Equilibrium condensation

It is instructive to consider just how mobile the surface atoms of a solid might be expected to be. Following the approach in Section III-2, one may first consider the evaporation-condensation equilibrium. The number of molecules hitting a 1-cm surface per second is from kinetic theory... 

Yet, it is reasonable to suppose that water molecules from the liquid are still evaporating, even at equilibrium. Molecules in the liquid have no way of knowing that the partial pressure of the vapor is equal to the vapor pressure. In the gas phase, the randomly moving molecules continue to strike the surface of the liquid and condense. Equilibrium corresponds to a perfect balance between this continuing evaporation and condensation. Then no net changes can be detected. ... 

In 1959 and 1960, Challa published the first results of quantitative experiments on the poly condensation equilibrium in PET [22, 41, 42], He determined the polycondensation equilibrium constant K at different temperatures and average degrees of polycondensation and found that this parameter depends only slightly on temperature, but increases significantly with increasing degree of polycondensation. The monomer BHET was found not to follow the principle of equal reactivity. 

Fontana, C. M., Poly condensation equilibrium and the kinetics of catalyzed transesterification in the formation of polyethylene terephthalate, J. Polym. Sci., Part A-l, 6, 2343-2358 (1968). 

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

The condensation equilibrium model allows us to eon-sider the equilibrium between unpolymerized protein X and its polymerie form P,... 

COOPERATIVITY CONCERTED PROCESS PRIMITIVE CHANGES ELEMENTARY REACTIONS SYNCHRONOUS Condensation equilibrium,... 

The effects described by Eqs. 4.1 to 4.4 apply to both stepwise addition and condensation polymerizations. In polycondensation, two further factors must be considered The condensation equilibrium and the exchange reactions. The condensation equilibrium limits the conversion and hence the average molecular weight. As in the case of esterification of monofunctional compounds, the corresponding polycondensations are to be treated as equilibrium reactions, governed by the law of mass action. For example, in the case of polyesterification, if... 

Since the number-average degree of polymerization P is reciprocally proportional to the free functional groups 1 - p still present (see Eq. 4.2), the upper limit of the degree of polymerization, when governed by the condensation equilibrium, is given by Eq. 4.7 ... 

The dianion [Ni6(CO)12]2- is stable to hydrolysis in alkaline aqueous solution however, in acidic conditions (pH = 3-6) it is converted quantitatively into the interstitial hydride complex [Ni12(CO)21H4 B]"- (n = 2,3).5 6 The complex readily reacts in solution with carbon monoxide according to the following degradation-condensation equilibrium 1... 

Salt concentrations were obtained by the addition of known weights of dried salt to the solvent mixture. The compositions of the condensed equilibrium vapor samples and the previously prepared ethanol-water charges to the still were determined as previously outlined. The mole fractions of the salt, ethanol, and water charged to the Othmer still were thus accurately determined by mass balance calculations. 

Mujtaba (1989) simulated the example considered by Boston et al. (1980) presented in section 4.2.4.1.1 using CMH model. The volume holdups used by Boston et al. were converted to molar holdups at the initial conditions. These were 0.00493 lbmol for each internal plates and 0.0493 lbmol for the condenser. Equilibrium k values were calculated using Antoine s vapour pressure correlation and enthalpies by the same procedure outlined in section 4.2.4.2.I. The simulation results are presented in Table 4.6. Note the slight differences in predictions (Table 4.4 and 4.6) are due to the use of different types of models (CVH and CMH) and thermodynamic property calculations. 

The condensation equilibrium is displaced to the right by removing the unsaturated cyano ester as it is formed by the addition of hydrogen cyanide The effect is analogous to the single-step formation and hydrogenation of a,/S-unsaturated cyanoacetic esters (method 394). The yields are good with most aliphatic ketones and aldehydes (49 75%), but poor results are obtained with aromatic carbonyl compounds and diisopropyl ketone. 

The pattern of side reactions in the polymerization of a-substituted lactams is slightly different. The keto timide structures (XV) formed in the Claisen type condensation have no acidic a-hydrogen so that the concentration of lactam anions cannot decrease so dramatically as with the acidic keto amides (X)—(XIV). Consequently, the position of the condensation equilibrium is shifted in favour of the initial components. Also the main products formed from af,a -disubstituted keto amides [136], scheme (52), are different from those of the monosubstituted keto amides, scheme (45). 

Solubility equilibria resemble the equilibria between volatile liquids (or solids) and their vapors in a closed container. In both cases, particles from a condensed phase tend to escape and spread through a larger, but limited, volume. In both cases, equilibrium is a dynamic compromise in which the rate of escape of particles from the condensed phase is equal to their rate of return. In a vaporization-condensation equilibrium, we assumed that the vapor above the condensed phase was an ideal gas. The analogous starting assumption for a dissolution-precipitation reaction is that the solution above the undissolved solid is an ideal solution. A solution in which sufficient solute has been dissolved to establish a dissolution-precipitation equilibrium between the solid substance and its dissolved form is called a saturated solution. 

Le Chatelier s principle applies to these equilibria, as it does to all equilibria. One way to exert a stress on a solubility equilibrium is to change the amount of solvent. Adding solvent reduces the concentration of dissolved substance more solid then tends to dissolve to restore the concentration of the dissolved substance to its equilibrium value. If an excess of solvent is added so that all of the solid dissolves, then obviously the solubility equilibrium ceases to exist and the solution is unsaturated. In a vaporization-condensation equilibrium, this corresponds to the complete evaporation of the condensed phase. Removing solvent from an already saturated solution forces additional solid to precipitate in order to maintain a constant concentration. A volatile solvent is often removed by simply letting a solution stand uncovered until the solvent evaporates. When conditions are right, the solid forms as crystals on the bottom and sides of the container (Fig. 16.1). 

Garst, J. F. Claisen ester condensation equilibriums - model calculations. J. Chem. Educ. 1979, 56, 721-722. 

Mechanism of the cyclization reaction and the nature of the acidolysisf condensation equilibrium... 

At first when the surface is bare, the number of molecules that condense exceeds the number of those that evaporate. As the surface becomes covered, other gas molecules have greater difficulty in finding unoccupied spaces, but, there is also an increase in the number of molecules escaping from the surface. When the rate of evaporation equals the rate of condensation, equilibrium is reached. The amount adsorbed at equilibrium is a function of the following factors, some of which are interrelated ... 

The gaseous phase issuing from the material tends to maintain a vaporisation-condensation equilibrium. Let Ovs b concentration of the vapour at the... 

If in imagination we remove all the micro-units, then the coacervated system consisting of two coexisting liquids assumes the character of a condensation equilibrium consisting of a colloid liquid (the coacervate) and a colloid vapour (the equilibrium liquid). See p. 12 Ch. I 4 c2. 

A special step polymerization involves an acyclic diene methathesis polymerization, ADMET [12]. A diene, CH2=CH(-CH2) -CH=CH2, sets up a condensation equilibrium, evolving ethylene in the presence of an ADMET catalyst and allows polymerization. Substituted dienes can produce precisely branched polymers [13]. 

Polycondensation reactions are equilibrium reactions. In most polycondensations, the condensation equilibrium is actually reached. Polycondensations usually take place through the elimination of a low-molecular-weight component. The polycondensation of dicarboxylic acids with diols is an example. According to the law of mass action, the concentrations of water, carboxyl, hydroxyl and ester groups are related by... 

Each condensation equilibrium for a polyphosphoric acid species that is additionally taken into account adds one additional component (see Section 12.2.1). Via the laws of mass action, each equilibrium also adds one additional relation between the molar fractions of the components. Accordingly, these additional composition variables are not independent. Therefore, for a phosphoric acid solution containing H2O, H3PO4, H4P2O7, H5P3O10, and so on, the number of independent components is still only two. 

In comparison to the usual ebulliometric equipment where the polymer solution is placed into the evaporator, only pure solvent is evaporated. The vapor flows through the cell and is condensed at its head-condenser to flow back into the reservoir at the bottom. The vapor pressure is kept constant using a manostat and is measured additionally outside the apparatus after the condenser. Equilibrium times decrease somewhat, degassing of the solvent is not necessary, air leakage does not play any role. 

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