Reaction pseudo-first

Fast reaction, pseudo-first order < Ha < E = tanh Ha... 

Isopropylbenzene (A) is alkylated with propylene (P) using HF catalyst. The mono (B), di (C), tri (D) and tetra (E) derivatives are formed. Relative specific rates are given by Rodiguin Rodiguina (Consecutive Chemical Reactions, 1964) for the case of a large excess of propylene which makes the reactions pseudo first order. The relative specific rates used here are kx = 1.0, k2 = 0.5, k3 = 0.3 and k4 0.2. The system of linear differential... 

When a = b = 1 in (1.42) the overall reaction is second-order. Even a quite small excess of one reagent (here B) can be used and pseudo first-order conditions will still pertain. As the reaction proceeds, the ratio of concentration of the excess to that of the deficient reagent progressively increases so that towards the end of the reaction, pseudo first-order conditions certainly hold. Even if [B] is maintained in only a two-fold excess over [A], the error in the computed second-order rate constant is 2% for 60% conversion. ... 

For reactions between ions of like charge, the term in xrc (1 + kR) 1 should be multiplied by a number 0.6—0.9, whereas for unlike charges, this number is 0.3—0.6 depending on R. Certainly, eqn. (58) is not the appropriate correction term. In eqn. (57), the ionic relaxation time for univalent ions is Tjon = 1/(477[rc Dn), where n is the electrolyte concentration. This is also the characteristic time for reaction (pseudo first-order decay time) of a univalent species reacting with one or other ion of the... 

The rate of product formation will be directly proportional to [A] but inversely proportional to [Br ]. By using an excess of Br so that its initial concentration [Br ]0 does not change appreciably over the course of the reaction, pseudo-first-order behavior can be achieved with /cobs = k2Keq/[Br ]0. 

Whenever a reactant is present in large excess, its concentration is virtually constant during the course of the reaction. Thus, in a second-order reaction A + B — P in which the concentration of B is very high and that of A is low, the reaction may appear to be first-order, because its rate will be nearly proportional to the concentration of A. This is an apparent or pseudo-first-order reaction. Pseudo-first-order reactions are common among biochemical reactions in which water is one of the reactants. Since the concentration of water is 55.5 M and far in excess of everything else, the reaction appears to behave like a first-order reaction. An example is the hydrolysis of an ester,... 

Using the above equation, we can calculate the rate constant k for various values of AG, shown in Table 2.2. The half-life of a unimolecular reaction is equal to (In 2) k or 0.693/, and a reaction is 97% complete after five half-lives. Table 2.2 uses the formula ln(c7c) = kt to relate the rate constant, k, and the original concentration, c°, to the concentration, c, at time t seconds for a unimolecular reaction. Reactant concentrations are very important in a bimolecular reaction. If reactant B in a bimolecular reaction is in large excess, then its concentration will not change significantly over the course of the reaction and can be considered a constant, making the reaction pseudo-first order. We can then use the above formula to calculate the concentration of A at time t by substituting the pseudo-first-order rate constant, k = [B]. 

Epoxide - alcohol reaction pseudo first order kinetics (k units of s k units of g eq s ). 

An excess alcohol makes the forward reaction pseudo-first order whereas reverse reaction second order in the case of com oil (Meher et al., 2006). When com oil is transesterified in a pressiuized batch reactor in the presence of sodium methoxide and methanol, higher conversion can be obtained. Kinetic constants of the stepwise reactions are increased in the direction of the progressing steps of the transesterification (Velazquez 2007). 

The effective rate law correctly describes the pressure dependence of unimolecular reaction rates at least qualitatively. This is illustrated in figure A3,4,9. In the lunit of high pressures, i.e. large [M], becomes independent of [M] yielding the high-pressure rate constant of an effective first-order rate law. At very low pressures, product fonnation becomes much faster than deactivation. A j now depends linearly on [M]. This corresponds to an effective second-order rate law with the pseudo first-order rate constant Aq ... 

The experiments were perfonued in a static reaction cell in a large excess of N2 (2-200 bar). An UV laser pulse (193 mu, 20 ns) started the reaction by the photodissociation of N2O to fonu O atoms in the presence of NO. The reaction was monitored via the NO2 absorption at 405 mu using a Hg-Xe high-pressure arc lamp, together with direct time-dependent detection. With a 20-200-fold excess of NO, the fonuation of NO2 followed a pseudo-first-order rate law ... 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

The effect of micelles of SDS, CTAB and C12E7 on the apparent second-order rate constants of the Diels-Alder reaction between nonionic 5.1a, anionic 5.1 f and cationic 5.1g with 5.2 is reported in Table 5.1. These apparent rate constants are calculated from the observed pseudo-first-order rate constants by dividing the latter by the overall concentration of 5.2. 

Herein [5.2]i is the total number of moles of 5.2 present in the reaction mixture, divided by the total reaction volume V is the observed pseudo-first-order rate constant Vmrji,s is an estimate of the molar volume of micellised surfactant S 1 and k , are the second-order rate constants in the aqueous phase and in the micellar pseudophase, respectively (see Figure 5.2) V is the volume of the aqueous phase and Psj is the partition coefficient of 5.2 over the micellar pseudophase and water, expressed as a ratio of concentrations. From the dependence of [5.2]j/lq,fe on the concentration of surfactant, Pj... 

Assuming complete binding of the dienophile to the micelle and making use of the pseudophase model, an expression can be derived relating the observed pseudo-first-order rate constant koi . to the concentration of surfactant, [S]. Assumirg a negligible contribution of the reaction in the aqueous phase to the overall rate, the second-order rate constant in the micellar pseudophase lq is given by ... 

When the dienophile does not bind to the micelle, reaction will take place exclusively in the aqueous phase so that the second-order rate constant of the reaction in the this phase (k,) is directly related to the ratio of the observed pseudo-first-order rate constant and the concentration of diene that is left in this phase. 

The integrated form of the rate law for equation 13.4, however, is still too complicated to be analytically useful. We can simplify the kinetics, however, by carefully adjusting the reaction conditions. For example, pseudo-first-order kinetics can be achieved by using a large excess of R (i.e. [R]o >> [A]o), such that its concentration remains essentially constant. Under these conditions... 

The concentration of nitromethane, CH3NO2, can be determined from the kinetics of its decomposition in basic solution. In the presence of excess base the reaction is pseudo-first-order in nitromethane. For a standard solution of 0.0100 M nitromethane, the concentration of nitromethane after 2.00 s was found to be 4.24 X 10 M. When a sample containing an unknown amount of nitromethane was analyzed, the concentration remaining after 2.00 s was found to be 5.35 X 10 M. What is the initial concentration of nitromethane in the sample ... 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

Direct-Computation Rate Methods Rate methods for analyzing kinetic data are based on the differential form of the rate law. The rate of a reaction at time f, (rate)f, is determined from the slope of a curve showing the change in concentration for a reactant or product as a function of time (Figure 13.5). For a reaction that is first-order, or pseudo-first-order in analyte, the rate at time f is given as... 

The concentration of aluminum in serum can be determined by adding 2-hydroxy-1-naphthaldehyde p-methoxybenzoyl-hydrazone and measuring the initial rate of the resulting complexation reaction under pseudo-first-order conditions.The rate of reaction is monitored by the fluorescence of the metal-ligand complex. Initial rates, with units of emission intensity per second, were measured for a set of standard solutions, yielding the following results... 

In a curve-fitting method the concentration of a reactant or product is monitored continuously as a function of time, and a regression analysis is used to fit an appropriate differential or integral rate equation to the data. Eor example, the initial concentration of analyte for a pseudo-first-order reaction, in which the concentration of a product is followed as a function of time, can be determined by fitting a rearranged form of equation 13.12... 

The analysis is carried out under conditions in which the reaction s kinetics are pseudo-first-order in picrate. Show that under these conditions, a plot of potential as a function of time will be linear. 

We know from equation 13.6 that for a pseudo-first-order reaction, the concentration of picrate at time t is... 

As carried out the rate of the reaction is pseudo-first-order in picrate and... 

Equation 13.14 shows how [A]o is determined for a two-point fixed-time integral method in which the concentration of A for the pseudo-first-order reaction... 

The concentration of phenylacetate can be determined from the kinetics of its pseudo-first-order hydrolysis reaction in an ethylamine buffer. When a standard solution of 0.55 mM phenylacetate is analyzed, the concentration of phenylacetate after 60 s is found to be 0.17 mM. When an unknown is analyzed, the concentration of phenylacetate remaining after 60 s is found to be 0.23 mM. What is the initial concentration of phenylacetate in the unknown ... 

When D and H3O+ are present in excess, the kinetics of the reaction are pseudo-first-order in H2O2, and can be used to determine the concentration of H2O2 by following the production of I2 with time. In one analysis the absorbance of the solution was measured after 240 s at 348 nm (where Beer s law holds for I2). When a set of standard solutions of H2O2 was analyzed, the following results were obtained... 

The concentration of chromic acid can be determined from its reduction by alcohols under conditions when the kinetics are pseudo-first-order in analyte. One approach is to monitor the absorbance of the solution at a wavelength of 355 nm. A standard solution of 5.1 X lO " M chromic acid yields absorbances of 0.855 and 0.709 at, 100 s and 300 s, respectively, after the reaction s initiation. When a sample with an unknown amount of chromic acid is analyzed under... 

The following data were collected for a reaction known to be pseudo-first-order in analyte. A, during the time in which the reaction is monitored. 

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