Equilibrium ration

Relations for the equilibrium rations and the mole fraction are entered ... 

For certain simplified cases it is possible to calculate directly the number of stages required to attain a desired product composition for a given set of feed conditions. For example, if equilibrium is attained in all stages and if the underflow mass rate is constant, both the equilibrium and operating lines on a modified McCabe-Thiele diagram are straight, and it is possible to calculate direc tly the number of ideal stages required to accommodate arw rational set of terminal flows and compositions (McCabe, Smith, and Harriott, op. cit.) ... 

Compounds in which conformational, rather than configurational, equilibria are influenced by the anomeric effect are depicted in entries 4—6. Single-crystal X-ray dilfiaction studies have unambiguously established that all the chlorine atoms of trans, cis, ira j-2,3,5,6-tetrachloro-l,4-dioxane occupy axial sites in the crystal. Each chlorine in die molecule is bonded to an anomeric carbon and is subject to the anomeric effect. Equally striking is the observation that all the substituents of the tri-0-acetyl-/ -D-xylopyranosyl chloride shown in entry 5 are in the axial orientation in solution. Here, no special crystal packing forces can be invoked to rationalize the preferred conformation. The anomeric effect of a single chlorine is sufficient to drive the equilibrium in favor of the conformation that puts the three acetoxy groups in axial positions. 

The anomalous iodoacetamide-fluoride reaction violates this rule, in that a less stable -halonium complex (18) must be involved, which then opens to (19) in the Markownikoff sense. This has been rationalized in the following way estimates of nonbonded destabilizing interactions in the possible products suggest that the actual product (16) is more stable than the alternative 6)5-fluoro-5a-iodo compound, so the reaction may be subject to a measure of thermodynamic control in the final attack of fluoride ion on the iodonium intermediate. To permit this, the a- and -iodonium complexes would have to exist in equilibrium with the original olefin, product formation being determined by a relatively high rate of attack upon the minor proportion of the less stable )9-iodonium ion. 

All the deseribed results [64-66] pointed out that the standard dynamie seahng formalism developed for the deseription of rough interfaees [60] is suitable for the rationalization of the interfaee behavior in reaetive systems far from equilibrium sueh as the ZGB model. However, mueh work remains to be done in order to elarify the role of high surfaee mobility of A speeies in the behavior of the reaetion interfaees. 

It might also be expected that enamines would be less basic than the corresponding saturated tertiary amines as a consequence of the delocalization of the nonbonded electron pair of the nitrogen. The older literature (/—/), which involved measurements in aqueous or partly aqueous solution, led to the opposite conclusion. This unexpected increase in basicity was rationalized in terms of an equilibrium between the enamine and the quaternary iminium hydroxide ... 

N2O4 has been extensively studied as a nonaqueous solvent system and it is uniquely useful for preparing anhydrous metal nitrates and nitrato complexes (p. 468). Much of the chemistry can be rationalized in terms of a selfionization equilibrium similar to that observed for... 

C. The structure, which involves two bridging carbonyl groups as shown in Fig. 26.8a, can perhaps be most easily rationalized on the basis of a bent Co-Co bond arising from overlap of angled metal orbitals (d sp hybrids). However, in solution this structure is in equilibrium with a second form (Fig. 26.8b) which has no bridging carbonyls and is held together solely by a Co-Co bond. 

Next, examine the equilibrium structure of acetamide (see also Chapter 16, Problem 8). Are the two NH protons in different chemical environments If so, would you expect interconversion to be easy or difficult Calculate the barrier to interconversion (via acetamide rotation transition state). Rationalize your result. Hint Examine the highest-occupied molecular orbital (HOMO) for both acetamide and its rotation transition state. Does the molecule incorporate a n bond. If so, is it disrupted upon rotation ... 

Repeat your analysis for tautomeric equilibria between 4-hydroxypyridine and 4-pyridone, 2-hydroxypyrimidine and 2-pyrimidone and 4-hydroxypyrimidine and 4-pyrimidone. For each, identify the favored (lower-energy) tautomer, and then use equation (1) to calculate the ratio of tautomers present at equilibrium. Point out any major differences among the four systems and rationalize what you observe. (Hint Compare dipole moments and electrostatic potential maps of the two pyridones and the two pyrimidones. How are these related to molecular stability )... 

It has been proposed that protonation or complex formation at the 2-nitrogen atom of 14 would enhance the polarization of the r,6 -7i system and facilitate the rearrangement leading to new C-C bond formation. The equilibrium between the arylhydrazone and its ene-hydrazine tautomer is continuously promoted to the right by the irreversible rearomatization in stage II of the process. The indolization of arylhydrazones on heating in the presence of (or absence of) solvent under non-catalytic conditions can be rationalized by the formation of the transient intermediate 14 (R = H). Under these thermal conditions, the equilibrium is continuously pushed to the right in favor of indole formation. Some commonly used catalysts in this process are summarized in Table 3.4.1. 

A series of oxidative rearrangements of tetrahydro-j8-carbolines may be rationalized on the basis of a general reaction of 2,3-disub-stituted indoles which was recently recognized by Taylor. Attack at the 4a-position of the tetrahydrocarboline (341) by an electrophile yields the indolenine derivative 342, which is in equilibrium with the isomeric species 342a. Compounds of structure 342 and 342a can undergo a variety of reactions leading to different products. 

One of the most rational means for displacing a broad zone is electrolyte desorption under the conditions of decreasing degree of ionization, i.e., when counterions are converted into dipolar ions, uncharged molecules and coions. This conversion corresponds to a sharp decrease in distribution coefficients of the desorbed substance. Hence, the displacement of equilibrium parame ters at a high rate of mass-exchange is one of the methods of selective stepwise chromatography. 

K 1), corresponding to a free energy of activation of 13.7,17.2 and 22.2 keal/mol, respectively. Theoretical investigations rationalize the dependence of the equilibrium on the nature of the cation for the 2-butenyl anion 129. 

In addition to the influence of the complexation equilibrium constant K, the observed reaction rate of arenediazonium salts in the presence of guest complexing reagents is influenced by the intrinsic reaction rate of the complexed arenediazonium ion. This system of reactions can be rationalized as in Scheme 11-1. Here we are specifically interested in the numerical value of the intrinsic rate constant k3 of the complexed diazonium ion relative to the rate constant k2 of the free diazonium ion. 

Since a first-order rate constant does not depend on [A]o, one need not know either the initial concentration or the exact instant at which the reaction began. This characteristic should not be used to rationalize experimentation on impure materials. These features do allow, however, a procedure in which measurements of slower reactions are not taken until the sample has reached temperature equilibrium with the thermostating bath. The first sample is simply designated as t = 0. Likewise, for rapidly decaying reaction transients, knowing the true zero time is immaterial. 

The precatalysts, Pt(IV) or Pt(II) salts, were found to be reduced in a series of steps by excess P(CH20H)5 to give Pt[P(CH20H)5]4, which in aqueous solution exists in equilibrium with the five-coordinate cationic hydride [PtL4H][OH] [L = P(CH20H)3]. Since reaction mixtures are basic [rationalized by the formation of hemiacetals from P(CH20H)3 and formaldehyde], the major Pt species present during catalysis is ze-... 

Table 6.11 Variation of equilibrium conversion with feed ration for the production of ethyl acetate.

Our determined anisotropy parameters for 226 nm photolysis agree favorably with the reported values of Syage, where a (3 value of 1.2 was measured for the fast 0(3P2) products. Syage observed a less anisotropic distribution for the slow 0(3P2) atoms, with a reported (3 value of 0.4. The f3 value of 1.2 for the high velocity component was rationalized by a prompt dissociation from the equilibrium ground state of ozone following an B I >2 <— X A i transition. 

For three-dimensional expansion in the air-filled section with the initial air volume equal to at least 200 times that of the initial water volume and with no partitions, baffles, or other types of compartments present, the air shock pressure is smaller than the final quasi-steady equilibrium pressure buildup. It can therefore be rationalized that the design of containment for a reactor is governed by equilibrium pressure only. 

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