Equilibrium saturation method

The signal strength increases with the rf power as long as relaxation effects are adequate to restore equilibrium. The method is therefore limited by saturation. 

The solubility of a material is usually determined by the equilibrium solubility method, which employs a saturated solution of the material, obtained by stirring an excess of the material in the solvent for a prolonged period until equilibrium is achieved. Common solvents used for solubility determination are ... 

In the gas saturation method, a carrier gas such as helium or air is bubbled slowly through the sample, coming to equilibrium with it. The material exiting the apparatus is collected, and the amount of sample dissolved can be measured at the end of the experiment. Knowledge of the number of moles carried away, the number of moles of carrier gas used, and the pressure of equilibration allows calculation of the partial pressure of the sample at equilibrium, which is approximately its vapor pressure. Care must be taken to ensure that all of the carrier gas is equilibrated with the sample and to prevent premature condensation before the solute is collected. This method is typically applied for vapor pressures below about 3 kPa, and may achieve 1% accuracy with careful use. 

For the gas saturation method, the error sources and their approximate values are very similar to previous column techniques. [At 95% confidence, temperature control = +0.05°K (normal), lack of vapor-liquid equilibrium = -5% (beta), trapping efficiency =... 

This moisture content has been shewn to result In a marked lowering of the T for many fibers. Further reductions In T occur when the flblr Is allowed to wet out In water until equilibrium saturation Is reached. These lowered T s are of significance In the processing and care of textile products. Several methods particularly useful for measuring the wet and dry T of fibers... 

The usual method of measuring hydrocarbon solubility in water is to ensure equilibrium saturation with an excess of hydrocarbon. If the vapor pressure of an organic compound is known, its solubility can be determined without knowing whether the water is truly saturated. The... 

If the concentration of a solution can be measured at a given temperature, and the corresponding equilibrium saturation concentration is known, then it is a simple matter to calculate the supersaturation (equations 3.67-3.69). Just as there are many methods of measuring concentration (section 3.9.2) so there are also many ways of measuring supersaturation, but not all of these are readily applicable to industrial crystallization practice. 

Coordination of solvent molecules in the outer sphere may also play a role during the dissolution and reactions of coordinatively saturated complexes. Various spectroscopic and equilibrium measurement methods can be employed to study outer-sphere solvation and some examples will be presented. 

In Eqs. (3.80) to (3.85), the concentrations are those of the equilibrium saturated solutions. In each case, the second of the equation pairs permits calculation of Aab Ask from the data, and the first then gives Aab-Colburn and Schoenborn (7) have given a graphical solution of the van Laar set. A similar graphical solution could be worked out for the Margules equations, but the additional parameter of Va/Vb in the Scatchard-Hamer equations would make such a method awkward. 

Isobaric-isothermal methods are often also called dynamic methods. One or more fluid streams are pumped continuoirsly into a thermostated equilibriirm cell. The pressure is kept constant during the experiment by controlling an effluent stream, irsually of the vapor phase. One can distinguish between continuorrs-flow methods and semi-flow methods. In continuous-flow methods, both phases flow throrrgh the eqrrihbrirrm cell. They can be used only for systems where the time needed to attain phase equilibrium is sufficiently short. Therefore, such equipment is usually not applied to polymer solutions. In semi-flow methods, only one phase is flowing while the other stays in the equilibrium phase. They are sometimes called gas-saturation methods or pure-gas circulation methods and can be used to measure gas solubilities in liquids and melts or solubilities of liquid or solid substances in supercritical fluids. 

For most SPR appHcations the dissociation constant is calculated from the Kd = koff/kon proportion. It can also be evaluated from the steady-state phase (equilibrium). This method, however, is apphcable only for kinetically fast interactions. The time required for reaching the equihbrium at a protein concentration equal to JCj can be expressed as l/ko . For an interaction with off =1x10 s it will take approximately 1 h to reach equilibrium. The steady state is reached faster with increased protein concentrations. Using a high protein concentration results, however, in the collection of only a narrow range of Req points, close to saturation (Rmax)- In this situation the Kj is... 

However, the total number of equilibrium stages N, N/N,n, or the external-reflux ratio can be substituted for one of these three specifications. It should be noted that the feed location is automatically specified as the optimum one this is assumed in the Underwood equations. The assumption of saturated reflux is also inherent in the Fenske and Underwood equations. An important limitation on the Underwood equations is the assumption of constant molar overflow. As discussed by Henley and Seader (op. cit.), this assumption can lead to a prediction of the minimum reflux that is considerably lower than the actual value. No such assumption is inherent in the Fenske equation. An exact calculational technique for minimum reflux is given by Tavana and Hansen [Jnd. E/ig. Chem. Process Des. Dev., 18, 154 (1979)]. A computer program for the FUG method is given by Chang [Hydrocarbon Process., 60(8), 79 (1980)]. The method is best applied to mixtures that form ideal or nearly ideal solutions. 

Figure 18.4 The hanging-drop method of protein crystallization, (a) About 10 pi of a 10 mg/ml protein solution in a buffer with added precipitant—such as ammonium sulfate, at a concentration below that at which it causes the protein to precipitate—is put on a thin glass plate that is sealed upside down on the top of a small container. In the container there is about 1 ml of concentrated precipitant solution. Equilibrium between the drop and the container is slowly reached through vapor diffusion, the precipitant concentration in the drop is increased by loss of water to the reservoir, and once the saturation point is reached the protein slowly comes out of solution. If other conditions such as pH and temperature are right, protein crystals will occur in the drop, (b) Crystals of recombinant enzyme RuBisCo from Anacystis nidulans formed by the hanging-drop method. (Courtesy of Janet Newman, Uppsala, who produced these crystals.)...

If the one-point calibration in ambient air is not sufficient, the next best approach is to use the calibration box method.- The air state is created in a closed box made of nonhygroscopic material, like metal or plastic. A controlled state of humidity is maintained by exposing the air in the box to a liquid surface of a saturated salt solution. In practice, a dish containing the saturated water solution of a salt is placed on supports at the bottom of the box. The air in the box is circulated by means of a small fan. The box should be airtight and positioned in a constant temperature environment. The calibrated instruments are placed in the box. A dewpoint hygrometer can be used as a reference. A wide range of humidity can be created by using solutions of different salts. Table 12.5 shows a few examples of equilibrium humidities achieved with different salt solutions. 

---