The class used to define conditions to be satisfied at chemical equilibrium. More...

#include <EquilibriumSpecs.hpp>

Public Member Functions
	EquilibriumSpecs (ChemicalSystem const &system)
	Construct an EquilibriumSpecs object.

auto	temperature () -> void
	Specify that the temperature of the system is given at chemical equilibrium. More...

auto	pressure () -> void
	Specify that the pressure of the system is given at chemical equilibrium. More...

auto	volume () -> void
	Specify that the volume of the system is given at chemical equilibrium. More...

auto	internalEnergy () -> void
	Specify that the internal energy of the system is given at chemical equilibrium. More...

auto	enthalpy () -> void
	Specify that the enthalpy of the system is given at chemical equilibrium. More...

auto	gibbsEnergy () -> void
	Specify that the Gibbs energy of the system is given at chemical equilibrium. More...

auto	helmholtzEnergy () -> void
	Specify that the Helmholtz energy of the system is given at chemical equilibrium. More...

auto	entropy () -> void
	Specify that the entropy of the system is given at chemical equilibrium. More...

auto	charge () -> void
	Specify that the electric charge is given at chemical equilibrium.

auto	elementAmount (StringOrIndex const &element) -> void
	Specify that the amount of an element is given at chemical equilibrium. More...

auto	elementAmountInPhase (StringOrIndex const &element, StringOrIndex const &phase) -> void
	Specify that the amount of an element in a phase is given at chemical equilibrium. More...

auto	elementMass (StringOrIndex const &element) -> void
	Specify that the mass of an element is given at chemical equilibrium. More...

auto	elementMassInPhase (StringOrIndex const &element, StringOrIndex const &phase) -> void
	Specify that the mass of an element in a phase is given at chemical equilibrium. More...

auto	phaseAmount (StringOrIndex const &phase) -> void
	Specify that the amount of a phase is given at chemical equilibrium. More...

auto	phaseMass (StringOrIndex const &phase) -> void
	Specify that the mass of a phase is given at chemical equilibrium. More...

auto	phaseVolume (StringOrIndex const &phase) -> void
	Specify that the volume of a phase is given at chemical equilibrium. More...

auto	unknownTemperature () -> void
	Specify that the temperature of the system is unknown in the chemical equilibrium calculation. More...

auto	unknownPressure () -> void
	Specify that the pressure of the system is unknown in the chemical equilibrium calculation. More...

auto	chemicalPotential (String substance) -> void
	Specify that the chemical potential of a substance is given at chemical equilibrium. More...

auto	lnActivity (Species const &species) -> void
	Specify that the ln activity of a species is given at chemical equilibrium. More...

auto	lnActivity (String species) -> void
	Specify that the ln activity of a species is given at chemical equilibrium. More...

auto	lgActivity (String species) -> void
	Specify that the lg activity of a species is given at chemical equilibrium. More...

auto	activity (String species) -> void
	Specify that the activity of a species is given at chemical equilibrium. More...

auto	fugacity (String gas) -> void
	Specify that the fugacity of a gaseous species is given at chemical equilibrium. More...

auto	pH () -> void
	Specify that the pH is given at chemical equilibrium. More...

auto	pMg () -> void
	Specify that pMg is given at chemical equilibrium. More...

auto	pE () -> void
	Specify that pE is given at chemical equilibrium. More...

auto	Eh () -> void
	Specify that Eh is given at chemical equilibrium. More...

auto	openTo (ChemicalFormula const &substance) -> void
	Specify that the chemical system is open to a substance. More...

auto	addUnknownTitrantAmount (ChemicalFormula const &substance) -> void
	Specify that the chemical system is open to a given chemical state. // TODO: Implement EquilibriumSpecs::auto openTo(ChemicalState const& state). More...

auto	numInputs () const -> Index
	Return the number of introduced input variables.

auto	numControlVariables () const -> Index
	Return the number of all introduced control variables.

auto	numControlVariablesP () const -> Index
	Return the number of introduced p control variables.

auto	numControlVariablesQ () const -> Index
	Return the number of introduced q control variables.

auto	numTitrants () const -> Index
	Return the number of all introduced explicit and implicit titrants.

auto	numTitrantsExplicit () const -> Index
	Return the number of all introduced explicit titrants.

auto	numTitrantsImplicit () const -> Index
	Return the number of all introduced implicit titrants.

auto	numEquationConstraints () const -> Index
	Return the number of all introduced equation constraints.

auto	numReactivityConstraints () const -> Index
	Return the number of all introduced reactivity constraints.

auto	numConstraints () const -> Index
	Return the number of all introduced equation, reactivity, and chemical potential constraints.

auto	numConservativeComponents () const -> Index
	Return the number of the conservative components in the equilibrium problem specifications.

auto	namesInputs () const -> Strings
	Return the names of the introduced input variables.

auto	namesControlVariables () const -> Strings
	Return the names of all introduced control variables.

auto	namesControlVariablesP () const -> Strings
	Return the names of introduced p control variables.

auto	namesControlVariablesQ () const -> Strings
	Return the names of introduced q control variables.

auto	namesTitrants () const -> Strings
	Return the names of all introduced explicit and implicit titrants.

auto	namesTitrantsExplicit () const -> Strings
	Return the names of all introduced explicit titrants.

auto	namesTitrantsImplicit () const -> Strings
	Return the names of all introduced implicit titrants.

auto	namesConstraints () const -> Strings
	Return the names of all introduced equation and chemical potential constraints.

auto	namesConservativeComponents () const -> Strings
	Return the names of the conservative components in the equilibrium problem specifications.

auto	addControlVariableQ (ControlVariableQ const &qvar) -> void
	Add a q control variable in the specification of the chemical equilibrium problem.

auto	addControlVariableP (ControlVariableP const &pvar) -> void
	Add a p control variable in the specification of the chemical equilibrium problem.

auto	addConstraint (EquationConstraint const &constraint) -> void
	Add an equation constraint to be satisfied at chemical equilibrium.

auto	addConstraints (EquationConstraints const &constraints) -> void
	Add a system of equation constraints to be satisfied at chemical equilibrium.

auto	addReactivityConstraint (ReactivityConstraint const &constraint) -> void
	Add a reactivity constraint to be satisfied at chemical equilibrium.

auto	addReactivityConstraints (ReactivityConstraints const &constraints) -> void
	Add a system of reactivity constraints to be satisfied at chemical equilibrium.

auto	addInput (String const &var) -> Index
	Add a new input variable for the chemical equilibrium problem with name `var`.

auto	system () const -> ChemicalSystem const &
	Return the chemical system associated with the equilibrium conditions.

auto	inputs () const -> Strings const &
	Return the input variables in the chemical equilibrium specifications.

auto	isTemperatureUnknown () const -> bool
	Return true if temperature is unknown in the chemical equilibrium specifications.

auto	isPressureUnknown () const -> bool
	Return true if pressure is unknown in the chemical equilibrium specifications.

auto	indexTemperatureAmongInputVariables () const -> Index
	Return the index of temperature in the vector of w input variables if it is an input, otherwise `Index(-1)` if unknown.

auto	indexTemperatureAmongControlVariablesP () const -> Index
	Return the index of temperature in the vector of p control variables if it is unknown, otherwise `Index(-1)` if known.

auto	indexPressureAmongInputVariables () const -> Index
	Return the index of pressure in the vector of w input variables if it is an input, otherwise `Index(-1)` if unknown.

auto	indexPressureAmongControlVariablesP () const -> Index
	Return the index of pressure in the vector of p control variables if it is unknown, otherwise `Index(-1)` if known.

auto	indexInputVariable (String const &name) const -> Index
	Return the index of a w input variable with given name if found, otherwise the number of w input variables.

auto	indexControlVariableP (String const &name) const -> Index
	Return the index of a p control variable with given name if found, otherwise the number of p control variables.

auto	indexControlVariableQ (String const &name) const -> Index
	Return the index of a q control variable with given name if found, otherwise the number of q control variables.

auto	controlVariablesQ () const -> Vec< ControlVariableQ > const &
	Return the q control variables in the chemical equilibrium specifications.

auto	controlVariablesP () const -> Vec< ControlVariableP > const &
	Return the q control variables in the chemical equilibrium specifications.

auto	titrants () const -> Vec< ChemicalFormula >
	Return the chemical formulas of the explicit and implicit titrant substances.

auto	titrantsExplicit () const -> Vec< ChemicalFormula >
	Return the chemical formulas of the explicit titrant substances.

auto	titrantsImplicit () const -> Vec< ChemicalFormula >
	Return the chemical formulas of the implicit titrant substances.

auto	equationConstraintsSingle () const -> Vec< EquationConstraint > const &
	Return the specified single equation constraints to be satisfied at chemical equilibrium.

auto	equationConstraintsSystem () const -> Vec< EquationConstraints > const &
	Return the specified systems of equation constraints to be satisfied at chemical equilibrium.

auto	reactivityConstraintsSingle () const -> Vec< ReactivityConstraint > const &
	Return the specified single reactivity constraints to be satisfied at chemical equilibrium.

auto	reactivityConstraintsSystem () const -> Vec< ReactivityConstraints > const &
	Return the specified systems of reactivity constraints to be satisfied at chemical equilibrium.

auto	assembleEquationConstraints () const -> EquationConstraints
	Assemble the complete system of equation constraints to be satisfied at chemical equilibrium. More...

auto	assembleReactivityConstraints () const -> ReactivityConstraints
	Assemble the complete system of reactivity constraints to be satisfied at chemical equilibrium. More...

auto	assembleReactivityConstraintsMatrixKn () const -> MatrixXd
	Assemble the coefficient matrix Kn of the reactivity constraints with respect to n species amount variables.

auto	assembleReactivityConstraintsMatrixKp () const -> MatrixXd
	Assemble the coefficient matrix Kp of the reactivity constraints with respect to p control variables.

auto	assembleConservationMatrix () const -> MatrixXd
	Assemble the conservation matrix for the chemical species with respect to the conservative components. More...

auto	assembleConservationMatrixN () const -> MatrixXd
	Assemble the conservation matrix for the n species amount variables with respect to the conservative components. More...

auto	assembleConservationMatrixQ () const -> MatrixXd
	Assemble the conservation matrix for the q control variables with respect to the conservative components.

auto	assembleConservationMatrixP () const -> MatrixXd
	Assemble the conservation matrix for the p control variables with respect to the conservative components.

Static Public Member Functions
static auto	TP (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given temperature (T) and pressure (P).

static auto	HP (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given enthalpy (H) and pressure (P).

static auto	TV (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given temperature (T) and volume (V).

static auto	UV (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given internal (U) energy and volume (V).

static auto	SP (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given entropy (S) and pressure (P).

static auto	SV (ChemicalSystem const &system) -> EquilibriumSpecs
	Return specifications for a chemical equilbrium problem with given entropy (S) and volume (V).

Detailed Description

The class used to define conditions to be satisfied at chemical equilibrium.

Explicit Titrants

The explicit titrants are the titrants introduced with method EquilibriumSpecs::openTo. In the code below, the names of the explicitly introduced titrants are shown:

using namespace Reaktoro;
EquilibriumSpecs specs(system); // for some ChemicalSystem object `system`
specs.openTo("H2S"); // a titrant named [H2S] will be introduced.
specs.openTo("CO2"); // a titrant named [CO2] will be introduced.

The amounts of these explicit titrants are unknown in the chemical equilibrium problem and computed together with the amounts of species.

Implicit Titrants

The implicit titrants are the titrants introduced with methods:

In the code below, the names of the implicitly introduced titrants are shown:

using namespace Reaktoro;
EquilibriumSpecs specs(system); // for some ChemicalSystem object `system`
specs.lnActivity("Ca+2"); // a titrant named [Ca+2] will be introduced.
specs.fugacity("O2");     // a titrant named [O2] will be introduced.
specs.pH();               // a titrant named [H+] will be introduced.
specs.pMg();              // a titrant named [Mg+2] will be introduced.
specs.pE();               // a titrant named [e-] will be introduced.
specs.Eh();               // a titrant named [e-] will be introduced.

The amounts of these implicit titrants are unknown in the chemical equilibrium problem and computed together with the amounts of species.

Control Variables

The control variables in a chemical equilibrium problem are unknowns introduced along with equilibrium constraints. These control variables can be:

temperature,
pressure, and
amounts of explicit and implicit titrants.

The number of these control variables depend whether temperature and/or pressure are unknown and if any titrant has been introduced, explicitly or implicitly. For example, if EquilibriumSpecs::temperature is not called, then temperature is unknown and computed in the chemical equilibrium calculation. The same applies for pressure in case EquilibriumSpecs::pressure is not called. Titrants are introduced either explicitly, with method EquilibriumSpecs::openTo, or implicitly, with methods:

The following example formulates a set of specifications for a chemical equilibrium problem in which temperature and the amount of titrant [CO2] are introduced control variables. Their values are not known in advance; they are computed as part of the chemical equilibrium calculation.

using namespace Reaktoro;
EquilibriumSpecs specs(system); // for some ChemicalSystem object `system`
specs.temperature(); // temperature is an input variable in the chemical equilibrium problem.
specs.pressure();    // pressure is an input variable in the chemical equilibrium problem.
specs.volume();      // volume is an input variable in the chemical equilibrium problem.
specs.openTo("CO2"); // a titrant named [CO2] is introduced, and its amount computed at the end of the equilibrium calculation.

Member Function Documentation

◆ temperature()

auto temperature ( ) -> void

Specify that the temperature of the system is given at chemical equilibrium.

This method introduces one input variable with name T. By calling this method, you are specifying that temperature is known in the equilibrium calculation (by default it is considered an unknown). Thus, it will not be considered as a control variable whose value needs to be computed as part of the equilibrium calculation.

See also: unknownTemperature

◆ pressure()

auto pressure ( ) -> void

Specify that the pressure of the system is given at chemical equilibrium.

This method introduces one input variable with name P. By calling this method, you are specifying that pressure is known in the equilibrium calculation (by default it is considered an unknown). Thus, it will not be considered as a control variable whose value needs to be computed as part of the equilibrium calculation.

See also: unknownPressure

◆ volume()

auto volume ( ) -> void

Specify that the volume of the system is given at chemical equilibrium.

This method introduces one input variable with name V. It also introduces an equation constraint with name volume to enforce a given volume value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ internalEnergy()

auto internalEnergy ( ) -> void

Specify that the internal energy of the system is given at chemical equilibrium.

This method introduces one input variable with name U. It also introduces an equation constraint with name internalEnergy to enforce a given internal energy value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ enthalpy()

auto enthalpy ( ) -> void

Specify that the enthalpy of the system is given at chemical equilibrium.

This method introduces one input variable with name H. It also introduces an equation constraint with name enthalpy to enforce a given enthalpy value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ gibbsEnergy()

auto gibbsEnergy ( ) -> void

Specify that the Gibbs energy of the system is given at chemical equilibrium.

This method introduces one input variable with name G. It also introduces an equation constraint with name gibbsEnergy to enforce a given Gibbs energy value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ helmholtzEnergy()

auto helmholtzEnergy ( ) -> void

Specify that the Helmholtz energy of the system is given at chemical equilibrium.

This method introduces one input variable with name A. It also introduces an equation constraint with name helmholtzEnergy to enforce a given Helmholtz energy value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ entropy()

auto entropy ( ) -> void

Specify that the entropy of the system is given at chemical equilibrium.

This method introduces one input variable with name S. It also introduces an equation constraint with name entropy to enforce a given entropy value for the chemical system at equilibrium.

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints.

◆ elementAmount()

auto elementAmount ( StringOrIndex const & element ) -> void

Specify that the amount of an element is given at chemical equilibrium.

Parameters

element The name or index of the element in the chemical system.

◆ elementAmountInPhase()

auto elementAmountInPhase	(	StringOrIndex const &	element,
		StringOrIndex const &	phase
	)		-> void

Specify that the amount of an element in a phase is given at chemical equilibrium.

Parameters

element	The name or index of the element in the chemical system.
phase	The name or index of the phase in the chemical system.

◆ elementMass()

auto elementMass ( StringOrIndex const & element ) -> void

Specify that the mass of an element is given at chemical equilibrium.

Parameters

element The name or index of the element in the chemical system.

◆ elementMassInPhase()

auto elementMassInPhase	(	StringOrIndex const &	element,
		StringOrIndex const &	phase
	)		-> void

Specify that the mass of an element in a phase is given at chemical equilibrium.

Parameters

element	The name or index of the element in the chemical system.
phase	The name or index of the phase in the chemical system.

◆ phaseAmount()

auto phaseAmount ( StringOrIndex const & phase ) -> void

Specify that the amount of a phase is given at chemical equilibrium.

Parameters

phase The name or index of the phase in the chemical system.

◆ phaseMass()

auto phaseMass ( StringOrIndex const & phase ) -> void

Specify that the mass of a phase is given at chemical equilibrium.

Parameters

phase The name or index of the phase in the chemical system.

◆ phaseVolume()

auto phaseVolume ( StringOrIndex const & phase ) -> void

Specify that the volume of a phase is given at chemical equilibrium.

Parameters

phase The name or index of the phase in the chemical system.

◆ unknownTemperature()

auto unknownTemperature ( ) -> void

Specify that the temperature of the system is unknown in the chemical equilibrium calculation.

This method introduces one p control variable with name T. By calling this method, you are specifying that temperature is unknown and to be computed as part of the chemical equilibrium calculation.

◆ unknownPressure()

auto unknownPressure ( ) -> void

Specify that the pressure of the system is unknown in the chemical equilibrium calculation.

This method introduces one p control variable with name P. By calling this method, you are specifying that pressure is unknown and to be computed as part of the chemical equilibrium calculation.

◆ chemicalPotential()

auto chemicalPotential ( String substance ) -> void

Specify that the chemical potential of a substance is given at chemical equilibrium.

This method introduces one input variable with name u[substance] (e.g., u[H2O] if substance is "H2O"). It also introduces a chemical potential constraint with same name to enforce a given chemical potential value for the substance at chemical equilibrium. This method also indicates that the chemical system is open to substance (e.g., the system is open to mass in/out of H₂O). Thus an implicit titrant is introduced with name [substance] (e.g., [H2O]).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

substance The chemical formula of the substance (e.g., H2O, CO2, H+, Mg+2).

◆ lnActivity() [1/2]

auto lnActivity ( Species const & species ) -> void

Specify that the ln activity of a species is given at chemical equilibrium.

This method introduces one input variable with name lnActivity[speciesName] (e.g., lnActivity[CO2(aq)] if species is a Species object with name "CO2(aq)"). It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for the natural log activity of the species at chemical equilibrium. This method also indicates that the chemical system is open to the underlying substance of the species, not the species itself. For example, the system is open to mass in/out of CO₂ if the Species object species is CO2(aq), CO2(g) or CO2(l)). Thus an implicit titrant is introduced with name [substance] (e.g., [CO2]).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

species The chemical species as an Species object.

◆ lnActivity() [2/2]

auto lnActivity ( String species ) -> void

Specify that the ln activity of a species is given at chemical equilibrium.

For more details, check the documentation of EquilibriumSpecs::lnActivity(Species const&).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

species The name of the chemical species as found in the database in use.

Note: The chemical species does not need to be in the chemical system; only in the database.

Warning: An error will be thrown if the database does not contain a species with given name.

◆ lgActivity()

auto lgActivity ( String species ) -> void

Specify that the lg activity of a species is given at chemical equilibrium.

For more details, check the documentation of EquilibriumSpecs::lnActivity(Species const&).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

species The name of the chemical species as found in the database in use.

Note: The chemical species does not need to be in the chemical system; only in the database.

Warning: An error will be thrown if the database does not contain a species with given name.

◆ activity()

auto activity ( String species ) -> void

Specify that the activity of a species is given at chemical equilibrium.

For more details, check the documentation of EquilibriumSpecs::lnActivity(Species const&).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

species The name of the chemical species as found in the database in use.

Note: The chemical species does not need to be in the chemical system; only in the database.

Warning: An error will be thrown if the database does not contain a species with given name.

◆ fugacity()

auto fugacity ( String gas ) -> void

Specify that the fugacity of a gaseous species is given at chemical equilibrium.

This method introduces one input variable with name f[gas] (e.g., f[O2] if gas is "O2"). It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for the fugacity of the gas at chemical equilibrium. This method also indicates that the chemical system is open to gas (e.g., the system is open to mass in/out of O₂). Thus an implicit titrant is introduced with name [substance] (e.g., [O2]).

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

gas	The name of the gaseous species as found in the database in use.

Note: The gaseous species does not need to be in the chemical system; only in the database.

Warning: An error will be thrown if the database does not contain a gaseous species with given name.

◆ pH()

auto pH ( ) -> void

Specify that the pH is given at chemical equilibrium.

This method introduces one input variable with name pH. It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for pH at chemical equilibrium. This method also indicates that the chemical system is open to mass in/out of H⁺. Thus an implicit titrant is introduced with name [H+]. The code below demonstrate the use of this method and its effect on the list of input variables, titrants and control variables.

using namespace Reaktoro;
EquilibriumSpecs specs(system); // for some ChemicalSystem object `system`
specs.enthalpy();                     // introduces input variable `H` and constraint `enthalpy`
specs.pressure();                     // introduces input variable `P`
specs.pH();                           // introduces input variable `pH`, constraint `pH`, and titrant `[H+]`
print(specs.namesInputs());      // H, P, pH
print(specs.namesTitrants());         // [H+]
print(specs.namesControlVariables()); // T, n[H+]
print(specs.namesContraints());       // enthalpy, pH

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Warning: An error will be thrown if the system does not contain an aqueous species with formula H+.

◆ pMg()

auto pMg ( ) -> void

Specify that pMg is given at chemical equilibrium.

This method introduces one input variable with name pMg. It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for pMg at chemical equilibrium. This method also indicates that the chemical system is open to mass in/out of Mg²⁺. Thus an implicit titrant is introduced with name [Mg+2].

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Warning: An error will be thrown if the system does not contain an aqueous species with formula Mg+2.

◆ pE()

auto pE ( ) -> void

Specify that pE is given at chemical equilibrium.

This method introduces one input variable with name pE. It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for pE at chemical equilibrium. This method also indicates that the chemical system is open to mass in/out of e^- (the electron substance). Thus an implicit titrant is introduced with name [e-].

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

◆ Eh()

auto Eh ( ) -> void

Specify that Eh is given at chemical equilibrium.

This method introduces one input variable with name Eh. It also introduces a chemical potential constraint with same name that is equivalent to enforcing a given value for Eh at chemical equilibrium. This method also indicates that the chemical system is open to mass in/out of e^- (the electron substance). Thus an implicit titrant is introduced with name [e-].

See also: EquilibriumSpecs::namesInputs, EquilibriumSpecs::namesConstraints, EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

◆ openTo()

auto openTo ( ChemicalFormula const & substance ) -> void

Specify that the chemical system is open to a substance.

Use this method to specify that the system is titrated with an unknown amount of a substance to be able to attain chemical equilibrium with given conditions. Its use introduces an explicit titrant with name [substance] (e.g., H2S is substance is "H2S"). The amount of this titrant is an unknown control variable which is computed in the chemical equilibrium calculation.

The code below demonstrate the use of this method and its effect on the list of titrants and control variables.

using namespace Reaktoro;
EquilibriumSpecs specs(system); // for some ChemicalSystem object `system`
specs.volume();
specs.pressure();
specs.openTo("H2S");
specs.openTo("CO2");
print(specs.namesTitrants()); // [H2S], [CO2]
print(specs.namesControlVariables()); // T, [H2S], [CO2]

Note: The code above is for demonstration purposes only. The given specifications do not produce a valid chemical equilibrium problem!

See also: EquilibriumSpecs::namesTitrants, EquilibriumSpecs::namesControlVariables

Parameters

substance The chemical formula of the substance.

◆ addUnknownTitrantAmount()

auto addUnknownTitrantAmount ( ChemicalFormula const & substance ) -> void

Specify that the chemical system is open to a given chemical state. // TODO: Implement EquilibriumSpecs::auto openTo(ChemicalState const& state).

Specify that the chemical system is open to a given material. // TODO: Implement EquilibriumSpecs::auto openTo(Material const& material). Specify that the chemical system is open to a titrant substance and its amount is unknown.

◆ assembleEquationConstraints()

auto assembleEquationConstraints ( ) const -> EquationConstraints

Assemble the complete system of equation constraints to be satisfied at chemical equilibrium.

This method assembles a system of equation constraints that considers first the evaluation of the provided single equations via addConstraint and then the provided systems of equations via method addConstraints.

◆ assembleReactivityConstraints()

auto assembleReactivityConstraints ( ) const -> ReactivityConstraints

Assemble the complete system of reactivity constraints to be satisfied at chemical equilibrium.

This method assembles a system of reactivity constraints that considers first the evaluation of the provided single constraints via addReactivityConstraint and then the provided systems of constraints via method addReactivityConstraints.

◆ assembleConservationMatrix()

auto assembleConservationMatrix ( ) const -> MatrixXd

Assemble the conservation matrix for the chemical species with respect to the conservative components.

This method is equivalent to assembleConservationMatrixN

◆ assembleConservationMatrixN()

auto assembleConservationMatrixN ( ) const -> MatrixXd

Assemble the conservation matrix for the n species amount variables with respect to the conservative components.

This conservative matrix of the chemical equilibrium problem is a matrix whose upper rows contains the formula matrix of the species with respect to elements and electric charge, and the lower rows contains the coefficients of the reactivity constraints (e.g., the stoichiometric matrix of the restricted reactions in the equilibrium computation). This matrix is used to compute the amounts of the conservative components in the chemical equilibrium problem, which are elements, electric charge, and the extend of the restricted reactions.

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

Reaktoro/Equilibrium/EquilibriumSpecs.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Explicit Titrants

Implicit Titrants

Control Variables

Member Function Documentation

◆ temperature()

◆ pressure()

◆ volume()

◆ internalEnergy()

◆ enthalpy()

◆ gibbsEnergy()

◆ helmholtzEnergy()

◆ entropy()

◆ elementAmount()

◆ elementAmountInPhase()

◆ elementMass()

◆ elementMassInPhase()

◆ phaseAmount()

◆ phaseMass()

◆ phaseVolume()

◆ unknownTemperature()

◆ unknownPressure()

◆ chemicalPotential()

◆ lnActivity() [1/2]

◆ lnActivity() [2/2]

◆ lgActivity()

◆ activity()

◆ fugacity()

◆ pH()

◆ pMg()

◆ pE()

◆ Eh()

◆ openTo()

◆ addUnknownTitrantAmount()

◆ assembleEquationConstraints()

◆ assembleReactivityConstraints()

◆ assembleConservationMatrix()

◆ assembleConservationMatrixN()