Equilibrium condition steady state comparison

The scheme in Fig. 5.5 indicates that the ligand, for example, oxalate, is adsorbed very fast in comparison to the dissolution reaction thus, adsorption equilibrium may be assumed. The surface chelate formed is able to weaken the original Al-oxygen bonds on the surface of the crystal lattice. The detachment of the oxalato-aluminum species is the slow and rate-determining step the initial sites are completely regenerated subsequent to the detachment step provided that the concentrations of the reactants are kept constant, steady state conditions with regard to the oxide surface species are established (Table 5.1). If, furthermore, the system is far from dissolution equilibrium, the back reaction can be neglected, and constant dissolution rates occur. 

Thus, for hydrophilic molecules, there is a clear correlation between the CSF/ serum ratio and the hydrodynamic radius of the molecule. This is applicable only in the presence of a steady-state equilibrium (i.e., when the serum concentration is stable and the exchange conditions at the blood-CSF barrier are undisturbed) (Tib). The ratio for water is by definition 1.0. The concentration of the smaller chloride ion is higher in CSF than in serum therefore, in barrier dysfunction, it decreases in comparison to larger molecules. For most amino acids, active... 

A Comparison of Steady State Procedures and Equilibrium Conditions in the Reversible Reaction... 

COMPARISON OF STEADY STATE PROCEDURES AND EQUILIBRIUM CONDITIONS... 

For the types of comparisons reported here it has generally been convenient to use steady state assumptions, but these clearly do not apply to conditions after forest spraying. Monitoring studies typically report rapid penetration of pesticides to forest streams followed by rapid dissipation of residues by a number of processes. Most published bioconcentration equations do not contain a time term and so they cannot readily be applied to short intervals when only a small fraction of the time to reach equilibrium would apply. The rate constants and other descriptive equations offer the possibility of predicting bioconcentration under non-equilibrium conditions. 

Comparison of equations 3 and 10 shows the essential difference between the stationary states of closed and continuous, open systems. For the closed system, equilibrium is the time-invariant condition. The total of each independently variable constituent and the equilibrium constant (a function of temperature, pressure, and composition) for each independent reaction (ATab in the example) are required to define the equilibrium composition Ca- For the continuous, open system, the steady state is the time-invariant condition. The mass transfer rate constant, the inflow mole number of each independently variable constituent, and the rate constants (functions of temperature, pressure, and composition) for each independent reaction are requir to define the steady-state composition Ca- It is clear that open-system models of natural waters require more information than closed-system models to define time-invariant compositions. An equilibrium model can be expected to describe a natural water system well when fluxes are small, that is, when flow time scales are long and chemical reaction time scales are short. 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

WET-BULB TEMPERATURE. The wet-bulb temperature is the steady-state, non-equilibrium temperature reached by a small mass of liquid immersed under adiabatic conditions in a continuous stream of gas. The mass of the liquid is so small in comparison with the gas phase that there is only a negligible change in the properties of the gas, and the effect of the process is confined to the liquid. The method of measuring the wet-bulb temperature is shown in Fig. 23.4. A thermometer, or an equivalent temperature-measuring device such as a thermocouple, is covered by a wick, which is saturated with pure liquid and immersed in a stream of gas having a definite temperature T and humidity ff. Assume that initially the temperature of the liquid is about that of the gas. Since the gas is not saturated, liquid evaporates, and because the process is adiabatic, the latent heat is supplied at first by cooling the liquid. As the temperature of the liquid decreases below that of the gas, sensible heat is transferred to the liquid. Ultimately a steady... 

HCo(CO)4 is held below its equilibrium value for the reaction in eq (3.2-1), which is only achieved after the alkene is fully consumed. The results for propylene hydroformylation in supercritical CO2 have been compared [53] with those of Mirbach [55] for the reaction of 1-octene in methylcyclohexane solution. Under comparable conditions, the steady-state concentrations of the intermediates do not differ greatly (i.e. by little more than a factor of three), and the overall hydroformylation rates are quite similar, d[aldehyde]/dt = 1.2 x 10" M s and 0.77 x 10 M s , for the methylcyclohexane and CO2 systems, respectively. Although different alkenes were used in the two studies, the comparisons are believed to be meaningful, as Wender et al. [56] have shown that hydroformylation rates for a wide range of straight-chain terminal alkenes vary only slightly with chain length for cobalt catalysts. 

The critical nucleus of a new phase (Gibbs) is an activated complex (a transitory state) of a system. The motion of the system across the transitory state is the result of fluctuations and has the character of Brownian motion, in accordance with Kramers theory, and in contrast to the inertial motion in Eyring s theory of chemical reactions. The relationship between the rate (probability) of the direct and reverse processes—the growth and the decrease of the nucleus—is determined from the condition of steadiness of the equilibrium distribution, which leads to an equation of the Fourier-Fick type (heat conduction or diffusion) in a rod of variable cross-section or in a stream of variable velocity. The magnitude of the diffusion coefficient is established by comparison with the macroscopic kinetics of the change of nuclei, which does not consider fluctuations (cf. Einstein s application of Stokes law to diffusion). The steady rate of nucleus formation is calculated (the number of nuclei per cubic centimeter per second for a given supersaturation). For condensation of a vapor, the results do not differ from those of Volmer. 

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