Equilibria concentration effects

A theoretical or equihbrium stage is a device or combination of devices that accomplishes the effect of intimately mixing two immiscible liquids until equilibrium concentrations are reached, then physically separating the two phases into clear layers. Crosscurrent extraction (Fig. 15-4) is a cascade, or series of stages, in which the raffinate R from one extraction stage is contacted with additional fresh solvent S in a subsequent stage. 

Hundreds of metabohc reac tions take place simultaneously in cells. There are branched and parallel pathways, and a single biochemical may participate in sever distinct reactions. Through mass action, concentration changes caused by one reac tion may effect the kinetics and equilibrium concentrations of another. In order to prevent accumulation of too much of a biochemical, the product or an intermediate in the pathway may slow the production of an enzyme or may inhibit the ac tivation of enzymes regulating the pathway. This is termed feedback control and is shown in Fig. 24-1. More complicated examples are known where two biochemicals ac t in concert to inhibit an enzyme. As accumulation of excessive amounts of a certain biochemical may be the key to economic success, creating mutant cultures with defective metabolic controls has great value to the produc tion of a given produc t. 

Catalysts increase the rate of reactions. It is found experimentally that addition of a catalyst to a system at equilibrium does not alter the equilibrium state. Hence it must be true that any catalyst has the same effect on the rates of the forward and reverse reactions. You will recall that the effect of a catalyst on reaction rates can be discussed in terms of lowering the activation energy. This lowering is effective in increasing the rate in both directions, forward and reverse. Thus, a catalyst produces no net change in the equilibrium concentrations even though the system may reach equilibrium much more rapidly than it did without the catalyst. 

We are not satisfied with the conclusion that this change or that change affects the equilibrium concentrations. We would also like to predict the direction of the effect (does it favor products or reactants ) and the magnitude of the effect (how much does it favor products or reactants ). The first desire, to know the qualitative effects, is answered by a generalization first proposed by a French chemist, Henry Louis Le Chatelier, and now called Le Chatelier s Principle. 

Predict the effect on equilibrium concentrations of an increase in (a) Temperature, (b) Pressure... 

What effect would the following changes have on the equilibrium concentration of Cl2 Give your reasons for each answer. 

Each of the following systems has come to equilibrium. What would be the effect on the equilibrium concentration (increase, decrease, no change) of each substance in the system when the listed reagent is added ... 

Since the system is far from equilibrium (the actual C02 concentration even at the exit of the bed is about 2 ppm whereas the equilibrium concentration is 10"4 ppm), K is small compared with Kp and the term [1 — f (K/Kp)] becomes unity, i.e. the effect of the reverse reaction can be ignored. Equation 1 then becomes... 

The profile of the concentration of a solute in both the mobile and stationary phases is Gaussian in form and this will be shown to be true when dealing later with basic chromatography column theory. Thus, the flow of mobile phase will slightly displace the concentration profile of the solute in the mobile phase relative to that in the stationary phase the displacement depicted in figure 1 is grossly exaggerated to demonstrate this effect. It is seen that, as a result of this displacement, the concentration of solute in the mobile phase at the front of the peak exceeds the equilibrium concentration with respect to that in the stationary phase. It follows that there is a net transfer of solute from the mobile phase in the front part of the peak to the... 

Table 10-10 Equilibrium model effect of complex formation on distribution of metals (all concentrations are given as — log(M)). pH = 8.0, T = 25°C. Ligands pS04 1.95 pHCOa 2.76 pCOs 4.86 pCl 0.25.

A question of practical interest is the amount of electrolyte adsorbed into nanostructures and how this depends on various surface and solution parameters. The equilibrium concentration of ions inside porous structures will affect the applications, such as ion exchange resins and membranes, containment of nuclear wastes [67], and battery materials [68]. Experimental studies of electrosorption studies on a single planar electrode were reported [69]. Studies on porous structures are difficult, since most structures are ill defined with a wide distribution of pore sizes and surface charges. Only rough estimates of the average number of fixed charges and pore sizes were reported [70-73]. Molecular simulations of nonelectrolyte adsorption into nanopores were widely reported [58]. The confinement effect can lead to abnormalities of lowered critical points and compressed two-phase envelope [74]. 

CO in the synthesis gas mixture for the methanol synthesis does not seem to take part directly in the reaction, but it does influence the process through two effects First the water-gas shift reaction and, secondly, through its effect on the surface morphology (and possibly also composition). For thermodynamic reasons, however, it would be desirable if CO could be hydrogenated directly via Eq (18) instead of going through two coupled equations (3) and (19), since it would yield a higher equilibrium concentration of methanol at the reactor exit. 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

It is a very important conclusion following from Eq. (13.8) that in the case considered, the rate of the overall reaction is determined wholly by the kinetic parameters of the first step ( i and k i), while the second step influences this rate only through the equilibrium concentration of the intermediate B. We say, therefore, that the first step (with its low value of parameter k.j) is the rate-determining step (RDS) of this reaction. Sometimes the term slow step is used, but this term is not very fortunate, inasmuch as the effective rates, and Uj, of the two steps actually are identical. Analogously, when k k2, we have... 

Indeed our scale makes it possible to make a more subtle comparison of risk levels, which allows us to classify substances in ascending risk order and can be directly interpreted (an ii value of 4.62% for instance means that with a vapour equilibrium concentration at 21 C in air this concentration cannot exceed 4.62% of LEL value, which is equivalent to the reading of the dial of an explosimeter). Note in particular that it is clearly seen by examining the tables for these substances that the same code 11 set by the regulations or 3 by NFPA hide very different risk situations, which is well shown by II code. Vice versa, the threshold effects of these codes tend to overestimate insignificant risk differences (for instance between ethylbenzene and styrene). 

Using the equation, very strong concentration effects in small systems have been calculated. For instance, if the macroaqueous phase contains 1 M NaCl and 1 /rM NaTPB, the concentration of this electrolyte in the micro-organic phase at partition equilibrium is 1390/rM [14] This approach is valid if the phases in small systems are thick enough (> 1 /rm), in comparison to the Debye screening length, to fulfill the electroneutrality conditions. 

Experimental results have indicated that within the activity coefficients of much resembling redox couples, although their standard redox potentials may differ appreciably, certain compensating effects can be expected, especially in the equilibrium state (E = 0), between the equimolecular starting concentrations hence the logarithmic term of the activity coefficients can be neglected with respect of the final ratio of equilibrium concentrations. 

Step 4 Estimate the effectiveness factor i) for the removal and the cleanup time required to obtain a residual toluene concentration of 150 mg/L. The phase distribution calculations carried out in Step 2 indicate that the equilibrium concentration of toluene in the gas phase is Ca equil = 109 mg/L (see Table 14.4). The concentration measured in the extracted air during the field tests is lower, at Q,flew = 78 mg/L, indicating that the removal effectiveness is limited either as a result of mass transfer phenomena or the existence of uncontaminated zones in the airflow pattern. The corresponding effectiveness factor is T = 78/109 = 0.716. 

The slopes of the peaks in the dynamic adsorption experiment is influenced by dispersion. The 1% acidified brine and the surfactant (dissolved in that brine) are miscible. Use of a core sample that is much longer than its diameter is intended to minimize the relative length of the transition zone produced by dispersion because excessive dispersion would make it more difficult to measure peak parameters accurately. Also, the underlying assumption of a simple theory is that adsorption occurs instantly on contact with the rock. The fraction that is classified as "permanent" in the above calculation depends on the flow rate of the experiment. It is the fraction that is not desorbed in the time available. The rest of the adsorption occurs reversibly and equilibrium is effectively maintained with the surfactant in the solution which is in contact with the pore walls. The inlet flow rate is the same as the outlet rate, since the brine and the surfactant are incompressible. Therefore, it can be clearly seen that the dynamic adsorption depends on the concentration, the flow rate, and the rock. The two parameters... 

The concentration of X is essentially constant throughout the reaction [see part (t )J. The equilibrium constant of part () is amended to include that constant concentration the new constant is K. That constant is just as effective in calculating the equilibrium concentration of Y as is the original constant, K. This is the same effect as using Ka, not K and [H.O], for weak acid and weak base equilibrium calculations. 

The reaction can, however, be made preparative for (91) by a continuous distillation/siphoning process in a Soxhlet apparatus equilibrium is effected in hot propanone over solid Ba(OH)2 (as base catalyst), the equilibrium mixture [containing 2% (91)] is then siphoned off. This mixture is then distilled back on to the Ba(OH)2, but only propanone (b.p. 56°) will distil out, the 2% of 2-methyl-2-hydroxypentan-4-one ( diacetone alcohol , 91, b.p. 164°) being left behind. A second siphoning will add a further 2% equilibrium s worth of (91) to the first 2%, and more or less total conversion of (90) — (91) can thus ultimately be effected. These poor aldol reactions can, however, be accomplished very much more readily under acid catalysis. The acid promotes the formation of an ambient concentration of the enol form (93) of, for example, propanone (90), and this undergoes attack by the protonated form of a second molecule of carbonyl compound, a carbocation (94) ... 

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