Equilibration Times of Dissolved Inorganic Carbon During pH Transitions

Equilibration times of dissolved inorganic carbon (DIC) depend on conversion reactions between CO2(aq) and the dissociation products of carbonic acid [S = (H2CO3) + (HCO3−) + (CO32−)]. Here, we develop analytical equations and a numerical model to calculate chemical equilibration times of DIC during pH transitions in buffered and unbuffered solutions. We approximate the equilibration degree of the DIC reservoir by the smaller of the CO2(aq) and S pools at the new pH, since the smaller pool is always farther from equilibrium during the chemical evolution. Both the amount of DIC converted and the rate of conversion differ between a pH increase and decrease, leading to distinct equilibration times for these general cases. Alkalinity perturbations in unbuffered solutions initially drive pH overshoots (increase or decrease) relative to the new equilibrium pH. The increased rates of DIC conversion associated with the pH overshoot yield shorter equilibration times compared to buffered solutions. Salinity has opposing effects on buffered and unbuffered solutions, decreasing and increasing equilibration times, respectively.

Redox hysteresis of super-Earth exoplanets from magma ocean circulation

<div class="page" title="Page 1"> <div class="section"> <div class="layoutArea"> <div class="column"> <p>Internal redox reactions may irreversibly alter the mantle composition and volatile inventory of terrestrial and super-Earth exoplanets and affect the prospects for atmospheric observations. The global efficacy of these mechanisms, however, hinges on the transfer of reduced iron from the molten silicate mantle to the metal core. Scaling analysis indicates that turbulent diffusion in the internal magma oceans of sub- Neptunes can kinetically entrain liquid iron droplets and quench core formation. This suggests that the chemical equilibration between core, mantle, and atmosphere may be energetically limited by convective overturn in the magma flow. Hence, molten super-Earths possibly retain a compositional memory of their accretion path. Redox control by magma ocean circulation is positively correlated with planetary heat flow, internal gravity, and planet size. The presence and speciation of remanent atmospheres, surface mineralogy, and core mass fraction of atmosphere-stripped exoplanets may thus constrain magma ocean dynamics.</p> </div> </div> </div> </div>

Using the elastic properties of zircon-garnet host-inclusion pairs for thermobarometry of the ultrahigh-pressure Dora-Maira whiteschists: problems and perspectives

The ultrahigh-pressure (UHP) whiteschists of the Brossasco-Isasca unit (Dora-Maira Massif, Western Alps) provide a natural laboratory in which to compare results from classical pressure (P)–temperature (T) determinations through thermodynamic modelling with the emerging field of elastic thermobarometry. Phase equilibria and chemical composition of three garnet megablasts coupled with Zr-in-rutile thermometry of inclusions constrain garnet growth within a narrow P–T range at 3–3.5 GPa and 675–720 °C. On the other hand, the zircon-in-garnet host-inclusion system combined with Zr-in-rutile thermometry would suggest inclusion entrapment conditions below 1.5 GPa and 650 °C that are inconsistent with the thermodynamic modelling and the occurrence of coesite as inclusion in the garnet rims. The observed distribution of inclusion pressures cannot be explained by either zircon metamictization, or by the presence of fluids in the inclusions. Comparison of the measured inclusion strains with numerical simulations shows that post-entrapment plastic relaxation of garnet from metamorphic peak conditions down to 0.5 GPa and 600–650 °C, on the retrograde path, best explains the measured inclusion pressures and their disagreement with the results of phase equilibria modelling. This study suggests that the zircon-garnet couple is more reliable at relatively low temperatures (< 600 °C), where entrapment conditions are well preserved but chemical equilibration might be sluggish. On the other hand, thermodynamic modelling appears to be better suited for higher temperatures where rock-scale equilibrium can be achieved more easily but the local plasticity of the host-inclusion system might prevent the preservation of the signal of peak metamorphic conditions in the stress state of inclusions. Currently, we cannot define a precise threshold temperature for resetting of inclusion pressures. However, the application of both chemical and elastic thermobarometry allows a more detailed interpretation of metamorphic P–T paths.

Technical note: CO₂ is not like CH₄ – limits of and corrections to the headspace method to analyse <i>p</i>CO₂ in fresh water

Headspace analysis of CO2 frequently has been used to quantify the concentration of CO2 in fresh water. According to basic chemical theory, not considering chemical equilibration of the carbonate system in the sample vials will result in a systematic error. By analysing the potential error for different types of water and experimental conditions, we show that the error incurred by headspace analysis of CO2 is less than 5 % for typical samples from boreal systems which have low alkalinity (< 900 µmol L−1), with pH < 7.5, and high pCO2 (> 1000 µatm). However, the simple headspace calculation can lead to high error (up to −300 %) or even impossibly negative values in highly undersaturated samples equilibrated with ambient air, unless the shift in carbonate equilibrium is explicitly considered. The precision of the method can be improved by lowering the headspace ratio and/or the equilibration temperature. We provide a convenient and direct method implemented in an R script or a JMP add-in to correct CO2 headspace results using separately measured alkalinity.

Technical note: CO₂ is not like CH₄ – limits of and corrections to the headspace method to analyse <i>p</i>CO₂ in water

Headspace analysis of CO2 frequently has been used to quantify the concentration of CO2 in freshwater. According to basic chemical theory, not considering chemical equilibration of the carbonate system in the sample vials will result in a systematic error. In this paper we provide a method to quantify the potential error resulting from simple application of Henry's law to headspace CO2 samples. By analysing the potential error for different types of water and experimental conditions we conclude that the error incurred by headspace analysis of CO2 is less than 5 % for samples with pH

Compression–Expansion Processes for Chemical Energy Storage: Thermodynamic Optimization for Methane, Ethane and Hydrogen

Several methods for chemical energy storage have been discussed recently in the context of fluctuating energy sources, such as wind and solar energy conversion. Here a compression–expansion process, as also used in piston engines or compressors, is investigated to evaluate its potential for the conversion of mechanical energy to chemical energy, or more correctly, exergy. A thermodynamically limiting adiabatic compression–chemical equilibration–expansion cycle is modeled and optimized for the amount of stored energy with realistic parameter bounds of initial temperature, pressure, compression ratio and composition. As an example of the method, initial mixture compositions of methane, ethane, hydrogen and argon are optimized and the results discussed. In addition to the stored exergy, the main products (acetylene, benzene, and hydrogen) and exergetic losses of this thermodynamically limiting cycle are also analyzed, and the volumetric and specific work are discussed as objective functions. It was found that the optimal mixtures are binary methane argon mixtures with high argon content. The predicted exergy losses due to chemical equilibration are generally below 10%, and the chemical exergy of the initial mixture can be increased or chemically up-converted due to the work input by approximately 11% in such a thermodynamically limiting process, which appears promising.

Chemical heterogeneities in the mantle: progress towards a general quantitative description

Chemical equilibration between two different assemblages (peridotite type and gabbro–eclogite type) has been determined using basic thermodynamic principles and certain constraints and assumptions regarding mass and reaction exchange. When the whole system (defined by the sum of the two subsystems) is in chemical equilibrium the two assemblages will not be homogenized, but they will preserve distinctive chemical and mineralogical differences. Furthermore, the mass transfer between the two subsystems defines two petrological assemblages that separately are also in local thermodynamic equilibrium. In addition, when two assemblages previously equilibrated as a whole in a certain initial mass ratio are held together assuming a different proportion, no mass transfer occurs and the two subsystems remain unmodified. By modeling the chemical equilibration results of several systems of variable initial size and different initial composition it is possible to provide a quantitative framework to determine the chemical and petrological evolution of two assemblages from an initial state, in which the two are separately in chemical equilibrium, to a state of equilibration of the whole system. Assuming that the local Gibbs energy variation follows a simple transport model with an energy source at the interface, a complete petrological description of the two systems can be determined over time and space. Since there are no data to constrain the kinetics of the processes involved, the temporal and spatial scale is arbitrary. The evolution model should be considered only a semiempirical tool that shows how the initial assemblages evolve while preserving distinct chemical and petrological features. Nevertheless, despite the necessary simplification, a 1-D model illustrates how chemical equilibration is controlled by the size of the two subsystems. By increasing the initial size of the first assemblage (peridotite like), the compositional differences between the initial and the final equilibrated stage become smaller, while on the eclogite-type side the differences tend to be larger. A simplified 2-D dynamic model in which one of the two subsystems is allowed to move with a prescribed velocity shows that after an initial transient state, the moving subsystem tends to preserve its original composition defined at the influx side. The composition of the static subsystem instead progressively diverges from the composition defining the starting assemblage. The observation appears to be consistent for various initial proportions of the two assemblages, which somehow simplify the development of potential tools for predicting the chemical equilibration process from real data and geodynamic applications. Four animation files and the data files of three 1-D and two 2-D numerical models are available following the instructions in the Supplement.