Equilibrium distribution measurement

Since 1961 [20], determination of the composition of complex species present in an anion-exchanger phase has been sought through the analysis of equilibrium distribution measurements between resins and solutions. The distribution ratio of a metal ion, M , defined as the rado of total concentrations of the metal in the two phases of a system containing a monovalent anion as ligand, L, can be represented by... 

In principle, one should solve the Boltzmann equation Eq. (65) in order to arrive at explicit expressions for the pressure tensor p and heat flux q, which proves not possible, not even for the simple BGK equation Eq. (11). However, one can arrive at an approximate expression via the Chapman Enskog expansion, in which the distribution function is expanded about the equilibrium distribution function fseq, where the expansion parameter is a measure of the variation of the hydrodynamic fields in time and space. To second order, one arrives at the familiar expression for p and q... 

Measurement of the equilibrium distribution of deuterium relative to hydrogen atoms in a proton-exchanging site compared with the distribution in the solvent or some other standard is a particularly subtle probe that can provide important information about the nature of the environment of the... 

The term within the square brackets in equation 11.79 is the normalized (equilibrium) distribution coefficient between the minerals a and )3 (cf section 10.8) at the closure condition of the mineral isochron. Ganguly and Ruitz (1986) have shown it to be essentially equal to the observed (disequilibrium) distribution coefficient between the two minerals as measured at the present time. can be assumed to be 1, within reasonable approximation. Equation 11.79 can be calibrated by opportunely expanding AG° over P and T ... 

A enzyme kinetic technique, introduced by Britton and co-workers "", that permits one to measure the equilibrium distribution of enzyme-bound substrate(s), inter-mediate(s), and product(s). In this procedure, radiolabeled substrate or product is initially permitted to react with enzyme for sufficient time to equilibrate. At thermodynamic equilibrium, all the different enzyme-bound species will be present at concentrations reflecting their stability relative to each other. One can then add a large excess of unlabeled substrate. Under this condition, any unbound or newly released radiolabel will mix with the large unlabeled pool of substrate or product, where it will undergo substantial reduction in its radiospecific activity. This dilution effectively reduces or eliminates any significant recycling of released radiolabel. One can then... 

Lipophilicity is a measure of solubility in nonpolar solvents It is determined from the equilibrium distribution of a drug between water and octanol. 

For unknown solute properties, a derivation from the association laws is used to adjust experimental results Chrastil has published the most popular one [6], An example is given in Fig. 6.6-6, comparing measured and calculated equilibrium data for rapeseed oil in C02, showing the dominating influence of the solvent density. This equation is very useful for describing the equilibrium distribution of natural substances in dense gases. 

From frequency dependent dielectric loss measurements, the transitions associated with solvent dipole reorientations occur on a timescale of 10-n -10-13 s. By contrast, the time response of the electronic contribution to the solvent polarization is much more rapid since it involves a readjustment in electron clouds . The difference in timescales for the two types of polarization is of paramount importance in deciding what properties of the solvent play a role in electron transfer. The electronic component of the polarization adjusts rapidly and remains in equilibrium with the charge distribution while electron transfer occurs. The orientational component arising from solvent dipoles must adopt a non-equilibrium distribution before electron... 

If there is a bottleneck at r=30, the system is much more likely to find it and suddenly leak through if not, one has a least measured the equilibrium distribution of r in a region where it would be too low to measure directly. The normalizing factor Q/Q, necessary to make the connection between p and p, can found be from the histograms via eq. 20 or, more accurately, by eqs. 12a and 12b of reference 17. 

In nimen-listulaled experimental animals, it has been observed that for certain distribution ratios of chloride in ihc ruminal fluids and hlood plasma, the calculated equilibrium potential Tor chloride is relatively the same as that measured directly with KCI-agar bridges and calomel electrodes However, in many circumstances, the calculated and measured values have been found lo be significantly different, an observation that could only be accounted for by the presence of an active transport mechanism responsible for the movement of chloride out of its equilibrium distribution. 

As we have seen, the HPLC determination of MIP selectivity is of limited value. The question naturally arises as to whether a better method is available. Since this is not the subject of this chapter, we mention only briefly that batch distribution measurements of the template (or of any other substance, separately or in mixture) appear to be useful due to the equilibrium nature of the batch method. The correct... 

---