Kinetics linear

This limit is called linear kinetics. On the other hand, if the surface overpotential is large, one of the exponential terms is negligible. This limit is called Tafel kinetics. The relationship was found empirically. In the anodic Tafel region... 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

The chemistry in this case is the irreversible conversion of A to B, which follows simple, linear kinetics. When we write the time-dependent mass balances for this system we have ... 

First, we begin by solving for the concentrations with linear kinetics, and we do this in complete form. We will do this with DSolve as an exercise, even though the equations are... 

When we solved the transient, well-mixedbatch reactor with linear kinetics, we obtained the same solution functionally, but instead of kab x, we had kabt as the argument of the... 

AT is the change in kinetic energy, made up of a change in linear kinetic energy and rotational kinetic energy. 

In some circumstances, the reaction rates may not be exactly parabolic, and even initially parabolic rates may be influenced by changes within the oxide scale with time. As an oxide scale grows, the build-up of inherent growth stresses, externally applied strains and chemical changes to either oxide scale or metal may all compromise the initial protection offered by the scale, leading to scale breakdown and ultimately partial or complete loss of protection paralinear, or linear kinetics may ensue. In other circumstances, as will be seen later in this chapter, very small additions of contaminants to... 

Ward et a/."" have shown that, under cyclical loading, the oxidation rate of steels is similar to that under unstressed isothermal conditions, provided the fatigue stress is below the stress required to exceed the scale failure strain. If, however, the failure strain is exceeded, the oxidation rate is accelerated due to repetitive scale failure, and linear kinetics are observed. 

In sulphur dioxide linear kinetics are generally observed due to control by phase boundary reactions, i.e. adsorption of SOj. RahmeF suggested that this is one of the conditions which favours simultaneous nucleation of sulphide and oxide at the gas/scale interface. The main reaction products are NiO, NijSj, Ni-S,j, and NiS04, depending on the temperature and gas pressure for example, according to the following reaction ... 

The kinetics of alkylation by triphenylmethyl compounds have been studied. Hart and Cassis353 found that the alkylation of phenol and o-cresol by triphenylmethyl chloride in o-dichlorobenzene gave non-linear kinetic plots which were, however, rendered linear by presaturation of the reaction mixture with hydrogen chloride, precise third-order kinetics, equation (182)... 

Visual proof of linear kinetics, making obvious the occurrence of undesirable conditions such as substrate depletion or lag phase non-linearity. Visual display of changes in the reaction rate. Maximum accuracy as the measurement can be made in the region of maximum linear velocity. 

The model assumes a well-mixed gas phase composition in the recycle loop, a well justified assumption in view of the very high (10-200) recycle ratio values used in the present work. For the batch electrocatalytic version we also neglect volume changes and assume linear kinetics for steps 1,3 and 4 of the consecutive OCM network (1), i.e. ... 

A. Rescigno, Mathematical foundations of linear kinetics. In Pharmacokinetics Mathematical and Statistical Approaches to Metabolism and Distribution of Chemicals and Drugs. (J. Eisenfeld and M. Witten, Eds.), North-Holland, Amsterdam, 1988. 

Fig. 1.16. The qualitative type of dependencies ait) (curve 1) and flit) (curve 2) in case of linear kinetics of chemisorption of donors.

Simple hydrodynamic analysis of the in vitro mechanism indicates that the elution concentration, in the absence of absorption, is a linear kinetic process, with a release profile that scales as the ratio of the tear production to the volume of the tear reservoir, fV/f V. Specifically ... 

WASP/TOXIWASP/WASTOX. The Water Quality Analysis Simulation Program (WASP, 3)is a generalized finite-difference code designed to accept user-specified kinetic models as subroutines. It can be applied to one, two, and three-dimensional descriptions of water bodies, and process models can be structured to include linear and non-linear kinetics. Two versions of WASP designed specifically for synthetic organic chemicals exist at this time. TOXIWASP (54) was developed at the Athens Environmental Research Laboratory of U.S. E.P.A. WASTOX (55) was developed at HydroQual, with participation from the group responsible for WASP. Both codes include process models for hydrolysis, biolysis, oxidations, volatilization, and photolysis. Both treat sorption/desorption as local equilibria. These codes allow the user to specify either constant or time-variable transport and reaction processes. 

Marcus AH. 1985b. Multicompartment kinetic models for lead II. Linear kinetics and variable absorption in humans without excessive lead exposure. Environ Res 36 459-472. 

P sh2+ va ues to be calculated from the kinetic plots by curve-fitting 258 for instance, the quite reasonable value of —1.038 0.090 was obtained for [16]. The resulting linear kinetic plots according to equation (54), i.e. assuming full substrate protonation, are shown in Fig. 15. 

Mahaney, J. E., Thomas, D. D. and Froehlich, J. P. The time-dependent distribution of phosphorylated intermediates in native sarcoplasmic reticulum Ca2+-ATPase from skeletal muscle is not compatible with a linear kinetic model. Biochemistry 43 4400-4416, 2004. 

This approach assumes that fe is known, the change in CL and k are proportional to CLcr, renal disease does not alter drug metabolism, any metabolites are inactive and nontoxic, the drug obeys first-order (linear) kinetic principles, and the drug is adequately described by a one-compartment model. The kinetic parameter/dosage adjustment factor (Q) can be calculated as ... 

The E-Z Solve software may also be used to solve Example 12-7 (see file exl2-7.msp). In this case, user-defined functions account for the addition of fiesh glucose, so that a single differential equation may be solved to desenbe the concentration-time profiles over the entire 30-dry period. This example file, with die user-defined functions, may be used as the basis for solution of a problem involving the nonlinear kinetics in equation (A), in place of the linear kinetics in (B) (see problem 12-17). 

The SFM is applied to a (single-stage) CSTR in Chapter 14, to a PFR in Chapter 15, and to an LFR in Chapter 16. In these cases, E(t) is known in exact analytical form. It is shown that the SFM gives equivalent results for a PFR and an LFR for any kinetics. For a CSTR, however, it gives an equivalent result only for first-order (i.e., linear) kinetics. This raises the question as to the usefulness of the SFM both for arbitrary kinetics and for arbitrary flow through a vessel. We first consider two methods of using equation 13.5-2 in conjunction with discrete experimental tracer data from a pulse input. 

A brief overview on why most of the autoxidation reactions develop complicated kinetic patterns is given in Section II. A preliminary survey of the literature revealed that the majority of autoxidation studies were published on a small number of substrates such as L-ascor-bic acid, catechols, cysteine and sulfite ions. The results for each of these substrates will be discussed in a separate section. Results on other metal ion mediated autoxidation reactions are collected in Section VII. In recent years, non-linear kinetic features were discovered in some systems containing dioxygen. These reactions form the basis of a new exciting domain of autoxidation chemistry and will be covered in Section VIII. 

The oxidation of benzaldehyde with dioxygen in the presence of Co(II) and bromide ion also shows non-linear kinetic phenomena. The net reaction of the oxidation process is given as follows ... 

In later work, Roelofs and co-workers discovered further details of the reaction by investigating the sub-systems, and they suggested a 21 step chemical model (RWJ model) to explain the observed non-linear kinetic patterns (163). According to the experimental observations, the oscillation process can be divided into two distinct alternating stages, the stoichiometries of which can be approximated as follows ... 

A distinction is to be drawn between situations in which (a) the flow pattern is known in detail (b) only the residence time distribution is known or can be calculated from tracer response data. Different networks of reactor elements can have similar RTDs, but fixing the network also fixes the RTD. Accordingly reaction conversions in a known network will be unique for any type of rate equation, whereas conversions figured when only the RTD is known proceed uniquely only for linear kinetics, although they can be bracketed in the general case. 

Linear combination of atomic orbitals (LCAO) method, 16 736 Linear condensation, in silanol polycondensation, 22 557-558 Linear congruential generator (LCG), 26 1002-1003 Linear copolymers, 7 610t Linear density, 19 742 of fibers, 11 166, 182 Linear dielectrics, 11 91 Linear elastic fracture mechanics (LEFM), 1 509-510 16 184 20 350 Linear ethoxylates, 23 537 Linear ethylene copolymers, 20 179-180 Linear-flow reactor (LFR) polymerization process, 23 394, 395, 396 Linear free energy relationship (LFER) methods, 16 753, 754 Linear higher a-olefins, 20 429 Linear internal olefins (LIOs), 17 724 Linear ion traps, 15 662 Linear kinetics, 9 612 Linear low density polyethylene (LLDPE), 10 596 17 724-725 20 179-211 24 267, 268. See also LLDPE entries a-olefin content in, 20 185-186 analytical and test methods for,... 

Upon the administration of 1 gram of an aminoglycoside every 12 hours, the Cmj v, was found to be 8 mcg/mL. The plasma concentration at time zero was 63 mcg/mL and elimination rate constant was 0.14 hour 1. If it is desired to increase the Cmin ss to 10 mcg/mL, what should be the dose of the drug, and the new Cmax ss Assume that the drug follows linear kinetics. 

When a single 25-mg bolus dose of an antibiotic is given, the C0 was found to be 2.5 mcg/mL and the elimination half-life was 2.5 hours. What would be the dose required to achieve a new minimum steady-state concentration of 0.45 mcg/mL with a dosing interval of 6 hours Also what would be the new maximum steady-state concentration Assume that the antibiotic follows linear kinetics ... 

Intravenous bolus dose of a 500-mg dose of an antibiotic every six hours in a patient produces minimum steady-state concentration of 10 meg/ mL. If the desired minimum steady-state concentration in this patient is 16 mcg/mL, calculate the size of dose needed to change this concentration. Assume that the drug follows linear kinetics. 

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