Chemical equilibrium line

When the pressure decreases, the chemical equilibrium line intersects the liquid-liquid envelope within the physically relevant composition space. Consequently, the chemical equilibrium line coincides with one of the tie lines with the phase-splitting region (see the enlarged region of Fig. 4.9(b)). 

Figure 4.23 shows the curves according to Eq. (83) and Eq. (85) for various sweep gas flow rates G and vanishing liquid phase mass transfer resistance (i.e., Kiiq = 1). The points of intersection with the chemical equilibrium line mark the concentrations at which reactive arheotropes exist As can be seen, the reactive arheotrope... 

By increasing the Damkohler number, the influence of the chemical reaction is fortified. For Da = 10 (Fig. 5.16b) the shape of trajectories starting with a relatively high mole fraction of MeOH is still similar to those of distillation without reaction, so that pure MeOH remains a stable node in the system. Near the MTBE vertex, the conditions change remarkably. The reaction vector is pointed towards the chemical equilibrium line (dashed curve). As a consequence, the stable node moves from... 

The pseudohomogeneous chemical equilibrium (PCE) for the cyclohexanol reaction system is illustrated in Fig. 5.21a and the non-reactive isobaric L-L phase diagram is plotted in Fig. 5.21b. The rafSnate phase is very dose to the pure water vertex (see enlarged view in the right block). The two L-L envelopes intersect the PCE at two points x = (0.3466, 0.1840) and x = (0.0003, 0.9969). The two parts of the PCE outside the L-L region and the so called unique reactive liquid-liquid tie line [19] comprise the heterogeneous chemical equilibrium line (HCE), which is the bold line in Fig. 5.21b. 

When k c = kg = 1, the off-diagonal elements of [k ] are equal to zero and the RD process discussed in Section 5.3.2 (case b) is recovered. Then, the location of the attainable product composition only depends on the vapor-liquid equilibria. In Fig. 5.24, singular point curves for the attainable bottom products of the depicted counter-current pervaporative reactor are given as a function of ky c (Fig. 5.24a) and kg (Fig. 5.24b). For each set of membrane permeabilities there is one curve of possible singular points. The ftill circles on the singular point curves indicate stable nodes, that is th mark attainable bottom products. For the system considered, stable nodes are only obtained below the chemical equilibrium line. 

Fig. 5.24. Attainable regions of the bottom products (gray) of a pervaporative reactor (left) at different relative membrane permeabilities (dashed line chemical equilibrium line at K — 5, Damkohler number Da — 0...

At the reactive azeotrope A, the stoichiometric line forms a tangent to the residuum line. Points of tangential contact constitute a line whose point of intersection with the chemical equilibrium line is the reactive azeotrope. With this condition existence and location of reactive azeotropes can be identified (Frey and Stichlmair... 

The starting point of this sequence is the reactive mixture xi (depicted conventionally on the chemical equilibrium line in figure 2.2). This liquid mixture is in phase equilibrium with the vapor y, which is totally condensed to x. ... 

Figure 2.2. Representation of stoichiometric and reactive distillation lines for the reactive system A-B-C undergoing the reaction A+B C. Remark tt denotes the pole at which stoichiometric lines coincide, XiT, = VijT,Vj. Legend dashed line stoichiometric line dotted line phase-equilibrium hne continuous line chemical equilibrium line. System feature ...

The starting point of this sequence is the reactive mixture xi on the chemical equilibrium line. This liquid mixture is in phase equilibrium with the vapor yl, which is totally condensed to x. Since this mixture is apart from the chemical equilibrium line, it reacts along the stoichiometric line to the equilibrium composition X2- As can be seen in figure 2.2, the difference of the slope between the stoichiometric and liquid-vapor equilibrium lines defines the orientation of the reactive distillation lines. This difference in behavior allows one to identify a point, at which both the phase equilibrium and stoichiometric lines are collinear and where liquid concentration remains unchanged. This special point (labelled A in figure 2.2) is conventionally referred to as reactive azeotrope and is surveyed in section 2.4. 

It is clear that Xj falls between zero and one (1 > X/ > 0). When x/= 1, we have unity for the transformed variable X/ = 1 and, similarly, x = 1 gives X/ = 0. Consider the ternary space in Figure 6.16a where the solid line represents the chemical equilibrium line and the dashed line is the corresponding vapor line (in vapor liquid equilibrium with liquid composition in the chemical equilibrium line). The transformation of... 

For a symmetrical separation of component h from c, Brian Staged Cascades in Chemical Processing, Prentice-Hall, Englewood Cliffs, N.J., 1972) reported that the ratio of wash solvent to extraction solvent W /S should be set equal to the geometric mean of the two slopes of the equilibrium lines [Eq. (15-35)]. 

Our sun is, of course, a star. It is a relatively cool star and, as such, contains a number of diatomic molecules (see Figure 25-3). There are many stars, however, with still lower surface temperatures and these contain chemical species whose presence can be understood in terms of the temperatures and the usual chemical equilibrium principles. For example, as the star temperature drops, the spectral lines attributed to CN and CH become more prominent. At lower temperatures, TiO becomes an important species along with the hydrides MgH, SiH, and A1H, and oxides ZrO, ScO, YO, CrO, AlO, and BO. 

The relationship between the line shape of an NMR spectrum and the lifetime of chemical processes is provided by the Bloch equations. Let us imagine that there is a chemical equilibrium... 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

Le Chatelier s principle Le ChOtelier s principle states that if a chemical system at equilibrium is stressed (disturbed), it will reestablish equilibrium by shifting of the reactions involved, limiting reactant The limiting reactant is the reactant that is used up first in a chemical reaction, line spectrum A line spectrum is a series of fine lines of colors representing wavelengths of photons that are characteristic of a particular element, liquid A liquid is a state of matter that has a definite volume but no definite shape, macromolecules Macromolecules are extremely large molecules. 

NewtonRaphson.m, a 30 line code function that solves chemical equilibrium problems of any degree of complexity. 

Consider a mixture of AX and BX at chemical equilibrium. When, for example, radioisotopes are used as tracers, they are injected into the equilibrium mixture in the form of a very small amount of B X. At various times, either (BX + B X) or (AX + A X) is separated from the mixture and analyzed. When nmr line broadening is used to monitor the exchange the tracer is already present e.g. H or O (or an additional amount can be added) and the exchange is monitored in situ and assessed from the shape of the nmr signals (Sec. 3.9.6). If the concentration of (AX + A X) is a and the concentration of (BX + B X) is b, and the fraction of exchange at time t is F, it is not difficult to show that the gross or overall rate of X transfer between AX and BX, (M s ) is given by ... 

Figure 24.9a shows a plot of measured total carbon (CO plus CO2, mole percent) versus equivalence ratio. The solid line was calculated assuming chemical equilibrium at the measured temperatures. The data points represent the measured CO and CO2 mole fractions (dry basis) using the fast extractive-sampling system. Horizontal bars represent the uncertainty in (f> due to reading and calibration errors vertical bars represent the uncertainty in the CO and CO2 mole-fraction sum due to line strength and absorption measurement uncertainty. The data are consistent to within 4% of the equilibrium predictions at all values of (p, indicating reliable operation of the system. 

Figure 24.9 illustrates measured CO and CO2 mole fractions as a function of equivalence ratio. The solid lines represent chemical equilibrium calculations of CO and CO2 mole fractions at measured temperatures. The vertical bars represent the uncertainty in measured CO and CO2 mole fractions due to line... 

In Fig. 1.14, the dotted lines for each curve show the activity of the coexisting phases at chemical equilibrium. Similarly in Fig. 1.16 the dotted line BDF shows the activity of the coexisting phases (5 = 0.185 and 0.815). The coexisting phases, which have the same structure, differ in the concentration of vacancies. This phenomenon is generally called phase separation or spinodal decomposition (it is observed not only in the solid phases but also in the liquid phases), and originates from the sign of the interaction energy... 

There is a special case of the EE mechanism in which the reversible electrode reactions are coupled to a very fast chemical reaction such that the chemical equilibrium is quickly reestablished at the electrode surface in line with the following reaction scheme [51] ... 

In fuel-rich flames, the CO should be in local chemical equilibrium, and hence the partial pressure of CO can be calculated from the local temperature and the measured fuel and air flowrates. Thus, a comparison between measured and calculated CO levels can serve as a validation of the diode laser technique for flame measurements. Such a comparison is shown in Figure 5 for equivalence ratios in the range <(> = 1.04 - 1.37. The data points shown represent the average of several observations on separate lines including ground state (v" = 0) and excited state (v" = 1) transitions. The agreement is consistently within the experimental uncertainty of 5%. 

Equation (81) can also be used to predict the existence of reactive arheotropes provided that the mixture is in permanent chemical equilibrium - that is, the Damkohler number is sufficiently large. The condition which must be fulfilled has been given by Frey and Stichlmair [30], who concluded that the slope of the nonreacting residue curve must coincide with the slope of the stoichiometric lines of the chemical reaction, given by the stoichiometric coefficients vu... 

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