A simple thermodynamic model for estimating the solubility of H2O in magmas

Abstract

A symmetrical, strictly regular solution model is used to estimate H2O solubilities in silicate melts. The standard state chemical potential of dissolved H2O and the adjustable parameter in the activity coefficient are determined by least squares analyses of data on H2O solubility in silicate melts. The adjustable parameter in the expression for the activity coefficient (Inγ) is a function only of the anhydrous melt composition and eleven values are provided for melts ranging in composition from picrite to rhyolite. At the 95% confidence level, the model should estimate H2O contents to within 4.8% of the amount present if the amount present is less than 10 wt.%. This compares to the reproducibility of 2.25% of the amount present for experimental determinations. To apply the model to rocks and magmas estimates ofT, P, and the fugacity of H2O are required. Variation of the H2O content of the melt changes the activity of other components. Knowledge of this variation removes the requirement that the fugacity of H2O be estimated. Application of the properties of exact differentials to the Gibbs function for the hydrous melt provides an expression relating the chemical potential of a feldspar component to the H2O content of the melt. This expression contains a second adjustable parameter which depends on the anhydrous melt composition. Using this second expression, the H2O content can be estimated ifT, P, and feldspar composition are known. Data are too meagre to evaluate the quantitative success of the second method.