Nomenclature

Species

Species are real things that exist in solution, for instance HCO$_{3}^{-}$, CO$_{2}$(aq), CaHCO$_{3}^{+}$. They never have negative mass.

Phase

A phase is a region of space that is physically distinct, mechanically separable, and homogeneous in its composition and properties. In geochemical systems, the phases are:

• a fluid phase composed of water and its dissolved constituents;

• potentially, a separate phase corresponding to each of the minerals in contact with the fluid phase;

• potentially, separate gas phases. If different gases (CO$_{2}$, O$_{2}$, etc) are buffered separately with known fugacity, as is assumed in geochemistry, each gas counts as a distinct phase.

Components

Components are useful abstractions. They might or might not be real things, so can even have negative mass. For instance, consider an alkaline solution (more OH$^{-}$ than H$^{+}$). Choose H$_{2}$O and H$^{+}$ to be the component basis set. Each hydroxyl ion, $\mathrm{H}_{2}\mathrm{O} - \mathrm{H}^{+} \rightarrow \mathrm{OH}^{-}$, is made up of a water molecule less a hydrogen ion. Since this is an alkaline solution, the overall composition has a positive amount of water and a negative amount of H$^{+}$. The molality of the H$^{+}$ species is positive, however.

A complete set of components forms a basis for the reaction system.

Basis

The set of components used in a geochemical model is the calculation's basis. There is no unique basis that describes a system, but the basis must satisfy these rules:

1. each species and phase considered in the model must be a combination of the components in the basis;

2. the number of components is minimal to satisfy (1)

3. the components must be linearly independent of one another, that is, no reactions exist to form one component from the others.

That is, the basis is a linearly-independent complete set of components: every other chemical in the system is composed of these components, and none of these components can be composed from the others.

The number of components in the basis is $1 + N_{i} + N_{k} + N_{m} + N_{p}$ (the "1" comes from the water component), while the number of phases is $1 + N_{k} + N_{m} + N_{p}$. The Gibbs phase rule, with fixed temperature and pressure, states that the number of degrees of freedom is the difference of these, or just $N_{i}$. Hence, given a constraint on the concentration or activity of each basis species, the system's equilibrium state can be determined. However, calculating the extent of the system — the amounts of fluid, minerals, gases and sorption sites — that are present, requires the extra $1 + N_{k} + N_{m} + N_{p}$ pieces of information.

Moles

A measure of the amount of a substance.

$$\mathrm{number\ of\ moles} = \frac{\mathrm{number\ of\ particles\ (molecules,\ atoms,\ ions,\ etc)}}{\mathcal{N}_{A}} \ ,$$ where $\mathcal{N}_{A}$ is Avogadro's number.

Mole fraction

A measure of the amount of a constituent relative to the mixture.

$$\mathrm{mole\ fraction} = \frac{\mathrm{number\ of\ moles\ of\ constituent}}{\mathrm{number\ of\ moles\ of\ all\ constituents\ in\ the\ mixture}}$$

Molality

A measure of concentration of a constituent.

$$\mathrm{molality} = \frac{\mathrm{number\ of\ moles\ of\ constituent}}{\mathrm{mass\ (kg)\ of\ solvent\ (water)}}$$

Chemical potential

The partial derivative of the free energy, $G$, with respect to the number of moles of that species: $\mu = \partial G/\partial n$, where temperature, pressure and the number of moles of other species are held fixed.

Activity

Defined in terms of the chemical potential, $$\mu = \mu^{0} + RT\log a \ ,$$ where

• $\mu$ [J.mol$^{-1}$] is the chemical potential

• $\mu^{0}$ [J.mol$^{-1}$] is the chemical potential in a standard state (it is independent of temperature, pressure, other constituents, etc)

• $R = 8.314\ldots\,$J.K$^{-1}$.mol$^{-1}$ is the gas constant

• $T$ (K) is temperature

• $\log$ is the natural logarithm

• $a$ [dimensionless] is the activity

For species equilibrium reactions, the activity is a dimensionless measure of effective concentration of a constituent in a solution $$a = \gamma m/m_{\mathrm{ref}} \ ,$$ where $\gamma$ is the activity coefficient, $m$ is the molality, and $m_{\mathrm{ref}}=1\,$mol.kg$^{-1}$.

For minerals in $A_{k}$, $a=1$.

For gases, the activity is proportional to the fugacity.

Mass action

This is an equation for the equilibrium constant of a reaction in terms of the activities of the reaction's species.

Saturation index

$\mathrm{SI} = \log_{10}(Q/K)$, where $Q$ is the activity product and $K$ is the equilibrium constant of the reaction. If $\mathrm{SI}>0$, the mineral is supersaturated, which means the system will try to precipitate the mineral.

Redox reaction

This involves the transfer of electrons. For instance $\mathrm{Fe}^{2+} + 0.25\mathrm{O}_{2} + \mathrm{H}^{+} \rightleftharpoons \mathrm{Fe}^{3+} + 0.5\mathrm{H}_{2}\mathrm{O}$, where charge is transferred between $\mathrm{Fe}^{2+}$ and $\mathrm{O}_{2}$. $\mathrm{Fe}^{2+}$ has lost an electron: it is oxidised. Often these reactions are split into half reactions that show the release/gain of an electron, e.g. $\mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+} + \mathrm{e}^{-}$. A redox couple is a reduced species and its corresponding oxidised form, e.g. $\mathrm{Fe}^{2+}$ / $\mathrm{Fe}^{3+}$.

Nernst potential

Quantifies the redox potential for a redox half-reaction with activity product $Q$ and equilibrium constant $K$: $$\mathrm{Eh} = -\frac{RT}{nF}\log(Q/K) = \mathrm{Eh}^{0} - \frac{RT}{nF}\log Q \ .$$ Here $R$ is the gas constant, $T$ is the temperature (in Kelvin), $F$ is the Faraday constant, $n$ is the number of electrons consumed in the half reaction, Eh$^{0}$ is the standard potential, and $\log$ has base e.