Dynamic equilibrium curve

As a result of the recent investigations of the pseudo-binary systems of the substance sulphur we obtain the diagram shown in Fig. 67. Here, the points A, D, and G represent the ideal freezing-points of monoclinic, rhombic, and nacreous sulphur respectively, or the temperatures at which these three crystalline forms are in equilibrium with pure molten Sa. The curve HEB represents the dynamic equilibrium curve for Sa, S i, and S,r in molten sulphur and the points B, E, and H, where this equilibrium curve cuts the freezing-point curves, represent the natural freezing-points of the three modifications of sulphur. 

It was also clarified that Thermodynamic Equilibrium conversion is only related to TRs (closed systems), and has nothing to do with MRs (open systems). The conversion limit of MRs has been indicated as a Dynamic Equilibrium curve, which represents the reaction not limited by any kind of chemical kinetics (no kinetic resistance, that is, all molecules in contact with the catalyst are considered to react with an infinite velocity) and thus the feed gas is assumed to be continuously at equilibrium inside the MR. 

A feature of the phase diagram in Fig. 8.12 is that the liquid-vapor boundary comes to an end at point C. To see what happens at that point, suppose that a vessel like the one shown in Fig. 8.13 contains liquid water and water vapor at 25°C and 24 Torr (the vapor pressure of water at 25°C). The two phases are in equilibrium, and the system lies at point A on the liquid-vapor curve in Fig. 8.12. Now let s raise the temperature, which moves the system from left to right along the phase boundary. At 100.°C, the vapor pressure is 760. Torr and, at 200.°C, it has reached 11.7 kTorr (15.4 atm, point B). The liquid and vapor are still in dynamic equilibrium, but now the vapor is very dense because it is at such a high pressure. 

Finally, the data gave a clear indication of the reversibility of the assembly process. As illustrated in the magnified portion of the assembly curve in Fig. 7a (see inset), the path of the curve was not smooth but exhibited occasional upward stretches, indicating that in an overall assembly process there were occasional dissociation steps involving a few nucleosomes at a time. Thus, we believe that we see the first real-time demonstration of the dynamic equilibrium between an assembled and a disassembled state of individual nucleosomes in the fiber context such equilibrium has been previously suggested on the basis of... 

Fig. 14 Equilibrium curve demonstrating the dynamic behavior of the sensor system during a 1-ppm increase in concentration of benzene in aqueous solution, initially present at a concentration of 4 ppm [55]...

The dynamics of the /J-cdl model now depends on the point of intersection between the equilibrium curve for the fast subsystem [the solution to Eqs. (12) and (13)] and the so-called null-cline for the slow subsystem [the solution to Eq. (12)]. If this point falls on one of the fully drawn branches of the equilibrium curve, the equilibrium for the three-dimensional model is stable, and the model produces neither bursting nor spiking dynamics. If, as sketched in Fig. 2.7c, the two curves intersect in a point of unstable behavior for the fast subsystem, the equilibrium point for the full model is also unstable. The null-cline in Fig. 2.7c is drawn as a dashed curve. Below the null-cline for the slow subsystem, dS/dt < 0, and the slow... 

Our picture of the transitions between centres is very incomplete so far, based on studies of distribution curve shapes in the products. When a monomer is polymerized by a living mechanism on two or more centres of widely differing reactivity, chains of characteristic legth are produced on each centre type. In a strictly living medium where centres of one type are not transformed to another, a product with a bi- or multimodal distribution curve of degrees of polymerization is formed. When the various centre types are in a dynamic equilibrium where the centre type changes in the course of propagation, the distribution curve of the product will be broader than the width of either of the peaks in the previous case, but narrower than the overall... 

The upper curve shows a current transient produced by a voltage step applied to an unilluminated sample. The applied field was 107Vm-1 for a sample 6.5 pm. thick measured at 298 K. The lower curve shows a TOF transient recorded under the same conditions, and the points represent a theoretical fit using an analytical form based on an error function. This function is a reasonable approximation at high temperatures, when the photo-generated carriers rapidly achieve a dynamic equilibrium in the Gaussian DOS of the DEH molecules. 

Fig. 5. II — A curve of bovine serum albumin on distilled water at 20°C. Curve on left is equilibrium curve, assuming no desorption. Curve on right is dynamic curve, which would be obtained if no expulsion of segments from interface occurred. From MacRitchie (1977a), reproduced with permission.

Analysis of the fluorescence decay curves in water indicated that the intracoil process is static and that anthryl aggregation induces non-exponentiality in the fluorescence decay associated with a dynamic equilibrium between the singlet diphenyl-anthracene and a non-fluorescent dimer state. Further evidence was also presented to show that these polymers self-organise into hydrophobic and hydrophilic regions Energy migration in alternative and random copolymers of 2-vinylnaphthalene and methyl methacrylat methacrylic acid... 

The dynamic adsorption capacity of the annular bed was calculated by integrating the concentration vs. time curves up to a point close to the dynamic equilibrium time. Typical results of the dynamic adsorption capacity as a function of the SO2 inlet partial pressure, the feed flow rate and the feed concentration are shown in Figures 3 to 5. The effect of temperature on the dynamic adsorption capacity is shown in Figure 6 where the higher temperature data were taken from reference (5). 

This investigation resulted in the creation of the database of the equilibrium and kinetic characteristics of the zeolite tuffs using dynamic breakthrough curve. The computer-controlled system was developed in order to obtain experiment breakthrough curves, to carry out their mathematical treatment and to calculate necessary characteristics. The effective equilibrium and kinetic coefficients of some Russian clinoptilolite-containing tuffs from different deposits for the sorption of ammonium-ions were evaluated using this method, the data base was created. The chemical composition, the content of ciinoptilolite in tuffs and total cation-exchange capacity of tuffs have been also included in the data base. 

SCHEME 8.R.3 Using the curved arrow method to describe the reaction that forms H30 and OH in water. As indicated by the two arrows at the bottom of the drawing, the process is reversible and goes in both directions, what chemists call a dynamic equilibrium. The longer backwards arrow indicates that, at any given time, the concentration of discrete water molecules is larger than that of the ions. 

As can be observed in these curves, for infinitely long time, the equilibrium of the reaction is reached (i.e., dynamic equilibrium of the exchange), the conductive flow is equal to zero, and the substance amount reaches its equilibrium value, given by... 

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