Extent of reaction completion

Table Al.l Extent of reaction completion for a first order reaction at different time intervals corresponding to different multiples of x and tll2...

The two time constants x and tV2 define time intervals in which a specific extent of reaction has been completed. In some applications one may wish to define a time point associated with a certain other extent of reaction completion. That is, how much time is required for the reaction to go to, say, 75% or 90% completion. This can be calculated using rearranged forms of Equations (A.16) through (A.21). For convenience, in Table Al.l we tabulate the extent of reaction completion for different time intervals, as multiples of x and ty2. 

By line 5, the reaction has reached 80% completion and the number average value of the degree of polymerization is 5. Although we have considered this slowly evolving polymer in terms of the extent of reaction, another question starts to be worrisome How long is this going to take ... 

In considering step polymerisation with polyfunctional molecules a number of assumptions are made. They are (i) that all functional groups are equally reactive, (ii) that reactivity is independent of molar mass or solution viscosity, and (iii) that all reactions occur between functional groups on different molecules, i.e. there are no intramolecular reactions. It is found experimentally that these assumptions are not completely valid and tend to lead to an underestimate of the extent of reaction required to bring about gelation. 

The high conversion test is operated to ensure that essentially complete conversion of the HBr is possible, and to study the fate of the feed contaminants. In this test, the conditions are selected to ensure complete conversion of the HBr. Several reaction pathways are then available to feed contaminants. They may undergo combustion, react with HBr, or react with the bromine formed. The extent of reaction via any of these pathways will depend on the nature of the contaminants and the temperature. Information concerning the fate of the contaminants can then be gained by analyzing the gas, bromine, and aqueous phases exiting the reactor. 

For complete rigor the distribution previously presented (Eqs. 1, 2, and 3 and Figs. 51 and 52) for linear polymer chains should be modified through substitution of p for the over-all extent of reaction p. Thus, for example, Eq. (3) for the weight fraction should be replaced with... 

Coulometric detection describes amperometry in which the reaction of the analyte proceeds to completion.59 The extent of reaction is a function of cell geometry, flow rate, and analyte concentration, so all cells can be made coulometric by stopping the flow.59 Several designs for coulometric cells that are independent of flow rate have been described.46... 

Hydroxy-terminated PDMS, however, has disadvantages. The monofunctional ends limit the number of connections between the polymer (or oligomer) molecule and the glass network to two. This limitation raises the possibility that some PDMS molecules are not tied at both ends to the glass network if the polycondensation does not go to completion i.e. there may be "dangling" or loose PDMS chains in the final sol-gel material. This occurance of free ends would indeed be anticipated since the extent of reaction most likely is not 100%. Hence, the physical properties, specifically the mechanical behavior of the overall material, would be expected to suffer as a result of loose PDMS chains in the system. Disregarding this potential problem, the mechanical behavior of the sol-gel hybrids are, ultimately, influenced by the mechanical behavior of the modifying elastomer ... 

When the extent of reactions such as these is studied, it is found that the reaction with HC104 progresses farther to the right than with any of the other acids. By this means, it is possible to rank even the strong acids that all react completely with water in terms of strength as shown in Table 9.1. 

The reaction is usually complete after 3-6 hours at reflux. Owing to dissolved pyrrolidine, the aqueous layer amounts to 35-45 ml., and thus its volume is not a good measure of the extent of reaction. 

Figure 4.6 The value of the Gibbs function AG decreases as the extent of reaction until, at (eq), there is no longer any energy available for reaction, and AG = 0. =0 represents no reaction and = 1 mol represents complete reaction...

Since the moles of trioxide will be less than the amount of nitroaromatic in the initial period of the process, trioxide will usually limit the extent of reaction. Later, the amount of trioxide will be larger. Therefore the maximum temperature that could be reached by complete conversion of the trioxide, MTSR, is... 

If isocyanate remains unextracted, the extent of reaction would apparently decrease with the extraction time. However, the amount of naphthylamine is obviously constant in the range of extraction duration studied, supporting complete removal of the unreacted isocyanate from the film. 

The points in Figure 4 do not show a tendency for p - e tend to zero as p tends to zero. That is, even in the limit of a perfect gelling system, inelastic loops are formed post-gel. Extrapolation to Pr,c = 0 gives Pr,e> extent of reaction leading to inelastic loops at complete reaction in the perfect gelling system. The values of p grange from about 9% to 18% for the system studied. As expected from considerations of pre-gel intramolecular reaction, the values of p g are smaller for f=3 compared with f=4 and they increase as v decreases, there being less opportunity for intramolecular reaction at lower functionalities(14). 

The situation is not so clear-cut in some polymer reactions. Reaction often occurs at crystal surfaces, and this leads to subsequent penetration of a small reactant into the crystalline regions. Complete penetration of the crystalline regions occurs if the reaction times are sufficiently long, although the extent of reaction may be lower in the crystalline regions compared to the amorphous regions. 

Esters (and certain other compounds) may be susceptible to hydrolysis by low or especially high pH, or in the presence of alkaline metal or alkaline earth salts. In the presence of acid, i.e., anion and hydrogen ion, the reaction is at equilibrium. However, in the presence of base and the associated cations, the reaction is driven to completion (e.g., acetyl salicylic acid and the effect of sodium and magnesium salts on the rate and extent of reaction). 

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