Thermodynamics and kinetics of the isotopic equilibration of nitrogen gas (<scp>N₂</scp>) in water: Implications for biological <scp>N₂</scp> fixation experiments

Abstract Better characterization of biological N 2 fixation along with its controlling factors is needed for improved projections of the feedbacks between nitrogen cycling, ecosystems productivity, and climate dynamics. Building on an ongoing community effort to refine estimates of biological N 2 fixation, we outline several considerations aimed at improving 15 N 2 incubation measurements. We first show based on a theoretical analysis that the bias associated with equilibrium isotopic fractionation is within the uncertainty of 15 N 2 incubation experiments, even under conditions with a large headspace to aqueous ratio, such as in soil or sediment incubations. Second, we empirically determine the effects of temperature and agitation on the equilibration kinetics. Shaking intensity seems to be a dominant control on the kinetics of equilibration. Our results show that nearly complete equilibration of dissolved 15 N 2 is achieved within 4 min of vigorous shaking at 20°C at atmospheric pressure, but significantly slower at lower temperatures. The equations presented in our study are adaptable to varying 15 N 2 incubation conditions and other trace gas isotope addition experiments.