Equilibrium distribution measurement procedure

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... 

Procedures. Procedures were developed for measuring plutonium distribution coefficients for batch equilibrium adsorption measurements and for measuring plutonium breakthrough concentrations for column flow-through adsorption experiments. 

These concepts have been applied by Ben-Shaul et al., 1972a, b to analysis of product energy distributions and to the definition of apparent temperatures for non-equilibrium product distributions. Their procedure may be illustrated with a treatment of vibrational distribution of products, as measured in infrared chemiluminescence studies. The quantities measurable in this case are and v. It is convenient to introduce fractional energies fx = EJE, where fT + fv + fR = 1. The probabilities actually determined are conditional probabilities P(/v ) for fixed . The surprisal is... 

The equilibrium distribution of NH3 and NH is a function of the hydrogen ion concentration (H+) in the water, and the equilibrium shifts to NH3 as the concentration or activity of is reduced. In water quality studies the H+ activity commonly is reported in terms of pH, where pH is the negative of the common logarithm of the H+ activity. (Most natural ffeshwaters have a pH in the range 6-8. The pH of seawater is about 8.1.) At steady state the concentrations of NH3 and NH4 are equal at a pH of 9.3, and the [NH3]/[NH4 ] ratio increases by a factor of 10 whenever the pH increases by one unit. Thus water that is virtually harmless at a pH of 7 might become extremely toxic if the pH is raised to 9. Because of this fact, it is of relatively little use in water quality work to assay merely for NH3 -h NH (by standard procedures) without simultaneously measuring the pH. 

In a single-component system the time dependency of the interfacial tension is determined by the time needed for the molecnles in the interfacial region to attain their equilibrium distribution. Except for solids (as discussed earlier), this is a fast process typically on the order of milliseconds, so that essentially all measuring procedures yield the equilibrium interfacial tension. However, for solutions containing surface-active compound(s), adsorption and desorption processes usually determine the rate of relaxation of the interface. Depending on the system and the conditions, the time scale may be much longer, say, on the order of seconds up to hours. We return to this in Section 17.4. 

The interpration of the ultrasonic relaxation spectrum in terms of the multistep mechanism is complicated but gives detailed kinetic information. It requires, however, a basic knowledge of the equilibrium distribution. In practice the ultrasonic technique is often used to the investigate ion of systems for which the equilibrium properties cannot be measured by other experimental means and hence the detailed equilibrium description is not known. In those situations it is still possible to obtain some information about the rates involved by using the two state consideration (13). It must be stated, that the rate constants obtained by this procedure are sort of mean values that may differ somewhat from the individual true rate constants. 

In a static partition, the atom (necessarily radioactive in the present context) is distributed between two immiscible phases (liquid and/or solid). Since this procedure is sequential, the accuracy in the measurement of the average concentrations increases with the number of trials. For a given system, under given conditions, the determination of one partition coefficient (D) requires numerous repetitive experiments, even for the more simple case involving only one chemical species in each phase. The experimental conditions must always ensure that at the end of the experiment, the atom has reached permanent partition equilibrium between the two phases. Moreover, the short half-life of the nucleus does not bring any perturbation since there is only one alternative either the measurement indicates in which phase the atom is or the atom has disintegrated before the measurement and no information is obtained. 

Several chemical reactions, including calcium carbonate and hydroxyapatite precipitation, have been studied to determine their relationship to observed water column and sediment phosphorus contents in hard water regions of New York State. Three separate techniques have been used to Identify reactions important in the distribution of phosphorus between the water column and sediments 1) sediment sample analysis employing a variety of selective extraction procedures 2) chemical equilibrium calculations to determine ion activity products for mineral phases involved in phosphorus transport and 3) seeded calcium carbonate crystallization measurements in the presence and absence of phosphate ion. 

Capillary condensation provides the possibility of blocking pores of a certain size with the liquid condensate simply by adjusting the vapor pressure. A permporometry lest usually begins at a relative pressure of 1, thus all pores filled and no unhindered gas transport. As the pressure is reduced, pores with a size corresponding to the vapor pressure applied become emptied and available for gas transport. The gas flow through the open mesopores is dominated by Knudsen diffusion as will be discussed in Section 4.3.2 under Transport Mechanisms of Porous Membranes. The flow rate of the noncondensable gas is measured as a function of the relative pressure of the vapor. Thus it is possible to express the membrane permeability as a function of the pore radius and construct the size distribution of the active pores. Although the adsorption procedure can be used instead of the above desorption procedure, the equilibrium of the adsorption process is not as easy to attain and therefore is not preferred. 

Determination of the distribution of Ag between the antibody-bound and free fractions, in radioimmunoassay procedures, requires a separation step which isolates Ag from Ag -Ab. Once separated, measurement of the radioactivity of the label in one or both the fractions provides a signal that is approximately exponentially related to the concentration of unlabeled antigen. The graphical relationship can have either a positive or a negative slope depending on whether the antibody-bound or free fraction is measured. The exact shape of the calibration curve however, is dependent on the antibody-binding equilibrium constant. ... 

A close set of equations was formulated in Ref. 16, related to the capillary pressure isotherms determined by the method of standard porosimetry [60], In the latter procedure, the equilibrium amount of the wetting liquid is measured in the porous sample under study. Simultaneously, the amount of the wetting liquid is measured in the standard specimen with a genuine porous structure, in which the capillary equilibrium is established. The standards are kept in thermodynamic equilibrium with the sample. The comparison of the amount of wetting liquid in the membrane with the pore-radius distribution in the standards, enables one to record (with a minimum of theoretical assumptions), the volume-size and surface-size distribution curves, specific pore-space surface area, and absorption isotherm in the membrane of interest, for various wetting liquids. 

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