Relative addition rate

T. Ingestad, Relative addition rate and external concentration driving variables used in plant nutrition research. Plant Cell Environ. 5 443 (1982). 

Table 12. Relative addition rates of singlet and triplet 69 4)...

Goransson A. (1993) Growth and nutrition of small Betula-pendula plants at different relative addition rates of iron. Trees-Struct. Funct. 8, 31—38. 

When one wants to make a copolymer with a given build-in ratio of both monomers, one has to consider the difference in relative addition rates of each monomer. This is determined by the ratio p = 4r I r. ... 

Figure 4 Illustrative examples of steric effects in the addition of the cyclohexyl radical to various alkenes. Relative addition rate coefficients (/Cadd) for the major isomer (anti-Markovnikov) were measured at 20 °C, and regioselectivity for this isomer is given in parentheses/ (See color plate.)...

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

Since the catalyst is so important to the cracking operation, its activity, selectivity, and other important properties should be measured. A variety of fixed or fluidized bed tests have been used, in which standard feedstocks are cracked over plant catalysts and the results compared with those for standard samples. Activity is expressed as conversion, yield of gasoline, or as relative activity. Selectivity is expressed in terms of carbon producing factor (CPF) and gas producing factor (GPF). These may be related to catalyst addition rates, surface area, and metals contamination from feedstocks. 

This relatively steady rate of addition of new generic names has resulted in books which are quite uniform in size, at least after accounting for the text which was used to bring the subject up to date. The individual chapter titles do not show a corresponding uniformity the composition of... 

As a result of the conclusions reached in these studies, a simple competition method was devised 12, 32) to determine relative rates of hydride transfer reactions rather accurately. For example, to obtain relative reaction rates of ethyl ions with various additives, a suitable source of fully deuterated ethyl ions such as C3D8 or iso-C4Di0 was irradiated in the presence of a perprotonated additive (RH), leading to the formation of C2D6 and C2D5H by Reactions 2 and 3. 

This aromatic alcohol has been an effective preservative and still is used in several ophthalmic products. Over the years it has proved to be a relatively safe preservative for ophthalmic products [138] and has produced minimal effects in various tests [99,136,139]. In addition to its relatively slower rate of activity, it imposes a number of limitations on the formulation and packaging. It possesses adequate stability when stored at room temperature in an acidic solution, usually about pH 5 or below. If autoclaved for 20-30 minutes at a pH of 5, it will decompose about 30%. The hydrolytic decomposition of chlorobutanol produces hydrochloric acid (HC1), resulting in a decreasing pH as a function of time. As a result, the hydrolysis rate also decreases. Chlorobutanol is generally used at a concentration of 0.5%. Its maximum water solubility is only about 0.7% at room temperature, which may be lowered by active or excipients, and is slow to dissolve. Heat can be used to increase dissolution rate but will also cause some decomposition and loss from sublimation. Concentrations as low as 0.125% have shown antimicrobial activity under the proper conditions. 

Recently, an example of cycloamylose-induced catalysis has been presented which may be attributed, in part, to a favorable conformational effect. The rates of decarboxylation of several unionized /3-keto acids are accelerated approximately six-fold by cycloheptaamylose (Table XV) (Straub and Bender, 1972). Unlike anionic decarboxylations, the rates of acidic decarboxylations are not highly solvent dependent. Relative to water, for example, the rate of decarboxylation of benzoylacetic acid is accelerated by a maximum of 2.5-fold in mixed 2-propanol-water solutions.6 Thus, if it is assumed that 2-propanol-water solutions accurately simulate the properties of the cycloamylose cavity, the observed rate accelerations cannot be attributed solely to a microsolvent effect. Since decarboxylations of unionized /3-keto acids proceed through a cyclic transition state (Scheme X), Straub and Bender suggested that an additional rate acceleration may be derived from preferential inclusion of the cyclic ground state conformer. This process effectively freezes the substrate in a reactive conformation and, in this case, complements the microsolvent effect. 

TABLE 6. Relative bimolecular addition rates for the reaction of initiator derived radicals obtained by polymer end group analysis15 163... 

Fig. 9. Effect of the chain length of hydrocarbons on the adsorption enthalpy and rates of desorption. (A) Hydrocarbon in interaction with zeolite framework. Methyl groups interact with the framework oxygen protons exhibit an additional attractive force. (B) Heat of adsorption as a function of carbon number for zeolites MFI and FAU in the acidic and non-acidic form. (C) Relative desorption rates of a C12, Ci6, and C20 alkane compared to octane at 348 K. Values calculated from the linear extrapolation of the heat of adsorption values shown in (B).

FIG. 15 A comprehensive stability map illustrating the general relationship between the occurrence of various reactions important in foods, as a function of water activity, superimposed on a sorption isotherm. M, mold Y, yeast B, bacteria. The isotherm is plotted as moisture content (left y axis) versus water activity, whereas all other curves are plotted as relative reaction rate (right y axis) versus water activity. Additional information corresponding to regions I, II, and III is given in Table IV. 

In addition to fluids, solid forms of drugs may be given by SC injection. This has been done with compressed pellets of testosterone placed under the skin, which are absorbed at a relatively constant rate over a long period. 

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