how activity coefficients of ionic and neutral species, \(\gamma_i\) and \(\gamma_n\) respectively, as well as the activity of solvent water, \(a_\mathsf{H_2O(l)}\), are calculated using the Debye–Hückel activity model.

The activity coefficients of ionics species are calculated using the following modified Debye–Hückel equation[5]:

\[\log\gamma_{i}=-\dfrac{AZ_{i}^{2}\sqrt{I}}{1+B\mathring{a}_{i}\sqrt{I}}+b_{i}I,\]

while the activity coefficients of neutral species are calculated using:

\[\log\gamma_{n}=b_{n}I.\]

In these equations, \(Z_i\) is the electrical charge of the ionic species; \(\mathring{a}_i\) is the size or an effective diameter of the ionic species (in units of \(\mathrm{Å}\), where \(1 \mathrm{Å}=10^{-10}\text{m}\)); \(I\) is the ionic strength of the aqueous solution (in units of molality), calculated using:

\[I=\frac{1}{2}\sum_{j}m_{j}Z_{j}^{2},\]

with \(m_{j}\) denoting the molality of the \(j\)th ion. The constants \(A\) and \(B\) in the Debye–Hückel model are calculated using (see Anderson and Crerar (1993)[1], page 439, and Langmuir (1997)[5], page 128):

\[A=1.824829238\cdot10^{6}\rho_{\mathrm{H_{2}O}}^{1/2}(\epsilon_{\mathrm{H_{2}O}}T)^{-3/2}\]

and

\[B=50.29158649\rho_{\mathrm{H_{2}O}}^{1/2}(\epsilon_{\mathrm{H_{2}O}}T)^{-1/2},\]

with \(A\) in units of \(\mathrm{(mol/kg)^{-1/2}}\) and \(B\) in units of \(\mathrm{(mol/kg)^{-1/2}}/\mathrm{Å}\). In these equations, \(T\) is temperature (in units of K); \(\epsilon_{\mathrm{H_{2}O}}\) is the dielectric constant of pure water (dimensionless), calculated using the Johnson and Norton (1991) model (see waterElectroStateJohnsonNorton); and \(\rho_{\mathrm{H_{2}O}}\) is the density of pure water (in units of \(\mathrm{g/cm^{3}}\)), calculated using either the equation of state of Haar–Gallagher–Kell (1984)[3] or the equation of state of Wagner and Pruss (2002)[7] (see waterThermoStateHGK and waterThermoStateWagnerPruss).

The activity of water is calculated using the following equation:

\[\log a_{w}=-\frac{1}{n_{w}^{\circ}}\left[\frac{m_{\Sigma}}{2.303}+\sum_{i}^{{\scriptscriptstyle \mathrm{ions}}}m_{i}\log\gamma_{i}+\frac{2}{3}AI^{\frac{3}{2}}\sum_{i}^{{\scriptscriptstyle \mathrm{ions}}}\sigma(\Lambda_{i})-I^{2}\sum_{i}^{{\scriptscriptstyle \mathrm{ions}}}\frac{b_{i}}{Z_{i}^{2}}\right],\]

which is thermodynamically consistent with the previous equations for the activity coefficients of both ionic and neutral species, since it was derived from the Gibbs–Duhem equation. In this equation, \(n_{w}^{\circ}=55.508472\) is the number of moles of water per kilogram; \(m_{\Sigma}\) is the sum of the molalities of all solutes (both ionic and neutral species); and \(\sigma(\Lambda_{i})\) is defined as:

\[\sigma(\Lambda_{i})=\frac{3}{(\Lambda_{i}-1)^{3}}\left[(\Lambda_{i}-1)(\Lambda_{i}-3)+2\ln \Lambda_{i}\right],\]

with \(\Lambda_{i}\) given by:

\[\Lambda_{i}=1+B\mathring{a}_{i}\sqrt{I}.\]

Usage Example:**

Use member methods aion and bion to set the effective ion-size parameter, \(\mathring{a}_i\), and the parameter \(b_i\) in the previous equations. Use method bneutral to set the parameter \(b_n\) of a neutral species.

using namespace Reaktoro; {delete}
DebyeHuckelParams debyehuckel;
debyehuckel.aion("Ca++", 5.0);
debyehuckel.bion("Ca++", 0.165);
debyehuckel.bneutral("O2(aq)", 0.2);

#include <AqueousChemicalModelDebyeHuckel.hpp>

Public Member Functions

 DebyeHuckelParams ()
 Construct a default DebyeHuckelParams instance.
 
auto aiondefault (double value) -> void
 Set the default ion-size parameter value to be used for ionic species lacking such data. More...
 
auto aiondefault () const -> double
 Return the default ion-size parameter value to be used for ionic species lacking such data.
 
auto aion (std::string name, double value) -> void
 Set the ion-size parameter value of a given ionic species (in units of Å). More...
 
auto aion (const std::map< std::string, double > &pairs) -> void
 Set the ion-size parameter values of several ionic species (in units of Å). More...
 
auto aion (double value) -> void
 Set the ion-size parameter of all ionic species to a common value. More...
 
auto aion (std::string name) const -> double
 Return the ion-size parameter value of a given ionic species (in units of Å). More...
 
auto biondefault (double value) -> void
 Set the default Debye–Hückel parameter b to be used for ionic species lacking such data. More...
 
auto biondefault () const -> double
 Return the default Debye–Hückel parameter b to be used for ionic species lacking such data.
 
auto bion (std::string name, double value) -> void
 Set the value of the Debye–Hückel parameter b of a given ionic species. More...
 
auto bion (const std::map< std::string, double > &pairs) -> void
 Set the value of the Debye–Hückel parameter b of several ionic species (in units of Å). More...
 
auto bion (double value) -> void
 Set the Debye–Hückel parameter b of all ionic species to a common value. More...
 
auto bion (std::string name) const -> double
 Return the value of the b parameter of a given ionic species. More...
 
auto bneutraldefault (double value) -> void
 Set the default value of the b parameter to be used neutral species lacking such data. More...
 
auto bneutraldefault () const -> double
 Return the default value of the b parameter to be used neutral species lacking such data.
 
auto bneutral (std::string name, double value) -> void
 Set the value of the b parameter of a given neutral species. More...
 
auto bneutral (const std::map< std::string, double > &pairs) -> void
 Set the value of the b parameter of several neutral species. More...
 
auto bneutral (double value) -> void
 Set the value of the b parameter of all neutral species to a common value. More...
 
auto bneutral (std::string name) const -> double
 Return the value of the b parameter of a given neutral species. More...
 
auto setLimitingLaw () -> void
 Set the Debye–Hückel limiting law model for the ionic species. More...
 
auto setKielland1937 () -> void
 Set the ion-size parameters according to the values given in Kielland (1937)[4]. More...
 
auto setWATEQ4F () -> void
 Set the Debye–Hückel parameters and b of the ionic species according to WATEQ4F[6] [2]. More...
 
auto setPHREEQC () -> void
 Set the Debye–Hückel parameters and b of the species according to PHREEQC v3. More...
 

Member Function Documentation

auto Reaktoro::DebyeHuckelParams::aiondefault ( double  value) -> void

Set the default ion-size parameter value to be used for ionic species lacking such data.

Parameters
valueThe default ion-size parameter value
auto Reaktoro::DebyeHuckelParams::aion ( std::string  name,
double  value 
) -> void

Set the ion-size parameter value of a given ionic species (in units of Å).

Parameters
nameThe name of the ionic species
valueThe ion-size parameter value (in units of Å)
auto Reaktoro::DebyeHuckelParams::aion ( const std::map< std::string, double > &  pairs) -> void

Set the ion-size parameter values of several ionic species (in units of Å).

Parameters
pairsThe pairs (name, value) for the ion-size parameters of the ionic species
auto Reaktoro::DebyeHuckelParams::aion ( double  value) -> void

Set the ion-size parameter of all ionic species to a common value.

Warning
This method overwrites all previously assigned ion-size parameter values. It also overwrites the default value of the ion-size parameter that is used for those ions lacking such data.
Parameters
valueThe common ion-size parameter value (in units of Å)
auto Reaktoro::DebyeHuckelParams::aion ( std::string  name) const -> double

Return the ion-size parameter value of a given ionic species (in units of Å).

Parameters
nameThe name of the ionic species
auto Reaktoro::DebyeHuckelParams::biondefault ( double  value) -> void

Set the default Debye–Hückel parameter b to be used for ionic species lacking such data.

Parameters
valueThe default parameter b value for ionic species
auto Reaktoro::DebyeHuckelParams::bion ( std::string  name,
double  value 
) -> void

Set the value of the Debye–Hückel parameter b of a given ionic species.

Parameters
nameThe name of the ionic species
valueThe value of the b parameter
auto Reaktoro::DebyeHuckelParams::bion ( const std::map< std::string, double > &  pairs) -> void

Set the value of the Debye–Hückel parameter b of several ionic species (in units of Å).

Parameters
pairsThe pairs (name, value) for the parameter b of the ionic species
auto Reaktoro::DebyeHuckelParams::bion ( double  value) -> void

Set the Debye–Hückel parameter b of all ionic species to a common value.

Warning
This method overwrites all previously assigned values for the b parameter of ionic species. It also overwrites the default b value that is used for those ions lacking such data.
Parameters
valueThe common value for the b parameter of the ionic species
auto Reaktoro::DebyeHuckelParams::bion ( std::string  name) const -> double

Return the value of the b parameter of a given ionic species.

Parameters
nameThe name of the ionic species
auto Reaktoro::DebyeHuckelParams::bneutraldefault ( double  value) -> void

Set the default value of the b parameter to be used neutral species lacking such data.

Parameters
valueThe default parameter b value for neutral species
auto Reaktoro::DebyeHuckelParams::bneutral ( std::string  name,
double  value 
) -> void

Set the value of the b parameter of a given neutral species.

Parameters
nameThe name of the neutral species
valueThe value of the b parameter
auto Reaktoro::DebyeHuckelParams::bneutral ( const std::map< std::string, double > &  pairs) -> void

Set the value of the b parameter of several neutral species.

Parameters
pairsThe pairs (name, value) for the parameter b of the neutral species
auto Reaktoro::DebyeHuckelParams::bneutral ( double  value) -> void

Set the value of the b parameter of all neutral species to a common value.

Warning
This method overwrites all previously assigned values for the b parameter of neutral species. It also overwrites the default b value that is used for those neutral species lacking such data.
Parameters
valueThe common value for the b parameter of neutral species
auto Reaktoro::DebyeHuckelParams::bneutral ( std::string  name) const -> double

Return the value of the b parameter of a given neutral species.

Note
This method returns the default b value for the neutral species if the given speciesof the b parameter for the neutral species that was previously define
Parameters
nameThe name of the neutral species
auto Reaktoro::DebyeHuckelParams::setLimitingLaw ( ) -> void

Set the Debye–Hückel limiting law model for the ionic species.

Use this method to indicate that the activity coefficients of the ionic species are calculated using the Debye–Hückel limiting law equation.

Warning
This method sets the default values of the Debye–Hückel parameters and b of the ionic species to zero. It also overwrites previously set values for and b of the ionic species.
Note
This method is equivalent to calling methods aion and bion with argument 0.0. For example, params.aion(0.0); params.bion(0.0);.
See also
aion, bion
auto Reaktoro::DebyeHuckelParams::setKielland1937 ( ) -> void

Set the ion-size parameters according to the values given in Kielland (1937)[4].

This method sets the values of ion-size parameters of the ionic species according to those given in Kielland (1937)[4], which is summarized in the following table:

Ion (Ångström)
H+ 9
Li+ 6
Rb+, Cs+, NH4+, Tl+, Ag+ 2.5
K+, Cl-, Br-, I-, CN-, NO2-, NO3- 3
OH-, F-, NCS-, NCO-, HS-, ClO3-, ClO4-, BrO3-, IO4-, MnO4- 3.5
Na+, CdCl+, ClO2-, IO3-, HCO3-, H2PO4-, HSO3-, H2AsO4-, Co(NH3)4(NO2)2+ 4-4.5
Hg2++, SO4--, S2O3--, S2O6--, S2O8--, SeO4--, CrO4--, HPO4-- 4
Pb++, CO3--, SO3--, MoO4--, Co(NH3)5Cl++, Fe(CN)5NO-- 4.5
Sr++, Ba++, Ra++, Cd++, Hg++, S--, S2O4--, WO4-- 5
Ca++, Cu++, Zn++, Sn++, Mn++, Fe++, Ni++, Co++ 6
Mg++, Be++ 8
PO4---, Fe(CN)6---, Cr(NH3)6+++, Co(NH3)6+++, Co(NH3)5H2O+++ 4
Al+++, Fe+++, Cr+++, Sc+++, Y+++, La+++, In+++, Ce+++, Pr+++, Nd+++, Sm+++ 9
Fe(CN)6---- 5
Co(S2O3)(CN)5---- 6
Th++++, Zn++++, Ce++++, Sn++++ 11
Co(SO3)2(CN)4----- 9
Warning
This method overwrites previously assigned values of for those ionic species in the table above.
Note
This method leaves unchanged the Debye–Hückel parameters b of the ionic species.
auto Reaktoro::DebyeHuckelParams::setWATEQ4F ( ) -> void

Set the Debye–Hückel parameters and b of the ionic species according to WATEQ4F[6] [2].

This method sets both and b of ionic species according to the ones used in WATEQ4F (Ball and Nordstrom [2], Truesdell and Jones cite Truesdell1974), which is listed in the following table:

Ion (Å) b
Ca++ 5.0 0.165
Mg++ 5.5 0.20
Na+ 4.0 0.075
K+ 3.5 0.015
Cl- 3.5 0.015
SO4-- 5.0 -0.04
HCO3- 5.4 0.0
CO3-- 5.4 0.0
Sr++ 5.26 0.121
H+ 9.0 0.0
OH- 3.5 0.0
SrHCO3+ 5.4 0.0
SrOH+ 5.0 0.0
Cu(S4)2--- 23.0 0.0
CuS4S5--- 25.0 0.0
S2-- 6.5 0.0
S3-- 8.0 0.0
S4-- 10.0 0.0
S5-- 12.0 0.0
S6-- 14.0 0.0
Ag(S4)2--- 22.0 0.0
AgS4S5--- 24.0 0.0
Ag(HS)S4-- 15.0 0.0

These values for and b are empirical. They were determined by fitting the modified Debye–Hückel equation to experimental mean-salt activity coefficient data.

Warning
This method overwrites previously assigned values of and b for those ionic species in the table above.

References:

  • Ball, J. W., Nordstrom, D. K. (1991). User’s Manual for WATEQ4F, with revised thermodynamic data base and test cases for calculating speciation of major, trace, and redox elements in natural waters. U.S. Geological Survey Water-Resources Investigations Report, 91–183, 1–188.
  • Truesdell, A. H., Jones, B. F. (1974). WATEQ–A computer program for calculating chemical equilibrium of natural waters. U.S. Geological Survey, Journal of Research, 2(2), 233–248.
auto Reaktoro::DebyeHuckelParams::setPHREEQC ( ) -> void

Set the Debye–Hückel parameters and b of the species according to PHREEQC v3.

This method sets the ion-size parameters and the parameter b of the ionic species according to those used in PHREEQC v3 when the phreeqc.dat database file is used, which are listed in the following table:

Ion (Å) b Ion (Å) b
Al(OH)2+ 5.4 0 Al(OH)4- 4.5 0
Al(SO4)2- 4.5 0 Al+++ 9 0
AlF++ 5.4 0 AlF2+ 5.4 0
AlF4- 4.5 0 AlOH++ 5.4 0
AlSO4+ 4.5 0 Ba++ 4 0.153
BaOH+ 5 0 Br- 3 0
CO3-- 5.4 0 Ca++ 5 0.165
CaH2PO4+ 5.4 0 CaHCO3+ 6 0
CaPO4- 5.4 0 Cl- 3.63 0.017
Cu+ 2.5 0 Cu++ 6 0
CuCl+ 4 0 CuCl2- 4 0
CuCl3- 4 0 CuCl3-- 5 0
CuCl4-- 5 0 CuOH+ 4 0
F- 3.5 0 Fe(OH)2+ 5.4 0
Fe(OH)3- 5 0 Fe(OH)4- 5.4 0
Fe++ 6 0 Fe+++ 9 0
FeCl++ 5 0 FeCl2+ 5 0
FeF++ 5 0 FeF2+ 5 0
FeH2PO4+ 5.4 0 FeH2PO4++ 5.4 0
FeHPO4+ 5 0 FeOH+ 5 0
FeOH++ 5 0 FeSO4+ 5 0
H+ 9 0 H2PO4- 5.4 0
H2SiO4-- 5.4 0 H3SiO4- 4 0
HCO3- 5.4 0 HPO4-- 5 0
HS- 3.5 0 K+ 3.5 0.015
KHPO4- 5.4 0 KSO4- 5.4 0
Li+ 6 0 LiSO4- 5 0
Mg++ 5.5 0.2 MgF+ 4.5 0
MgH2PO4+ 5.4 0 MgHCO3+ 4 0
MgOH+ 6.5 0 MgPO4- 5.4 0
Mn(OH)3- 5 0 Mn++ 6 0
Mn+++ 9 0 MnCl+ 5 0
MnCl3- 5 0 MnF+ 5 0
MnHCO3+ 5 0 MnOH+ 5 0
NH4+ 2.5 0 NO2- 3 0
NO3- 3 0 Na+ 4.08 0.082
NaHPO4- 5.4 0 NaSO4- 5.4 0
OH- 3.5 0 PO4--- 4 0
S-- 5 0 SO4-- 5 -0.04
SiF6-- 5 0 Sr++ 5.26 0.121
SrHCO3+ 5.4 0 SrOH+ 5 0
Zn++ 5 0 ZnCl+ 4 0
ZnCl3- 4 0 ZnCl4-- 5 0
Note
This method also sets the default value of b for neutral species to 0.1, which is the default value used in PHREEQC.

References:

  • Parkhurst, D. L., Appelo, C. A. J. (2013). Description of input and examples for PHREEQC version 3 — A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. In Groundwater Book 6, Modeling Techniques (p. 497). U.S. Geological Survey Techniques and Methods.

The documentation for this class was generated from the following files: