Chemical drive concentration dependence

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

Whilst the fundamental driving force for crystallisation, the true thermodynamic supersaturation, is the difference in chemical potential, in practice supersaturation is generally expressed in terms of solution concentrations as given in equations 15.1-15.3. Mullin and Sohnel(19) has presented a method of determining the relationship between concentration-based and activity-based supersaturation by using concentration-dependent activity-coefficients. 

The driving force for transport within the zeolite crystals appears to be the gradient of chemical potential rather than the concentration gradient, and, for systems with a nonlinear equilibrium isotherm, the diffusivity is therefore concentration dependent (6-8). 

The primary difference between D and D is a thermodynamic factor involving the concentration dependence of the activity coefficient of component 1. The thermodynamic factor arises because mass diffusion has a chemical potential gradient as a driving force, but the diffusivity is measured proportional to a concentration gradient and is thus influenced by the nonideality of the solution. This effect is absent in self-diffusion. 

Here q is the concentration of species i, and the quantity RT/ci has been absorbed into the diffusion coefficient D. Eq. (6.3.4) is known as Pick s Law of diffusion. The coefficient is clearly concentration dependent. In Eq. (6.3.4) the concentration gradient serves as the driving force , but in actuality it is the gradient in chemical potential that activates the particle flow, as shown in Eq. (6.3.3). 

The interactions of ions with water molecules and other ions affect the concentration-dependent (colligative) properties of solutions. Colligative properties include osmotic pressure, boiling point elevation, freezing point depression, and the chemical potential, or activity, of the water and the ions. The activity is the driving force of reactions. Colligative properties and activities of solutions vary nonlinearly with concentration in the real world of nonideal solutions. 

One expects that Dg and Dt will have a different concentration dependence. Comparisons between PFG NMR, QENS, and MD simulations could only be made in the past at the level of Dg. At equihbriiun, one can now obtain experimentally Dt using coherent neutron scattering. From equihbrium MD simulations, one cannot derive Dt, but one can determine the corrected diffusivity Do. These two diffusivities are linked by considering that the driving force for diffusion is the chemical potential gradient, and not the concentration gradient... 

In this section we will deal with the analysis of adsorption kinetics of a multicomponent system. First we will deal with the case of a single zeolite crystal to investigate the effect of the interaction of diffusion of all species inside a zeolite crystal. This interaction of diffusion is characterized by a diffusivitv matrix which is in general a function of the concentrations of all species involved. This concentration dependence will take a special functional form if we assume that the driving force for the diffusion inside the zeolite crystal is the chemical potential gradient and that the mobility coefficients of all species are constant. Only in the limit of low concentration such that the partition between the fluid phase and the adsorbed phase is linear, the diffusivity matrix will become a constant matrix. 

Fig. 7 Driving force dependence of (fobs obtained for the reduction of ZnPor+ in benzene by various redox couples in the aqueous phase as probed by SECM in the presence of a full monolayer of ClO-lipid (a). As the driving force increases, fcobs increases in the presence of Fe(CN)6 (curve 1), but decreases for Co (II) sepalchrate (curve 2) and V + (curve 3). A similar analysis is presented in (b) but in the absence of the C-10 lipids and for substantially smaller concentration of the aqueous redox couple. The curve in (c) was obtained from photocurrent measurements at the polarizable water DCE interface in the presence of water-soluble porphyrin dimer (ZnTPPSiZnTMFVP) and ferrocene (Fc), dimethylferrocene (DMFc), butylferrocene (ButylFc), diferrocenylethane (DfcEt), and decamethylferrocene (DCMFc). (Figs, a, b and c were reprinted from Refs. [32, 34], respectively, with permission from the American Chemical Society.)...

Interpretation of concentration dependence of micropore diffusion coefficient in terms of chemical potential driving force model... 

In processing, it is frequently necessary to separate a mixture into its components and, in a physical process, differences in a particular property are exploited as the basis for the separation process. Thus, fractional distillation depends on differences in volatility. gas absorption on differences in solubility of the gases in a selective absorbent and, similarly, liquid-liquid extraction is based on on the selectivity of an immiscible liquid solvent for one of the constituents. The rate at which the process takes place is dependent both on the driving force (concentration difference) and on the mass transfer resistance. In most of these applications, mass transfer takes place across a phase boundary where the concentrations on either side of the interface are related by the phase equilibrium relationship. Where a chemical reaction takes place during the course of the mass transfer process, the overall transfer rate depends on both the chemical kinetics of the reaction and on the mass transfer resistance, and it is important to understand the relative significance of these two factors in any practical application. 

What Are the Key Ideas The tendency of electrons to be transferred in a chemical reaction depends on the species involved and their concentrations. When the process is spontaneous and reduction and oxidation occur at different locations, the reaction can do work and drive electrons through an external circuit. 

Diffusion as referred to here is molecular diffusion in interstitial water. During early diagenesis the chemical transformation in a sediment depends on the reactivity and concentration of the components taking part in the reaction. Chemical transformations deplete the original concentration of these compounds, thereby setting up a gradient in the interstitial water. This gradient drives molecular diffusion. Diffusional transport and the kinetics of the transformation reactions determine the net effectiveness of the chemical reaction. 

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