Concentration Dependence of Chemical Drive

We can now use what we have learned to easily show how shifts in concentration affect the chemical drive to react. Observe the following reaction 

If all the substances are present in small concentrations, we can apply the mass action equation for all of them  

6 Mass Action and Concentration Dependence of Chemical Potential 

The mass action term JL summarizes the deviations from the basic value of the individual substances which are caused by mass action. 

We will explain the influence of concentration shifts upon the chemical drive using the example of cleavage of cane sugar, 

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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 ... 

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. 

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

Several possibilities exist to determine the influence of transport phenomena. The measurement of gas consumption in dependence on the interfacial area, the physical absorption coefficient, the rate of a chemical reaction following the absorption, and the concentration gradient (as the driving force of the absorption) allows decisions to be made on which regime is, in fact, in existence [40]. 

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). 

In summary, the chemical potential of a substance depends on its concentration, the pressure, the electrical potential, and gravity. We can compare the chemical potentials of a substance on two sides of a barrier to decide whether it is in equilibrium. If fij is the same on both sides, we would not expect a net movement of species / to occur spontaneously across the barrier. The relative values of the chemical potential of species / at various locations are used to predict the direction for spontaneous movement of that chemical substance (toward lower /a ), just as temperatures are compared to predict the direction for heat flow (toward lower T). We will also find that Afij from one region to another gives a convenient measure of the driving force on species /. 

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. 

In this chapter we will consider some additional fundamental aspects of chemical reactions, i.e., how they occur, the driving forces behind them, and their dependence upon specifics of molecular structure and conditions of reaction, such as temperature and concentration. There are two aspects of chemical reactions which, though interrelated, are dealt with as separate topics. The first of these is the study of the reaction from its initiation to the point where the system seems to undergo no further change, called chemical kinetics. The second deals with the system after all apparent change has stopped, and is called chemical equilibrium. Following those topics we will examine some specific aspects of chemical equilibria involving oxidation-reduction reactions in aqueous solutions and combustion reactions. 

Now, it is instructive to re-analyze the unsteady-state macroscopic mass balance on an isolated solid pellet of pure A with no chemical reaction. The rate of output due to interphase mass transfer from the solid particle to the liquid solution is expressed as the product of a liquid-phase mass transfer coefficient c, liquids a Concentration driving force (Ca, — Ca), and the surface area of one spherical pellet, 4nR. The unsteady-state mass balance on the solid yields an ordinary differential equation for the time dependence of the radius of the peUet. For example,... 

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