Sequential solutions equilibrium equations

As is true in the design of many separation techniques, the choice of specified design variables controls the choice of the design method. For the flash chamber, we can use either a sequential solution method or a simultaneous solution method. In the sequential procedure, we solve the mass balances and equilibrium relationships first and then solve the energy balances and enthalpy equations. In the simultaneous solution method, all equations must be solved at the same time. In both cases, we solve for flow rates, compositions, and temperatures before we size the flash drum. 

In the sequential solution procedure, we first solve the mass balance and equilibrium relationships, and then we solve the energy balance and enthalpy equations. In other words, the two sets of equations are uncoupled. The sequential solution procedure is applicable when the last degree of freedom is used to specify a variable that relates to the conditions in the flash drum Possible choices are ... 

If the temperature of the feed to the drum, Tp, is the specified variable, the mass and energy balances and the equilibrium equations must be solved simultaneously. You can see from the energy balance, Eq. (2-7 why this is true. The feed enthalpy, hp, can be calculated, but the vapor and liquid enthalpies, and depend upon x, which are unknown. Thus a sequential solution is not possible. 

While the redox titration method is potentiometric, the spectroelectrochemistry method is potentiostatic [99]. In this method, the protein solution is introduced into an optically transparent thin layer electrochemical cell. The potential of the transparent electrode is held constant until the ratio of the oxidized to reduced forms of the protein attains equilibrium, according to the Nemst equation. The oxidation-reduction state of the protein is determined by directly measuring the spectra through the tranparent electrode. In this method, as in the redox titration method, the spectral characterization of redox species is required. A series of potentials are sequentially potentiostated so that different oxidized/reduced ratios are obtained. The data is then adjusted to the Nemst equation in order to calculate the standard redox potential of the proteic species. Errors in redox potentials estimated with this method may be in the order of 3 mV. 

This means that permeation is a sequential process, starting with solution of the gas on the outer surface of the polymer (where equilibrium nearly exists), followed by slow inward diffusion ("reaction with pre-established equilibrium"). For all three physical quantities P, S and D, the temperature dependence can be described by a Van t Hoff-Arrhenius equation ... 

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