Nomenclature
The symbols of the formulas of this documentation, grouped by subject. A symbol that means different things in different chapters is listed once for each meaning, with the pages where that meaning holds; a meaning listed without pages holds everywhere else. The value of a physical constant is the one ChemistryLab computes with, read from the library when this page is built.
Hovering an equation on any page shows the symbols it holds, with their meaning on that page.
Typography
A scalar, and a component of a vector or a matrix, is set in italic:
Physical constants
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| molar gas constant, 8.314462618 J/(mol K) | J/(mol K) | ||
| Faraday constant, 96485.33212 C/mol | C/mol | ||
| Avogadro constant, 6.02214076e+23 1/mol | 1/mol | ||
| Boltzmann constant, 1.380649e-23 J/K | J/K | ||
| elementary charge, 1.602176634e-19 C | C | theory/activity_models | |
| vacuum permittivity, 8.854187813e-12 F/m | F/m |
State and thermodynamic functions
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| temperature | K | ||
| pressure | Pa (bar in the tables) | ||
| reference temperature of the standard properties, 298.15 K | K | ||
| reference pressure of the standard properties, 1 bar | Pa | ||
| Gibbs energy | J | ||
| enthalpy | J | ||
| Hessian of the Gibbs energy at the solution, ∇²G | manual/solving, tutorials/reaktoro_comparison | ||
| entropy | J/K | ||
| internal energy | J | ||
| volume | m³ | ||
| heat capacity at constant pressure | J/K (J/(mol K) for a species) | ||
| chemical potential | J/mol | ||
| equilibrium constant of a reaction, ln K = −ΔᵣG°/RT | 1 | ||
| change of a quantity: between two states, or by a reaction (Δᵣ) or a formation (Δ_f) | |||
| stoichiometry of the kinetic reactions, restricted to their non-aqueous participants | 1 | manual/kinetics_syntax | |
| reaction quotient, the product of the activities raised to their coefficients | 1 | ||
| extent of a reaction, dnᵢ = νᵢ dξ | mol | ||
| heat released by a paste or recorded by a calorimeter | J | ||
| orthonormal basis of the tangent space of the phase's composition | theory/solid_solutions | ||
| affinity of a reaction, −ΔᵣG | J/mol | ||
| saturation ratio of a phase, the ion activity product over K | 1 | ||
| heat received by the system, or released by the reactions | J | theory/the_two_laws, examples/lavergne2018 | |
| work received by the system | J | theory/the_two_laws | |
| factor multiplying every amount (the Gibbs energy is homogeneous of degree one) | 1 | theory/energies_and_potentials | |
| standard state (superscript) | |||
| of formation from the elements (subscript, as in Δ_fG°) | |||
| of reaction (subscript, as in ΔᵣG°) | |||
| pressure parameter of the HKF equations of state, 2600 bar | bar | theory/thermodynamics | |
| Born coefficient of an aqueous species (HKF) | J/mol | theory/thermodynamics |
Amounts and composition
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| amount of a species | mol | ||
| amounts of the species, one per species | mol | ||
| stoichiometric coefficients: those of one reaction as a vector, one row per reaction as a matrix | 1 | ||
| mole fractions of the members of a phase | 1 | theory/solid_solutions | |
| charge numbers of the species | 1 | ||
| vector of ones | 1 | ||
| budget of the components: the amounts the conservation matrix must return | mol | ||
| conservation matrix: one row per component, one column per species | 1 | ||
| stoichiometric coefficient, positive for a product | 1 | ||
| mole fraction | 1 | ||
| molality of a solute | mol/kg of water | ||
| molar mass | kg/mol | ||
| total amount of the sites of a site family | mol | theory/surface_complexation, theory/standard_states, manual/surfaces, examples/surface_langmuir | |
| total amount of a phase, the sum of its members' amounts | mol | theory/equilibrium, theory/solid_solutions | |
| water/cement ratio, by mass | g/g | ||
| bound water per gram of binder | g/g | examples/thermogravimetry |
Aqueous solutions
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| activity | 1 | ||
| activity of water | 1 | ||
| activity coefficient | 1 | ||
| ionic strength, ½ Σ mᵢ zᵢ² | mol/kg | ||
| charge number of a species | 1 | ||
| ion size of the extended Debye–Hückel model | Å | ||
| Debye–Hückel limiting slope, a property of water | (kg/mol)^½ | theory/activity_models, examples/activity_models_compared, examples/pitzer_model | |
| Debye–Hückel coefficient of the ion size, a property of water | Å⁻¹ (kg/mol)^½ | ||
| linear term of the B-dot model | kg/mol | ||
| osmotic coefficient | 1 | ||
| inverse Debye length of the solution | 1/m | ||
| relative permittivity of water | 1 | ||
| SIT interaction coefficient ε(i, k) of two ions | kg/mol | theory/activity_models | |
| distance from the central ion | m | theory/activity_models | |
| constant of the activity model (Davies, SIT, Pitzer), or the linear term of B-dot | kg/mol | theory/activity_models, examples/activity_models_compared | |
| density (of water, unless stated) | kg/m³ | ||
| mean charge density around an ion (Poisson's equation) | C/m³ | theory/activity_models | |
| mean electrostatic potential around an ion (Poisson's equation) | V | theory/activity_models | |
| Pitzer interaction parameters of a pair of ions | kg/mol | theory/activity_models, examples/pitzer_model | |
| water (subscript) |
Surfaces
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| charge density of the surface | C/m² | ||
| electrostatic potential of the surface plane | V | ||
| capacitance of the surface (constant-capacitance model) | F/m² | theory/surface_complexation, manual/surfaces | |
| area of the surface | m² | theory/surface_complexation, manual/surfaces | |
| Gouy–Chapman prefactor, √(8 εᵣ ε₀ RT ρ) | C m⁻² (kg/mol)^½ | theory/surface_complexation, examples/hfo_diffuse_layer | |
| sites per host formula unit | 1 | theory/surface_complexation, theory/standard_states | |
| drive of an occupied state of a site, from the proton activity | 1 | examples/surface_langmuir |
Solid solutions
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| interaction parameter of a regular solution | J/mol | ||
| matrix of the interaction parameters of a regular solution, or of those of one site | J/mol | theory/solid_solutions | |
| coupling of two sites by the reference surface: the G°/RT of the compounds projected on their tangent spaces | 1 | theory/solid_solutions | |
| a direction of change of the composition, in the tangent space of the simplex | 1 | theory/solid_solutions | |
| Redlich–Kister (Guggenheim) coefficients of the excess Gibbs energy | J/mol | theory/solid_solutions, examples/solid_solution_models, examples/miscibility_gap | |
| site fraction of a moiety on a sublattice | 1 | theory/solid_solutions, examples/sublattice_csh, examples/cashplus_csh | |
| site fractions of the moieties on the sublattices | 1 | theory/solid_solutions, examples/sublattice_csh, examples/cashplus_csh | |
| fictive activity coefficient of an end-member of a sublattice model | 1 | theory/solid_solutions, examples/sublattice_csh | |
| molar Gibbs energy of mixing of a binary | J/mol | examples/miscibility_gap | |
| fraction of vacant bridging sites of an end-member | 1 | examples/sublattice_csh | |
| multiplicity of site s in the formula unit of a sublattice model | 1 | theory/solid_solutions | |
| reference surface of the compound energy formalism: the standard Gibbs energies of the compounds interpolated in the site fractions | J/mol | theory/solid_solutions | |
| number of mixing sites of a compound-energy model | 1 | theory/solid_solutions |
Equilibrium and the solver
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| multiplier of a conservation row, minus the potential of its primary species in RT units | 1 | theory/equilibrium, theory/thermodynamics, manual/solving | |
| multipliers of the conservation rows | 1 | theory/equilibrium, theory/thermodynamics, manual/solving, theory/partial_equilibrium_kinetics | |
| potentials the multipliers give the species, u = −Aᵀy, in RT units | 1 | theory/equilibrium, theory/thermodynamics | |
| potential the multipliers give a species, a component of u | 1 | theory/equilibrium, theory/thermodynamics | |
| any change of the amounts | mol | theory/equilibrium | |
| basis of the null space of the conservation matrix | 1 | tutorials/reaktoro_comparison | |
| equilibrium map: the equilibrium amounts nₑ of a budget bₑ | tutorials/coupling, tutorials/kinetics, tutorials/reaktoro_comparison, examples/coupled_hydration, theory/partial_equilibrium_kinetics | ||
| number of element potentials, the unknowns of the outer Newton iteration | 1 | theory/equilibrium |
Kinetics and hydration
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| exponent of the van Genuchten retention curve, m = 1/b | 1 | tutorials/self_desiccation | |
| pressure parameter of the van Genuchten retention curve | MPa | tutorials/self_desiccation | |
| the matrix KᵀK of the kinetic stoichiometry | 1 | manual/kinetics_syntax | |
| surface tension of water | N/m | tutorials/self_desiccation | |
| reactive surface area of a dissolving mineral | m² | theory/kinetics | |
| time | s (days in the cement pages) | ||
| degree of reaction (of hydration, for a clinker phase) | 1 | ||
| degree of hydration at which hydration stops (Powers) | 1 | ||
| rate of a kinetic reaction | mol/s | ||
| rates of the kinetic reactions | mol/s | ||
| extents of the kinetic reactions | mol | ||
| amounts of the species of the equilibrium partition | mol | ||
| amounts of the kinetic species | mol | ||
| budget of the components held by the equilibrium partition | mol | ||
| conservation matrix restricted to the equilibrium partition | 1 | ||
| activation energy | J/mol | ||
| specific surface (Blaine fineness) of the material | m²/kg | theory/kinetics, examples/cement_clinker_kinetics | |
| heat loss of the calorimeter against the temperature difference | W | manual/kinetics_syntax, examples/lavergne2018, examples/cement_clinker_kinetics | |
| linear coefficient of the heat loss of the calorimeter, φ = aΔT + bΔT² | W/K | manual/kinetics_syntax, examples/lavergne2018, examples/cement_clinker_kinetics | |
| quadratic coefficient of the heat loss of the calorimeter, φ = aΔT + bΔT² | W/K² | manual/kinetics_syntax, examples/lavergne2018, examples/cement_clinker_kinetics | |
| normalized degree of hydration, α/αₘₐₓ | 1 | theory/kinetics | |
| time at which the material is half reacted | d | theory/kinetics | |
| heat capacity of the calorimeter and of what it holds besides the paste | J/K | examples/lavergne2018 | |
| bound water per unit degree of hydration | g/g | theory/cement_water_budget, tutorials/self_desiccation, tutorials/self_desiccation_kinetics | |
| chemical shrinkage per unit degree of hydration | cm³/g | theory/cement_water_budget, tutorials/self_desiccation, tutorials/self_desiccation_kinetics | |
| Powers coefficient, b + s S_/(1 − S_) | g/g | theory/cement_water_budget, tutorials/self_desiccation | |
| degree of saturation of the pores | 1 | tutorials/self_desiccation, tutorials/self_desiccation_kinetics, theory/cement_water_budget | |
| degree of saturation at which hydration stops | 1 | ||
| porosity, referred to the initial volume | 1 | manual/recipes, theory/recipe_bookkeeping | |
| mass in a recipe: of a constituent (m_c), of the binder (m_b), of the equilibrium (m_eq) | g | theory/recipe_bookkeeping | |
| mass fraction of a material in the binder | 1 | theory/recipe_bookkeeping | |
| mass fraction of a constituent in its material | 1 | theory/recipe_bookkeeping | |
| mass fraction of an oxide in a constituent known by its analysis | 1 | theory/recipe_bookkeeping | |
| an oxide decomposed over the primaries of the system, per formula unit | 1 | theory/recipe_bookkeeping | |
| the oxides of a constituent whose element the system has a primary for | theory/recipe_bookkeeping | ||
| state of the differential system of a kinetic run | theory/partial_equilibrium_kinetics | ||
| right-hand side of the differential system, a function of its state | theory/partial_equilibrium_kinetics | ||
| Jacobian of the right-hand side with respect to the state | theory/partial_equilibrium_kinetics | ||
| optimality conditions of the minimization, stationarity and conservation | theory/partial_equilibrium_kinetics | ||
| residual of the energy balance of a semi-adiabatic cell | J | theory/partial_equilibrium_kinetics | |
| heat lost through the walls of the cell, against the temperature difference | W | theory/partial_equilibrium_kinetics | |
| heat capacity of the vessel and of what it holds besides the paste | J/K | theory/partial_equilibrium_kinetics | |
| heat capacity of the cell at equilibrium, the shift of the partition included | J/K | theory/partial_equilibrium_kinetics | |
| change of the enthalpy of a calorimeter cell since the start | J | theory/partial_equilibrium_kinetics |
Cement chemist notation
| Symbol | Meaning | Unit | Where |
|---|---|---|---|
| CaO, in cement chemist notation | manual/cement_notation, examples/bogue_calculation, examples/cem2_blended, examples/cem4_pozzolanic |