Equilibrium constants static methods

A rate and equilibrium study of the cis/trans isomerization of tris(l,l,l-trifluoro-2,4-pentanedionato)chromium(III) in the vapour phase has been reported.761 The equilibrium constant 3.56 was independent of temperature in the range 118-144.8 °C, the same value being measured by both static and kinetic methods. The activation energies for isomerization were both less than 115 kJmol-1 the Cr—O bond energy is 210 kJ mol-1. On these grounds, a bond-rupture mechanism was rejected. A similar mechanism may operate for the isomerization in solution. 

The dynamic methods depend on the fact that certain vibrations of a liquid cause periodic extensions and contractions of its surface, which are resisted or assisted by the surface tension. Surface tension therefore forms an important part, or the whole, of the restoring force which is concerned in these vibrations, and may be calculated from observations of their periodicity. Dynamic methods include determination of the wave-length of ripples, of the oscillations of jets issuing from non-circular orifices, and of the oscillations of hanging drops. Dynamic methods may measure a different quantity from the static methods, in the case of solutions, as the surface is constantly being renewed in some of these methods, and may not be old enough for adsorption to have reached equilibrium. In the formation of ripples there is so little interchange of material between the surface and interior, and so little renewal of the surface, that the surface tension measured is the static tension ( 12. ... 

In principle, a continuous procedure can be used to construct the isotherm under quasi-equilibrium conditions the pure adsorptive is admitted (or removed) at a slow and constant rate and a volumetric or gravimetric technique used to follow the variation of the amount adsorbed with increase (or decrease) in pressure. A carrier gas technique, making use of conventional gas chromatrographic equipment, may be employed to measure the amount adsorbed provided that the adsorption of the carrier gas is negligible. In all types of measurement involving gas flow it is essential to confirm that the results are not affected by change in flow rate and to check the agreement with representative isotherms determined by a static method. 

Some static headspace methods do not require an external calibration and are based on measurements performed at thermodynamic equilibrium between liquid and gas phase. In the phase ratio variation method (PRV) described by Ettre and Collaborators (1993), the partition coefficient calculation is based on the fact that the headspace concentration changes as a function of the phase volume ratio (gas and liquid phases), while the partition coefficient remains constant. This method has been recently applied to study the interactions between aroma compounds and macromolecules in different food systems (Savary et al. 2006, 2007) but so far not to the wine. 

Undoubtedly, NMR is one of the methods of choice to study atropisomerism. Together with crystallography (2.1), HPLC (2.11), and theoretical calculations (2.14), NMR is the technique that has contributed most to the understanding of this phenomenon. We have separated, in some cases rather artificially, the use of NMR to study static aspects of atropisomerism (torsion angles, preferred conformation, equilibrium constants) from its dynamic use (barriers, 2.9). 

In the static method, a sample of known mass is allowed to reach equilibrium with air maintained at a constant relative humidity and temperature. The moisture content of the sample at equilibrium is measured and is defined as the EMC. The constant relative humidity environments are usually created using saturated salt solutions in containers [13]. A container with a 10- to 15-g sample suspended in the environment above the saturated salt solution is kept at a constant temperature. The experiment must be repeated at several temperatures and relative humidities. The sample is weighed at a regular interval of 3-12 h until the change in sample mass between two successive readings is less than 0.01 g (at this stage it is assumed that the sample has reached equilibrium). Depending on the vapor pressure of the moisture in the seeds and the vapor pressure of the... 

If we measure the acid constant for this system by a static method, equilibrium having been attained, the total concentration of undissociated acid is [SH] -f [HS] and the measured equilibrium constant is... 

In the static method, a sample of known mass is allowed to reach equilibrium with air maintained at a constant relative humidity and temperature. The moisture content of the sample at equilibrium is measured and is defined as the EMC. The constant relative humidity environments are usually created using saturated salt solutions in containers [13]. 

In the static method, a liquid mixture is charged to an evacuated equilibrium cell, immersed in a constant-temperature bath. Equilibration of the phases is brought about by vigorous stirring of the liquid phase or, in some designs, by rocking the cell. 

The method includes the mass unit vent flow capacity per unit area. G. This allows using any applicable vent capacity calculation method. The method incorporates the equilibrium rate model (ERM) for vent flow capacity when friction is negligible. Additionally, a coiTection factor is used for longer vent lines of constant diameter and with negligible static head change. ... 

The key advantage of this headspace method, compared to static headspace analysis, is the sensitivity obtained. While static headspace shows the status at equilibrium and can measure thermodynamic constants, purge-and-trap or dynamic headspace can measure the kinetics of... 

Table 3.3 shows the effect of method on ka values. The type of method clearly affected the ka values and, although not shown, the time required for equilibrium in potassium adsorption to be reached. In earlier work, Ogwada and Sparks (1986a) had found that with the vortex batch method, diffusion was reduced significantly and the rate coefficients one obtained approximated reaction-controlled rate constants. The data in Table 3.3 show clearly that significant diffusion exists with the static and miscible displacement methods because of limited mixing. 

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... 

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