Steady state chemical

Model of Pb, Bi, and Po degassing. For a purpose of clarity, it is considered here that the degassing reservoir has reached a chemical steady-state (i.e., radionuclide activities in the degassing reservoir are constant, that is d(Ik)iydt = 0 in Eqn. 4). This assumption usually is valid for very active basaltic systems like Stromboli, where erupted products display an almost constant chemical composition as shown above, and where the degassing reservoir is quickly and continuously replenished with deep undegassed magma. 

The main inconvenient of this methodology is that the results cannot be considered stricto sensu as obtained in operando conditions, because the system was perturbed from the steady state to reveal hidden species. It could be even hypothesized that such compounds are uniquely due to the particular test conditions and not to the real reaction pathway. A method to discard such kind of criticism is to maintain the chemical steady state of the reaction, while introducing a perturbation via a sudden exchange of one... 

Meunier, F.C., Tibiletti, D., Goguet, A., Shekhtman, S., Hardacre, C., and Burch, R. 2007. On the complexity of the water-gas shift reaction mechanism over a Pt/Ce02 catalyst Effect of the temperature on the reactivity of formate surface species studied by operando DRIFT during isotopic transient at chemical steady-state. Catal. Today 126 143 17. 

The method of isotopic transient reaction kinetics (see 5), applied in a chemical steady state is an elegant application of the true steady state measurement. 

This situation applies when the total flux of chemical into an organism equals the total flux out with no net change in mass or concentration of the chemical. Steady-state differs from equilibrium in that it is achieved as a result of a balance of transport and transformation... 

The approach of Prasad and Huntress (1980a, b) might be called the chemical time dependent approach because it utilizes fixed physical conditions. However, the chemical evolution to steady-state takes so long that it may be unwise to maintain fixed physical conditions. Time scales more rapid that the 107 years needed to reach chemical steady-state include the grain adsorption time and the free-fall collapse time. Thus, in the simplest approximation, chemical steady-state can never be reached because the gas phase will be adsorbed into the grains and the cloud will have collapsed to form, presumably, a star. The observed facts that clouds do not form stars as rapidly as the free fall model and that they do possess a gas phase, both demonstrate that... 

For a typical dense cloud with nH2 = 104 cm-3, t = 3 x 105 yrs. Since the grains are quite cold, it is customarily assumed that hitting and sticking are one and the same for heavy species. The number we have calculated for t is a factor of 30 below the time needed to reach chemical steady state (see Section 4) and, indeed, is comparable to the time needed for peak complex molecule abundances to be achieved in the gas phase model of Leung, Herbst, and Huebner (1984). However, t is also much smaller than customarily assumed cloud lifetimes, based on star formation rates, of 107 yrs (see, e.g., Leger, Jura, and Omont 1985). If this latter number is correct, then a gas phase can exist if and only if at least one of the following criteria is met ... 

Lerman, A. Time to chemical steady states in lakes and oceans. In Hem, J.D., editor. Nonequilibrium Systems in Natural Water Chemistry. Advan. Chem. Ser. 106, American Chemical Society, Washington, DC, pp. 30-76, 1971. 

By means of Eq. (22) the percentage of chemical steady-state level in relation to time of chemical uptake in half-lives was calculated and presented in Table 1. Furthermore, as an example the uptake of TCDD in medaka was calculated. 95% of the steady-state TCDD level is reached if the time of uptake is 4.3 X half-Hfe and 98.4% is reached in 6 x half-life. This means that for TCDD in medaka (10% Hpid content) 95% of steady-state TCDD level is reached in 1.8 years and 98.4% in 2.5 years, respectively. The experimentally determined half-Hfe of TCDD in medaka was 154 days [28]. 

However, the removal of NO by the reaction shown in Equation (19) is much slower (e.g., 3 d). Thus, we can use the chemical steady-state approximation (which equates chemical production to chemical loss only) to define the ratio of NO to NO2. We must however take full account of transport in calculating [NOJ. Similar arguments hold for the odd oxygen ([0 J = [O] + [O3]) and odd hydrogen ([HOJ = [H] -b [OH] -b [HO2]) families. 

Time to Chemical Steady-States in Lakes and Ocean... 

In water and sediments, the time to chemical steady-states is controlled by the magnitude of transport mechanisms (diffusion, advection), transport distances, and reaction rates of chemical species. When advection (water flow, rate of sedimentation) is weak, diffusion controls the solute dispersal and, hence, the time to steady-state. Models of transient and stationary states include transport of conservative chemical species in two- and three-layer lakes, transport of salt between brine layers in the Dead Sea, oxygen and radium-226 in the oceanic water column, and reacting and conservative species in sediment. 

Rate of change in concentration (C2) in layer h2. Ci° and C2° are initial concentrations in layers hi and h2 identified in the inset. Upper and lower layer assumed well mixed linear concentration gradient in middle layer. Equation 10, with Equations 7 and 9. Thickness of water layers hi = h2 = 25 m, Ah = JO m. Concentration-time curves were computed for the following diffusion coefficients, from left to right K = 5 X 10 2, 1 X 10 2y and 5 X 10 2 cm2 sec 1. Higher value of eddy diffusivity in the middle layer results in a faster attainment of chemical steady-state, indicated by equal concentrations in the three water layers (dashed line in the inset). 

Such changes, disturbing the existing chemical steady-state, would cause the concentration of the species to vary as a function of time until a new steady-state has been established. The time required to attain a new steady-state for Ra-226 in the sediment will be evaluated for a simple, but hypothetical, case of the Ra-226 concentration at the sediment-water interface increasing by a factor of 1.6. Such an increase would keep the Ra-226/Th-230 atom ratio at the sediment-water interface at the value of 1.6/100, which is still below the equilibrium value of approximately 2/100 the present-day ratio is near 1/100. 

Figure 2.1 illustrates one of the many possible feedback scenarios. For example, climate changes, mechanical compaction, or heat transport can cause or change ground-water flow. Groundwater flow brings about advection and dispersion of solutes. Mass fluxes across spatial domains cause changes of chemical concentrations, and perturb chemical equilibrium or a chemical steady state, which leads to chemical reactions. 

Hydrodynamic dispersion may however be significant in small, local hydrogeological problems, such as a point source contamination (Plummer et al., 1992). Another instance where diffusion may play an important role in water chemistry is the diffusion from permeable to less permeable parts of the aquifer, or matrix diffusion. This process appears to be important in fractured aquifers (Maloszewski and Zuber, 1991 Neretnieks, 1981), volcanic rock aquifers, aquifers adjacent to confining units (Sudicky and Frind, 1981), and sand layers inter-stratified with confining clay layers (Sanford, 1997). In systems in which a chemical steady state (see below) has not been reached, matrix diffusion effects may severely limit the applicability of inverse mass balance modeling to those systems. 

A chemical steady state is a sufficient, although not necessary, assumption because the underlying mathematical equations to be solved in inverse modeling are the integrated forms of mass conservation (Lichtner, 1996, p. 61). In other words, we have... 

Steady states for flow and for chemistry are different concepts and are often confused steady-state flow means constant directions and magnitudes of velocities steady-state chemistry means constant concentration distributions. Local equilibrium can possibly maintain a chemical steady state for reactive constituents in a transient flow regime (e.g., Ca2+ and HCCTj" in a Karst aquifer). However, if kinetics plays a significant role, e.g., the dissolution rate of feldspars or oxidation of organic carbon, then the chemical state in a transient flow field depends on competing factors of kinetic rates and velocity changes. Thus, chemical steady state may be achieved for some constituents but not others. 

Note that this is a situation where the solute concentrations vary in both space and time. Therefore, the chemical steady state assumption that is necessary for inverse modeling may be violated. 

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