# Electrochemistry (thermo.electrochem)¶

This module contains models for:

• Pure substance electrical conductivity lookups

• Correlations for aqueous electrolyte heat capacity, density, and viscosity

• Aqueous electrolyte conductivity

• Water equilibrium constants

• Balancing experimental ion analysis results so as to meet the electroneutrality condition

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker.

## Aqueous Electrolyte Density¶

thermo.electrochem.Laliberte_density(T, ws, CASRNs)[source]

Calculate the density of an aqueous electrolyte mixture using the form proposed by [1]. Parameters are loaded by the function as needed. Units are Kelvin and Pa*s.

$\rho_m = \left(\frac{w_w}{\rho_w} + \sum_i \frac{w_i}{\rho_{app_i}}\right)^{-1}$
Parameters
Tfloat

Temperature of fluid [K]

wsarray

Weight fractions of fluid components other than water

CASRNsarray

CAS numbers of the fluid components other than water

Returns
rhofloat

Solution density, [kg/m^3]

Notes

Temperature range check is not used here.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_density(273.15, [0.0037838838], ['7647-14-5'])
1002.62501201

thermo.electrochem.Laliberte_density_mix(T, ws, c0s, c1s, c2s, c3s, c4s)[source]

Calculate the density of an aqueous electrolyte mixture using the form proposed by [1]. All parameters must be provided to the function. Units are Kelvin and Pa*s.

$\rho_m = \left(\frac{w_w}{\rho_w} + \sum_i \frac{w_i}{\rho_{app_i}}\right)^{-1}$
Parameters
Tfloat

Temperature of fluid [K]

wsarray

Weight fractions of fluid components other than water

c0s

Fit coefficient, [-]

c1s

Fit coefficient, [-]

c2s

Fit coefficient, [-]

c3s

Fit coefficient, [1/degC]

c4s

Fit coefficient, [degC]

Returns
rhofloat

Solution density, [kg/m^3]

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_density_mix(T=278.15, ws=[0.00581, 0.002], c0s=[-0.00324112223655149, 0.967814929691928], c1s=[0.0636354335906616, 5.540434135986], c2s=[1.01371399467365, 1.10374669742622], c3s=[0.0145951015210159, 0.0123340782160061], c4s=[3317.34854426537, 2589.61875022366])
1005.6947727219

thermo.electrochem.Laliberte_density_i(T, w_w, c0, c1, c2, c3, c4)[source]

Calculate the density of a solute using the form proposed by Laliberte [1]. Parameters are needed, and a temperature, and water fraction. Units are Kelvin and Pa*s.

$\rho_{app,i} = \frac{(c_0[1-w_w]+c_1)\exp(10^{-6}[t+c_4]^2)} {(1-w_w) + c_2 + c_3 t}$
Parameters
Tfloat

Temperature of fluid [K]

w_wfloat

Weight fraction of water in the solution, [-]

c0float

Fit coefficient, [-]

c1float

Fit coefficient, [-]

c2float

Fit coefficient, [-]

c3float

Fit coefficient, [1/degC]

c4float

Fit coefficient, [degC]

Returns
rho_ifloat

Solute partial density, [kg/m^3]

Notes

Temperature range check is not used here.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> params = [-0.00324112223655149, 0.0636354335906616, 1.01371399467365, 0.0145951015210159, 3317.34854426537]
>>> Laliberte_density_i(273.15+0, 1-0.0037838838, *params)
3761.8917585

thermo.electrochem.Laliberte_density_w(T)[source]

Calculate the density of water using the form proposed by [1]. No parameters are needed, just a temperature. Units are Kelvin and kg/m^3.

$\rho_w = \frac{\left\{\left([(-2.8054253\times 10^{-10}\cdot t + 1.0556302\times 10^{-7})t - 4.6170461\times 10^{-5}]t -0.0079870401\right)t + 16.945176 \right\}t + 999.83952} {1 + 0.01687985\cdot t}$
Parameters
Tfloat

Temperature of fluid [K]

Returns
rho_wfloat

Water density, [kg/m^3]

Notes

Original source not cited No temperature range is used.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_density_w(298.15)
997.0448954179155
>>> Laliberte_density_w(273.15 + 50)
988.0362916114763


## Aqueous Electrolyte Heat Capacity¶

thermo.electrochem.Laliberte_heat_capacity(T, ws, CASRNs)[source]

Calculate the heat capacity of an aqueous electrolyte mixture using the form proposed by [1]. Parameters are loaded by the function as needed.

$Cp_m = w_w Cp_w + \sum w_i Cp_i$
Parameters
Tfloat

Temperature of fluid [K]

wsarray

Weight fractions of fluid components other than water

CASRNsarray

CAS numbers of the fluid components other than water

Returns
Cpfloat

Solution heat capacity, [J/kg/K]

Notes

A temperature range check is not included in this function. Units are Kelvin and J/kg/K.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_heat_capacity(273.15+1.5, [0.00398447], ['7647-14-5'])
4186.575407596064

thermo.electrochem.Laliberte_heat_capacity_mix(T, ws, a1s, a2s, a3s, a4s, a5s, a6s)[source]

Calculate the heat capacity of an aqueous electrolyte mixture using the form proposed by [1]. All parameters must be provided to this function.

$Cp_m = w_w Cp_w + \sum w_i Cp_i$
Parameters
Tfloat

Temperature of fluid [K]

wsarray

Weight fractions of fluid components other than water

CASRNsarray

CAS numbers of the fluid components other than water

Returns
Cpfloat

Solution heat capacity, [J/kg/K]

Notes

A temperature range check is not included in this function. Units are Kelvin and J/kg/K.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_heat_capacity_mix(T=278.15, ws=[0.00581, 0.002], a1s=[-0.0693559668993322, -0.103713247177424], a2s=[-0.0782134167486952, -0.0647453826944371], a3s=[3.84798479408635, 2.92191453087969], a4s=[-11.2762109247072, -5.48799065938436], a5s=[8.73187698542672, 2.41768600041476], a6s=[1.81245930472755, 1.32062411084408])
4154.788562680796

thermo.electrochem.Laliberte_heat_capacity_i(T, w_w, a1, a2, a3, a4, a5, a6)[source]

Calculate the heat capacity of a solute using the form proposed by [1] Parameters are needed, and a temperature, and water fraction.

$Cp_i = a_1 e^\alpha + a_5(1-w_w)^{a_6}$
$\alpha = a_2 t + a_3 \exp(0.01t) + a_4(1-w_w)$
Parameters
Tfloat

Temperature of fluid [K]

w_wfloat

Weight fraction of water in the solution

a1-a6floats

Function fit parameters

Returns
Cp_ifloat

Solute partial heat capacity, [J/kg/K]

Notes

Units are Kelvin and J/kg/K. Temperature range check is not used here.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> params = [-0.0693559668993322, -0.0782134167486952, 3.84798479408635, -11.2762109247072, 8.73187698542672, 1.81245930472755]
>>> Laliberte_heat_capacity_i(1.5+273.15, 1-0.00398447, *params)
-2930.73539458

thermo.electrochem.Laliberte_heat_capacity_w(T)[source]

Calculate the heat capacity of pure water in a fast but similar way as in [1]. [1] suggested the following interpolatative scheme, using points calculated from IAPWS-97 at a pressure of 0.1 MPa up to 95 °C and then at saturation pressure. The maximum temperature of [1] is 140 °C.

$Cp_w = Cp_1 + (Cp_2-Cp_1) \left( \frac{t-t_1}{t_2-t_1}\right) + \frac{(Cp_3 - 2Cp_2 + Cp_1)}{2}\left( \frac{t-t_1}{t_2-t_1}\right) \left( \frac{t-t_1}{t_2-t_1}-1\right)$

In this implementation, the heat capacity of water is calculated from a chebyshev approximation of the scheme of [1] up to ~92 °C and then the heat capacity comes directly from IAPWS-95 at higher temperatures, also at the saturation pressure. There is no discontinuity between the methods.

Parameters
Tfloat

Temperature of fluid [K]

Returns
Cp_wfloat

Water heat capacity, [J/kg/K]

Notes

Units are Kelvin and J/kg/K.

References

1(1,2,3,4)

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_heat_capacity_w(273.15+3.56)
4208.878727051538


## Aqueous Electrolyte Viscosity¶

thermo.electrochem.Laliberte_viscosity(T, ws, CASRNs)[source]

Calculate the viscosity of an aqueous mixture using the form proposed by [1]. Parameters are loaded by the function as needed. Units are Kelvin and Pa*s.

$\mu_m = \mu_w^{w_w} \Pi\mu_i^{w_i}$
Parameters
Tfloat

Temperature of fluid, [K]

wsarray

Weight fractions of fluid components other than water, [-]

CASRNsarray

CAS numbers of the fluid components other than water, [-]

Returns
mufloat

Viscosity of aqueous mixture, [Pa*s]

Notes

Temperature range check is not used here. Check is performed using NaCl at 5 degC from the first value in [1]’s spreadsheet.

References

1(1,2)

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_viscosity(273.15+5, [0.005810], ['7647-14-5'])
0.0015285828581961414

thermo.electrochem.Laliberte_viscosity_mix(T, ws, v1s, v2s, v3s, v4s, v5s, v6s)[source]

Calculate the viscosity of an aqueous mixture using the form proposed by [1]. All parameters must be provided in this implementation.

$\mu_m = \mu_w^{w_w} \Pi\mu_i^{w_i}$
Parameters
Tfloat

Temperature of fluid, [K]

wsarray

Weight fractions of fluid components other than water, [-]

v1s

Fit parameter, [-]

v2s

Fit parameter, [-]

v3s

Fit parameter, [-]

v4s

Fit parameter, [1/degC]

v5s

Fit parameter, [-]

v6s

Fit parameter, [-]

Returns
mufloat

Viscosity of aqueous mixture, [Pa*s]

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_viscosity_mix(T=278.15, ws=[0.00581, 0.002], v1s=[16.221788633396, 69.5769240055845], v2s=[1.32293086770011, 4.17047793905946], v3s=[1.48485985010431, 3.57817553622189], v4s=[0.00746912559657377, 0.0116677996754397], v5s=[30.7802007540575, 13897.6652650556], v6s=[2.05826852322558, 20.8027689840251])
0.0015377348091189648

thermo.electrochem.Laliberte_viscosity_i(T, w_w, v1, v2, v3, v4, v5, v6)[source]

Calculate the viscosity of a solute using the form proposed by [1] Parameters are needed, and a temperature. Units are Kelvin and Pa*s.

$\mu_i = \frac{\exp\left( \frac{v_1(1-w_w)^{v_2}+v_3}{v_4 t +1}\right)} {v_5(1-w_w)^{v_6}+1}$
Parameters
Tfloat

Temperature of fluid, [K]

w_wfloat

Weight fraction of water in the solution, [-]

v1float

Fit parameter, [-]

v2float

Fit parameter, [-]

v3float

Fit parameter, [-]

v4float

Fit parameter, [1/degC]

v5float

Fit parameter, [-]

v6float

Fit parameter, [-]

Returns
mu_ifloat

Solute partial viscosity, [Pa*s]

Notes

Temperature range check is outside of this function. Check is performed using NaCl at 5 degC from the first value in [1]’s spreadsheet.

References

1(1,2)

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> params = [16.221788633396, 1.32293086770011, 1.48485985010431, 0.00746912559657377, 30.7802007540575, 2.05826852322558]
>>> Laliberte_viscosity_i(273.15+5, 1-0.005810, *params)
0.004254025533308794

thermo.electrochem.Laliberte_viscosity_w(T)[source]

Calculate the viscosity of a water using the form proposed by [1]. No parameters are needed, just a temperature. Units are Kelvin and Pa*s. t is temperature in degrees Celcius.

$\mu_w = \frac{t + 246}{(0.05594t+5.2842)t + 137.37}$
Parameters
Tfloat

Temperature of fluid, [K]

Returns
mu_wfloat

Water viscosity, [Pa*s]

Notes

Original source or pure water viscosity is not cited. No temperature range is given for this equation.

References

1

Laliberte, Marc. “A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data.” Journal of Chemical & Engineering Data 54, no. 6 (June 11, 2009): 1725-60. doi:10.1021/je8008123

Examples

>>> Laliberte_viscosity_w(298)
0.000893226448703328


## Aqueous Electrolyte Thermal Conductivity¶

thermo.electrochem.thermal_conductivity_Magomedov(T, P, ws, CASRNs, k_w)[source]

Calculate the thermal conductivity of an aqueous mixture of electrolytes using the form proposed by Magomedov [1]. Parameters are loaded by the function as needed. Function will fail if an electrolyte is not in the database.

$\lambda = \lambda_w\left[ 1 - \sum_{i=1}^n A_i (w_i + 2\times10^{-4} w_i^3)\right] - 2\times10^{-8} PT\sum_{i=1}^n w_i$
Parameters
Tfloat

Temperature of liquid [K]

Pfloat

Pressure of the liquid [Pa]

wsarray

Weight fractions of liquid components other than water

CASRNsarray

CAS numbers of the liquid components other than water

k_wfloat

Liquid thermal condiuctivity or pure water at T and P, [W/m/K]

Returns
klfloat

Liquid thermal condiuctivity, [W/m/K]

Notes

Range from 273 K to 473 K, P from 0.1 MPa to 100 MPa. C from 0 to 25 mass%. Internal untis are MPa for pressure and weight percent.

An example is sought for this function. It is not possible to reproduce the author’s values consistently.

References

1

Magomedov, U. B. “The Thermal Conductivity of Binary and Multicomponent Aqueous Solutions of Inorganic Substances at High Parameters of State.” High Temperature 39, no. 2 (March 1, 2001): 221-26. doi:10.1023/A:1017518731726.

Examples

>>> thermal_conductivity_Magomedov(293., 1E6, [.25], ['7758-94-3'], k_w=0.59827)
0.548654049375

thermo.electrochem.Magomedov_mix(T, P, ws, Ais, k_w)[source]

Calculate the thermal conductivity of an aqueous mixture of electrolytes using the correlation proposed by Magomedov [1]. All coefficients and the thermal conductivity of pure water must be provided.

$\lambda = \lambda_w\left[ 1 - \sum_{i=1}^n A_i (w_i + 2\times10^{-4} w_i^3)\right] - 2\times10^{-8} PT\sum_{i=1}^n w_i$
Parameters
Tfloat

Temperature of liquid [K]

Pfloat

Pressure of the liquid [Pa]

ws

Weight fractions of liquid components other than water, [-]

Ais

Ai coefficients which were regressed, [-]

k_wfloat

Liquid thermal condiuctivity or pure water at T and P, [W/m/K]

Returns
klfloat

Liquid thermal condiuctivity, [W/m/K]

Notes

Range from 273 K to 473 K, P from 0.1 MPa to 100 MPa. C from 0 to 25 mass%. Internal untis are MPa for pressure and weight percent.

References

1

Magomedov, U. B. “The Thermal Conductivity of Binary and Multicomponent Aqueous Solutions of Inorganic Substances at High Parameters of State.” High Temperature 39, no. 2 (March 1, 2001): 221-26. doi:10.1023/A:1017518731726.

Examples

>>> Magomedov_mix(293., 1E6, [.25], [0.00294], k_w=0.59827)
0.548654049375


## Aqueous Electrolyte Electrical Conductivity¶

thermo.electrochem.dilute_ionic_conductivity(ionic_conductivities, zs, rhom)[source]

This function handles the calculation of the electrical conductivity of a dilute electrolytic aqueous solution. Requires the mole fractions of each ion, the molar density of the whole mixture, and ionic conductivity coefficients for each ion.

$\lambda = \sum_i \lambda_i^\circ z_i \rho_m$
Parameters
ionic_conductivities

Ionic conductivity coefficients of each ion in the mixture [m^2*S/mol]

zs

Mole fractions of each ion in the mixture, [-]

rhomfloat

Overall molar density of the solution, [mol/m^3]

Returns
kappafloat

Electrical conductivity of the fluid, [S/m]

Notes

The ionic conductivity coefficients should not be equivalent coefficients; for example, 0.0053 m^2*S/mol is the equivalent conductivity coefficient of Mg+2, but this method expects twice its value - 0.0106. Both are reported commonly in literature.

Water can be included in this caclulation by specifying a coefficient of 0. The conductivity of any electrolyte eclipses its own conductivity by many orders of magnitude. Any other solvents present will affect the conductivity extensively and there are few good methods to predict this effect.

References

1

Haynes, W.M., Thomas J. Bruno, and David R. Lide. CRC Handbook of Chemistry and Physics, 95E. Boca Raton, FL: CRC press, 2014.

Examples

Complex mixture of electrolytes [‘Cl-’, ‘HCO3-’, ‘SO4-2’, ‘Na+’, ‘K+’, ‘Ca+2’, ‘Mg+2’]:

>>> ionic_conductivities = [0.00764, 0.00445, 0.016, 0.00501, 0.00735, 0.0119, 0.01061]
>>> zs = [0.03104, 0.00039, 0.00022, 0.02413, 0.0009, 0.0024, 0.00103]
>>> dilute_ionic_conductivity(ionic_conductivities=ionic_conductivities, zs=zs, rhom=53865.9)
22.05246783663

thermo.electrochem.conductivity_McCleskey(T, M, lambda_coeffs, A_coeffs, B, multiplier, rho=1000.0)[source]

This function handles the calculation of the electrical conductivity of an electrolytic aqueous solution with one electrolyte in solution. It handles temperature dependency and concentrated solutions. Requires the temperature of the solution; its molality, and four sets of coefficients lambda_coeffs, A_coeffs, B, and multiplier.

$\Lambda = \frac{\kappa}{C} \Lambda = \Lambda^0(t) - A(t) \frac{m^{1/2}}{1+Bm^{1/2}} \Lambda^\circ(t) = c_1 t^2 + c_2 t + c_3 A(t) = d_1 t^2 + d_2 t + d_3$

In the above equations, t is temperature in degrees Celcius; m is molality in mol/kg, and C is the concentration of the elctrolytes in mol/m^3, calculated as the product of density and molality.

Parameters
Tfloat

Temperature of the solution, [K]

Mfloat

Molality of the solution with respect to one electrolyte (mol solute / kg solvent), [mol/kg]

lambda_coeffs

List of coefficients for the polynomial used to calculate lambda; length-3 coefficients provided in [1], [-]

A_coeffs

List of coefficients for the polynomial used to calculate A; length-3 coefficients provided in [1], [-]

Bfloat

Empirical constant for an electrolyte, [-]

multiplierfloat

The multiplier to obtain the absolute conductivity from the equivalent conductivity; ex 2 for CaCl2, [-]

rhofloat, optional

The mass density of the aqueous mixture, [kg/m^3]

Returns
kappafloat

Electrical conductivity of the solution at the specified molality and temperature [S/m]

Notes

Coefficients provided in [1] result in conductivity being calculated in units of mS/cm; they are converted to S/m before returned.

References

1(1,2,3)

McCleskey, R. Blaine. “Electrical Conductivity of Electrolytes Found In Natural Waters from (5 to 90) °C.” Journal of Chemical & Engineering Data 56, no. 2 (February 10, 2011): 317-27. doi:10.1021/je101012n.

Examples

A 0.5 wt% solution of CaCl2, conductivity calculated in mS/cm

>>> conductivity_McCleskey(T=293.15, M=0.045053, A_coeffs=[.03918, 3.905,
... 137.7], lambda_coeffs=[0.01124, 2.224, 72.36], B=3.8, multiplier=2)
0.8482584585108555

thermo.electrochem.ionic_strength(mis, zis)[source]

Calculate the ionic strength of a solution in one of two ways, depending on the inputs only. For Pitzer and Bromley models, mis should be molalities of each component. For eNRTL models, mis should be mole fractions of each electrolyte in the solution. This will sum to be much less than 1.

$I = \frac{1}{2} \sum M_i z_i^2 I = \frac{1}{2} \sum x_i z_i^2$
Parameters
mislist

Molalities of each ion, or mole fractions of each ion [mol/kg or -]

zislist

Charges of each ion [-]

Returns
Ifloat

ionic strength, [?]

References

1

Chen, Chau-Chyun, H. I. Britt, J. F. Boston, and L. B. Evans. “Local Composition Model for Excess Gibbs Energy of Electrolyte Systems. Part I: Single Solvent, Single Completely Dissociated Electrolyte Systems.” AIChE Journal 28, no. 4 (July 1, 1982): 588-96. doi:10.1002/aic.690280410

2

Gmehling, Jurgen. Chemical Thermodynamics: For Process Simulation. Weinheim, Germany: Wiley-VCH, 2012.

Examples

>>> ionic_strength([0.1393, 0.1393], [1, -1])
0.1393


## Pure Liquid Electrical Conductivity¶

thermo.electrochem.conductivity(CASRN, method=None)[source]

This function handles the retrieval of a chemical’s conductivity. Lookup is based on CASRNs. Will automatically select a data source to use if no method is provided; returns None if the data is not available.

Function has data for approximately 100 chemicals.

Parameters
CASRNstr

CASRN [-]

Returns
kappafloat

Electrical conductivity of the fluid, [S/m]

T

Temperature at which conductivity measurement was made or None if not available, [K]

Other Parameters
methodstr, optional

A string for the method name to use, as defined by constants in conductivity_methods

Notes

Only one source is available in this function. It is:

• ‘LANGE_COND’ which is from Lange’s Handbook, Table 8.34 Electrical Conductivity of Various Pure Liquids’, a compillation of data in [1]. The individual datapoints in this source are not cited at all.

References

1

Speight, James. Lange’s Handbook of Chemistry. 16 edition. McGraw-Hill Professional, 2005.

Examples

>>> conductivity('7732-18-5')
(4e-06, 291.15)

thermo.electrochem.conductivity_methods(CASRN)[source]

Return all methods available to obtain electrical conductivity for the specified chemical.

Parameters
CASRNstr

CASRN, [-]

Returns
methods

Methods which can be used to obtain electrical conductivity with the given inputs.

thermo.electrochem.conductivity_all_methods = ['LANGE_COND']

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

## Water Dissociation Equilibrium¶

thermo.electrochem.Kweq_Arcis_Tremaine_Bandura_Lvov(T, rho_w)[source]

Calculates equilibrium constant for OH- and H+ in water, according to [1].

$Q = \rho \exp(\alpha_0 + \alpha_1 T^{-1} + \alpha_2 T^{-2} \rho^{2/3})$
$- \log_{10} K_w = -2n \left[ \log_{10}(1+Q) - \frac{Q}{Q+1} \rho (\beta_0 + \beta_1 T^{-1} + \beta_2 \rho) \right] -\log_{10} K_w^G + 2 \log_{10} \frac{18.015268}{1000}$
Parameters
Tfloat

Temperature of water [K]

rho_wfloat

Density of water at temperature and pressure [kg/m^3]

Returns
Kweqfloat

Ionization constant of water, [-]

Notes

Formulation is in terms of density in g/cm^3; density is converted internally.

n = 6; alpha0 = -0.864671; alpha1 = 8659.19; alpha2 = -22786.2; beta0 = 0.642044; beta1 = -56.8534; beta2 = -0.375754

References

1

Arcis, Hugues, Jane P. Ferguson, Jenny S. Cox, and Peter R. Tremaine. “The Ionization Constant of Water at Elevated Temperatures and Pressures: New Data from Direct Conductivity Measurements and Revised Formulations from T = 273 K to 674 K and p = 0.1 MPa to 31 MPa.” Journal of Physical and Chemical Reference Data 49, no. 3 (July 23, 2020): 033103. https://doi.org/10.1063/1.5127662.

Examples

>>> -1*log10(Kweq_Arcis_Tremaine_Bandura_Lvov(600, 700))
11.138236348

thermo.electrochem.Kweq_IAPWS(T, rho_w)[source]

Calculates equilibrium constant for OH- and H+ in water, according to [1]. This is the most recent formulation available.

$Q = \rho \exp(\alpha_0 + \alpha_1 T^{-1} + \alpha_2 T^{-2} \rho^{2/3})$
$- \log_{10} K_w = -2n \left[ \log_{10}(1+Q) - \frac{Q}{Q+1} \rho (\beta_0 + \beta_1 T^{-1} + \beta_2 \rho) \right] -\log_{10} K_w^G + 2 \log_{10} \frac{18.015268}{1000}$
Parameters
Tfloat

Temperature of water [K]

rho_wfloat

Density of water at temperature and pressure [kg/m^3]

Returns
Kweqfloat

Ionization constant of water, [-]

Notes

Formulation is in terms of density in g/cm^3; density is converted internally.

n = 6; alpha0 = -0.864671; alpha1 = 8659.19; alpha2 = -22786.2; beta0 = 0.642044; beta1 = -56.8534; beta2 = -0.375754

References

1

Bandura, Andrei V., and Serguei N. Lvov. “The Ionization Constant of Water over Wide Ranges of Temperature and Density.” Journal of Physical and Chemical Reference Data 35, no. 1 (March 1, 2006): 15-30. doi:10.1063/1.1928231

Examples

Example from IAPWS check:

>>> -1*log10(Kweq_IAPWS(600, 700))
11.203153057603775

thermo.electrochem.Kweq_IAPWS_gas(T)[source]

Calculates equilibrium constant for OH- and H+ in water vapor, according to [1]. This is the most recent formulation available.

$-log_{10} K_w^G = \gamma_0 + \gamma_1 T^{-1} + \gamma_2 T^{-2} + \gamma_3 T^{-3}$
Parameters
Tfloat

Temperature of H2O [K]

Returns
K_w_Gfloat

Notes

gamma0 = 6.141500E-1; gamma1 = 4.825133E4; gamma2 = -6.770793E4; gamma3 = 1.010210E7

References

1

Bandura, Andrei V., and Serguei N. Lvov. “The Ionization Constant of Water over Wide Ranges of Temperature and Density.” Journal of Physical and Chemical Reference Data 35, no. 1 (March 1, 2006): 15-30. doi:10.1063/1.1928231

Examples

>>> Kweq_IAPWS_gas(800)
1.4379721554798815e-61

thermo.electrochem.Kweq_1981(T, rho_w)[source]

Calculates equilibrium constant for OH- and H+ in water, according to [1]. Second most recent formulation.

$\log_{10} K_w= A + B/T + C/T^2 + D/T^3 + (E+F/T+G/T^2)\log_{10} \rho_w$
Parameters
Tfloat

Temperature of fluid [K]

rho_wfloat

Density of water, [kg/m^3]

Returns
Kweqfloat

Ionization constant of water, [-]

Notes

Density is internally converted to units of g/cm^3.

A = -4.098; B = -3245.2; C = 2.2362E5; D = -3.984E7; E = 13.957; F = -1262.3; G = 8.5641E5

References

1

Marshall, William L., and E. U. Franck. “Ion Product of Water Substance, 0-1000 degree C, 1010,000 Bars New International Formulation and Its Background.” Journal of Physical and Chemical Reference Data 10, no. 2 (April 1, 1981): 295-304. doi:10.1063/1.555643.

Examples

>>> -1*log10(Kweq_1981(600, 700))
11.274522047


## Balancing Ions¶

thermo.electrochem.balance_ions(anions, cations, anion_zs=None, cation_zs=None, anion_concs=None, cation_concs=None, rho_w=997.1, method='increase dominant', selected_ion=None)[source]

Performs an ion balance to adjust measured experimental ion compositions to electroneutrality. Can accept either the actual mole fractions of the ions, or their concentrations in units of [mg/L] as well for convinience.

The default method will locate the most prevalent ion in the type of ion not in excess - and increase it until the two ion types balance.

Parameters
anionslist(ChemicalMetadata)

List of all negatively charged ions measured as being in the solution; ChemicalMetadata instances or simply objects with the attributes MW and charge, [-]

cationslist(ChemicalMetadata)

List of all positively charged ions measured as being in the solution; ChemicalMetadata instances or simply objects with the attributes MW and charge, [-]

anion_zslist, optional

Mole fractions of each anion as measured in the aqueous solution, [-]

cation_zslist, optional

Mole fractions of each cation as measured in the aqueous solution, [-]

anion_concslist, optional

Concentrations of each anion in the aqueous solution in the units often reported (for convinience only) [mg/L]

cation_concslist, optional

Concentrations of each cation in the aqueous solution in the units often reported (for convinience only) [mg/L]

rho_wfloat, optional

Density of the aqueous solutionr at the temperature and pressure the anion and cation concentrations were measured (if specified), [kg/m^3]

methodstr, optional

The method to use to balance the ionimbalance; one of ‘dominant’, ‘decrease dominant’, ‘increase dominant’, ‘proportional insufficient ions increase’, ‘proportional excess ions decrease’, ‘proportional cation adjustment’, ‘proportional anion adjustment’, ‘Na or Cl increase’, ‘Na or Cl decrease’, ‘adjust’, ‘increase’, ‘decrease’, ‘makeup’].

selected_ionChemicalMetadata, optional

Some methods adjust only one user-specified ion; this is that input. For the case of the ‘makeup’ method, this is a tuple of (anion, cation) ChemicalMetadata instances and only the ion type not in excess will be used.

Returns
anionslist[ChemicalMetadata]

List of all negatively charged ions measured as being in the solution; ChemicalMetadata instances after potentially adding in an ion which was not present but specified by the user, [-]

cationslist[ChemicalMetadata]

List of all positively charged ions measured as being in the solution; ChemicalMetadata instances after potentially adding in an ion which was not present but specified by the user, [-]

anion_zs

Mole fractions of each anion in the aqueous solution after the charge balance, [-]

cation_zs

Mole fractions of each cation in the aqueous solution after the charge balance, [-]

z_water

Mole fraction of the water in the solution, [-]

Notes

The methods perform the charge balance as follows:

• ‘dominant’ : The ion with the largest mole fraction in solution has its concentration adjusted up or down as necessary to balance the solution.

• ‘decrease dominant’ : The ion with the largest mole fraction in the type of ion with excess charge has its own mole fraction decreased to balance the solution.

• ‘increase dominant’ : The ion with the largest mole fraction in the type of ion with insufficient charge has its own mole fraction decreased to balance the solution.

• ‘proportional insufficient ions increase’ : The ion charge type which is present insufficiently has each of the ions mole fractions increased proportionally until the solution is balanced.

• ‘proportional excess ions decrease’ : The ion charge type which is present in excess has each of the ions mole fractions decreased proportionally until the solution is balanced.

• ‘proportional cation adjustment’ : All cations have their mole fractions increased or decreased proportionally as necessary to balance the solution.

• ‘proportional anion adjustment’ : All anions have their mole fractions increased or decreased proportionally as necessary to balance the solution.

• ‘Na or Cl increase’ : Either Na+ or Cl- is added to the solution until the solution is balanced; the species will be added if they were not present initially as well.

• ‘Na or Cl decrease’ : Either Na+ or Cl- is removed from the solution until the solution is balanced; the species will be added if they were not present initially as well.

• ‘adjust’ : An ion specified with the parameter selected_ion has its mole fraction increased or decreased as necessary to balance the solution. An exception is raised if the specified ion alone cannot balance the solution.

• ‘increase’ : An ion specified with the parameter selected_ion has its mole fraction increased as necessary to balance the solution. An exception is raised if the specified ion alone cannot balance the solution.

• ‘decrease’ : An ion specified with the parameter selected_ion has its mole fraction decreased as necessary to balance the solution. An exception is raised if the specified ion alone cannot balance the solution.

• ‘makeup’ : Two ions ase specified as a tuple with the parameter selected_ion. Whichever ion type is present in the solution insufficiently is added; i.e. if the ions were Mg+2 and Cl-, and there was too much negative charge in the solution, Mg+2 would be added until the solution was balanced.

Examples

>>> anions_n = ['Cl-', 'HCO3-', 'SO4-2']
>>> cations_n = ['Na+', 'K+', 'Ca+2', 'Mg+2']
>>> cations = [identifiers.pubchem_db.search_name(i) for i in cations_n]
>>> anions = [identifiers.pubchem_db.search_name(i) for i in anions_n]
>>> an_res, cat_res, an_zs, cat_zs, z_water = balance_ions(anions, cations,
... anion_zs=[0.02557, 0.00039, 0.00026], cation_zs=[0.0233, 0.00075,
... 0.00262, 0.00119], method='proportional excess ions decrease')
>>> an_zs
[0.02557, 0.00039, 0.00026]
>>> cat_zs
[0.01948165456267761, 0.0006270918850647299, 0.0021906409851594564, 0.0009949857909693717]
>>> z_water
0.9504856267761288


## Fit Coefficients and Data¶

All of these coefficients are lazy-loaded, so they must be accessed as an attribute of this module.

In [1]: from thermo.electrochem import Magomedovk_thermal_cond, cond_data_McCleskey, CRC_aqueous_thermodynamics, electrolyte_dissociation_reactions, Laliberte_data

In [2]: Magomedovk_thermal_cond
Out[2]:
Formula               Chemical       Ai
CASRN
497-19-8       Na2CO3      Sodium carbonate  -0.00050
584-08-7        K2CO3   Potassium carbonate   0.00160
7447-39-4       CuCl2      Cuprous chloride   0.00360
7488-54-2      Rb2SO4      Rubidium sulfate   0.00134
7601-89-0      NaClO4    Sodium perchlorate   0.00250
7646-79-9       CoCl2    Cobaltous chloride   0.00320
7664-93-9       H2SO4          Acid sulfate   0.00305
7699-45-8       ZnBr2          Zinc bromide   0.00410
7718-54-9       NiCl2    Nickelous chloride   0.00330
7758-94-3       FeCl2      Ferrous chloride   0.00294
7761-88-8       AgNO3        Silver nitrate   0.00190
7775-09-9      NaClO3       Sodium chlorate   0.00240
7778-50-9     K2Cr2O7  Potassium dichromate   0.00188
7786-81-4       NiSO4     Nickelous sulfate   0.00140
7789-00-6      K2CrO4    Potassium chromate   0.00130
7789-23-3          KF    Potassium fluoride   0.00180
7789-38-0      NaBrO3        Sodium bromate   0.00170
7789-39-1        RbBr      Rubidium bromide   0.00305
7789-42-6       CdBr2       Cadmium bromide   0.00274
7789-46-0       FeBr2       Ferrous bromide   0.00375
7790-29-6         RbI       Rubidium iodide   0.00322
7790-80-9        CdI2        Cadmium iodide   0.00302
7791-11-9        RbCl     Rubidium chloride   0.00238
10042-76-9   Sr(NO3)2     Strontium nitrate   0.00153
10043-01-3  Al2(SO4)3      Aluminum sulfate   0.00335
10099-74-8   Pb(NO3)2          Lead nitrate   0.00138
10102-68-8       CaI2        Calcium iodide   0.00340
10139-47-6       ZnI2           Zinc iodide   0.00410
10325-94-7   Cd(NO3)2       Cadmium nitrate   0.00155
10377-51-2        LiI        Lithium iodide   0.00435
10377-58-9       MgI2      Magnesium iodide   0.00417
10476-81-0      SrBr2     Strontium bromide   0.00290
10476-85-4      SrCl2    Strontium chloride   0.00170
10476-86-5       SrI2      Strontium iodide   0.00311
12027-06-4       NH4I       Ammonium iodide   0.00480
13126-12-0      RbNO3      Rubidium nitrate   0.00214
13462-88-9      NiBr2     Nickelous bromide   0.00396
13462-90-3       NiI2      Nickelous iodide   0.00393
15238-00-3       CoI2      Cobaltous iodide   0.00384

In [3]: cond_data_McCleskey
Out[3]:
formula        c1     c2  ...       d3      B  multiplier
CASRN                                  ...
7447-40-7        KCl  0.009385  2.533  ...    44.11   1.70           1
7647-14-5       NaCl  0.008967  2.196  ...    44.55   1.30           1
7647-01-0        HCl -0.006766  6.614  ...    48.53   0.01           1
7447-41-8       LiCl  0.008784  1.996  ...    42.79   1.00           1
7647-17-8       CsCl  0.010080  2.479  ...    41.29   1.40           1
12125-02-9     NH4Cl  0.006575  2.684  ...    30.00   0.70           1
10043-52-4     CaCl2  0.011240  2.224  ...   137.70   3.80           2
7786-30-3      MgCl2  0.009534  2.247  ...   129.80   3.10           2
10361-37-2     BaCl2  0.010380  2.346  ...   111.80   2.40           2
10476-85-4     SrCl2  0.009597  2.279  ...    60.18   0.80           2
7664-93-9      H2SO4 -0.019850  7.421  ...  1869.00  11.50           2
7757-82-6     Na2SO4  0.009501  2.317  ...   135.50   2.20           2
7778-80-5      K2SO4  0.008819  2.872  ...   247.10   5.30           2
10294-54-9    Cs2SO4  0.012730  2.457  ...   187.40   3.30           2
7778-18-9      CaSO4  0.011920  2.564  ...   644.40   9.60           2
7646-93-7      KHSO4 -0.003092  9.759  ...  1776.00   8.20           1
298-14-6       KHCO3  0.007807  2.040  ...    38.58   0.90           1
584-08-7       K2CO3  0.011450  2.726  ...    81.12   2.10           2
144-55-8      NaHCO3  0.012600  1.543  ...    52.94   1.10           1
497-19-8      Na2CO3  0.022960  5.211  ...   455.80   4.80           2
1310-73-2       NaOH  0.006936  3.872  ...    56.76   0.20           1
7681-49-4        NaF  0.007346  2.032  ...    69.99   2.30           1
7789-23-3         KF  0.007451  2.294  ...    39.40   0.90           1
7758-02-3        KBr  0.007076  2.612  ...    29.49   0.60           1
7757-79-1       KNO3  0.009117  2.309  ...    49.12   0.70           1
7779-88-6   Zn(NO3)2  0.015260  4.519  ...   302.90   4.00           2

[26 rows x 9 columns]

In [4]: CRC_aqueous_thermodynamics
Out[4]:
Formula                            Name  ...  S(aq)  Cp(aq)
CAS                                                         ...
57-12-5                CN-                     Cyanide ion  ...   94.1     NaN
71-47-6              CHOO-                     Formate ion  ...   92.0   -87.9
71-50-1            CH3COO-                     Acetate ion  ...   86.6    -6.3
71-52-3              HCO3-                 Bicarbonate ion  ...   91.2     NaN
302-04-5              SCN-                 Thiocyanate ion  ...  144.3   -40.2
...                    ...                             ...  ...    ...     ...
117412-24-5         BeO2-2           Beryllium dioxide ion  ... -159.0     NaN
127622-32-6        Y(OH)+2           Yttrium hydroxide ion  ...    NaN     NaN
129466-35-9       Te(OH)3+  Tellurium(IV) trihydroxide ion  ...  111.7     NaN
186449-38-7         InOH+2            Indium hydroxide ion  ...  -88.0     NaN
2099995000-00-0  Y2(OH)2+4         Yttrium dihydroxide ion  ...    NaN     NaN

[173 rows x 7 columns]

In [5]: electrolyte_dissociation_reactions
Out[5]:
Electrolyte name Electrolyte CAS  ... Cation charge Cation count
0    Diammonium Hydrogen phosphate       7783-28-0  ...             1            2
1                 Ammonium Sulfate       7783-20-2  ...             1            2
2                 ammonium sulfite      10196-04-0  ...             1            2
3               Ammonium phosphate      10361-65-6  ...             1            3
4     Ammonium siliconhexafluoride      16919-19-0  ...             1            2
..                             ...             ...  ...           ...          ...
259                  Zinc selenite      13597-46-1  ...             2            1
260                  Zinc selenate      13597-54-1  ...             2            1
261                   Zinc Nitrate       7779-88-6  ...             2            1
262                  Zinc Chloride       7646-85-7  ...             2            1
263                   Zinc Sulfate       7733-02-0  ...             2            1

[264 rows x 11 columns]

In [6]: Laliberte_data
Out[6]:
Name    Formula  ...   Max w.2  No of points in corr.2
CASRN                                     ...
7783-20-2    Ammonium Sulfate  (NH4)2SO4  ...       NaN                     NaN
10043-01-3   Aluminum Sulfate  Al2(SO4)3  ...       NaN                     NaN
7446-70-0   Aluminum Chloride      AlCl3  ...       NaN                     NaN
10022-31-8     Barium Nitrate   Ba(NO3)2  ...  0.047274                    96.0
10361-37-2    Barium Chloride      BaCl2  ...  0.248237                    16.0
...                       ...        ...  ...       ...                     ...
57-50-1               Sucrose    Sucrose  ...       NaN                     NaN
13825-74-6    Titanyl Sulfate     TiOSO4  ...       NaN                     NaN
7779-88-6        Zinc Nitrate   Zn(NO3)2  ...  0.077132                   144.0
7646-85-7       Zinc Chloride      ZnCl2  ...       NaN                     NaN
7733-02-0        Zinc Sulfate      ZnSO4  ...       NaN                     NaN

[109 rows x 32 columns]