Equilibria laboratory experiments

Constraints on Li isotopic fractionation from equilibrium laboratory experiments in magmatic-hydrothermal systems have been examined in only one instance (Lynton 2003). This study examined Li in a quartz-muscovite-aqueous fluid system at conditions of formation of magmatic hydrothermal porphyry-type deposits (400-500°C, 100 MPa). In the presence of a fluid containing L-SVEC (5T i = 0), quartz showed rapid shift from 5 Li = +27 in the starting material to c. +10 at both run temperatures. Muscovite (initial 5 Li = +9), shifted more sharply at 500°C (to c. +20) than at 400°C (to c. +13). Although the results are difficult to put directly into the context of a natural mineral deposit, they do indicate that over geologically relevant time scales, minerals in magmatic-hydrothermal systems should show appreciable Li isotopic fractionation, and that this may permit the composition and/or temperature of ore... 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

Simulation runs are typically short (t 10 - 10 MD or MC steps, correspondmg to perhaps a few nanoseconds of real time) compared with the time allowed in laboratory experiments. This means that we need to test whether or not a simulation has reached equilibrium before we can trust the averages calculated in it. Moreover, there is a clear need to subject the simulation averages to a statistical analysis, to make a realistic estimate of the errors. 

The initial set of experiments and the first few textbook chapters lay down a foundation for the course. The elements of scientific activity are immediately displayed, including the role of uncertainty. The atomic theory, the nature of matter in its various phases, and the mole concept are developed. Then an extended section of the course is devoted to the extraction of important chemical principles from relevant laboratory experience. The principles considered include energy, rate and equilibrium characteristics of chemical reactions, chemical periodicity, and chemical bonding in gases, liquids, and solids. The course concludes with several chapters of descriptive chemistry in which the applicability and worth of the chemical principles developed earlier are seen again and again. 

Research into the aquatic chemistry of plutonium has produced information showing how this radioelement is mobilized and transported in the environment. Field studies revealed that the sorption of plutonium onto sediments is an equilibrium process which influences the concentration in natural waters. This equilibrium process is modified by the oxidation state of the soluble plutonium and by the presence of dissolved organic carbon (DOC). Higher concentrations of fallout plutonium in natural waters are associated with higher DOC. Laboratory experiments confirm the correlation. In waters low in DOC oxidized plutonium, Pu(V), is the dominant oxidation state while reduced plutonium, Pu(III+IV), is more prevalent where high concentrations of DOC exist. Laboratory and field experiments have provided some information on the possible chemical processes which lead to changes in the oxidation state of plutonium and to its complexation by natural ligands. 

The mechanisms by which Pu(IV) is oxidized in aquatic environments is not entirely clear. At Oak Ridge, laboratory experiments have shown that oxidation occurs when small volumes of unhydrolyzed Pu(IV) species (i.e., Pu(IV) in strong acid solution as a citric acid complex or in 45 percent Na2Coj) are added to large volumes of neutral-to-alkaline solutions(23). In repeated experiments, the ratios of oxidized to reduced species were not reproducible after dilution/hydrolysis, nor did the ratios of the oxidation states come to any equilibrium concentrations after two months of observation. These results indicate that rapid oxidation probably occurs at some step in the hydrolysis of reduced plutonium, but that this oxidation was not experimentally controllable. The subsequent failure of the various experimental solutions to converge to similar high ratios of Pu(V+VI)/Pu(III+IV) demonstrated that the rate of oxidation is extremely slow after Pu(IV) hydrolysis reactions are complete. 

Polythermal reaction models (Section 14.1), however, are commonly applied to closed systems, as in studies of groundwater geothermometry (Chapter 23), and interpretations of laboratory experiments. In hydrothermal experiments, for example, researchers sample and analyze fluids from runs conducted at high temperature, but can determine pH only at room temperature (Fig. 2.2). To reconstruct the original pH (e.g., Reed and Spycher, 1984), assuming that gas did not escape from the fluid before it was analyzed, an experimentalist can calculate the equilibrium state at room temperature and follow a polythermal path to estimate the fluid chemistry at high temperature. 

The great value of kinetic theory is that it frees us from many of the constraints of the equilibrium model and its variants (partial equilibrium, local equilibrium, and so on see Chapter 2). In early studies (e.g., Lasaga, 1984), geochemists were openly optimistic that the results of laboratory experiments could be applied directly to the study of natural systems. Transferring the laboratory results to field situations, however, has proved to be much more challenging than many first imagined. 

Many minerals have been found to dissolve and precipitate in nature at dramatically different rates than they do in laboratory experiments. As first pointed out by Paces (1983) and confirmed by subsequent studies, for example, albite weathers in the field much more slowly than predicted on the basis of reaction rates measured in the laboratory. The discrepancy can be as large as four orders of magnitude (Brantley, 1992, and references therein). As we calculate in Chapter 26, furthermore, the measured reaction kinetics of quartz (SiC>2) suggest that water should quickly reach equilibrium with this mineral, even at low temperatures. Equilibrium between groundwater and quartz, however, is seldom observed, even in aquifers composed largely of quartz sand. 

There is no certainty, furthermore, that the reaction or reaction mechanism studied in the laboratory will predominate in nature. Data for reaction in deionized water, for example, might not apply if aqueous species present in nature promote a different reaction mechanism, or if they inhibit the mechanism that operated in the laboratory. Dove and Crerar (1990), for example, showed that quartz dissolves into dilute electrolyte solutions up to 30 times more quickly than it does in pure water. Laboratory experiments, furthermore, are nearly always conducted under conditions in which the fluid is far from equilibrium with the mineral, although reactions in nature proceed over a broad range of saturation states across which the laboratory results may not apply. 

The importance of equilibrium versus kinetic effects has yet to be addressed in any coherent way by the limited laboratory experiments conducted for Li isotope study. It is clear from the study of other stable isotope systems that kinetic effects may dominate the fractionation pathways under many circumstances (e.g., Johnson and Bullen 2004), especially in laboratory simulations of low-temperature natural phenomena (Beard and Johnson 2004). The clarification of how kinetic effects on Li isotopic compositions are manifested remains a major area for future study in natural, synthetic and theoretical systems. 

In the laboratory experiments of Seyfried et al. (1998), naturally altered sea floor basalt (5 Li = +7.4) was reacted with Li-free alkali-chloride aqueous fluid at 350°C for 890 hours (initial fluid/solid mass ratio 2). Samples of the fluid were taken throughout the experiment, and showed initial rapid influx of isotopically heavy-enriched Li released by early-dissolving alteration minerals. However, with progressive reaction, isotopic composition of the fluid decreased and Li concentration reaehed apparent steady state. Although an equilibrium model applies best to the synthetic results, Rayleigh distillation was considered most likely to apply in hydrothermal reactions occurring in nature. 

CAI s that were once molten (type B and compact type A) apparently crystallized under conditions where both partial pressures and total pressures were low because they exhibit marked fractionation of Mg isotopes relative to chondritic isotope ratios. But much remains to be learned from the distribution of this fractionation. Models and laboratory experiments indicate that Mg, O, and Si should fractionate to different degrees in a CAI (Davis et al. 1990 Richter et al. 2002) commensurate with the different equilibrium vapor pressures of Mg, SiO and other O-bearing species. Only now, with the advent of more precise mass spectrometry and sampling techniques, is it possible to search for these differences. Also, models prediet that there should be variations in isotope ratios with growth direction and Mg/Al content in minerals like melilite. Identification of such trends would verify the validity of the theory. Conversely, if no correlations between position, mineral composition, and Mg, Si, and O isotopic composition are found in once molten CAIs, it implies that the objects acquired their isotopic signals prior to final crystallization. Evidence of this nature could be used to determine which objects were melted more than once. 

Accordingly, isotopic equilibration for Cr and Se species is expected to be much slower than for the aqueous Fe(III)-Fe(II) couple, which reaches equilibrium within minutes in laboratory experiments (Beard and Johnson 2004). Additionally, Cr(III) and Se(0) are highly insoluble and their residence times in solution are small, which further decreases the likelihood of isotopic equilibration. In the synthesis below, isotopic fractionations are assumed to be kinetically controlled unless otherwise stated. However, definitive assessments of this assumption have not been done, and future studies may find that equilibrium fractionation is attained for some reactions or rmder certain conditions. 

Equation 2-4, [Oj] = kJNOjJ/JlTj [NO], should be tested in the real atmosphere, as well as in laboratory experiments. Simultaneous measurements of the concentrations of ozone, nitric oxide, and nitrogen dioxide and of the intensity of sunlight for a variety of conditions will provide a much-needed check on this dynamic equilibrium. 

A series of laboratory experiments with a pure substance (shown in Figure 2-2) will result in data for pressure, temperature, and volume. A similar series of experiments with a two-component system will result in data for additional variables. The composition of the overall mixture, the composition of the equilibrium liquid, and the composition of the equilibrium gas are all important. Therefore, in addition to plotting combinations of temperature, pressure, and volume, additional graphs with these variables plotted against composition are possible. 

Hydrate formation from free gas will likely initiate at a gas-liquid interface, as observed in the laboratory experiments of Chapter 6. As indicated in Chapter 3, either initial hydrate formation or a solid phase can serve as nucleation sites for additional formation from the gas and aqueous liquid phases. However, most geochemists (Claypool and Kaplan, 1974 Finley et al., 1987, etc.) suggest hydrates form from gas (either at equilibrium or supersaturated) dissolved in the liquid phase, without a free gas. 

Even if the linear equilibrium assumption is accepted, Rvalues measured in laboratory experiments will be sensitive to the solution chemistry and experimental design. If conservative predictions of the barrier time-to-breakthrough are desired, the supporting laboratory experiments should be carefully designed, as discussed in the following section. 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

The substance-specific kinetic constants, kx and k2, and partition coefficient Ksw (see Equations 3.1 and 3.2) can be determined in two ways. In theory, kinetic parameters characterizing the uptake of analytes can be estimated using semiempirical correlations employing mass transfer coefficients, physicochemical properties (mainly diffusivities and permeabilities in various media), and hydro-dynamic parameters.38 39 However, because of the complexity of the flow of water around passive sampling devices (usually nonstreamlined objects) during field exposures, it is difficult to estimate uptake parameters from first principles. In most cases, laboratory experiments are needed for the calibration of both equilibrium and kinetic samplers. 

In applying the model, some mineral parameters, such as numbers, n, and mean radii, Rq of various mineral particles may be estimated by mineralogical techniques. For physical properties such as phase equilibrium constants, K, published ternary and binary data may be used on an approximate basis. Kinetic parameters such as reaction rate constants, k, or mass transfer coefficients can be very roughly estimated based on laboratory experiments. Their values may then be varied in a series of computer runs until the results match pilot plant data. A reasonably good match will, at the same time, confirm the remaining variables, rate equations and other assumptions. 

---