Equilibrium degree of conversion

The degree of dissociation a is the equilibrium degree of conversion, i.e. the fraction of the number of molecules originally present that dissociated at the given concentration. The degree of dissociation depends directly on the given dissociation constant. Obviously a = [Bz+]/v+c = [Az ]/v c, [Bv+Av ] = c(l - a) and the dissociation constant is then given as... 

This equation can be easily modified if the equilibrium degree of conversion at T = Tiisequal, notto 1, but to some value dp < 1. 

The values of the modulus of the end product depend on temperature therefore it is necessary to introduce the equilibrium degree of conversion as a reference point ... 

To illustrate the concept, Figure 2.3 represents the dependences of and tj as a function of P, at stoichiometric ratio (1 0.5 mol) between B and N2. It can be seen that at 1 atm, equilibrium degree of conversion equals to 0.5 and only at P = 100 atm, it approaches unity. It means that, due to dissociation of the product, having sufficient amount of nitrogen in the system does not guarantee full conversion. It also can be seen that adiabatic combustion temperature is extremely... 

Assume that the dependence of the equilibrium constant on temperature is known. This relationship can be obtained by means of one of the methods described in Chapter 3. The equilibrium degree of conversion and temperature Tmust satisfy a set of two non-linear equations... 

All relaxation curves exhibited more than one phase at various degrees of conversion and at different temperatures. This clearly rules out the all-or-none mechanism (AON) although the AON model is able to fit easily to the measured equilibrium transition curve. However, a mechanism has been proposed which allows the existence of side... 

Several methods have been developed for the quantitative description of such systems. The partition function of the polymer is computed with the help of statistical thermodynamics which finally permits the computation of the degree of conversion 0. In the simplest case, it corresponds to the linear Ising model according to which only the nearest segments interact cooperatively149. The second possibility is to start from already known equilibrium relations and thus to compute the relevant degree of conversion 0. 

Both Qv(x) and Q°(x) decrease as the polymerization proceeds and, after a definite conversion Qv(x) may reach the value of Qx(x). Since the dilution of a gel cannot be greater than its equilibrium degree of swelling, the excess of solvent should separate from the gel phase resulting in the syneresis, i.e. in phase separation. The condition for incipient phase separation during copolymerization of divinyl/vinyl monomers is given by [107]... 

Figure 2.12 Calculated curves for ee (starting upper left comer) and ee (starting lower left comer) for a resolution with =100 and three different equilibrium constants, 10 000, 5 and 0.5. With a large the reaction is irreversible and the progress curves looks like the examples of Figure 2.9. For reactions with smaller K q-values a dramatic effect is observed for ee. The curve reaches a maximum, as the reaction progresses further ee is reduced and the curve never reaches 100%. The effect of reversibility on ee is not as dramatic. The curve dips down at an earlier degree of conversion when K is lowered.

Fig. 1. Degree of conversion n 1 at equilibrium for the nearest-neighbor case (.kik-sjkik-s ) = (k ki)2 as a function of the parameters K0 = (k /k,) 12, - (kjki)1 2. Note that the cooperative transition region corresponds to K0 and K, being very large and about equal. For very small values of K0 and K, the conversion is about 1/2 and the strictly alternating polymer... 01010. .. is preferred. K0 and K, completely determine the equilibrium distribution.

Fig. 2. Degree of conversion n as a function of reduced time k,t. Initial equilibrium corresponds to K0 = Ki = 1, for example, to kt = k2 = k3 = kt = k2 = k3. Stepwise transition to...

For reasonable accuracy by the flow method it is necessary to maintain the degree of conversion at between 30 and 50% of complete conversion from the initial to the equilibrium ortho-para ratio at the reactor temperature. This may be done by varying the amount of catalyst or the flow rate of the hydrogen. Catalyst masses of from 10 mg to 10 g and monitored flow rates of 0.1 to 1 cm3 s-1 (STP) have often been used. Atmospheric pressure has been used for many of the reported results. 

Figure 4.16. Temperature dependence of the equilibrium value of the "rheological" degree of conversion. Points - experimental solid line calculated.

Figure 5.14 Enantioselectivity as a function of degree of conversion x and equilibrium constant (Rakels, 1993).

Whereas a high value for e.e.s can always be achieved with irreversible reachons (maybe only in case of high degree of conversion), this is not possible in the case of reversible reactions. However, an optimal value for e.e.s can be found which depends on E and K. As expected, the maximum e.e.p value is reached at a zero degree of conversion and does not depend on K at a degree of conversion of zero, the reachon is far from equilibrium. 

Table 4.11 Equilibrium constants and compositions for ideal-gas reaction (4.14) at P° = 1 bar. x is a mol fraction of a component, is a degree of conversion...

A more detailed picture of hydroisomerization of n-octane and n-nonane is given in Table II in which product distributions are listed for different degrees of conversion along with thermodynamic equilibrium values. The latter have been calculated from Gibbs free energy data available in literature (F7) the accuracy of which, however, is not known. From Table II the following conclusions may be drawn ... 

Tobolsky and Owen (15) extended the Tobolsky-Eisenberg (16) general treatment of homopolymerization equilibria to copolymerization and applied their equations to the copolymerization data of Schenk (14) on selenium and sulfur. In this work the equilibrium degree of polymerization is measured as a function of temperature for total conversion of monomer to polymer. Equilibrium constants for initiation and propagation are derived from homopolymerization experiments. 

Polymerization in the liquid crystal state involves a major increase in the molecular weight of the polymer, reaching the hundreds of thousands. The thermodynamic equilibrium between the monomer in smectic liquid crystals and the polymer is shifted completely toward formation of the polymer up to the melting point of the crystal (138°C.). The polymerization rate does not change with the degree of conversion... 

If one assumes that all macromolecules are bound to stable complexes at an equimolar ratio of poly(methacrylic acid) and poly(ethylene glycol), the reaction yield must be practically 100%. However, the experimentally determined degree of conversion 6 — (Co - Cx)/Co (where Co is the total concentration of CQOH groups in solution, C, the concentration of COOH groups not associated with PEG) is about 0.7. Such a discrepancy between theoretical and experimental degrees of conversion may be explained if one takes into account the possibility of the following equilibrium in the complex particle on link level ... 

---