Reaction rate approximations

Chlorendic anhydride is the common name of the Diels-Alder adduct of maleic anhydride and hexachlorocyclopentadiene, 3,4,5,6,7,7-hexachloroendomethylene-l,2,3,6-tetrahydrophthahc anhydride (HET). The resultant resins from HET contribute to the flame retardancy of the alkyd coatings. HET gives a greater reaction rate than phthaUc anhydride, to the extent that at 204—210°C the reaction rate approximates that of phthaUc anhydride at a temperature of 238°C (8). However, the resins tend to develop darker color, particularly at high processing temperature. Tetrachlorophthahc anhydride [117-08-8] made by conventional chlorination of phthaUc anhydride, would also impart flame retardancy to its alkyds. However, it is appreciably less soluble in the usual processing solvents than is phthaUc anhydride, and is reported to be of appreciably lower chemical reactivity (8). 

There is clearly uncertainty in relying on knowledge of the same material in different applications or conditions. If performance is known under one set of conditions it may be a relatively modest step to predict performance under different conditions. As an illustration, if performance has been proven at 60 °C, the rule of thumb whereby reaction rates approximately double for each 10 °C rise in temperature, might be applied to estimate performance at 70°C (for a justification of this rule for many polymers see [8]). To what extent this approach proves useful or successful will depend on the closeness of the different circumstances and on a general understanding of the potential reasons for any discrepancy. 

This step is called the rate-limiting step. Reaction rate approximation can be found in the form of power series (by/j. or r. ) (see Lazman and Yablonskii, 1988, 1991). 

The cyclic characteristic C is small in the vicinity of thermodynamic equilibrium. We can find the overall reaction rate approximation in the vicinity of equilibrium either directly from kinetic polynomial or by expanding the reaction rate in power series by the small parameter C. The explicit expression for the first term is presented by Lazman and Yablonskii (1988, 1991). It is written as follows ... 

The PhRMA guidance and Alsante et al. (21) have recommended a conservative approach of assuming that for every 10°C increase in temperature the reaction rate approximately doubles. This is approximately equivalent to assuming an E l of 12 kcal/mol. 

In the absence of compound specific data on temperature effects, Equation 26 can still be useful for approximate corrections using assumed values of Ea. Thus, the rule-of-thumb that reaction rates approximately double for every 10°C increase in temperature, is justified because most reactions of organic substances in solution have anEa of about 50 kj /mol. Most reported rate constants probably overestimate environmental rates slightly because the former typically are measured near 25°C, and 15°C is more typical of natural waters. 

The red curve shows how the energy distribution is shifted at 100 °C. At 100 °C, many more molecules have the energy needed to overcome the energy barriers, especially the 80 kJ/mol barrier. For smaller temperature changes, chemists often use an approximation for reactions with typical activation energies of about 40 to 60 kJ/mol (10 to 15 kcal/mol), the reaction rate approximately doubles when the temperature is raised by 10 °C, as from 27 °C (near room temperature) to 37 °C (body temperature). 

For many reactions in organic chemistry, reaction rates approximately double for a I0°C increase in temperature. 

Carbonic anhydrase catalyses the hydration and dehydration reactions of CO2 and accelerates this reaction rate approximately 5000-fold. The results of earlier attempts to use carbonic anhydrase to improve sensor response time were mixed, probably because the response times of previous sensors were limited by slow diffusion through the gas-permeable membrane, and not by reaction kinetics [29, 30]. 

It seems that the reaction rate approximately doubled for each 10-degree temperature increase. The parent compound and its oxon are characterized by nearly equal activation energies at pH 3.1. However, under alkaline condition the E b value calculated for paraoxon is approximately 2.5 kcal mole" smaller than that calculated for the parent compound, parathion. 

Practically all of the monomer consumption results from the propagation reaction and virtually not at all by other reactions such as the start reaction and termination or transfer to monomer. This condition is always fulfilled for degrees of polymerization in excess of 100, since then the error resulting from monomer consumption by other reactions is less than 1%. In this case, the overall reaction rate approximates to that of the propagation reaction ... 

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