Analytic solutions to sets of first-order rate equations with up to six rate constants using a symbolic computer language SMP and application to biochemical kinetics

1988 ◽  
Vol 9 (6) ◽  
pp. 674-683 ◽  
Author(s):  
W. C. Kreye ◽  
Prem Batra ◽  
Gordon Skinner
Keyword(s):  
Rate Constants ◽  
Analytic Solutions ◽  
Rate Equations ◽  
Computer Language ◽  
First Order ◽  
Biochemical Kinetics ◽  
Order Rate

The Kinetics of Isotope Effects in a Model Solvolysis System Involving One Optically Active Ion Pair Intermediate

1974 ◽  
Vol 52 (10) ◽  
pp. 1937-1941 ◽  
Author(s):  
P. Christian Vogel
Keyword(s):  
Rate Constant ◽  
Rate Constants ◽  
Isotope Effects ◽  
Kinetic Scheme ◽  
Ion Pair ◽  
Rate Equations ◽  
Differential Analysis ◽  
First Order ◽  
Order Rate ◽  
Special Cases

The derivation of the observed first-order rate constants from the "exact" integrated rate equations for the kinetic scheme of reaction 1 is presented. It is shown that the solvolytic exponential first-order rate constant is a special case of the polarimetric rate constant and that the optical activity of the product is determined by a multiplicative ratio of rate constants for the optically important reactions of the ion pair intermediate. A form of the integrated first-order polarimetric rate equation with a linearly independent parameter set is presented. The functions for the first-order rate constants derived using the steady state approximation are special cases of the functions derived from the exact equations, as are the functions for the first-order rate constants for two systems which involve pre-equilibria followed by a slow product forming step. These functions cannot all be derived one from the other. A differential analysis of observed isotope effects as functions of isotope effects on the rate constants for reactions involving the intermediates is presented.

A kinetic standard for precise calibration of spectrophotometer cell temperature.

1981 ◽  
Vol 27 (5) ◽  
pp. 753-755 ◽  
Author(s):  
P A Adams ◽  
M C Berman
Keyword(s):  
Temperature Dependence ◽  
Rate Constants ◽  
Cell Temperature ◽  
First Order ◽  
Order Rate ◽  
Acid Catalyzed ◽  
Pseudo First Order ◽  
Hydrolysis Of

Abstract We describe a simple, highly reproducible kinetic technique for precisely measuring temperature in spectrophotometric systems having reaction cells that are inaccessible to conventional temperature probes. The method is based on the temperature dependence of pseudo-first-order rate constants for the acid-catalyzed hydrolysis of N-o-tolyl-D-glucosylamine. Temperatures of reaction cuvette contents are measured with a precision of +/- 0.05 degrees C (1 SD).

scholarly journals Compounds of 6, 13-Diamino-6, 13-Dimethyl-1, 4, 8, 11 - Tetraazacyclotetradecane

2021 ◽  
Author(s):  
◽  
Asokamali Siriwardena
Keyword(s):  
Rate Constants ◽  
Magnetic Measurements ◽  
Order Rate Constant ◽  
Acidic Solutions ◽  
First Order ◽  
Order Rate ◽  
Pendant Arm ◽  
Nickel Copper ◽  
13C Nuclear Magnetic Resonance ◽  
Kinetics Of

<p>The reaction of bis-(diaminoethane)nickel(II) chloride, ([Ni(en)2]Cl2 in methanol with formaldehyde and nitroethane in the presence of triethylamine proceeds readily to produce (6, 13-dimethyl-6, 13-dinitro-1, 4, 8, 11-tetraazacyclotetradecane)nickel(II) chloride, [Ni(dini)] - Cl2. Reduction of the nitro groups of this compound by catalytic hydrogenation yields three isomers of the pendant arm macrocyclic complex (6, 13-diamino-6, 13-dimethyl-1, 4, 8, 11-tetraazachyclotetradecane)nickel(II) chloride, designated a-, b- and c-[Ni(diam)]Cl2. These were separated by fractional crystallization. The aisomer was observed to isomerizes slowly in solution to the b- form. A parallel dissociation reaction of the a- isomer was also observed. The demetallation of a- and b- isomers of the diam complex of nickel by reaction with cyanide or concentrated acid at 140 degrees C produces the macrocycle meso-(6, 13-diamino-6, 13-dimethyl-1, 4, 8, 11-tetraazacyclotetra-decane), diam. A variety of hexamine, pentamine and tetramine complexes of diam with nickel(II), copper(II), cobalt(II) and (III), chromium(III), palladium(II), rhodium(III), zinc(II) and cadmium(II) were prepared. Hexamine and tetramine forms of labile metal complexes could be rapidly and reversibly interconverted by altering the pH. The hexamine cobalt(III) cation, [Co(diam)]3+ was by far the most inert of the prepared cobalt(III) complexes, remaining unaffected in hot acidic solutions. In contrast, a single pendant arm of the hexamine [Cr(diam)]3+ cation could be dissociated in acid. (Two possibly triamine complexes of lead were also prepared). These compounds were characterized by elemental analysis, magnetic measurements, electronic, infrared, 1H and 13C nuclear magnetic resonance spectra. The pendant arm protonation constants (log K) of diam and selected complexes of nickel, copper and palladium were calculated from potentiometric titration measurements at 25 degrees C. The log K values for diam at 25 degrees C (I = 0.1 M NaclO4) were 11.15, 9.7, 6.2 and 5.3. Kinetics of the parallel isomerization and dissociation of a-[Ni(dimH2)]4+ in HCl/NaCl solutions were monitored spectrophotometrically at 50 degrees C. The rate of reaction in acidic solutions showed a non-linear dependency on acid concentration. The observed first order rate constant (kobs) for disappearance of a-[Ni(diamH2)]4+ (by isomerization and dissociation) in 2.0 M HCl, 0.1 M NaOH and 2.0 M NaCl were 3.05 x 10-4, 2.0(3) x 10-2 and 5.0 x 10-5 s-1 respectively. The rate of the dissociation component of the reaction of a-[Ni(diamH2)]4+ in 2.0 M HCl at 50 degrees C was 1.82 x 10-7 s-1. Acid bydrolysis kinetics of (Cu[diamH2])(ClO4)4 in hydrochloric acid and perchloric acid at 50 and 70 degrees C were studied spectrophotometrically. The reactions were slow and the observed first order rate constants were to a first approximation independent of the particular acid or its concentration. The observed first order rate constants were 1 x 10-9 and 8 x 10-9 s-1 at 50 and 70 degrees C respectively. Questions about the nature of the reaction being followed have been raised.</p>

The thermal decompositions of carbamates. I. Ethyl N-Methyl-N-phenylcarbamate

1971 ◽  
Vol 24 (12) ◽  
pp. 2541 ◽  
Author(s):  
NJ Daly ◽  
F Ziolkowski
Keyword(s):  
Carbon Dioxide ◽  
Gas Phase ◽  
Rate Constants ◽  
Volume Ratio ◽  
Reaction Vessel ◽  
First Order ◽  
Order Rate

Ethyl N-methyl-N-phenylcarbamate decomposes in the gas phase over the range 329-380� to give N-methylaniline, carbon dioxide, and ethylene. The reaction is quantitative, and is first order in the carbamate. First-order rate constants are described by the equation ������������������� k1 = 1012.44 exp(-45,380/RT) (s-1) and are unaffected by the addition of cyclohexene or by increase in the surface to volume ratio of the reaction vessel. The reaction is considered to be unimolecular and likely to proceed by means of a mechanism of the type represented by the pyrolyses of acetates, xanthates, and carbonates.

HUMAN MEIZOTHROMBIN 1, ITS ISOLATION AND PROPERTIES

1987 ◽  
Author(s):  
Zbigniew S Latallo ◽  
Craig M Jackson
Keyword(s):  
Rate Constants ◽  
Antithrombin Iii ◽  
Order Rate Constant ◽  
Red Cross ◽  
Apparent Lack ◽  
First Order ◽  
Order Rate ◽  
Matching Grant ◽  
Echis Carinatus

Meizothrombin (MT) and meizothrombin des Fragment 1 (MT1) are intermediates in the conversion of prothrombin to α-thrombin (αTH). Due to their transient character, properties of these enzymes are difficult to establish. Isolation of MT1 was achieved by affinity chromatography on D-Phe-Pro-Arginal (FPRal)immobilized on Affi-Gel 10 as originally employed for thrombin purification (Patel et al. Biochim.Biophys. Acta 748,321 (1983)). Human prethrombin 1 was activated with the purified activator from Echis carinatus venom in the presence of Ca++;, benzamidine and FPRal gel at pH 7.8. After exhaustive washing the MT1 was eluted with 0.1 M hydroxylamine in 0.15 M Na acetate buffer, pH 5.5. Under these conditions the MT1 is stable and can bestored at -70°C. Upon changing the pH of the preparation to 8.0, complete conversion into aTH occurred atroom temperature within 48 hours. Homogeneity of both preparations wasdemonstrated by PAGE. The Km and ke, values for MT1 measured on Tos-Gly-Pro-Arg pNA(0.1 M NaCl, 0.01 M TRIS, 0.01 M HEPES, 0.1% PEG, pH 7.8, 25°C) were 15.7 /iM and 126 s-1. The kinetic con stants for the aTH resulting from autocatalytic degradation of MT1 were indistinguishable from those previously established forαTH obtained by Xa activation i.e. 4.77 /μM and 126 s-1. Clotting activity of MT1 was found to be only one fifth as high as that of the resulting μTH(746 u/mg vs. 3900 u/mg as tested using the NIH standard) .Inhibitionof MTl by antithrombin III was alsomuch less rapid than αTH andmost importantly, it was not affected by high affinity heparin( Mr20,300). Under conditions of the experiment (0.3 M NaCl, 0.0rl M TRIS, 0.01 M HEPES, 2.5 mM EDTA, 0.1% PEG, pH 7.8, 25°C; [ATIII] 100 nM, [E] 10 nM), the pseudo first order rate constants in the absence of heparin were 4.04 × 10-3V1 (MTl) and 1.13 × 10-3V1 (αTH), giving apparent second order rate constants of 4.04 × 103 and 1.13 × 10-4M-1s-1. In the presence of 4.5 nM of heparin the observed first order rate constant for MTl remained unchanged whereas it increased to 6.241 × 10-3s-1 (5.5 fold) for αTH. This apparent lack of an effect of heparin may be of significance in vivo.Supported by a Matching Grant from the American National Red Cross and by the Southeastern Michigan Blood Service.

The mercury(II)-induced aquation of trans-Chloroamminebis(dimethylglyoximato)cobalt(III) complex

1975 ◽  
Vol 28 (5) ◽  
pp. 1133 ◽  
Author(s):  
S Chan ◽  
S Tan
Keyword(s):  
Rate Constants ◽  
Aqueous Ethanol ◽  
Association Constants ◽  
First Order ◽  
Order Rate ◽  
Leaving Group ◽  
Pseudo First Order ◽  
Activated Complex

The pseudo first-order rate constants for the mercury(II)-induced aquation of trans-[Co(Hdmg)2(NH3)Cl] (Hdmg = dimethylglyoximate ion) have been measured in aqueous and aqueous ethanol solutions (ethanol- water mole ratio 1 : 5.1) containing various excess amounts of mercury(II)ion at 273.2 K. Association constants of the complex formed with mercury(II) ion and rate constants for dissociation of the activated complex in both solutions have been calculated. The kinetic results are discussed in terms of formation of an activated complex Co-C1-Hg, followed by a simple rate-determining aquation in which HgCl+ acts as the leaving group.

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