Internal Reference Documentation¶
Activity Correction API¶
pyEQL activity correction library
This file contains functions for computing molal-scale activity coefficients of ions and salts in aqueous solution.
Individual functions for activity coefficients are defined here so that they can be used independently of a pyEQL solution object. Normally, these functions are called from within the get_activity_coefficient method of the Solution class.
copyright: | 2013-2015 by Ryan S. Kingsbury |
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license: | LGPL, see LICENSE for more details. |
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pyEQL.activity_correction.
_debye_parameter_B
(temperature='25 degC')¶ Return the constant B used in the extended Debye-Huckel equation
Parameters: temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
Notes
The parameter B is equal to: [1]
\[B = ( {8 \pi N_A e^2 \over 1000 \epsilon k T} ) ^ {1 \over 2}\][1] Bockris and Reddy. /Modern Electrochemistry/, vol 1. Plenum/Rosetta, 1977, p.210. Examples
>>> _debye_parameter_B() 0.3291...
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pyEQL.activity_correction.
_debye_parameter_activity
(temperature='25 degC')¶ Return the constant A for use in the Debye-Huckel limiting law (base 10)
Parameters: temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
Returns: Quantity The parameter A for use in the Debye-Huckel limiting law (base e)
See also
Notes
The parameter A is equal to: [2]
\[A^{\gamma} = {e^3 ( 2 \pi N_A {\rho})^{0.5} \over (4 \pi \epsilon_o \epsilon_r k T)^{1.5}}\]Note that this equation returns the parameter value that can be used to calculate the natural logarithm of the activity coefficient. For base 10, divide the value returned by 2.303. The value is often given in base 10 terms (0.509 at 25 degC) in older textbooks.
References
[2] Archer, Donald G. and Wang, Peiming. “The Dielectric Constant of Water and Debye-Huckel Limiting Law Slopes.” /J. Phys. Chem. Ref. Data/ 19(2), 1990. Examples
>>> _debye_parameter_activity() 1.17499...
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pyEQL.activity_correction.
_debye_parameter_osmotic
(temperature='25 degC')¶ Return the constant A_phi for use in calculating the osmotic coefficient according to Debye-Huckel theory
Parameters: temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
See also
Notes
Not to be confused with the Debye-Huckel constant used for activity coefficients in the limiting law. Takes the value 0.392 at 25 C. This constant is calculated according to: [3] [4]
\[A^{\phi} = {1 \over 3} A^{\gamma}\]References
[3] Kim, Hee-Talk and Frederick, William Jr, 1988. “Evaluation of Pitzer Ion Interaction Parameters of Aqueous Electrolytes at 25 C. 1. Single Salt Parameters,” //J. Chemical Engineering Data// 33, pp.177-184. [4] Archer, Donald G. and Wang, Peiming. “The Dielectric Constant of Water and Debye-Huckel Limiting Law Slopes.” /J. Phys. Chem. Ref. Data/ 19(2), 1990. Examples
>>> _debye_parameter_osmotic() 0.3916...
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pyEQL.activity_correction.
_debye_parameter_volume
(temperature='25 degC')¶ Return the constant A_V, the Debye-Huckel limiting slope for apparent molar volume.
Parameters: temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
See also
Notes
Takes the value 1.8305 cm ** 3 * kg ** 0.5 / mol ** 1.5 at 25 C. This constant is calculated according to: [5]
\[A_V = -2 A_{\phi} R T [ {3 \over \epsilon} {{\partial \epsilon \over \partial p} } - {{1 \over \rho}{\partial \rho \over \partial p} }]\]NOTE: at this time, the term in brackets (containing the partial derivatives) is approximate. These approximations give the correct value of the slope at 25 degC and produce estimates with less than 10% error between 0 and 60 degC.
The derivative of epsilon with respect to pressure is assumed constant (for atmospheric pressure) at -0.01275 1/MPa. Note that the negative sign does not make sense in light of real data, but is required to give the correct result.
The second term is equivalent to the inverse of the bulk modulus of water, which is taken to be 2.2 GPa. [6]
References
[5] Archer, Donald G. and Wang, Peiming. “The Dielectric Constant of Water and Debye-Huckel Limiting Law Slopes.” /J. Phys. Chem. Ref. Data/ 19(2), 1990. [6] http://hyperphysics.phy-astr.gsu.edu/hbase/permot3.html Examples
TODO
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pyEQL.activity_correction.
_pitzer_B_MX
(ionic_strength, alpha1, alpha2, beta0, beta1, beta2)¶ Return the B_MX coefficient for the Pitzer ion interaction model.
\[B_MX = \beta_0 + \beta_1 f1(\alpha_1 I ^ {0.5}) + \beta_2 f2(\alpha_2 I ^ {0.5})\]Parameters: ionic_strength: number
The ionic strength of the parent solution, mol/kg
alpha1, alpha2: number
Coefficients for the Pitzer model, kg ** 0.5 / mol ** 0.5
beta0, beta1, beta2: number
Coefficients for the Pitzer model. These ion-interaction parameters are specific to each salt system.
Returns: float
The B_MX parameter for the Pitzer ion interaction model.
See also
References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
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pyEQL.activity_correction.
_pitzer_B_phi
(ionic_strength, alpha1, alpha2, beta0, beta1, beta2)¶ Return the B^Phi coefficient for the Pitzer ion interaction model.
\[B^\Phi = \beta_0 + \beta1 \exp(-\alpha_1 I ^{0.5}) + \beta_2 \exp(-\alpha_2 I ^ {0.5})\]or
\[B^\Phi = B^\gamma - B_{MX}\]Parameters: ionic_strength: number
The ionic strength of the parent solution, mol/kg
alpha1, alpha2: number
Coefficients for the Pitzer model, kg ** 0.5 / mol ** 0.5
beta0, beta1, beta2: number
Coefficients for the Pitzer model. These ion-interaction parameters are specific to each salt system.
Returns: float
The B^Phi parameter for the Pitzer ion interaction model.
References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
Beyer, R., & Steiger, M. (2010). Vapor Pressure Measurements of NaHCOO + H 2 O and KHCOO + H 2 O from 278 to 308 K and Representation with an Ion Interaction (Pitzer) Model. Journal of Chemical & Engineering Data, 55(2), 830–838. doi:10.1021/je900487a
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pyEQL.activity_correction.
_pitzer_f1
(x)¶ The function of ionic strength used to calculate eta_MX in the Pitzer ion intercation model.
\[f(x) = 2 [ 1- (1+x) \exp(-x)] / x ^ 2\]References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
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pyEQL.activity_correction.
_pitzer_f2
(x)¶ The function of ionic strength used to calculate eta_gamma in the Pitzer ion intercation model.
\[f(x) = -{2 \over x ^ 2} [ 1 - ({1+x+ x^2 \over 2}) \exp(-x)] \]References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
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pyEQL.activity_correction.
_pitzer_log_gamma
(ionic_strength, molality, B_MX, B_phi, C_phi, z_cation, z_anion, nu_cation, nu_anion, temperature='25 degC', b=<Quantity(1.2, 'kilogram ** 0.5 / mole ** 0.5')>)¶ Return the natural logarithm of the binary activity coefficient calculated by the Pitzer ion interaction model.
\[\ln \gamma_{MX} = -{|z_+ z_-| A^{Phi} ( I ^ {0.5} \over (1 + b I ^ {0.5})} + {2 \over b }\ln (1 + b I ^ {0.5}) )+ + {m (2 \nu_+ \nu_-) \over (\nu_+ + \nu_-)} (B_{MX} + B_{MX}^\Phi) + {m^2(3 (\nu_+ \nu_-)^{1.5} \over (\nu_+ + \nu_-))} C_{MX}^\Phi \]Parameters: ionic_strength: Quantity
The ionic strength of the parent solution, mol/kg
molality: Quantity
The concentration of the salt, mol/kg
B_MX,B_phi,C_phi: Quantity
Calculated paramters for the Pitzer ion interaction model.
z_cation, z_anion: int
The formal charge on the cation and anion, respectively
nu_cation, nu_anion: int
The stoichiometric coefficient of the cation and anion in the salt
temperature: str Quantity
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
b: number, optional
Coefficient. Usually set equal to 1.2 kg ** 0.5 / mol ** 0.5 and considered independent of temperature and pressure
Returns: float
The natural logarithm of the binary activity coefficient calculated by the Pitzer ion interaction model.
References
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
May, P. M., Rowland, D., Hefter, G., & Königsberger, E. (2011). A Generic and Updatable Pitzer Characterization of Aqueous Binary Electrolyte Solutions at 1 bar and 25 °C. Journal of Chemical & Engineering Data, 56(12), 5066–5077. doi:10.1021/je2009329
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pyEQL.activity_correction.
get_activity_coefficient_davies
(ionic_strength, formal_charge=1, temperature='25 degC')¶ Return the activity coefficient of solute in the parent solution according to the Davies equation.
Parameters: formal_charge : int, optional
The charge on the solute, including sign. Defaults to +1 if not specified.
ionic_strength : Quantity
The ionic strength of the parent solution, mol/kg
temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
Returns: float
The mean molal (mol/kg) scale ionic activity coefficient of solute
See also
Notes
Activity coefficient is calculated according to: [7]
\[\ln \gamma = A^{\gamma} z_i^2 ({\sqrt I \over (1 + \sqrt I)} + 0.2 I)\]Valid for 0.1 < I < 0.5
References
[7] Stumm, Werner and Morgan, James J. Aquatic Chemistry, 3rd ed, pp 103. Wiley Interscience, 1996.
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pyEQL.activity_correction.
get_activity_coefficient_debyehuckel
(ionic_strength, formal_charge=1, temperature='25 degC')¶ Return the activity coefficient of solute in the parent solution according to the Debye-Huckel limiting law.
Parameters: formal_charge : int, optional
The charge on the solute, including sign. Defaults to +1 if not specified.
ionic_strength : Quantity
The ionic strength of the parent solution, mol/kg
temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
Returns: float
The mean molal (mol/kg) scale ionic activity coefficient of solute
See also
Notes
Activity coefficient is calculated according to: [8]
\[\ln \gamma = A^{\gamma} z_i^2 \sqrt I\]Valid only for I < 0.005
References
[8] Stumm, Werner and Morgan, James J. Aquatic Chemistry, 3rd ed, pp 103. Wiley Interscience, 1996.
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pyEQL.activity_correction.
get_activity_coefficient_guntelberg
(ionic_strength, formal_charge=1, temperature='25 degC')¶ Return the activity coefficient of solute in the parent solution according to the Guntelberg approximation.
Parameters: formal_charge : int, optional
The charge on the solute, including sign. Defaults to +1 if not specified.
ionic_strength : Quantity
The ionic strength of the parent solution, mol/kg
temperature : str Quantity, optional
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
Returns: float
The mean molal (mol/kg) scale ionic activity coefficient of solute
See also
Notes
Activity coefficient is calculated according to: [9]
\[\ln \gamma = A^{\gamma} z_i^2 {\sqrt I \over (1 + \sqrt I)}\]Valid for I < 0.1
References
[9] Stumm, Werner and Morgan, James J. Aquatic Chemistry, 3rd ed, pp 103. Wiley Interscience, 1996.
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pyEQL.activity_correction.
get_activity_coefficient_pitzer
(ionic_strength, molality, alpha1, alpha2, beta0, beta1, beta2, C_phi, z_cation, z_anion, nu_cation, nu_anion, temperature='25 degC', b=1.2)¶ Return the activity coefficient of solute in the parent solution according to the Pitzer model.
Parameters: ionic_strength: Quantity
The ionic strength of the parent solution, mol/kg
molality: Quantity
The molal concentration of the parent salt, mol/kg
alpha1, alpha2: number
Coefficients for the Pitzer model. This function assigns the coefficients proper units of kg ** 0.5 / mol ** 0.5 after they are entered.
beta0, beta1, beta2, C_phi: number
Coefficients for the Pitzer model. These ion-interaction parameters are specific to each salt system.
z_cation, z_anion: int
The formal charge on the cation and anion, respectively
nu_cation, nu_anion: int
The stoichiometric coefficient of the cation and anion in the salt
temperature: str Quantity
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
b: number, optional
Coefficient. Usually set equal to 1.2 and considered independent of temperature and pressure. If provided, this coefficient is assigned proper units of kg ** 0.5 / mol ** 0.5 after entry.
Returns: float
The mean molal (mol/kg) scale ionic activity coefficient of solute, dimensionless
See also
_debye_parameter_activity
,_pitzer_B_MX
,_pitzer_B_gamma
,_pitzer_B_phi
,_pitzer_log_gamma
References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
May, P. M., Rowland, D., Hefter, G., & Königsberger, E. (2011). A Generic and Updatable Pitzer Characterization of Aqueous Binary Electrolyte Solutions at 1 bar and 25 °C. Journal of Chemical & Engineering Data, 56(12), 5066–5077. doi:10.1021/je2009329
Beyer, R., & Steiger, M. (2010). Vapor Pressure Measurements of NaHCOO + H 2 O and KHCOO + H 2 O from 278 to 308 K and Representation with an Ion Interaction (Pitzer) Model. Journal of Chemical & Engineering Data, 55(2), 830–838. doi:10.1021/je900487a
Examples
>>> get_activity_coefficient_pitzer(0.5*unit('mol/kg'),0.5*unit('mol/kg'),1,0.5,-.0181191983,-.4625822071,.4682,.000246063,1,-1,1,1,b=1.2) 0.61915...
>>> get_activity_coefficient_pitzer(5.6153*unit('mol/kg'),5.6153*unit('mol/kg'),3,0.5,0.0369993,0.354664,0.0997513,-0.00171868,1,-1,1,1,b=1.2) 0.76331...
NOTE: the examples below are for comparison with experimental and modeling data presented in the May et al reference below.
10 mol/kg ammonium nitrate. Estimated result (from graph) = 0.2725
>>> get_activity_coefficient_pitzer(10*unit('mol/kg'),10*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.22595 ...
5 mol/kg ammonium nitrate. Estimated result (from graph) = 0.3011
>>> get_activity_coefficient_pitzer(5*unit('mol/kg'),5*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.30249 ...
18 mol/kg ammonium nitrate. Estimated result (from graph) = 0.1653
>>> get_activity_coefficient_pitzer(18*unit('mol/kg'),18*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.16241 ...
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pyEQL.activity_correction.
get_apparent_volume_pitzer
(ionic_strength, molality, alpha1, alpha2, beta0, beta1, beta2, C_phi, V_o, z_cation, z_anion, nu_cation, nu_anion, temperature='25 degC', b=1.2)¶ Return the apparent molar volume of solute in the parent solution according to the Pitzer model.
Parameters: ionic_strength: Quantity
The ionic strength of the parent solution, mol/kg
molality: Quantity
The molal concentration of the parent salt, mol/kg
alpha1, alpha2: number
Coefficients for the Pitzer model. This function assigns the coefficients proper units of kg ** 0.5 / mol ** 0.5 after they are entered.
beta0, beta1, beta2, C_phi: number
Pitzer coefficients for the apparent molar volume. These ion-interaction parameters are specific to each salt system.
V_o: number
The V^o Pitzer coefficient for the apparent molar volume.
z_cation, z_anion: int
The formal charge on the cation and anion, respectively
nu_cation, nu_anion: int
The stoichiometric coefficient of the cation and anion in the salt
temperature: str Quantity
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
b: number, optional
Coefficient. Usually set equal to 1.2 and considered independent of temperature and pressure. If provided, this coefficient is assigned proper units of kg ** 0.5 / mol ** 0.5 after entry.
Returns: float
The apparent molar volume of the solute, cm ** 3 / mol
See also
References
May, P. M., Rowland, D., Hefter, G., & Königsberger, E. (2011). A Generic and Updatable Pitzer Characterization of Aqueous Binary Electrolyte Solutions at 1 bar and 25 °C. Journal of Chemical & Engineering Data, 56(12), 5066–5077. doi:10.1021/je2009329
Krumgalz, Boris S., Pogorelsky, Rita (1996). Volumetric Properties of Single Aqueous Electrolytes from Zero to Saturation Concentration at 298.15 K Represented by Pitzer’s Ion-Interaction Equations. Journal of Physical Chemical Reference Data, 25(2), 663-689.
Examples
NOTE: the example below is for comparison with experimental and modeling data presented in the Krumgalz et al reference below.
0.25 mol/kg CuSO4. Expected result (from graph) = 0.5 cm ** 3 / mol
>>> get_apparent_volume_pitzer(1.0*unit('mol/kg'),0.25*unit('mol/kg'),1.4,12,0.001499,-0.008124,0.2203,-0.0002589,-6,2,-2,1,1,b=1.2) 0.404...
1.0 mol/kg CuSO4. Expected result (from graph) = 4 cm ** 3 / mol
>>> get_apparent_volume_pitzer(4.0*unit('mol/kg'),1.0*unit('mol/kg'),1.4,12,0.001499,-0.008124,0.2203,-0.0002589,-6,2,-2,1,1,b=1.2) 4.424...
10.0 mol/kg ammonium nitrate. Expected result (from graph) = 50.3 cm ** 3 / mol
>>> get_apparent_volume_pitzer(10.0*unit('mol/kg'),10.0*unit('mol/kg'),2,0,0.000001742,0.0002926,0,0.000000424,46.9,1,-1,1,1,b=1.2) 50.286...
20.0 mol/kg ammonium nitrate. Expected result (from graph) = 51.2 cm ** 3 / mol
>>> get_apparent_volume_pitzer(20.0*unit('mol/kg'),20.0*unit('mol/kg'),2,0,0.000001742,0.0002926,0,0.000000424,46.9,1,-1,1,1,b=1.2) 51.145...
NOTE: the examples below are for comparison with experimental and modeling data presented in the Krumgalz et al reference below.
0.8 mol/kg NaF. Expected result = 0.03
>>> get_apparent_volume_pitzer(0.8*unit('mol/kg'),0.8*unit('mol/kg'),2,0,0.000024693,0.00003169,0,-0.000004068,-2.426,1,-1,1,1,b=1.2) 0.22595 ...
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pyEQL.activity_correction.
get_osmotic_coefficient_pitzer
(ionic_strength, molality, alpha1, alpha2, beta0, beta1, beta2, C_phi, z_cation, z_anion, nu_cation, nu_anion, temperature='25 degC', b=1.2)¶ Return the osmotic coefficient of water in an electrolyte solution according to the Pitzer model.
Parameters: ionic_strength: Quantity
The ionic strength of the parent solution, mol/kg
molality: Quantity
The molal concentration of the parent salt, mol/kg
alpha1, alpha2: number
Coefficients for the Pitzer model. This function assigns the coefficients proper units of kg ** 0.5 / mol ** 0.5 after they are entered.
beta0, beta1, beta2, C_phi
Coefficients for the Pitzer model. These ion-interaction parameters are specific to each salt system.
z_cation, z_anion: int
The formal charge on the cation and anion, respectively
nu_cation, nu_anion: int
The stoichiometric coefficient of the cation and anion in the salt
temperature: str Quantity
String representing the temperature of the solution. Defaults to ‘25 degC’ if not specified.
b: number, optional
Coefficient. Usually set equal to 1.2 and considered independent of temperature and pressure. If provided, this coefficient is assigned proper units of kg ** 0.5 / mol ** 0.5 after entry.
Returns: Quantity
The osmotic coefficient of water, dimensionless
See also
_debye_parameter_activity
,_pitzer_B_MX
,_pitzer_B_gamma
,_pitzer_B_phi
,_pitzer_log_gamma
References
Scharge, T., Munoz, A.G., and Moog, H.C. (2012). Activity Coefficients of Fission Products in Highly Salinary Solutions of Na+, K+, Mg2+, Ca2+, Cl-, and SO42- : Cs+. /Journal of Chemical& Engineering Data (57), p. 1637-1647.
Kim, H., & Jr, W. F. (1988). Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25 degree C. 1. Single salt parameters. Journal of Chemical and Engineering Data, (2), 177–184.
May, P. M., Rowland, D., Hefter, G., & Königsberger, E. (2011). A Generic and Updatable Pitzer Characterization of Aqueous Binary Electrolyte Solutions at 1 bar and 25 °C. Journal of Chemical & Engineering Data, 56(12), 5066–5077. doi:10.1021/je2009329
Beyer, R., & Steiger, M. (2010). Vapor Pressure Measurements of NaHCOO + H 2 O and KHCOO + H 2 O from 278 to 308 K and Representation with an Ion Interaction (Pitzer) Model. Journal of Chemical & Engineering Data, 55(2), 830–838. doi:10.1021/je900487a
Examples
Experimental value according to Beyer and Stieger reference is 1.3550
>>> get_osmotic_coefficient_pitzer(10.175*unit('mol/kg'),10.175*unit('mol/kg'),1,0.5,-.0181191983,-.4625822071,.4682,.000246063,1,-1,1,1,b=1.2) 1.3552 ...
Experimental value according to Beyer and Stieger reference is 1.084
>>> get_osmotic_coefficient_pitzer(5.6153*unit('mol/kg'),5.6153*unit('mol/kg'),3,0.5,0.0369993,0.354664,0.0997513,-0.00171868,1,-1,1,1,b=1.2) 1.0850 ...
NOTE: the examples below are for comparison with experimental and modeling data presented in the May et al reference below.
10 mol/kg ammonium nitrate. Estimated result (from graph) = 0.62
>>> get_osmotic_coefficient_pitzer(10*unit('mol/kg'),10*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.6143 ...
5 mol/kg ammonium nitrate. Estimated result (from graph) = 0.7
>>> get_osmotic_coefficient_pitzer(5*unit('mol/kg'),5*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.6925 ...
18 mol/kg ammonium nitrate. Estimated result (from graph) = 0.555
>>> get_osmotic_coefficient_pitzer(18*unit('mol/kg'),18*unit('mol/kg'),2,0,-0.01709,0.09198,0,0.000419,1,-1,1,1,b=1.2) 0.5556 ...
Water Properties API¶
pyEQL water properties library
This file contains functions for retrieving various physical properties of water substance
copyright: | 2013-2015 by Ryan S. Kingsbury |
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license: | LGPL, see LICENSE for more details. |
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pyEQL.water_properties.
water_density
(temperature=<Quantity(25, 'degC')>, pressure=<Quantity(1, 'atmosphere')>)¶ Return the density of water in kg/m3 at the specified temperature and pressure.
Parameters: temperature : float or int, optional
The temperature in Celsius. Defaults to 25 degrees if not specified.
pressure : float or int, optional
The ambient pressure of the solution in Pascals (N/m2). Defaults to atmospheric pressure (101325 Pa) if not specified.
Returns: float
The density of water in kg/m3.
Notes
Based on the following empirical equation reported in [10]
\[\rho_W = 999.65 + 0.20438 T - 6.1744e-2 T ^ {1.5}\]Where T is the temperature in Celsius.
[10] Sohnel, O and Novotny, P. //Densities of Aqueous Solutions of Inorganic Substances.// Elsevier Science, Amsterdam, 1985. Examples
>>> water_density(25*unit('degC')) <Quantity(997.0415, 'kilogram / meter ** 3')>
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pyEQL.water_properties.
water_dielectric_constant
(temperature=<Quantity(25, 'degC')>)¶ Return the dielectric constant of water at the specified temperature.
Parameters: temperature : Quantity, optional
The temperature. Defaults to 25 degC if omitted.
Returns: float
The dielectric constant (or permittivity) of water relative to the permittivity of a vacuum. Dimensionless.
Notes
This function implements a quadratic fit of measured permittivity data as reported in the CRC Handbook [11]. The parameters given are valid over the range 273 K to 372 K. Permittivity should not be extrapolated beyond this range.
\[\epsilon(T) = a + b T + c T^2\]References
[11] “Permittivity (Dielectric Constant) of Liquids.” CRC Handbook of Chemistry and Physics, 92nd ed, pp 6-187 - 6-208. Examples
>>> water_dielectric_constant(unit('20 degC')) 80.15060...
Display an error if ‘temperature’ is outside the valid range
>>> water_dielectric_constant(-5*unit('degC'))
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pyEQL.water_properties.
water_specific_weight
(temperature=<Quantity(25, 'degC')>, pressure=<Quantity(1, 'atmosphere')>)¶ Return the specific weight of water in N/m3 at the specified temperature and pressure.
Parameters: temperature : Quantity, optional
The temperature. Defaults to 25 degC if omitted.
pressure : Quantity, optional
The ambient pressure of the solution. Defaults to atmospheric pressure (1 atm) if omitted.
Returns: Quantity
The specific weight of water in N/m3.
See also
Examples
>>> water_specific_weight() <Quantity(9777.637025975, 'newton / meter ** 3')>
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pyEQL.water_properties.
water_viscosity_dynamic
(temperature=<Quantity(25, 'degC')>, pressure=<Quantity(1, 'atmosphere')>)¶ Return the dynamic (absolute) viscosity of water in N-s/m2 = Pa-s = kg/m-s at the specified temperature.
Parameters: temperature : Quantity, optional
The temperature. Defaults to 25 degC if omitted.
pressure : Quantity, optional
The ambient pressure of the solution. Defaults to atmospheric pressure (1 atm) if omitted.
Returns: Quantity
The dynamic (absolute) viscosity of water in N-s/m2 = Pa-s = kg/m-s
Notes
Implements the international equation for viscosity of water as specified by NIST [12]
Valid for 273 < temperature < 1073 K and 0 < pressure < 100,000,000 Pa
References
[12] Sengers, J.V. “Representative Equations for the Viscosity of Water Substance.” J. Phys. Chem. Ref. Data 13(1), 1984.http://www.nist.gov/data/PDFfiles/jpcrd243.pdf Examples
>>> water_viscosity_dynamic(20*unit('degC')) <Quantity(0.000998588610804179, 'kilogram / meter / second')> >>> water_viscosity_dynamic(unit('100 degC'),unit('25 MPa')) <Quantity(0.00028165034364318573, 'kilogram / meter / second')> >>> water_viscosity_dynamic(25*unit('degC'),0.1*unit('MPa')) <Quantity(0.0008872817880143659, 'kilogram / meter / second')>
#TODO - check these again after I implement pressure-dependent density function
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pyEQL.water_properties.
water_viscosity_kinematic
(temperature=<Quantity(25, 'degC')>, pressure=<Quantity(1, 'atmosphere')>)¶ Return the kinematic viscosity of water in m2/s = Stokes at the specified temperature.
Parameters: temperature : Quantity, optional
The temperature. Defaults to 25 degC if omitted.
pressure : Quantity, optional
The ambient pressure of the solution. Defaults to atmospheric pressure (1 atm) if omitted.
Returns: Quantity
The kinematic viscosity of water in Stokes (m2/s)
See also
Examples
>>> water_viscosity_kinematic() <Quantity(8.899146003595295e-07, 'meter ** 2 / second')>