Isotope exchange, rate, with

The content of the material in a carbon reservoir is a measure of that reservoir s direct or indirect exchange rate with the atmosphere, although variations in solar also create variations in atmospheric content activity (Stuiver and Quay, 1980, 1981). Geologically important reservoirs (i.e., carbonate rocks and fossil carbon) contain no radiocarbon because the turnover times of these reservoirs are much longer than the isotope s half-life. The distribution of is used in studies of ocean circulation, soil sciences, and studies of the terrestrial biosphere. 

Derivation of rate equations is an integral part of the effective usage of kinetics as a tool. Novel mechanisms must be described by new equations, and famihar ones often need to be modified to account for minor deviations from the expected pattern. The mathematical manipulations involved in deriving initial velocity or isotope exchange-rate laws are in general quite straightforward, but can be tedious. It is the purpose of this entry, therefore, to present the currently available methods with emphasis on the more convenient ones. 

Annual isotopic variation is substantial in shallow lakes with relatively short residence times. These variations reflect the dominance of summer evaporation and spring snowmelt. In addition, these variations may prove useful for examining atmospheric exchange rates with lakes and for quantifying periods of episodic water input. 

It will be shown below that with the aid of liquid ammonia solutions of potassium amide, the acidity of hydrocarbons (including even saturated ones) cannot only be detected but also determined quantitatively from measurements of hydrogen isotope exchange rates. 

Table 17 lists rate coefficients for various acids. There is a substantial isotope effect, comparable with those which would be required to correlate either set of exchange rates with the exchange rates inferred from oxidation studies (Section 4.3) and with that calculated from an approximate spectroscopic treatment . ... 

Reaction of isotopic exchange Rate of exchange at 40 torr pressure /molecules 5 X 10- y cm sec / Activation energy / kcal ymole J Order of reaction With respect to With respect to O, CO, ... 

Identical experiments carried out with both s-MDH and m-MDH from beef heart resulted in similar changes in the isotopic exchange rates (76). For both enzymes, the data were compatible with a compulsory ordered mechanism involving binary complexes of the MDH s with the coenzyme but not with the dicarboxylic acid substrates (75). The isotopic exchange rates were very similar for m-MDH from pig or beef heart, and the results were qualitatively the same for s-MDH from beef heart... 

The compulsory ordered mechanism arrived at through isotopic exchange rates is basically in agreement with mechanisms postulated on the basis of initial velocity studies. Heyde and Ainsworth showed that for beef heart m-MDH the initial velocity pattern in the absence of products and the product inhibition pattern are consistent with an ordered mechanism (77). Raval and Wolfe obtained similar results with pig heart m-MDH data obtained by initial velocity studies in both directions are in agreement with a compulsory ordered mechanism (78,79). Substrate inhibition by oxaloacetate also occurs with pig heart m-MDH (80). Similar initial velocity studies on beef heart s-MDH did... 

Another application of pulse chromatographic methods is in studies of the kinetics of isotope-exchange reactions [75]. A deuterium-labelled compound was formed as a pulse of a volatile compound (reagent) passed through a column packed with Gas-Chrom A with 10% of Carbowax 6000 and 10% of KO H applied on its surface. The isotope exchange rate is a characteristic of the nature of the substance under investigation and is of... 

Simplified surface-area based rate model. A simple isotope exchange rate model derived by Northrop and Clayton (1966) was modified by Cole et al. (1983) to account for the surface area of the solid in experimental mineral-fluid systems. As a first approximation, this model assumes that the rate-limiting step involves the addition and removal of atoms (O, H, C) from the surface of the solid. The overall rate of reaction, R, can be expressed in the following pseudo-first order equation with the inclusion of a factor. As, representing the total surface area (m ) of the mineral... 

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