Applications Involving Chemical Equilibrium

The left side is the chemical potential of pure A outside the tube. The right side is the chemical potential of A inside the tube. Because we do not consider the gas phase we may omit the index The temperature is the same in both subsystems. The outside pressure is P, whereas the inside pressure is different i.e. P + n. Why  

Initially the tube may contain B only. Chemical equilibrium therefore requires flow of A across the membrane into the tube. For simplicity we assume that the 

Again it is assumed that incompressibility of the liquid is a good approximation, cf.(3.34). Combination of Eqs.(3.55) and (3.56) then yields 

This is the so called van t Hoff equation (Jacobus van t Hoff, first Nobel prize in chemistry for his work on chemical dynamics and osmotic pressure, 1901). Note that the osmotic pressure only depends on the molar concentration of component B and temperature (under the approximations we have made in the course of the derivation). Here osmotic pressure is another example for a colligative property. 

Remark Reverse Osmosis. According to our derivation leading to Eq.(3.61), it should be possible to apply extra pressure to the tube in Fig. 3.9 and by doing so reduce its solute content. A technical example is desalination of sea water, which is forced through a membrane using a pressure exceeding the osmotic pressure. This process is called reverse osmosis. 

---

Intelligent engineering can drastically improve process selectivity (see Sharma, 1988, 1990) as illustrated in Chapter 4 of this book. A combination of reaction with an appropriate separation operation is the first option if the reaction is limited by chemical equilibrium. In such combinations one product is removed from the reaction zone continuously, allowing for a higher conversion of raw materials. Extractive reactions involve the addition of a second liquid phase, in which the product is better soluble than the reactants, to the reaction zone. Thus, the product is withdrawn from the reactive phase shifting the reaction mixture to product(s). The same principle can be realized if an additive is introduced into the reaction zone that causes precipitation of the desired product. A combination of reaction with distillation in a single column allows the removal of volatile products from the reaction zone that is then realized in the (fractional) distillation zone. Finally, reaction can be combined with filtration. A typical example of the latter system is the application of catalytic membranes. In all these cases, withdrawal of the product shifts the equilibrium mixture to the product. 

The applications of non-equilibrium or cool plasmas are more recent ( 3). In both areas the lack of fundamental understanding of the physical and chemical processes involved results in a substantially empirical approach to new applications and the optimisation of the desired material. 

The development and application of a rigorous model for a chemically reactive system typically involves four steps (1) development of a thermodynamic model to describe the physical and chemical equilibrium (2) adoption and use of a modeling framework to describe the mass transfer and chemical reactions (3) parameterization of the mass-transfer and kinetic models based upon laboratory, pilot-plant, or commercial-plant data and (4) use of the integrated model to optimize the process and perform equipment design. 

Note that the qualitative analysis of cations by selective precipitation involves all the types of reactions we have discussed and represents an excellent application of the principles of chemical equilibrium. 

Both processes (86) and (87) apparently involve formation or destruction of the zwitterion dipole moment Therefore, application of an electric field must di lace the respective chemical equilibrium to some extent depending on the an e 0 between the directions of the zwitterion dipole and the field E. For 0 < 90° an increase of the number of zwitterions is favoured whereas for 0 > 90° this number will be decreased. Therefore, the whole system tends to develop preferential orientation of dipoles parallel to the field. Proton transfer of the kind involved here has generally been proved to be practically difiiision controlled so that the reaction rates could be extremely high. The chemical mechanism of dielectric polarization may thus be fast enough in comparison with the rotational difiusion of the zwitterion, especially if the latter is a macromolecule (e.g . a protein). 

---