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The sodium-rich feldspar mineral endmember.

An activity model in which distinct atomic positions in a crystal structure are occupied independently by specified species. For ideal random mixing, a pure mineral endmember requiring ${\nu }_s$ specified atoms on site type $s$ has thermodynamic activity $a={\prod }_s{X}_s^{{\nu }_s}$ relative to that pure endmember, with other occupations held fixed. Its mixing contribution to the chemical potential is $RT\ln a$. The powers count occupied positions per formula unit; they are not always the mole fraction of whole endmember formulae.

Under ideal independent mixing on crystallographic sites, a mineral endmember's thermodynamic activity is the product of its required site fractions, one factor per mixed site. Muscovite has one K and three Al per formula unit, sanidine has one K and one Al, and corundum has two Al. Interpreting the given Al fractions as the fractions on every relevant Al/Fe site givesThus $A_s=a_{\mathrm{san}}{a}_{\mathrm{cor}}/a_{\mathrm{mus}}=0.6237816764$. The cubic power for muscovite includes its tetrahedral Al site and two octahedral Al sites; if site-specific fractions differed, bulk Al/(Al+Fe) alone would not determine this activity. The calculation uses the uniform-site ideal-mixing interpretation intended by the given data.

At $P=5000\mathrm{bar}$ with ideal water, solvegiving $T_{\mathrm{eq}}=979.40\mathrm{K}=706.25{}^{\circ }\mathrm{C}$. Using the bulk mole fraction only once for a multisite mineral endmember would omit part of its ideal mixing chemical potential.

At the one-bar standard state, pure mineral endmembers and water vapour treated as an ideal gas all have unit thermodynamic activity. The Gibbs energy of reaction is ${\Delta }_r{G}^{\circ }={\Delta }_r{H}^{\circ }-T{\Delta }_r{S}^{\circ }$. Setting it to zero givesThe quantities are taken per mole of the reaction as written. The simplified result uses the stipulated temperature-independent enthalpy and entropy differences.

The compositions alone do not specify a unique thermodynamic activity model. Adopt the usual ideal, independent mixing on crystallographic sites approximation: three Mg–Fe positions per formula unit, with the other sites fixed at their stated endmember compositions. Then the mineral endmember activities areThe exponent counts the three mixing cations; treating each whole mineral formula as a single mixing site would be a different model. In particular, the magnesian biotite and garnet components here are phlogopite and pyrope.

For the written reaction, the reaction quotient iswith the other solid activities equal to one. The Gibbs energy of reaction balance therefore givesThe smaller product-endmember activity lowers the reaction chemical potential and lowers the equilibrium temperature in this model. Nonideal activity coefficients or unequal occupancies of crystallographic sites would require further information rather than a revised universal numerical answer.^[ref]

The magnesian biotite mineral endmember. Iron substitution on its magnesium-bearing positions produces a solid solution requiring an activity model when used in chemical equilibrium calculations.

The magnesian aluminium-bearing garnet mineral endmember. In an ideal Mg–Fe site model with other positions fixed, its thermodynamic activity is $X_{\mathrm{Mg}}^3$ because three magnesium positions occur per formula unit.

A high-temperature potassium feldspar mineral, with idealized composition $\mathrm{KAlS}{\mathrm{i}}_3{\mathrm{O}}_8$. Substitution on its K and Al sites changes the thermodynamic activity of that mineral endmember and therefore the chemical equilibrium of reactions involving it.