Abstract
Since the time of J. H. van’t Hoff [1], it has been known that chemical equilibrium is dynamic, meaning that at equilibrium, chemical reactions do not cease, but instead the forward and backward reaction rates are equal. The constant concentrations at equilibrium preclude the use of concentrations to measure reaction rates at equilibrium. Therefore, with the exception of a few special cases, no reaction rates at equilibrium have been published in the literature of chemistry, physics, or chemical engineering. Here we report dissolution and precipitation rates at equilibrium for quartz and barite with the isotope-doping method. Experimental data show that dissolution and precipitation rates are equal at equilibrium, indicating the principle of detailed balance (PDB) appear to be applicable at these experimental conditions. The PDB has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time, and its wide application in geochemistry has mostly been implicit and without experimental testing of its applicability. Nevertheless, many extrapolations based on PDB without experimental validation have far reaching impacts on society’s mega environmental enterprises. The isotope doping method appears to able to test its applicability for a variety of minerals at a wide range of conditions.
Highlights
The isotope doping technique introduces an enriched rare isotope of an element to an experimental solution that is interacting with a mineral or a suite of minerals that have normal or natural isotopic compositions [2]
We used the initial rate method [8] to find the rate of appearance of 28Si in solution, which gives the dissolution rate at equilibrium, and the rate of disappearance of 29Si, which gives the precipitation rate at equilibrium
One application of our experimental results is the validation of equilibrium constants for quartz solubility
Summary
The isotope doping technique introduces an enriched rare isotope of an element to an experimental solution that is interacting with a mineral or a suite of minerals that have normal or natural isotopic compositions [2]. The technique has been used in the past with various isotopes. Zuddas et al [3] and Seimbille et al [4] used 39K and 84Sr to simultaneously measure dissolution rates of K-feldspar, biotite, and plagioclase during the hydrothermal alteration of a granite; Beck et al [5] used Ca isotopes to study the reaction kinetics of calcite recrystallization at elevated temperature; and Curti et al [6] used radioactive barium isotopes to study isotope-exchange in barite. Gruber et al [7] measured albite dissolution rates with Si isotopes
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