First-order constants

The kinetics of lithium polystyrene polymerization obeys a first order law at constant concentration of TMTCT. The first order constant increases linearly with the concentration of this complexing agent149) and becomes constant for [TMTCT] [lithium polystyrene] as shown in Fig. 23. 

R ratio(H2O/TTIP)=150, synthesis temperature=180°C(HNO3) and 160 C(TENOH), dried at 105 C. obtained by Scherrer equation, apparent first-order constants(A ) of orange n. rutile structure... 

The dynamic error existing between and Cr depends on the relative magnitudes of the respective time constants. For the reactor, assuming a first-order, constant volume reaction... 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

Note that k and /c3 are second-order constants, whereas k2 is a pseudo-first-order constant. The pH versus rate profile can be constructed by considering, in turn, that one of the three kinetic terms is predominating, thus ... 

For such a mechanism, the overall second-order formation rate constant is given by the product of the first-order constant ktx and the equilibrium constant Kos. The characteristic solvent exchange rates are thus often useful for estimating the rates of formation of complexes of simple monodentate ligands but, as mentioned already, in some cases the situation for macrocyclic and other polydentate ligands is not so straightforward. 

In the range of linear adsorption behaviour, whatever the number of site types (see Section 2.3.1 for the merging of parameters of two sites), the surface concentration F is related to via an effective linear coefficient, Ah, while the first-order internalisation processes can also be described by an effective first-order constant, k. Thus, equation (39) can be recast, for instance, in terms of r as ... 

The values of pl+B calculated according to Equation (44) are also listed in Table 1. They show the same ranking as the kp, since the mB only vary from ca. 7-11 mold 1 but as they are first-order constants they cannot be compared with any second-order rate-constants obtained for the same monomers by chemical initiation. Therefore all the many attempts in the literature to make such comparisons are futile. 

The rate equation describes the variation in response variable R (with initial value of Rq) the measure response appears at a constant rate (zero order) of and is eliminafed by the first-order constant. The indirect response models will generally fall info fwo caf-egories inhibition or stimulation function. The inhibition response is classically described in ferms of IC q, fhe drug concenfration fhaf produce 50% of maximal inhibition (e.g., action of S5mfhefic glucocorticoid on adrenal glands or effecf of furosemide on sodium absorption in fhe loop of Henley) and is a number from 0 fo 1 where 1 represents total inhibition ... 

Mathematical Analysis. Reactions 3 to 5 are first-order or pseudo-first-order reactions. Thus, the pseudo-first-order constant for Reaction 3 is ksE. For brevity we rewrite the two intermediates (E2+ 02H A )2 and (+E—E+ 02H A )g as Ci and C2, respectively. We assume that the light intensity is proportional to C2 during any one run. Thus, dl/dt = dC2/dt and the calculated decay of C2 can be related to k0. 

Dr. MargerumrAn experimental comparison with the aquo ion was not made in this series because nickel hydroxide would precipitate. However, the Niglycine+ data provides a reference point which suggests all the ku values can be multiplied by a factor of about 10 to give the first-order constant for water dissociation. 

Changes in Relative Pseudo-First-Order Constants for HDS of Dibenzothiophene with Increasing Naphthalene Concentrations (NiMo/Al203, 32(f C, 2.5 MPa H2) (21, 41a, 133)... 

The units of k2 are M 1 s 1. If [B] is present at unit activity, the rate is /c2[A], a quantity with units of s We can see that the bimolecular, or second-order, rate constant for reaction of A with B may be compared with first-order constants when the second reactant B is present at unit activity. In many real situations, reactant B is present in large excess and in a virtually constant concentration. The reaction is pseudo-first order and the experimentally observed rate constant /c2[B] is an apparent first-order rate constant. The bimolecular rate constant k2 can be obtained by dividing the apparent constant by [B]. 

If M is unstable then ipb/fpf will be less than unity. Its magnitude will depend upon the scan rate, the value of the first-order constant k, and the conditions of the experiment. At fast scan rates the ratio ipb/ ip, may approach one if the time gate for the decomposition of M is small compared with the half-life of M-, (In 2jk). As the temperature is lowered, the magnitude of k may be sufficiently decreased for full reversible behaviour to be observed. The decomposition of M- could involve the attack of a solution species upon it, e.g. an electrophile. In such cases, ipb/ipf, will of course be dependent upon the concentration of the particular substrate (under pseudo-first-order conditions, k is kapparent). Quantitative cyclic voltammetric and related techniques allow the evaluation of the rate constants for such electrochemical—chemical, EC, processes. At the limit, the electron-transfer process is completely irreversible if k is sufficiently large with respect to the rate of heterogeneous electron transfer the electrochemical and chemical steps are concerted on the time-scale of the cyclic voltammetric experiment.1-3... 

This points up the desirability of using the dimensionless index variable x and of having the liberty of choosing h x) in Eq. 12. If h x) = x then k, the first-order constant, is being linearly distributed. If it is desirable to distribution kn linearly then h(x) = x[/(x)] 1 1. 

The first-order constant klG will now be expressed in terms of the rate constant kx of the reaction in the liquid phase. From equation 4.14, the rate of transfer of A per unit area of gas-liquid interface is >l(kxDA) CAi i.e. in terms of an enhanced mass transfer coefficient k L = V(kxDA) this rate of transfer is k LCAi. The rate of transfer per unit volume of dispersion JA is thus ... 

While comparing the pseudo-first order constant for the same polymers with the relative non-imprinted polymers ( MIP/ NIP),the rate increase dropped to 24 for carbonate and 11 for carbamate. The corresponding bulk polymers showed better results since the rate enhancement, due to the imprinted polymer, was 588 for the carbonate hydrolysis and 1,435 for the carbamate. However, when comparing the imprinted with the non-imprinted bulk, the ratio dropped to 10 for carbonate and 5.8 for carbamate, suggesting that the higher selectivity showed by the beads could be due to an enhanced accessibility of the active sites compared to the bulk. 

Remember that within any given experiment the reaction is strictly first order, see Problems 4.17 and 4.18, but the reaction moving to second order conditions will be shown up as the decreasing value of the first order constant. 

If we run the same readion starting from a 200 1 mole/mole mixture of A and B, the change in [A] will never be more than 0.5%, because even at full conversion there will still be 199 equivalents of A left. This means that [A] = [A]0, giving a pseudo first-order readion profile that depends only on [B]. In the corresponding rate equation (Eq. (2.57)), the pseudo first-order constant k = k[A]0. Pseudo order conditions are very useful for isolating the contribution of a chemical species to the rate-determining step. 

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