Solution Class Reference

This page contains detailed information on each of the methods, attributes, and properties in Solution. Use the sidebar on the right for easier navigation.

Solution

class pyEQL.Solution(solutes: list[list[str]] | dict[str, str] | None = None, volume: str | None = None, temperature: str = '298.15 K', pressure: str = '1 atm', pH: float = 7, pE: float = 8.5, balance_charge: str | None = None, solvent: str | list = 'H2O', engine: EOS | Literal['native', 'ideal', 'phreeqc'] = 'native', database: str | Path | Store | None = None, default_diffusion_coeff: float = 1.6106e-09, log_level: Literal['DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL'] | None = 'ERROR')

Class representing the properties of a solution. Instances of this class contain information about the solutes, solvent, and bulk properties.

__init__(solutes: list[list[str]] | dict[str, str] | None = None, volume: str | None = None, temperature: str = '298.15 K', pressure: str = '1 atm', pH: float = 7, pE: float = 8.5, balance_charge: str | None = None, solvent: str | list = 'H2O', engine: EOS | Literal['native', 'ideal', 'phreeqc'] = 'native', database: str | Path | Store | None = None, default_diffusion_coeff: float = 1.6106e-09, log_level: Literal['DEBUG', 'INFO', 'WARNING', 'ERROR', 'CRITICAL'] | None = 'ERROR')

Instantiate a Solution from a composition.

Parameters:

• solutes –

  dict, optional. Keys must be the chemical formula, while values must be str Quantity representing the amount. For example:

  {“Na+”: “0.1 mol/L”, “Cl-”: “0.1 mol/L”}

  Note that an older “list of lists” syntax is also supported; however this will be deprecated in the future and is no longer recommended. The equivalent list syntax for the above example is

  [[“Na+”, “0.1 mol/L”], [“Cl-”, “0.1 mol/L”]]

  Defaults to empty (pure solvent) if omitted

• volume – str, optional Volume of the solvent, including the unit. Defaults to ‘1 L’ if omitted. Note that the total solution volume will be computed using partial molar volumes of the respective solutes as they are added to the solution.

• temperature – str, optional The solution temperature, including the ureg. Defaults to ‘25 degC’ if omitted.

• pressure – Quantity, optional The ambient pressure of the solution, including the unit. Defaults to ‘1 atm’ if omitted.

• pH – number, optional Negative log of H+ activity. If omitted, the solution will be initialized to pH 7 (neutral) with appropriate quantities of H+ and OH- ions

• pE – the pE value (redox potential) of the solution. Lower values = more reducing, higher values = more oxidizing. At pH 7, water is stable between approximately -7 to +14. The default value corresponds to a pE value typical of natural waters in equilibrium with the atmosphere.

• balance_charge – The strategy for balancing charge during init and equilibrium calculations. Valid options are ‘pH’, which will adjust the solution pH to balance charge, ‘pE’ which will adjust the redox equilibrium to balance charge, or the name of a dissolved species e.g. ‘Ca+2’ or ‘Cl-’ that will be added/subtracted to balance charge. If set to None, no charge balancing will be performed either on init or when equilibrate() is called. Note that in this case, equilibrate() can distort the charge balance!

• solvent – Formula of the solvent. Solvents other than water are not supported at this time.

• engine – Electrolyte modeling engine to use. See documentation for details on the available engines.

• database – path to a .json file (str or Path) or maggma Store instance that contains serialized SoluteDocs. None (default) will use the built-in pyEQL database.

• log_level – Log messages of this or higher severity will be printed to stdout. Defaults to ‘ERROR’, meaning that ERROR and CRITICAL messages will be shown, while WARNING, INFO, and DEBUG messages are not. If set to None, nothing will be printed.

• default_diffusion_coeff –

  Diffusion coefficient value in m^2/s to use in calculations when there is no diffusion coefficient for a species in the database. This affects several important property calculations including conductivity and transport number, which are related to the weighted sums of diffusion coefficients of all species. Setting this argument to zero will exclude any species that does not have a tabulated diffusion coefficient from these calculations, possibly resulting in underestimation of the conductivity and/or inaccurate transport numbers.

  Missing diffusion coefficients are especially likely in complex electrolytes containing, for example, complexes or paired species such as NaSO4[-1]. In such cases, setting default_diffusion_coeff to zero is likely to result in the above errors.

  By default, this argument is set to the diffusion coefficient of NaCl salt, 1.61x10^-9 m2/s.

Examples

>>> s1 = pyEQL.Solution({'Na+': '1 mol/L','Cl-': '1 mol/L'},temperature='20 degC',volume='500 mL')
>>> print(s1)
Components:
Volume: 0.500 l
Pressure: 1.000 atm
Temperature: 293.150 K
Components: ['H2O(aq)', 'H[+1]', 'OH[-1]', 'Na[+1]', 'Cl[-1]']

balance_charge

Standardized formula of the species used for charge balancing.

water_substance

IAPWS instance describing water properties.

components

Special dictionary where keys are standardized formula and values are the moles present in Solution.

database

Store instance containing the solute property database.

solvent

Formula of the component that is set as the solvent (currently only H2O(aq) is supported).

property mass: Quantity

Return the total mass of the solution.

The mass is calculated each time this method is called.

Returns: The mass of the solution, in kg

property solvent_mass: Quantity

Return the mass of the solvent.

This property is used whenever mol/kg (or similar) concentrations are requested by get_amount()

Returns:

The mass of the solvent, in kg

See also

get_amount()

property volume: Quantity

Return the volume of the solution.

Returns:

the volume of the solution, in L

Return type:

Quantity

property temperature: Quantity

Return the temperature of the solution in Kelvin.

property pressure: Quantity

Return the hydrostatic pressure of the solution in atm.

property pH: float | None

Return the pH of the solution.

p(solute: str, activity=True) → float | None

Return the negative log of the activity of solute.

Generally used for expressing concentration of hydrogen ions (pH)

Parameters:

• solute – str String representing the formula of the solute

• activity – bool, optional If False, the function will use the molar concentration rather than the activity to calculate p. Defaults to True.

Returns:

Quantity

The negative log10 of the activity (or molar concentration if activity = False) of the solute.

property density: Quantity

Return the density of the solution.

Density is calculated from the mass and volume each time this method is called.

Returns:

The density of the solution.

Return type:

Quantity

property dielectric_constant: Quantity

Returns the dielectric constant of the solution.

Parameters:

None –

Returns:

the dielectric constant of the solution, dimensionless.

Return type:

Quantity

Notes

Implements the following equation as given by Zuber et al.

\[\epsilon = \epsilon_{solvent} \over 1 + \sum_i \alpha_i x_i\]

where \(\alpha_i\) is a coefficient specific to the solvent and ion, and \(x_i\) is the mole fraction of the ion in solution.

References

A. Zuber, L. Cardozo-Filho, V.F. Cabral, R.F. Checoni, M. Castier, An empirical equation for the dielectric constant in aqueous and nonaqueous electrolyte mixtures, Fluid Phase Equilib. 376 (2014) 116-123. doi:10.1016/j.fluid.2014.05.037.

property chemical_system: str

Return the chemical system of the Solution as a “-” separated list of elements, sorted alphabetically. For example, a solution containing CaCO3 would have a chemical system of “C-Ca-H-O”.

property elements: list

Return a list of elements that are present in the solution.

For example, a solution containing CaCO3 would return [“C”, “Ca”, “H”, “O”]

property cations: dict[str, float]

Returns the subset of components that are cations.

The returned dict is sorted by amount in descending order.

property anions: dict[str, float]

Returns the subset of components that are anions.

The returned dict is sorted by amount in descending order.

property neutrals: dict[str, float]

Returns the subset of components that are neutral (not charged).

The returned dict is sorted by amount in descending order.

property viscosity_dynamic: Quantity

Return the dynamic (absolute) viscosity of the solution.

Calculated from the kinematic viscosity

See also

viscosity_kinematic

property viscosity_kinematic: Quantity

Return the kinematic viscosity of the solution.

Notes

The calculation is based on a model derived from the Eyring equation and presented in

\[\ln \nu = \ln {\nu_w MW_w \over \sum_i x_i MW_i } + 15 x_+^2 + x_+^3 \delta G^*_{123} + 3 x_+ \delta G^*_{23} (1-0.05x_+)\]

Where:

\[\delta G^*_{123} = a_o + a_1 (T)^{0.75}\]

\[\delta G^*_{23} = b_o + b_1 (T)^{0.5}\]

In which \(\nu\) is the kinematic viscosity, MW is the molecular weight, \(x_{+}\) is the mole fraction of cations, and \(T\) is the temperature in degrees C.

The a and b fitting parameters for a variety of common salts are included in the database.

References

Vásquez-Castillo, G.; Iglesias-Silva, G. a.; Hall, K. R. An extension of the McAllister model to correlate kinematic viscosity of electrolyte solutions. Fluid Phase Equilib. 2013, 358, 44-49.

See also

viscosity_dynamic()

property conductivity: Quantity

Compute the electrical conductivity of the solution.

Returns:

The electrical conductivity of the solution in Siemens / meter.

Notes

Conductivity is calculated by summing the molar conductivities of the respective solutes.

\[EC = {F^2 \over R T} \sum_i D_i z_i ^ 2 m_i = \sum_i \lambda_i m_i\]

Where \(D_i\) is the diffusion coefficient, \(m_i\) is the molal concentration, \(z_i\) is the charge, and the summation extends over all species in the solution. Alternatively, \(\lambda_i\) is the molar conductivity of solute i.

Diffusion coefficients \(D_i\) (and molar conductivities \(\lambda_i\)) are adjusted for the effects of temperature and ionic strength using the method implemented in PHREEQC >= 3.4. [aq] [hc] See get_diffusion_coefficient for further details.

References

[aq]

https://www.aqion.de/site/electrical-conductivity

[hc]

http://www.hydrochemistry.eu/exmpls/sc.html

See also

ionic_strength get_diffusion_coefficient() get_molar_conductivity()

property ionic_strength: Quantity

Return the ionic strength of the solution.

Return the ionic strength of the solution, calculated as 1/2 * sum ( molality * charge ^2) over all the ions.

Molal (mol/kg) scale concentrations are used for compatibility with the activity correction formulas.

Returns:

The ionic strength of the parent solution, mol/kg.

Return type:

Quantity

See also

get_activity() get_water_activity()

Notes

The ionic strength is calculated according to:

\[I = \sum_i m_i z_i^2\]

Where \(m_i\) is the molal concentration and \(z_i\) is the charge on species i.

Examples

>>> s1 = pyEQL.Solution([['Na+','0.2 mol/kg'],['Cl-','0.2 mol/kg']])
>>> s1.ionic_strength
<Quantity(0.20000010029672785, 'mole / kilogram')>

>>> s1 = pyEQL.Solution([['Mg+2','0.3 mol/kg'],['Na+','0.1 mol/kg'],['Cl-','0.7 mol/kg']],temperature='30 degC')
>>> s1.ionic_strength
<Quantity(1.0000001004383303, 'mole / kilogram')>

property charge_balance: float

Return the charge balance of the solution.

Return the charge balance of the solution. The charge balance represents the net electric charge on the solution and SHOULD equal zero at all times, but due to numerical errors will usually have a small nonzero value. It is calculated according to:

\[CB = \sum_i C_i z_i\]

where \(C_i\) is the molar concentration, and \(z_i\) is the charge on species i.

Returns:

The charge balance of the solution, in equivalents (mol of charge) per L.

Return type:

float

property alkalinity: Quantity

Return the alkalinity or acid neutralizing capacity of a solution.

Returns:

The alkalinity of the solution in mg/L as CaCO3

Return type:

Quantity

Notes

The alkalinity is calculated according to [stm]

\[Alk = \sum_{i} z_{i} C_{B} + \sum_{i} z_{i} C_{A}\]

Where \(C_{B}\) and \(C_{A}\) are conservative cations and anions, respectively (i.e. ions that do not participate in acid-base reactions), and \(z_{i}\) is their signed charge. In this method, the set of conservative cations is all Group I and Group II cations, and the conservative anions are all the anions of strong acids.

References

[stm]

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

property hardness: Quantity

Return the hardness of a solution.

Hardness is defined as the sum of the equivalent concentrations of multivalent cations as calcium carbonate.

NOTE: at present pyEQL cannot distinguish between mg/L as CaCO3 and mg/L units. Use with caution.

Returns:

The hardness of the solution in mg/L as CaCO3

Return type:

Quantity

property total_dissolved_solids: Quantity

Total dissolved solids in mg/L (equivalent to ppm) including both charged and uncharged species.

The TDS is defined as the sum of the concentrations of all aqueous solutes (not including the solvent), except for H[+1] and OH[-1]].

property TDS: Quantity

Alias of total_dissolved_solids().

property debye_length: Quantity

Return the Debye length of a solution.

Debye length is calculated as [wk3]

\[\kappa^{-1} = \sqrt({\epsilon_r \epsilon_o k_B T \over (2 N_A e^2 I)})\]

where \(I\) is the ionic strength, \(\epsilon_r\) and \(\epsilon_r\) are the relative permittivity and vacuum permittivity, \(k_B\) is the Boltzmann constant, and \(T\) is the temperature, \(e\) is the elementary charge, and \(N_A\) is Avogadro’s number.

Returns The Debye length, in nanometers.

References

[wk3]

https://en.wikipedia.org/wiki/Debye_length#Debye_length_in_an_electrolyte

See also

ionic_strength dielectric_constant

property bjerrum_length: Quantity

Return the Bjerrum length of a solution.

Bjerrum length represents the distance at which electrostatic interactions between particles become comparable in magnitude to the thermal energy.:math:lambda_B is calculated as

\[\lambda_B = {e^2 \over (4 \pi \epsilon_r \epsilon_o k_B T)}\]

where \(e\) is the fundamental charge, \(\epsilon_r\) and \(\epsilon_r\) are the relative permittivity and vacuum permittivity, \(k_B\) is the Boltzmann constant, and \(T\) is the temperature.

Returns:

The Bjerrum length, in nanometers.

Return type:

Quantity

References

https://en.wikipedia.org/wiki/Bjerrum_length

Examples

>>> s1 = pyEQL.Solution()
>>> s1.bjerrum_length
<Quantity(0.7152793009386953, 'nanometer')>

See also

dielectric_constant

property osmotic_pressure: Quantity

Return the osmotic pressure of the solution relative to pure water.

Returns:

The osmotic pressure of the solution relative to pure water in Pa

See also

get_water_activity get_osmotic_coefficient get_salt

Notes

Osmotic pressure is calculated based on the water activity [sata] [wk]

\[\Pi = -\frac{RT}{V_{w}} \ln a_{w}\]

Where \(\Pi\) is the osmotic pressure, \(V_{w}\) is the partial molar volume of water (18.2 cm**3/mol), and \(a_{w}\) is the water activity.

References

[sata]

Sata, Toshikatsu. Ion Exchange Membranes: Preparation, Characterization, and Modification. Royal Society of Chemistry, 2004, p. 10.

[wk]

http://en.wikipedia.org/wiki/Osmotic_pressure#Derivation_of_osmotic_pressure

Examples

>>> s1=pyEQL.Solution()
>>> s1.osmotic_pressure
<Quantity(0.495791416, 'pascal')>

>>> s1 = pyEQL.Solution([['Na+','0.2 mol/kg'],['Cl-','0.2 mol/kg']])
>>> soln.osmotic_pressure
<Quantity(906516.7318131207, 'pascal')>

get_amount(solute: str, units: str = 'mol/L') → Quantity

Return the amount of ‘solute’ in the parent solution.

The amount of a solute can be given in a variety of unit types. 1. substance per volume (e.g., ‘mol/L’, ‘M’) 2. equivalents (i.e., moles of charge) per volume (e.g., ‘eq/L’, ‘meq/L’) 3. substance per mass of solvent (e.g., ‘mol/kg’, ‘m’) 4. mass of substance (e.g., ‘kg’) 5. moles of substance (‘mol’) 6. mole fraction (‘fraction’) 7. percent by weight (%) 8. number of molecules (‘count’) 9. “parts-per-x” units, where ppm = mg/L, ppb = ug/L ppt = ng/L

Parameters:

• solute – str String representing the name of the solute of interest

• units – str Units desired for the output. Examples of valid units are ‘mol/L’,’mol/kg’,’mol’, ‘kg’, and ‘g/L’ Use ‘fraction’ to return the mole fraction. Use ‘%’ to return the mass percent

Returns:

The amount of the solute in question, in the specified units

See also

mass add_amount() set_amount() get_total_amount() get_osmolarity() get_osmolality() get_total_moles_solute() pyEQL.utils.interpret_units()

get_components_by_element() → dict[str, list]

Return a list of all species associated with a given element.

Elements (keys) are suffixed with their oxidation state in parentheses, e.g.,

{“Na(1.0)”:[“Na[+1]”, “NaOH(aq)”]}

Species associated with each element are sorted in descending order of the amount present (i.e., the first species listed is the most abundant).

get_el_amt_dict()

Return a dict of Element: amount in mol.

Elements (keys) are suffixed with their oxidation state in parentheses, e.g. “Fe(2.0)”, “Cl(-1.0)”.

get_total_amount(element: str, units: str) → Quantity

Return the total amount of ‘element’ (across all solutes) in the solution.

Parameters:

• element – The symbol of the element of interest. The symbol can optionally be followed by the oxidation state in parentheses, e.g., “Na(1.0)”, “Fe(2.0)”, or “O(0.0)”. If no oxidation state is given, the total concentration of the element (over all oxidation states) is returned.

• units – str Units desired for the output. Any unit understood by get_amount can be used. Examples of valid units are ‘mol/L’,’mol/kg’,’mol’, ‘kg’, and ‘g/L’.

Returns:

The total amount of the element in the solution, in the specified units

See also

get_amount() pyEQL.utils.interpret_units()

add_solute(formula: str, amount: str)

Primary method for adding substances to a pyEQL solution.

Parameters:

• formula (str) – Chemical formula for the solute. Charged species must contain a + or - and

• charge ((for polyvalent solutes) a number representing the net) –

• amount (str) – The amount of substance in the specified unit system. The string should contain

• g/L'. (both a quantity and a pint-compatible representation of a ureg. e.g. '5 mol/kg' or '0.1) –

add_solvent(formula: str, amount: str)

Same as add_solute but omits the need to pass solvent mass to pint.

add_amount(solute: str, amount: str)

Add the amount of ‘solute’ to the parent solution.

Parameters:

• solute – str String representing the name of the solute of interest

• amount – str quantity String representing the concentration desired, e.g. ‘1 mol/kg’ If the units are given on a per-volume basis, the solution volume is not recalculated If the units are given on a mass, substance, per-mass, or per-substance basis, then the solution volume is recalculated based on the new composition

Returns:

Nothing. The concentration of solute is modified.

set_amount(solute: str, amount: str)

Set the amount of ‘solute’ in the parent solution.

Parameters:

• solute – str String representing the name of the solute of interest

• amount –

  str Quantity String representing the concentration desired, e.g. ‘1 mol/kg’ If the units are given on a per-volume basis, the solution volume is not recalculated and the molar concentrations of other components in the solution are not altered, while the molal concentrations are modified.

  If the units are given on a mass, substance, per-mass, or per-substance basis, then the solution volume is recalculated based on the new composition and the molal concentrations of other components are not altered, while the molar concentrations are modified.

Returns:

Nothing. The concentration of solute is modified.

get_total_moles_solute() → Quantity

Return the total moles of all solute in the solution.

get_moles_solvent() → Quantity

Return the moles of solvent present in the solution.

Returns:

The moles of solvent in the solution.

get_osmolarity(activity_correction=False) → Quantity

Return the osmolarity of the solution in Osm/L.

Parameters:

activity_correction – bool If TRUE, the osmotic coefficient is used to calculate the osmolarity. This correction is appropriate when trying to predict the osmolarity that would be measured from e.g. freezing point depression. Defaults to FALSE if omitted.

get_osmolality(activity_correction=False) → Quantity

Return the osmolality of the solution in Osm/kg.

Parameters:

activity_correction – bool If TRUE, the osmotic coefficient is used to calculate the osmolarity. This correction is appropriate when trying to predict the osmolarity that would be measured from e.g. freezing point depression. Defaults to FALSE if omitted.

get_salt() → Salt

Determine the predominant salt in a solution of ions.

Many empirical equations for solution properties such as activity coefficient, partial molar volume, or viscosity are based on the concentration of single salts (e.g., NaCl). When multiple ions are present (e.g., a solution containing Na+, Cl-, and Mg+2), it is generally not possible to directly model these quantities. pyEQL works around this problem by treating such solutions as single salt solutions.

The get_salt() method examines the ionic composition of a solution and returns an object that identifies the single most predominant salt in the solution, defined by the cation and anion with the highest mole fraction. The Salt object contains information about the stoichiometry of the salt to enable its effective concentration to be calculated (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).

Returns:

Salt object containing information about the parent salt.

See also

get_activity() get_activity_coefficient() get_water_activity() get_osmotic_coefficient() osmotic_pressure viscosity_kinematic

Examples

>>> s1 = Solution([['Na+','0.5 mol/kg'],['Cl-','0.5 mol/kg']])
>>> s1.get_salt()
<pyEQL.salt_ion_match.Salt object at 0x7fe6d3542048>
>>> s1.get_salt().formula
'NaCl'
>>> s1.get_salt().nu_cation
1
>>> s1.get_salt().z_anion
-1

>>> s2 = pyEQL.Solution([['Na+','0.1 mol/kg'],['Mg+2','0.2 mol/kg'],['Cl-','0.5 mol/kg']])
>>> s2.get_salt().formula
'MgCl2'
>>> s2.get_salt().nu_anion
2
>>> s2.get_salt().z_cation
2

get_salt_dict(cutoff: float = 0.01, use_totals: bool = True) → dict[str, dict]

Returns a dict of salts that approximates the composition of the Solution. Like components, the dict is keyed by formula and the values are the total moles present in the solution, e.g., {“NaCl(aq)”: 1}. If the Solution is pure water, the returned dict contains only ‘HOH’.

Parameters:

• cutoff – Lowest salt concentration to consider. Analysis will stop once the concentrations of Salts being analyzed goes below this value. Useful for excluding analysis of trace anions.

• use_totals – Whether to base the analysis on total element concentrations or individual species concentrations.

Notes

Salts are identified by pairing the predominant cations and anions in the solution, in descending order of their respective equivalent amounts.

Many empirical equations for solution properties such as activity coefficient, partial molar volume, or viscosity are based on the concentration of single salts (e.g., NaCl). When multiple ions are present (e.g., a solution containing Na+, Cl-, and Mg+2), it is generally not possible to directly model these quantities.

The get_salt_dict() method examines the ionic composition of a solution and simplifies it into a list of salts. The method returns a dictionary of Salt objects where the keys are the salt formulas (e.g., ‘NaCl’). The Salt object contains information about the stoichiometry of the salt to enable its effective concentration to be calculated (e.g., 1 M MgCl2 yields 1 M Mg+2 and 2 M Cl-).

Returns:

dict

A dictionary of Salt objects, keyed to the salt formula

See also

osmotic_pressure viscosity_kinematic get_activity() get_activity_coefficient() get_water_activity() get_osmotic_coefficient()

equilibrate(**kwargs) → None

Update the composition of the Solution using the thermodynamic engine.

Any kwargs specified are passed through to self.engine.equilibrate()

Returns:

Nothing. The .components attribute of the Solution is updated.

get_activity_coefficient(solute: str, scale: Literal['molal', 'molar', 'fugacity', 'rational'] = 'molal') → Quantity

Return the activity coefficient of a solute in solution.

The model used to calculate the activity coefficient is determined by the Solution’s equation of state engine.

Parameters:

• solute – The solute for which to retrieve the activity coefficient

• scale – The activity coefficient concentration scale

• 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 activity coefficient as a dimensionless pint Quantity

Return type:

Quantity

get_activity(solute: str, scale: Literal['molal', 'molar', 'rational'] = 'molal') → Quantity

Return the thermodynamic activity of the solute in solution on the chosen concentration scale.

Parameters:

• solute – String representing the name of the solute of interest

• scale – The concentration scale for the returned activity. Valid options are “molal”, “molar”, and “rational” (i.e., mole fraction). By default, the molal scale activity 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 thermodynamic activity of the solute in question (dimensionless Quantity)

Notes

The thermodynamic activity depends on the concentration scale used [rs] . By default, the ionic strength, activity coefficients, and activities are all calculated based on the molal (mol/kg) concentration scale.

References

[rs]

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

See also

ionic_strength get_activity_coefficient() get_salt()

get_osmotic_coefficient(scale: Literal['molal', 'molar', 'rational'] = 'molal') → Quantity

Return the osmotic coefficient of an aqueous solution.

The method used depends on the Solution object’s equation of state engine.

get_water_activity() → Quantity

Return the water activity.

Returns:

The thermodynamic activity of water in the solution.

Return type:

Quantity

See also

ionic_strength get_activity_coefficient() get_salt()

Notes

Water activity is related to the osmotic coefficient in a solution containing i solutes by:

\[\ln a_{w} = - \Phi M_{w} \sum_{i} m_{i}\]

Where \(M_{w}\) is the molar mass of water (0.018015 kg/mol) and \(m_{i}\) is the molal concentration of each species.

If appropriate Pitzer model parameters are not available, the water activity is assumed equal to the mole fraction of water.

References

Blandamer, Mike J., Engberts, Jan B. F. N., Gleeson, Peter T., Reis, Joao Carlos R., 2005. “Activity of water in aqueous systems: A frequently neglected property.” Chemical Society Review 34, 440-458.

Examples

>>> s1 = pyEQL.Solution([['Na+','0.3 mol/kg'],['Cl-','0.3 mol/kg']])
>>> s1.get_water_activity()
<Quantity(0.9900944932888518, 'dimensionless')>

get_chemical_potential_energy(activity_correction: bool = True) → Quantity

Return the total chemical potential energy of a solution (not including pressure or electric effects).

Parameters:

activity_correction – bool, optional If True, activities will be used to calculate the true chemical potential. If False, mole fraction will be used, resulting in a calculation of the ideal chemical potential.

Returns:

Quantity

The actual or ideal chemical potential energy of the solution, in Joules.

Notes

The chemical potential energy (related to the Gibbs mixing energy) is calculated as follows: [koga]

\[E = R T \sum_i n_i \ln a_i\]

or

\[E = R T \sum_i n_i \ln x_i\]

Where \(n\) is the number of moles of substance, \(T\) is the temperature in kelvin, \(R\) the ideal gas constant, \(x\) the mole fraction, and \(a\) the activity of each component.

Note that dissociated ions must be counted as separate components, so a simple salt dissolved in water is a three component solution (cation, anion, and water).

References

[koga]

Koga, Yoshikata, 2007. *Solution Thermodynamics and its Application to Aqueous Solutions:

A differential approach.* Elsevier, 2007, pp. 23-37.

_get_property(solute: str, name: str) → Any | None

Retrieve a thermodynamic property (such as diffusion coefficient) for solute, and adjust it from the reference conditions to the conditions of the solution.

Parameters:

• solute – str String representing the chemical formula of the solute species

• name – str The name of the property needed, e.g. ‘diffusion coefficient’

Returns:

The desired parameter or None if not found

Return type:

Quantity

get_transport_number(solute: str) → Quantity

Calculate the transport number of the solute in the solution.

Parameters:

solute – Formula of the solute for which the transport number is to be calculated.

Returns:

The transport number of solute, as a dimensionless Quantity.

Notes

Transport number is calculated according to :

\[t_i = {D_i z_i^2 C_i \over \sum D_i z_i^2 C_i}\]

Where \(C_i\) is the concentration in mol/L, \(D_i\) is the diffusion coefficient, and \(z_i\) is the charge, and the summation extends over all species in the solution.

Diffusion coefficients \(D_i\) are adjusted for the effects of temperature and ionic strength using the method implemented in PHREEQC >= 3.4. See get_diffusion_coefficient for further details.

References

Geise, G. M.; Cassady, H. J.; Paul, D. R.; Logan, E.; Hickner, M. A. “Specific ion effects on membrane potential and the permselectivity of ion exchange membranes.”” Phys. Chem. Chem. Phys. 2014, 16, 21673-21681.

See also

get_diffusion_coefficient() get_molar_conductivity()

get_lattice_distance(solute: str) → Quantity

Calculate the average distance between molecules.

Calculate the average distance between molecules of the given solute, assuming that the molecules are uniformly distributed throughout the solution.

Parameters:

solute – str String representing the name of the solute of interest

Returns:

The average distance between solute molecules

Return type:

Quantity

Examples

>>> soln = Solution([['Na+','0.5 mol/kg'],['Cl-','0.5 mol/kg']])
>>> soln.get_lattice_distance('Na+')
1.492964.... nanometer

Notes

The lattice distance is related to the molar concentration as follows:

\[d = ( C_i N_A ) ^ {-{1 \over 3}}\]

as_dict() → dict

Convert the Solution into a dict representation that can be serialized to .json or other format.

classmethod from_dict(d: dict) → Solution

Instantiate a Solution from a dictionary generated by as_dict().

classmethod from_preset(preset: Literal['seawater', 'rainwater', 'wastewater', 'urine', 'normal saline', 'Ringers lactate']) → Solution

Instantiate a solution from a preset composition.

Parameters:

preset (str) – String representing the desired solution. Valid entries are ‘seawater’, ‘rainwater’, ‘wastewater’, ‘urine’, ‘normal saline’ and ‘Ringers lactate’.

Returns:

A pyEQL Solution object.

Raises:

FileNotFoundError – If the given preset file doesn’t exist on the file system.

Notes

The following sections explain the different solution options:

• ‘rainwater’ - pure water in equilibrium with atmospheric CO2 at pH 6

• ‘seawater’ or ‘SW’- Standard Seawater. See Table 4 of the Reference for Composition [1]_

• ‘wastewater’ or ‘WW’ - medium strength domestic wastewater. See Table 3-18 of [2]_

• ‘urine’ - typical human urine. See Table 3-15 of [2]_

• ‘normal saline’ or ‘NS’ - normal saline solution used in medicine [3]_

• ‘Ringers lacatate’ or ‘RL’ - Ringer’s lactate solution used in medicine [4]_

References

[1]

Millero, Frank J. “The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale.” Deep-sea Research. Part I 55(1), 2008, 50-72.

[2]

Metcalf & Eddy, Inc. et al. Wastewater Engineering: Treatment and Resource Recovery, 5th Ed. McGraw-Hill, 2013.

[3]

https://en.wikipedia.org/wiki/Saline_(medicine)

[4]

https://en.wikipedia.org/wiki/Ringer%27s_lactate_solution

to_json() → str

Returns a json string representation of the MSONable object.

unsafe_hash()

Returns an hash of the current object. This uses a generic but low performance method of converting the object to a dictionary, flattening any nested keys, and then performing a hash on the resulting object

classmethod validate_monty_v1(_MSONable__input_value)

Pydantic validator with correct signature for pydantic v1.x

classmethod validate_monty_v2(_MSONable__input_value, _)

Pydantic validator with correct signature for pydantic v2.x

to_file(filename: str | Path) → None

Saving to a .yaml or .json file.

Parameters:

filename (str | Path) – The path to the file to save Solution. Valid extensions are .json or .yaml.

classmethod from_file(filename: str | Path) → Solution

Loading from a .yaml or .json file.

Parameters:

filename (str | Path) – Path to the .json or .yaml file (including extension) to load the Solution from. Valid extensions are .json or .yaml.

Returns:

A pyEQL Solution object.

Raises:

FileNotFoundError – If the given filename doesn’t exist on the file system.

print(mode: Literal['all', 'ions', 'cations', 'anions', 'neutrals'] = 'all', units: Literal['ppm', 'mol', 'mol/kg', 'mol/L', '%', 'activity'] = 'mol', places=4)

Print details about the Solution.

Parameters:

• mode – Whether to list the amounts of all solutes, or only anions, cations, any ion, or any neutral solute.

• units – The units to list solute amounts in. “activity” will list dimensionless activities instead of concentrations.

• places – The number of decimal places to round the solute amounts.

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