Effect on equilibrium curves

These pressure differences have no effect on heatup paths, Fig. 12.4 - and little effect on equilibrium curves and intercepts. Intercept temperature and % S02 oxidized both increase slightly with increasing pressure. 

Fig. 17.1 shows the effect of C02 on a 1st catalyst bed heatup path and intercept. C02 has no effect on equilibrium curves, Appendix F. 

Summing up, the influence of the kinetics of a chemical reaction on the vapor-liquid equilibrium is very complex. Physical distillation boundaries may disappear, while new kinetic stable and unstable nodes may appear. As result, the residue curve map with chemical reaction could look very different from the physical plots. As a consequence, evaluating the kinetic effects on residue curve maps is of great importance for conceptual design of reactive distillation systems. However, if the reaction rate is high enough such that the chemical equilibrium is reached quickly, the RCM simplifies considerably. But even in this case the analysis may be complicated by the occurrence of reactive azeotropes. 

Fig. 5. Isobaric volume v versus T, illustrating volume hysteresis effect. The equilibrium curve in the liquid well above Tg is unique. At a constant cooling rate g, the V falls out of equilibrium below Tg. When the sample is then annealed at constant T, the volume becomes densified and may reach a relaxed glass state, depending on the temperature. The lower portion of the solid curve represents the behavior after heating at constant q. Note c remains under its liquid value to T> Tg. This plot is similar to that found for amorphous Selenium in Ref. 71 and for a polymeric system in Ref. 79.

Figure 12.4 Effect of pressure on equilibrium curves and heatup path-equilibrium curve intercepts. Equilibrium curves and intercepts are affected by pressure. Heatup paths are not. Intercept temperature and % SO2 oxidized both increase shghtly with increasing pressure. The intercepts have been calculated as described in Appendix J.

Increasing the pressure may either increase or decrease the UCST and, thus, raise or lower the (liquid + liquid) equilibrium line. Figure 8.19, for example, shows the effect of pressure on the (liquid + liquid) equilibrium curves for (xin-CftHu + A2CH3OH).3 In this example, we see that increasing p increases the UCST. 

This equation shows that activity of Ca + is related to pH, concentration of H2CO3 and temperature. Because pH is related to the concentration of Cl for the equilibrium curves 1 and 2 in Fig. 2.14, the relationship between the concentrations of Ca " " and Cl" can be derived for calcite-albite-sericite-K-feldspar-quartz equilibrium (curves 4 and 7 in Fig. 2.14) and calcite-albite-sericite-Na-montmorillonite-quartz equilibrium (curves 5 and 8 in Fig. 2.14) with constant w2h2C03- The range of zh2C03 in the solution in equilibrium with calcite is assumed to be 10 to 10 . The other equilibrium curves for the assemblage including Ca minerals are also drawn (Fig. 2.14). These assemblages are wairakite-albite-sericite-K-feldspar-quartz (curve 3), Ca-montmotillonite-albite-sericite-Na-montmorillonite-quartz (curve 6), Ca-montmorillonite-albite-sericite-K-feldspar-quartz (curve 9) and anhydrite (curve 10). The effect of solid solution on the equilibrium curves is not considered because of the lack of thermochemical data of solid solution. 

The existence of dark matter (either baryonic or non-baryonic) is inferred from its gravitational effects on galactic rotation curves, the velocity dispersions and hydrostatic equilibrium of hot (X-ray) gas in clusters and groups of galaxies, gravitational lensing and departures from the smooth Hubble flow described by Eq. (4.1). This dark matter resides at least partly in the halos of galaxies such as our... 

The influence of the solubility of the gas on the shape of the equilibrium curve, and the effect on the film and overall coefficients, may be seen by considering three cases in turn — very soluble, almost insoluble, and moderately soluble gases. 

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