Susceptibility first-order

The kinetics of the reactions were complicated, but three broad categories were distinguished in some cases the rate of reaction followed an exponential course corresponding to a first-order form in others the rate of reaction seemed to be constant until it terminated abruptly when the aromatic had been consumed yet others were susceptible to autocatalysis of varying intensities. It was realised that the second category of reactions, which apparently accorded to a zeroth-order rate, arose from the superimposition of the two limiting kinetic forms, for all degrees of transition between these forms could be observed. 

Azobisnittiles are efficient sources of free radicals for vinyl polymerizations and chain reactions, eg, chlorinations (see Initiators). These compounds decompose in a variety of solvents at nearly first-order rates to give free radicals with no evidence of induced chain decomposition. They can be used in bulk, solution, and suspension polymerizations, and because no oxygenated residues are produced, they are suitable for use in pigmented or dyed systems that may be susceptible to oxidative degradation. 

Although reasonably stable at room temperature under neutral conditions, tri- and tetrametaphosphate ions readily hydrolyze in strongly acidic or basic solution via polyphosphate intermediates. The hydrolysis is first-order under constant pH. Small cycHc phosphates, in particular trimetaphosphate, undergo hydrolysis via nucleophilic attack by hydroxide ion to yield tripolyphosphate. The ring strain also makes these stmctures susceptible to nucleophilic ring opening by other nucleophiles. 

Some authors use O] instead of cr as the substituent constant in such correlations.) An example is provided by the aminolysis of phenyl esters in dioxane the substrates RCOOPh were reacted with -butylamine, and the observed first-order rate constants were related to amine concentration by = k2 [amine] kj [amine]. The rate constants kz and k could be correlated by means of Eq. (7-54), the reaction constants being p = +2.14, b = + 1.03 (for A 2) and p = -1-3.03,8 = -1-1.08 (for ks). Thus, the two reactions are about equally sensitive to steric effects, whereas the amine-catalyzed reaction is more susceptible to electronic effects than is the uncatalyzed reaction. 

If (A i[X ]/A 2[Y ]) is not much smaller than unity, then as the substitution reaction proceeds, the increase in [X ] will increase the denominator of Eq. (8-65), slowing the reaction and causing deviation from simple first-order kinetics. This mass-law or common-ion effect is characteristic of an S l process, although, as already seen, it is not a necessary condition. The common-ion effect (also called external return) occurs only with the common ion and must be distinguished from a general kinetic salt effect, which will operate with any ion. An example is provided by the hydrolysis of triphenylmethyl chloride (trityl chloride) the addition of 0.01 M NaCl decreased the rate by fourfold. The solvolysis rate of diphenylmethyl chloride in 80% aqueous acetone was decreased by LiCl but increased by LiBr. ° The 5 2 mechanism will also yield first-order kinetics in a solvolysis reaction, but it should not be susceptible to a common-ion rate inhibition. 

The first kinetic study appears to have been that of Martinsen148, who found that the sulphonation of 4-nitrotoluene in 99.4-100.54 wt. % sulphuric acid was first-order in aromatic and apparently zeroth-order in sulphur trioxide, the rate being very susceptible to the water concentration. By contrast, Ioffe149 considered the reaction to be first-order in both aromatic and sulphur trioxide, but the experimental data of both workers was inconclusive. The first-order dependence upon aromatic concentration was confirmed by Pinnow150, who determined the equilibrium concentrations of quinol and quinolsulphonic acid after reacting mixtures of these with 40-70 wt. % sulphuric acid at temperatures between 50 and 100 °C the first-order rate coefficients for sulphonation and desulphonation are given in Tables 34 and 35. The logarithms of the rate coefficients for sulphonation... 

The contribution of the electron to the diamagnetic susceptibility of the system can be calculated by the methods of quantum-mechanical perturbation theory, a second-order perturbation treatment being needed for the term in 3C and a first-order treatment for that in 3C". In case that the potential function in 3C° is cylindrical symmetrical about the s axis, the effect of 3C vanishes, and the contribution of the electron to the susceptibility (per mole) is given... 

The effect of temperature upon the situation in Fig. 5-5 is to modify the Boltzmann distribution. Lowering the temperature depopulates the higher-lying energy levels in favour of the lower. Therefore, susceptibility increases with decreasing temperature. Quantitative studies of the simple (first-order )... 

The more usual pattern found experimentally is that shown by B, which is called a sigmoid curve. Here the graph is indicative of a slow initial rate of kill, followed by a faster, approximately linear rate of kill where there is some adherence to first-order reaction kinetics this is followed again by a slower rate of kill. This behaviour is compatible with the idea of a population of bacteria which contains a portion of susceptible members which die quite rapidly, an aliquot of average resistance, and a residue of more resistant members which die at a slower rate. When high concentrations of disinfectant are used, i.e. when the rate of death is rapid, a curve ofthe type shown by C is obtained here the bacteria are dying more quickly than predicted by first-order kinetics and the rate constant diminishes in value continuously during the disinfection process. 

Organic peroxides and hydroperoxides decompose in part by a self-induced radical chain mechanism whereby radicals released in spontaneous decomposition attack other molecules of the peroxide.The attacking radical combines with one part of the peroxide molecule and simultaneously releases another radical. The net result is the wastage of a molecule of peroxide since the number of primary radicals available for initiation is unchanged. The velocity constant ka we require refers to the spontaneous decomposition only and not to the total decomposition rate which includes the contribution of the chain, or induced, decomposition. Induced decomposition usually is indicated by deviation of the decomposition process from first-order kinetics and by a dependence of the rate on the solvent, especially when it consists of a polymerizable monomer. The constant kd may be separately evaluated through kinetic measurements carried out in the presence of inhibitors which destroy the radical chain carriers. The aliphatic azo-bis-nitriles offer a real advantage over benzoyl peroxide in that they are not susceptible to induced decomposition. 

Bis(ethylacetoacetonate)-lanthanide(III) alkoxides, represented by structure (314), also initiate the well-controlled ROP of CL.895 Mn increases linearly with conversion (with Mw/Mn<1.10 throughout), and increasing [M]0/[I]o- Kinetic analysis implies a first order dependence on the lanthanide initiator, consistent with a non-aggregated active site. Block copolymers with moderately narrow polydispersities (1.25-1.45) have also been prepared using these initiators. NMR spectroscopy confirms well-controlled block sequences suggesting that these initiators are less susceptible to transesteriflcation than other lanthanide alkoxides. Initiation occurs exclusively at the alkoxide bond, and the tris(ethylacetoacetonate) analogs are inactive under the same conditions. 

For the latter two ions, the presence of low-lying excited states makes the inclusion of both the first-order contribution of the excited states and the second-order effects due to coupling of the ground / state with the excited states crucial in a correct estimation of the room-temperature values of xT. Indeed, second-order contribution in Van Vleck [9] expansion of the susceptibility is inversely proportional to the energy difference between the ground and the excited states ... 

Cytochrome P-450 from rat or human liver microsome preparations is inactivated when incubated anaerobically with carbon tetrachloride in the presence of NADPH and an oxygen-scavenging system (Manno et al. 1988 1992). Inactivation involved destruction of the heme tetrapyrrolic structure, and followed pseudo first-order kinetics with fast and slow half lives of 4.0 and 29.8 minutes. When compared with rat liver microsomes, the human preparations were 6-7 times faster at metabolizing carbon tetrachloride, and only about one- eighth as susceptible to suicide inactivation (about 1 enzyme molecule lost for every 196 carbon tetrachloride molecules metabolized). 

Many drugs are quite stable but functional groups such as esters and lactam rings which occur in some drugs are susceptible to hydrolysis and functional groups such as catechols and phenols are quite readily oxidised. The most common types of degradation which occur in pure and formulated drugs obey zero or first order kinetics. 

Additional information Procaine is formulated in injections and thus susceptible to aqueous phase hydrolysis, in simple solution its degradation is first order (Fig. 2.9). 

The rate of clearance of chlorhexidine from the mouth after one mouth rinse with 10 mL of a 0.2% aqueous solution follows approximately first-order kinetics, with a half-life of 60 minutes. This means that following application of a single rinse with a 0.2% chlorhexidine solution, the concentration of the compound exceeds the minimum inhibitory concentration (MIC) for oral streptococci (5 mg/mL) for almost 5 hours. The pronounced substantivity, along with the relative susceptibility of oral streptococci, may account for the great effectiveness of chlorhexidine in inhibiting supragingival plaque formation. 

Ac-susceptibility measurements by Morellon et al. (2000) showed, that (on heating) Gdj(Sio.iGeo.9)4 undergoes a first-order transition from a ferromagnetic to an antiferromagnetic state at 7c = 81 K, followed by a second-order transition to the paramagnetic state at 7n = 127 K. Measurements of the thermal dependence of the lattice parameters... 

Stoichiometry (28) is followed under neutral or in alkaline aqueous conditions and (29) in concentrated mineral acids. In acid solution reaction (28) is powerfully inhibited and in the absence of general acids or bases the rate of hydrolysis is a function of pH. At pH >5.0 the reaction is first-order in OH but below this value there is a region where the rate of hydrolysis is largely independent of pH followed by a region where the rate falls as [H30+] increases. The kinetic data at various temperatures both with pure water and buffer solutions, the solvent isotope effect and the rate increase of the 4-chloro derivative ( 2-fold) are compatible with the interpretation of the hydrolysis in terms of two mechanisms. These are a dominant bimolecular reaction between hydroxide ion and acyl cyanide at pH >5.0 and a dominant water reaction at lower pH, the latter susceptible to general base catalysis and inhibition by acids. The data at pH <5.0 can be rationalised by a carbonyl addition intermediate and are compatible with a two-step, but not one-step, cyclic mechanism for hydration. Benzoyl cyanide is more reactive towards water than benzoyl fluoride, but less reactive than benzoyl chloride and anhydride, an unexpected result since HCN has a smaller dissociation constant than HF or RC02H. There are no grounds, however, to suspect that an ionisation mechanism is involved. 

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