Dehydration equilibrium with ideal-gas fluid (${\Delta }_{r}G=0$)

For a mineral reaction producing one mole of water, let $H^{\circ },S^{\circ }$ refer to the $P^{\circ }$ standard state and let the solids’ volume change $\Delta V_s$ be constant. If $A_s$ is the product/reactant solid-activity ratio, the Gibbs energy of reaction isFor temperature-independent specified activities and fugacity, equilibrium givesThe gas pressure work is already represented by the fugacity term; adding a second constant water-volume term double counts it. For an ideal gas, $f=P$; a given fugacity coefficient gives $f={\varphi }_{f}P$. If these quantities depend on temperature, the equilibrium equation must instead be solved implicitly. Pressure units in the solid volume correction must match those used for $\Delta V_s$.