Internal module reference¶

These internal modules are used by Solution but typically are not directly accessed by the user.

Salt analysis module¶

pyEQL salt matching library.

This file contains functions that allow a pyEQL Solution object composed of individual species (usually ions) to be mapped to a solution of one or more salts. This mapping is necessary because some parameters (such as activity coefficient data) can only be determined for salts (e.g. NaCl) and not individual species (e.g. Na+)

copyright:: 2013-2023 by Ryan S. Kingsbury
license:: LGPL, see LICENSE for more details.

class pyEQL.salt_ion_match.Salt(cation, anion)[source]¶

Class to represent a salt.

get_effective_molality(ionic_strength)[source]¶

Calculate the effective molality according to [mistry].

\[2 I \over (\nu_+ z_+^2 + \nu_- z_- ^2)\]

Parameters:: ionic_strength (Quantity) – The ionic strength of the parent solution, mol/kg
Returns:: Quantity
Return type:: the effective molality of the salt in the parent solution

References

[mistry]

Mistry, K. H.; Hunter, H. a.; Lienhard V, J. H. Effect of composition and nonideal solution behavior on desalination calculations for mixed electrolyte solutions with comparison to seawater. Desalination 2013, 318, 34-47.

pyEQL.salt_ion_match._sort_components(Solution, type='all')[source]¶

Sort the components of a solution in descending order (by mol).

Parameters:

Solution (Solution object) –
type (The type of component to be sorted. Defaults to 'all' for all) – solutes. Other valid arguments are ‘cations’ and ‘anions’ which return sorted lists of cations and anions, respectively.

Returns:

A list whose keys are the component names (formulas) and whose
values are the component objects themselves

pyEQL.salt_ion_match.generate_salt_list(sol, unit='mol/kg')[source]¶

Generate a list of salts that represents the ionic composition of a solution.

Returns:: A dictionary of Salt objects, where Salt objects are the keys and the amounts are the values.
Return type:: dict

pyEQL.salt_ion_match.identify_salt(sol)[source]¶

Analyze the components of a solution and identify the salt that most closely approximates it. (e.g., if a solution contains 0.5 mol/kg of Na+ and Cl-, plus traces of H+ and OH-, the matched salt is 0.5 mol/kg NaCl).

Create a Salt object for this salt.

Return type:: A Salt object.

Activity Correction module¶

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:: 2013-2023 by Ryan S. Kingsbury
license:: LGPL, see LICENSE for more details.

pyEQL.activity_correction._debye_parameter_B(temperature='25 degC')[source]¶

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:

\[B = ( {8 \pi N_A e^2 \over 1000 \epsilon k T} ) ^ {1 \over 2}\]

References

Bockris and Reddy. /Modern Electrochemistry/, vol 1. Plenum/Rosetta, 1977, p.210.

Examples:¶

>>> _debye_parameter_B() 
0.3291...

pyEQL.activity_correction._debye_parameter_activity(temperature='25 degC')[source]¶

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.
Return type:: Quantity The parameter A for use in the Debye-Huckel limiting law (base e)

Notes

The parameter A is equal to:

\[A^{\gamma} = {e^3 ( 2 \pi N_A {\rho})^{0.5} \over (4 \pi \epsilon_o \epsilon_r k T)^{1.5}}\]

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

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...

See also

_debye_parameter_osmotic()

pyEQL.activity_correction._debye_parameter_osmotic(temperature='25 degC')[source]¶

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.

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: [kim] [arch]

\[A^{\phi} = {1 \over 3} A^{\gamma}\]

References

[kim]

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.

[arch]

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...

See also

_debye_parameter_activity()

pyEQL.activity_correction._debye_parameter_volume(temperature='25 degC')[source]¶

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.

Notes

Takes the value 1.8305 cm ** 3 * kg ** 0.5 / mol ** 1.5 at 25 C. This constant is calculated according to: [1]_

\[A_V = -2 A_{\phi} R T [ {3 \over \epsilon} {{\partial \epsilon \over \partial p} } - {{1 \over \rho}{\partial \rho \over \partial p} }]\]

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. [2]_

References

Speciation Engines module¶

pyEQL engines for computing aqueous equilibria (e.g., speciation, redox, etc.).

copyright:: 2013-2023 by Ryan S. Kingsbury
license:: LGPL, see LICENSE for more details.

class pyEQL.engines.EOS[source]¶

Abstract base class for pyEQL equation of state classes.

abstract equilibrate(solution)[source]¶

Adjust the speciation and pH of a Solution object to achieve chemical equilibrium.

The Solution should be modified in-place, likely using add_moles / set_moles, etc.

Parameters:: solution – pyEQL Solution object

Returns: Nothing. The speciation of the Solution is modified in-place.

Raises:

ValueError if the calculation cannot be completed, e.g. due to insufficient number of –
parameters or lack of convergence. –

abstract get_activity_coefficient(solution, solute)[source]¶

Return the molal scale activity coefficient of solute, given a Solution object.

Parameters:

solution – pyEQL Solution object
solute – str identifying the solute of interest

Returns: Quantity: dimensionless quantity object

Raises:

ValueError if the calculation cannot be completed, e.g. due to insufficient number of –
parameters. –

abstract get_osmotic_coefficient(solution)[source]¶

Return the molal scale osmotic coefficient of a Solution.

Parameters:: solution – pyEQL Solution object

Returns: Quantity: dimensionless molal scale osmotic coefficient

Raises:

ValueError if the calculation cannot be completed, e.g. due to insufficient number of –
parameters. –

abstract get_solute_volume()[source]¶

Return the volume of only the solutes.

Parameters:: solution – pyEQL Solution object

Returns: Quantity: solute volume in L

Raises:

ValueError if the calculation cannot be completed, e.g. due to insufficient number of –
parameters. –

class pyEQL.engines.IdealEOS[source]¶

Ideal solution equation of state engine.

equilibrate(solution)[source]¶: Adjust the speciation of a Solution object to achieve chemical equilibrium.

get_activity_coefficient(solution, solute)[source]¶: Return the molal scale activity coefficient of solute, given a Solution object.

get_osmotic_coefficient(solution)[source]¶: Return the molal scale osmotic coefficient of solute, given a Solution object.

get_solute_volume(solution)[source]¶: Return the volume of the solutes.

class pyEQL.engines.NativeEOS[source]¶

pyEQL’s native EOS. Uses the Pitzer model when possible, falls back to other models (e.g. Debye-Huckel) based on ionic strength if sufficient parameters are not available.

equilibrate(solution)[source]¶: Adjust the speciation of a Solution object to achieve chemical equilibrium.

get_activity_coefficient(solution, solute)[source]¶

Whenever the appropriate parameters are available, the Pitzer model [may] is used. If no Pitzer parameters are available, then the appropriate equations are selected according to the following logic: [stumm].

I <= 0.0005: Debye-Huckel equation 0.005 < I <= 0.1: Guntelberg approximation 0.1 < I <= 0.5: Davies equation I > 0.5: Raises a warning and returns activity coefficient = 1

The ionic strength, activity coefficients, and activities are all calculated based on the molal (mol/kg) concentration scale. If a different scale is given as input, then the molal-scale activity coefficient \(\gamma_\pm\) is converted according to [rbs]

\[f_\pm = \gamma_\pm * (1 + M_w \sum_i \nu_i \m_i)\]

\[y_\pm = m \rho_w / C \gamma_\pm\]

where \(f_\pm\) is the rational activity coefficient, \(M_w\) is the molecular weight of water, the summation represents the total molality of all solute species, \(y_\pm\) is the molar activity coefficient, \(\rho_w\) is the density of pure water, \(m\) and \(C\) are the molal and molar concentrations of the chosen salt (not individual solute), respectively.

Parameters:

solute – String representing the name of the solute of interest
scale – The concentration scale for the returned activity coefficient. Valid options are “molal”, “molar”, and “rational” (i.e., mole fraction). By default, the molal scale activity coefficient is returned.
verbose – If True, pyEQL will print a message indicating the parent salt that is being used for activity calculations. This option is useful when modeling multicomponent solutions. False by default.

Returns: The mean ion activity coefficient of the solute in question on the selected scale.

See also

get_ionic_strength get_salt activity_correction.get_activity_coefficient_debyehuckel activity_correction.get_activity_coefficient_guntelberg activity_correction.get_activity_coefficient_davies activity_correction.get_activity_coefficient_pitzer

Notes

For multicomponent mixtures, pyEQL implements the “effective Pitzer model” presented by Mistry et al. [mistry]. In this model, the activity coefficient of a salt in a multicomponent mixture is calculated using an “effective molality,” which is the molality that would result in a single-salt mixture with the same total ionic strength as the multicomponent solution.

\[m_effective = 2 I \over (\nu_{+} z_{+}^2 + \nu{_}- z_{-} ^2)\]

References

[may]

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

[stumm]

Stumm, Werner and Morgan, James J. Aquatic Chemistry, 3rd ed, pp 165. Wiley Interscience, 1996.

[rbs]

Robinson, R. A.; Stokes, R. H. Electrolyte Solutions: Second Revised Edition; Butterworths: London, 1968, p.32.

[mistry]

Mistry, K. H.; Hunter, H. a.; Lienhard V, J. H. Effect of composition and nonideal solution behavior on desalination calculations for mixed electrolyte solutions with comparison to seawater. Desalination 2013, 318, 34-47.

get_osmotic_coefficient(solution)[source]¶

Return the molal scale osmotic coefficient of solute, given a Solution object.

Osmotic coefficient is calculated using the Pitzer model. [may] If appropriate parameters for the model are not available, then pyEQL raises a WARNING and returns an osmotic coefficient of 1.

If the ‘rational’ scale is given as input, then the molal-scale osmotic coefficient \(\phi\) is converted according to [rbs]

\[g = - \phi * M_{w} \sum_{i} \nu_{i} \m_{i}) / \ln x_{w}\]

where \(g\) is the rational osmotic coefficient, \(M_{w}\) is the molecular weight of water, the summation represents the total molality of all solute species, and \(x_{w}\) is the mole fraction of water.

Parameters:

scale –
"molal" (The concentration scale for the returned osmotic coefficient. Valid options are) –

:param : :param “rational”: :type “rational”: i.e., mole fraction :param coefficient is returned.:

Returns

Quantity:: The osmotic coefficient

See also

get_water_activity get_ionic_strength get_salt

Notes

For multicomponent mixtures, pyEQL adopts the “effective Pitzer model” presented by Mistry et al. [mstry]. In this approach, the osmotic coefficient of each individual salt is calculated using the normal Pitzer model based on its respective concentration. Then, an effective osmotic coefficient is calculated as the concentration-weighted average of the individual osmotic coefficients.

For example, in a mixture of 0.5 M NaCl and 0.5 M KBr, one would calculate the osmotic coefficient for each salt using a concentration of 0.5 M and an ionic strength of 1 M. Then, one would average the two resulting osmotic coefficients to obtain an effective osmotic coefficient for the mixture.

(Note: in the paper referenced below, the effective osmotic coefficient is determined by weighting using the “effective molality” rather than the true molality. Subsequent checking and correspondence with the author confirmed that the weight factor should be the true molality, and that is what is implemented in pyEQL.)

References

[may]
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

[rbs]
Robinson, R. A.; Stokes, R. H. Electrolyte Solutions: Second Revised Edition; Butterworths: London, 1968, p.32.

[mstry]
Mistry, K. H.; Hunter, H. a.; Lienhard V, J. H. Effect of composition and nonideal solution behavior on desalination calculations for mixed electrolyte solutions with comparison to seawater. Desalination 2013, 318, 34-47.

Examples

>>> s1 = pyEQL.Solution([['Na+','0.2 mol/kg'],['Cl-','0.2 mol/kg']])
>>> s1.get_osmotic_coefficient()
<Quantity(0.923715281, 'dimensionless')>

>>> s1 = pyEQL.Solution([['Mg+2','0.3 mol/kg'],['Cl-','0.6 mol/kg']],temperature='30 degC')
>>> s1.get_osmotic_coefficient()
<Quantity(0.891409618, 'dimensionless')>

get_solute_volume(solution)[source]¶: Return the volume of the solutes.

Internal module reference¶

Salt analysis module¶

Activity Correction module¶

Examples:¶

Examples:¶

Examples:¶

See Also:¶

See Also:¶

See Also:¶

See Also:¶

See Also:¶

Speciation Engines module¶