Isotherm congruent

Fig. 11 shows master curves extrapolated with the model. These have the same general features as master curves plotted by shifting data isotherms. The two differ slightly because different assumptions are involved. The conventional method of shifting data makes all isotherms congruent the same viscoelastic processes are assumed at all temperatures. The phenomenological model is not limited to this assumption. When the thermal spread varies with frequency, the model extrapolates to isotherms like fig. 11. Note... 

The isothermal evaporation of a sat. soln. of two salts with a common ion leads to the separation of both salts, but with sat. soln. of three salts, this may or may not occur. The isothermal evaporation of solution II furnishes as solid phases the same three salts as are present as solutes. These soln. were called by W. Meyer-hofer congruent solutions, because, on isothermal evaporation, they furnish as solid phases the same salts as are present as solutes in soln. On the other hand, with solution I the salts which separate as solid phases are different from those present in soln., for sodium chloride appears in place of ammonium hydrocarbonate. In contrast with congruent soln., W. Meyerhofer styled them incongrucnt solutions here the sat. soln. contains a different salt from those which are present as solid phases. The gradual addition of sodium chloride to solution I changes the composition of the soln. until the incongruent solution I passes into II ammonium hydrocarbonate does not change when added in a similar manner to solution II. 

In the preceding cases the solidus and liquidus curves meet tangentially to an isothermal line at a congruent point the solution freezes at this temperature without any change in composition. Au—Ni alloys exhibit the behavior depicted in Fig. 3.15.2. Inasmuch as AHC > 0 for this case, the solid solution for T < Tc is less stable than a mixture of phases this is indicated by the dotted curve at the bottom of the diagram. 

In practice this means that the adsorption isotherm, should shift parallel along the x-axis when the temperature is changed. When this is indeed observed, the isotherms are called temperature-congruent the distance between them is... 

Adsorption isotherm of Phe vapors on CA-3 sample were obtained at different CO2 percentages, 0%, 10%, 15% and 30% at 150°C (see Fig 3). The adsorption isotherms are close to type I of the BDDT classification. It is observed that the adsorption is mainly produced in the molecular size pores of Phe and the presence of CO2 in the gas stream seems not to avoid the multilayer adsorption. The decrease on the Phe adsorption capacity when CO2 is added to the gas stream is probably due to a competitive effect between both molecules for the adsorption sites. It is also observed that the increase of the CO2 percentage from 10% to 30% does not seem to affect to Phe adsorption capacities. This fact is congruent with the results obtained by Yong et al who reported that the CO2 adsorption at high temperature on non-chemically modified carbonaceous materials, follows Henry s law with a negligible influence of CO2 partial pressure on its adsorption capacity. 

The shapes of these isotherms are controlled by surface heterogeneity, and thus provide a means of deducing the various modes of interfacial attraction presented by the substrates. Isotherms of pentane on unsized IM6 before and after plasma treatment are congruent. Pentane interacts only by dispersion force attraction, as does methylene iodide the registry of these isotherms is predicted by the similarity in ft obtained from wetting measurements. Pentane isotherms serve as a reference with which to assess the effect of additional modes of solid/vapor interaction with acidic and basic probes. 

Since the salts were originally present in equimolccular proportions, the final result of evaporation will be the pure double salt. If when the solution has reached the point E the salt A which had separated out is removed, double salt only will be left as solid phase. At a given temperature, however, a single solid phase can exist in equilibrium with solutions of different composition. If, therefore, isothermal evaporation is continued after the removal of the salt A, double salt will be deposited, and the composition of the solution will change in the direction EF. At the point F the salt B will separate out, and on evaporation both double salt and the salt B will be deposited. In the former case (when the salt A disappears on evaporation) we are dealing with an incoftgruently saturated solution but in the latter case, where both solid phases continue to be deposited, the solution is said to be congruently saturated -... 

A congruently saturated solution is one from which the solid phases are continuously deposited during isothermal evaporation to dryness, whereas in the case of incongruently saturated solutions, at least one of the solid phases disappears during the process of evaporation. 

Lastly, if the temperature lies outside the transition interval, isothermal evaporation of an unsaturated solution of the composition X (Fig. 127) will lead to the deposition of pure double salt from beginning to end. If a solution of the composition Y is evaporated, the component A will first be deposited and the composition of the solution will alter in the direction of E, at which point double salt will separate out. Since the solution at this point contains relatively more of A than is present in the double salt, both the double salt and the single salt A will be deposited on continued evaporation, in order that the composition of the solution shall remain unchanged. In the case of solution Z, first component B and afterwards the double salt will be deposited. The result will, therefore, be a mixture of double salt and the salt B (congruently saturated solutions). 

Today s data collection methods allow the registration of a great number of data and this simultaneously with a high time density. In consequence, numerical differentiation of a progressing value described by numerous discrete data points can be performed without making significant errors. Such a differentiation of the congruent X(h) curves of all three experiments with respect to the equivalent isothermal reaction time... 

The isothermal section of the Co-Sm-C system at 900 °C is shown in fig. 22. From a comparison of the liquidus projection and the isothermal section at 900°C, Sm5COiiC2 occurs on the liquidus projection and decomposes eutectoidally above 900°C, and SmCoC2 melts congruently. The compound Sm5CoiiC2 is hexagonal... 

Grahame-Parsons isotherm uses the electrode charge, a, whose value influences the parameter, related to the standard adsorption energy. Equation (75) predicts that the isotherms for different electrode charges must be congruent. 

Figure 12.5 Effect of temperature on the solubility curves and the co-crystal domain in the ternary phase diagram of (a) a congruently melting cocrystal (c/.. Figure 12.1(a)) and (b) an incongruently melting co-crystal cf, Figure 12.1(b)). Ideal miscibility of all components in the liquid phase is assumed. The eutectic grooves are indicated by continuous lines, the peritectic groove by a dashed line. The two-phase regions in the 75 °C isothermal cross section are shaded.

Figure 13.4 (a) is a stoichiometric compound with congruent fusion the metastable eutectic between A and B is not represented. Conversely, (b) shows a non-stoichiometric compound with congruent fusion (note that the composition of the melting point does not necessarily correspond to a stoichiometric composition) the metastable eutectic between A and B is not represented, (c) is a stoichiometric compound in the isothermal section of the ternary system A-B-C. (d) < AB> is a non-stoichiometric compound in the isothermal section of the ternary system A-B-C. The thin segments, representing the so-called tie lines, connect the compositions of the two phases in equilibrium crystals and their saturated liquid phase, u.s.s. is an unsaturated solution. 

At = const, when the adsorption isotherm is congruent with respect to the electrode potential and the surface coverage is low, the effective standard rate constant may be determined with the posterior correction for the double-layer effects. Besides, in some cases (for instance, in the case of M j M"" electrode), faradaic elements do not depend on the bulk concentration of M"" [18]. This effect may be useful in studies of Cjj in the presence of faradaic process. At last, no surface area of the electrode is required to obtain the parameter k (see Eq. (5.56)). Dependence of directly measured capacitance (unrelated to the surface unit) versus direct current (instead of i) may be used for this purpose. 

Let us assume that and Tlx are established when = const and the adsorption isotherms are congruent with respect to the electrode potential [8, 16]. Then, a question arises whether it is possible to combine Lqs. (1.2) and (7.11) with adsorption isotherms. Analysis of a number of isotherms showed that such consistency exists only in the case where the adsorption of the complex species obeys a Freundlich isotherm BjCj" = 9j, going over to a Henry isotherm with = 1, and also in the case of purely electrostatic adsorption. It can be proved that in the case of Freundlich isotherm, there exists the relationship between the three types of constants ... 

In the calculations of partial pressures (Hastie et al., 1968), ionization of dimeric molecules accompanied by loss of more than one atom (especially in reaction steps that can interfere with ionization of monomers) was assumed to be improbable. This assumption was experimentally confirmed in studies of the congruent evaporation of SmCl3 (Chervoimyi et al., 1974). Isothermal evaporation of a sample of known weight was carried out at several temperatures, and the saturated vapor pressure was determined by the Hertz-Knudsen equation. In each experiment, the state of an imsaturated vapor caused by the presence of an nonvolatile species ( 1.5% SmCl2) was determined in the end of... 

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