Temperature Dependence of the Azeotropic Composition

In [4], an equation is derived which describes how the azeotropic composition of a binary mixture depends on the temperature. Starting with the phase equilibrium for both components 

As the azeotropic composition itself is a function of temperature, differentiating with respect to T gives 

The factors (3ln y[/dx])T can be determined from Eq. (C.159), which can be written in logarithmic form as well  

Rearranging, using Eq. (C.16) and defining So Tq,Po) as a reference point at ideal gas conditions yields 

---

Note that the azeotropic conditions found in parts (a) and (b) are slightly different. This is a result of the difference in temperature between the two cases. Later in this section sve will show how this temperature dependence of the azeotropic composition can be used to advantage in. distillation. 

For the whole composition range and the different temperatures selected the results are shown in Figure 5.50. From the diagram it can be seen that a strong temperature (pressure) dependence of the azeotropic composition is observed (50 C 0.8 150 C Xi.az 0.2). This is mainly caused by the different... 

In this case the composition corresponding to the indifferent state which is here the azeotropic composition, depends upon the temperature. Thus if certain values of mj and m are given, it is in general possible to find a temperature such that the azeotropic composition satisfies (29.121). A closed system of this kind, chosen at random, can in general reach an indifferent state if one exists, but it cannot move along the indifferent line, for the other values of the composition along the line cannot be reached from the initial state. 

The temperature dependence of the separation factor (see Eq. (5.18)) and of the azeotropic composition of binary systems depends on the type of azeotrope (pressure maximum, pressure minimum), the temperature dependence of the vapor pressures, and the composition and temperature dependence of the activity coefficients. These dependencies can be described with the help of the heats of vaporization and partial molar excess enthalpies following the Clausius-Clapeyron respectively the Gibbs-Helmholtz equation [38] (derivation see Appendix C, B9) ... 

At 20 °C, for y-ray induced copolymerizations, r, 0.04 for monomer compositions containing 8-39% CO 7). At 120-130 °C, for (C2HsO)2 initiated copolymerizations, tj si 0.15 9). As Eq. (6) indicates, there exists one monomer ratio for which the copolymer composition equals the monomer composition, namely if + [C]/[E]) = 1. Using the above values of r, this azeotropic composition corresponds to 48.5 mol % CO for the y-ray induced copolymerizations at 20 °C (Fig. 1) 7), and si 46 mol % CO for the free radical initiated copolymerizations 9). The value of rj is dependent on the reaction temperature. For example, for the y-ray induced copolymerizations, the value of r2 increases from 0.04 at 20 °C to 0.31 at 157 °C 7). As expected, the value of rt at 135 °C was close to that observed for the free-radical initiated polymerization at that temperature. These results indicate that the copolymerization should be carried out at low temperatures in order to get copolymers with high CO contents. The azeotropic composition is also altered by pressure. For example, for (C2HsO)2 initiated copolymerizations the %CO in the azeotropic composition drops from 46% to 36% when the total gas pressure is lowered from 100 to 13.6 MPa (from 1000 to 136 atm) 9). 

The selection of acetonitrile versus methyl alcohol has several considerations even though their flammabilities and toxicities are relatively close. The advantages of using acetonitrile over methanol are (1) its lower UV absorbance cut-off. (2) its lower viscosity, (3) and its smaller viscosity dependence on temperature. The advantages of using methanol over acetonitrile are (1) its lower cost and lower cost fluctuation in the market place, and (2) its ease to recycle with water as a co-solvent (e.g. in reversed-phase chromatography) since methanol-water does not have an azeotrope as does acetonitrile-water. At a boiling point of 76.5°C, the azeotrope composition of acetonitrile-water is 83.7 16.3 [78]. 

The separation process depends on the nature of the vapor-liquid equilibrium relationships of the system, which can be represented on a ternary diagram. Figure 10.3a shows a ternary diagram at some fixed system pressure. Components A and B are close boilers, and A forms an azeotrope with the entrainer E. The curves in the triangle represent liquid isotherms. A corresponding vapor isotherm (not shown) could be drawn to represent the vapor at equilibrium with each liquid curve with tie lines joining vapor and liquid compositions at equilibrium. The temperature of the isotherms reaches a minimum at point Z that corresponds to the composition of the azeotrope formed between A and E. 

There are several ways to separate an azeotropic mixture into two components of the desired purities, and these are discussed in. other chemical engineering courses. However, one method will be mentioned here, and it is based on the fact that in general the two components will not have the same heat of vaporization, so that by the Clausius-Clapeyron equation the temperature dependence of their vapor pressures will be different. Since the dominant temperature dependence in vapor-liquid equilibrium is that of the pure component vapor pressures, the azeotropic composition will also change with temperature (and pressure). Therefore, what can be done is to use two distillation columns operating at different pressures. 

Figure 9.16 Different types of liquid-vapor phase diagrams for a binary liquid mixture of component A and B as functions of the mole fraction of the component with the higher boiling temperature, (a) The phase diagram for a system with a low-boiling azeotrope (minimum boiling point) and (b) the phase diagram for a system with a high-boiling azeotrope (maximum boiling point). The arrows show how the paths for various distillation processes depend upon the position of the initial composition relative to the azeotrope.

In order to relate yx and xu the bubblepoint temperatures are found over a series of values of xv Since the activity coefficients depend on the composition of the liquid and both activity coefficients and vapor pressures depend on the temperature, the calculation requires a respectable effort. Moreover, some vapor-liquid measurements must have been made for evaluation of a correlation of activity coefficients. The method does permit calculation of equilibria at several pressures since activity coefficients are substantially independent of pressure. A useful application is to determine the effect of pressure on azeotropic composition (Walas, 1985, p. 227). 

The condensate that collects on the cold surface is usually a completely homogeneous, or miscible, mixture of components. In general, the relative composition of the liquid components in the condensate is different from the composition in the vapor phase (except for an azeotropic mixture, where the condensate has the same exact molar concentration ratio as the vapor phase) [194]. The film that forms is not necessarily smooth but may show the appearance of streamers (or rivulets), waves, or droplets, depending on the particular mixture and its surface tension (which depends on the local wall temperature) [25,195,196]. If the condensate mixture is heterogeneous, or immiscible (as can occur when one component, for example, is aqueous and the other is organic), the pattern can be quite complex, looking somewhat like dropwise condensation [25,193,197]. These different condensate patterns affect the resulting fluid flow and heat transfer. 

---