A stable isotope doping method to test the range of applicability of detailed balance

The principle of detailed balance (PDB) has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time (Wegscheider, 1901; Lewis, 1925; Onsager, 1931), 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. Here we report an isotope doping method that independently measures simultaneous dissolution and precipitation rates and can test this principle. The technique reacts a solution enriched in a rare isotope of an element with a solid having natural isotopic abundances (Beck et al., 1992; Gaillardet, 2008; Gruber et al., 2013). Dissolution and precipitation rates are found from the changing isotopic ratios. Our quartz experiment doped with 29Si showed that the equilibrium dissolution rate remains unchanged at all degrees of undersaturation. We recommend this approach to test the validity of using the detailed balance relationship in rate equations for other substances.