Reaction rates pseudo-first-order reactions

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... 

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

Decomposition of diphenoylperoxide [6109-04-2] (40) in the presence of a fluorescer such as perylene in methylene chloride at 24°C produces chemiluminescence matching the fluorescence spectmm of the fluorescer with perylene was reported to be 10 5% (135). The reaction follows pseudo-first-order kinetics with the observed rate constant increasing with fluorescer concentration according to = k [flr]. Thus the fluorescer acts as a catalyst for peroxide decomposition, with catalytic decomposition competing with spontaneous thermal decomposition. An electron-transfer mechanism has been proposed (135). 

The numerical solution of these equations is shown in Fig. 23-28. This is a plot of the enhancement fac tor E against the Hatta number, with several other parameters. The factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption with zero concentration of A in the liquid. The uppermost line on the upper right represents the pseudo-first-order reaction, for which E = P coth p. 

A parameter such as a rate constant is usually obtained as a consequence of various arithmetic manipulations, and in order to estimate the uncertainly (error) in the parameter we must know how this error is related to the uncertainties in the quantities that contribute to the parameter. For example, Eq. (2-33) for a pseudo-first-order reaction defines k, which can be determined by a semilogarithmic plot according to Eq. (2-6). By a method to be described later in this section the uncertainty in itobs (expressed as its variance associated with cb. Thus, we need to know how the errors in fcobs and cb are propagated into the rate constant k. 

Danckwerts et al. (D6, R4, R5) recently used the absorption of COz in carbonate-bicarbonate buffer solutions containing arsenate as a catalyst in the study of absorption in packed column. The C02 undergoes a pseudo first-order reaction and the reaction rate constant is well defined. Consequently this reaction could prove to be a useful method for determining mass-transfer rates and evaluating the reliability of analytical approaches proposed for the prediction of mass transfer with simultaneous chemical reaction in gas-liquid dispersions. 

In experiments with [sulfone]o = 3.15 x 10 5 M and excess N2H4, the reaction follows pseudo-first-order kinetics. Values of k vary with [N2H4]. Formulate the rate law and evaluate the constants therein ... 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

Example 5.7 A CSTR is commonly used for the bulk pol5anerization of styrene. Assume a mean residence time of 2 h, cold monomer feed (300 K), adiabatic operation UAgxt = ), and a pseudo-first-order reaction with rate constant... 

The chemistry seems fairly simple. The water concentration is high and approximately constant so that the reaction is pseudo-first-order with respect to the epoxy. The rate is also proportional to the hydrogen ion concentration h. Thus,... 

The fact that the rate of silanization is influenced by the moisture content of the sUica supports the mechanism wherein a hydrolysis step is involved. The reaction follows pseudo first-order kinetics. Figure 29.1 shows the mechanism of the primary reaction. 

Fig. 2 shows the plot of ln[(CEcVCEc] vs. time during first 2 h. Quite good straight lines were obtained, and the pseudo first-order reaction rate constants for 120,130 and 140 °C were 0.002421, 0.002481 and 0.002545 h, respectively. From the Arrhenius plot of the first order reaction rate constants, one can estimate the activation energy as 41.5 kJ/mol. 

In this study, the absorption rates of carbon dioxide into the solution of GMA and Aliquat 336 in such organic solvents as toluene, N-methyl-2-pirrolidinone(NMP), and dimethyl sulfoxide(DMSO) was measured to determine the pseudo-first-order reaction constant, which was used to obtain the elementary reaction rate constants. 

From the results of experiment 2.1, we confirmed decomposition reaction is pseudo first-order, and calculated pseudo first-order decomposition rate constants. Then fixnn relationship between each first-order reaction rate constant and sodium hydroxide concentration, we confirmed that the reaction is expressed by second-order with expression first-orders for both of sodium hydroxide and fenitrothion. 

The absorbance data enabled the determination of extraction rate constants. For a pseudo-first-order reaction, the following equation describes the extraction process ... 

The demetalation kinetics of ZnTTP by an acidic aqueous phase have also been reported [61]. In this study, ZnTTP was considered to adsorb at the interface producing Zn and free base porphyrin by proton attack. The demetalation kinetics of ZnTTP were analyzed as a pseudo-first-order reaction, because the proton concentration in the aqueous phase was in large excess. The rate law was found to be described by... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

In aqueous solution the water concentration may be considered constant, so the reverse reaction follows pseudo first-order kinetics. The data below on this reaction have been taken from Emanuel and Knorre. Use them to determine the values of both first-order rate constants. 

Meehan and Bond (23) on the other hand, have taken an opposite view, namely that k3I1(C) k3I(C), while k3II(T) k3I(T). Thus, in this view, the hydrolysis occurs at external binding sites, while covalent binding occurs at intercalation sites. Furthermore, they reject the common intermediate model (Equation 2) on the basis of their belief that the rates of reaction for tetraol formation and adduct formation and the ratio of the products should be the same in such a model. While these rates of reaction are the same and the product ratios are observed to be different, this is fully consistent for a set of parallel pseudo-first order reactions involving a common intermediate (29) as pointed out above. Thus, the data of Meehan and Bond does not demonstrate the validity of the two-domain model (23). 

A mechanism for a pseudo-first-order reaction involving the hydrolysis of substrate S catalyzed by acid HA that is consistent with the observed rate law rs = kohscs, is as follows ... 

A liquid-phase reaction A + B -> 2C is conducted in a nonisothermal multitubular PFR. The reactor tubes (7 m long, 2 cm in diameter) are surrounded by a coolant which maintains a constant wall temperature. The reaction is pseudo-first-order with respect to A, with kA = 4.03 X 105 e 56WT s 1. The mass flow rate is constant at 0.06 kg s-1, the density is constant at 1.025 g cm-3, and the temperature at the inlet of the reactor (TJ is 350 K. 

A pulse-tracer experiment for a particular flow rate in a certain vessel (assume closed ) shows that the first (i) and the second (aj) moments of the RID are 15.4 min and 0.670, respectively. If a pseudo-first-order reaction, A + B products, with fcA = 0.299 min-1 at... 

The alkylation of toluene with acetylene in the presence of sulphuric acid is carried out in a batch reactor. 6000 kg of toluene is charged in each batch, together with the required amount of sulphuric acid and the acetylene is fed continuously to the reactor under pressure. Under circumstances of intense agitation, it may be assumed that the liquid is always saturated with acetylene, and that the toluene is consumed in a simple pseudo first-order reaction with a rate constant of 0.0011 s-1. 

The toluene is consumed in a simple pseudo first-order reaction with a rate constant of 0.0011 s 1... 

If the forward reaction is pseudo first order and the reverse reaction second order, then, as discussed in Sections 1.4.4 and 1.4.5 in Volume 3, the rate equation may be written as ... 

Describe the various mass transfer and reaction steps involved in a three-phase gas-liquid-solid reactor. Derive an expression for the overall rate of a catalytic hydrogenation process where the reaction is pseudo first-order with respect to the hydrogen with a rate constant k (based on unit volume of catalyst particles). 

Tests were performed on pyrolysis of an oil in a heated tubular reactor. The reaction is pseudo first order with an activation energy of 56630 cal/gmol, so the specific rate is represented by... 

A dilute aqueous solution of maleic anhydride is to be continuously hydrolyzed at 25 C. Because of the dilution the reaction is pseudo first order with k = 0.143 gmol/cc-min. A volumetric rate of 530 cc/min is to be processed with inlet concentration of 0,00015 gmol/cc. There are two 2.5 liter and one 5.0 liter stirred vessels available. Find the conversions for various arrangements of these vessels. 

A gas oil is cracked at 630 C and 1 atm by passing vaporized feed through a bed of silica-alumina catalyst spheres with radius 0.088 cm. At a feed rate of 0.2 mol/(h)(cc catalyst bed) conversion was 50%. The reaction is pseudo first order. The effective diffusivity is 0.0008 cm2/s. As an approximation, assume a constant volumetric flow rate. Find the effectiveness of the catalyst. 

A reagent in solution can enhance a mass transfer coefficient in comparison with that of purely physical absorption. The data of Tables 8.1 and 8.2 have been cited. One of the simpler cases that can be analyzed mathematically is that of a pseudo-first order reaction that goes to completion in a liquid film, problem P8.02.01. It appears that the enhancement depends on the specific rate of reaction, the diffusivity, the concentration of the reagent and physical mass transfer coefficient (MTC). These quantities occur in a group called the Hatta number,... 

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