Zero order meaning

Zero Order Zero order, meaning that the rate is independent of the concentration, may occur in two situations when the rate is intrinsically independent of concentration and when the species is in such abundant supply that its concentration is nearly constant during reaction. In the latter case the dependency of the rate on concentration cannot be detected, and apparent zero order prevails. Thus in the oxidation of NO iQ NO2 in the presence of a large excess of O2, the rate is zero order in O - ... 

For a rate law, zero order means that the exponent is zero. In other words, the reaction rate is just equal to a constant it doesn t change as time passes. 

Table 2 Zero-Order Mean Shape Potential of the Stationary Points Relative to Reactants (in kcal/mol)...

The integral under the heat capacity curve is an energy (or enthalpy as the case may be) and is more or less independent of the details of the model. The quasi-chemical treatment improved the heat capacity curve, making it sharper and narrower than the mean-field result, but it still remained finite at the critical point. Further improvements were made by Bethe with a second approximation, and by Kirkwood (1938). Figure A2.5.21 compares the various theoretical calculations [6]. These modifications lead to somewhat lower values of the critical temperature, which could be related to a flattening of the coexistence curve. Moreover, and perhaps more important, they show that a short-range order persists to higher temperatures, as it must because of the preference for unlike pairs the excess heat capacity shows a discontinuity, but it does not drop to zero as mean-field theories predict. Unfortunately these improvements are still analytic and in the vicinity of the critical point still yield a parabolic coexistence curve and a finite heat capacity just as the mean-field treatments do. 

The synnnetry selection rules discussed above tell us whether a particular vibronic transition is allowed or forbidden, but they give no mfonnation about the intensity of allowed bands. That is detennined by equation (Bl.1.9) for absorption or (Bl.1.13) for emission. That usually means by the Franck-Condon principle if only the zero-order tenn in equation (B 1.1.7) is needed. So we take note of some general principles for Franck-Condon factors (FCFs). 

This means that the eonversion is proportional to time. Eigure 3-4 shows plots of the zero order rate equations. Examples of zero order reaetions are the intensity of radiation within the vat for photoehemieal reaetions or the surfaee available in eertain solid eatalyzed gas reaetions. 

Cartesian tensors, i.e., tensors in a Cartesian coordinate system, will be discussed. Three Independent quantities are required to describe the position of a point in Cartesian coordinates. This set of quantities is X where X is (x, X2, X3). The index i in X has values 1,2, and 3 because of the three coordinates in three-dimensional space. The indices i and j in a j mean, therefore, that a j has nine components. Similarly, byi has 27 components, Cp has 81 components, etc. The indices are part of what is called index notation. The number of subscripts on the symboi denotes the order of the tensor. For example, a is a zero-order tensor... 

The rate equation is first-order in acetone, first-order in hydroxide, but it is independent of (i.e., zero order in) the halogen X2. Moreover, the rate is the same whether X2 is chlorine, bromine, or iodine. These results can only mean that the transition state of the rds contains the elements of acetone and hydroxide, but not of the halogen, which must enter the product in a fast reaction following the rds. Scheme VI satisfies these kinetic requirements. 

These two parameters describe the change in fraction unconverted with a percentage change in kt or in c0. The first sensitivity is also the slope of the curves in Fig. 28. The values of these sensitivities are given in Table IX. In a piston flow reactor where the conversion level is c/c0 = 0.1, the value of Stt is —0.23 for the first-order kinetics, —0.90 for the zero-order kinetics, and —4.95 for the negative first-order kinetics. In the stirred tank reactor, the value of the sensitivities Skt is —0.09 for the first-order kinetics, — 0.90 for the zero-order kinetics, and +0.11 for the negative first-order kinetics. A positive sensitivity means that as kt is increased, the fraction unconverted also increases, clearly an unstable situation. 

These simple values for the first few coefficients are the result of our choice of number density and temperature as multiplicative factors in the zero-order distribution function, and of defining the expansion variable in terms of the mean velocity and temperature. 

Note that all the zero-order rate constants are essentially equivalent except those for the poly-hydric alcohols which are exactly half the value of the others. Ingold et al (Ref 49a) interpret this to mean that the rate of attack of nitronium is the same for both OH groups of the glycol molecule. Since there are two such groups the overall rate constant k0 is Vi that for monohydric alcohols. The explanation for the observed k0 for glycerol is more complex. In essence it consists of postulating that the two outside OH s are readily nitrated, ie, the 1-OH is nitrated at the same rate as the 3-OH, but the middle OH is nitrated much more slowly... 

As given above, the statements that adjust the exponents m and n have been commented out and the initial values for these exponents are zero. This means that the program will fit the data to. = k. This is the form for a zero-order reaction, but the real purpose of running this case is to calculate the standard deviation of the experimental rate data. The object of the fitting procedure is to add functionality to the rate expression to reduce the standard deviation in a manner that is consistent with physical insight. Results for the zero-order fit are shown as Case 1 in the following data ... 

Simplifying, 1.0 = (10) how can this be We can treat this mathematically, but examining the data also gives the result. Changing the concentration of NO2 F has no effect on the initial rate, so the rate is independent of [NO2 F]. This means that [NO2 F] does not appear in the rate law. Mathematically, we set Z = 0. The reaction is zero order in NO2 F, and the rate law is as follows ... 

Here the point p belongs to the spherical surface A of radius R. In order to find the upper limit on the left hand side of this equality, let us recall that T is the disturbing potential. In other words, it is caused by the irregular distribution of masses whose sum is equal to zero. This means that its expansion in power series with Legendre s functions does not contain a zero term. The next term is also equal to zero, because the origin coincides with the center of mass. Therefore, the series describing the function T starts from the term, which decreases as r. This means that the product r T O if oo and... 

The reaction (Eqn. 5.4-65) takes place in the liquid phase. The molecules are transferred away from the interface to the bulk of the liquid, while reaction takes place simultaneously. Two limiting cases can be envisaged (1) reaction is very fast compared to mass transfer, which means that reaction only takes place in the film, and (2) reaction is very slow compared to mass transfer, and reaction only takes place in the liquid bulk. A convenient dimensionless group, the Hatta number, has been defined, which characterizes the situation compared to the limiting cases. For a reaction that is first order in the gaseous reactant and zero order in the liquid reactant (cm = 1, as = 0), Hatta is ... 

Other than possibly for the insensible perspiration they absorb, transdermal patches tend to operate as thermodynamically static systems, meaning as com-positionally fixed systems, from the moment they are applied until their removal. Marketed ethanol-driven estradiol and fentanyl patches are exceptions because they meter out ethanol and drive it into the stratum corneum to propel the absorption process. Compositional steadfastness is still the rule, however, and it is this feature that bestows the zero-order delivery attribute on the ordinary transdermal patch. Drug is present within the patches in reservoir amounts whether or not the reservoir compartment is easily distinguished, for there must be enough drug to sustain delivery over the full course of patch wear. 

The data lie on a straight line only for Plot (1), the graph of [HI] vs. t. Therefore, the reaction is zero order with respect to HI. The slope of the line = -0.00546 mM-s-1, using a least mean square regression fitting program. However, the slope can be estimated from any two points on the line. If we use the first and last points ... 

Capsules were equilibrated with a tracer solution overnight. A capsule pellet (0.2-0.5 ml) was then placed in 5 ml test buffer (PBS or RPMI-1640 medium, Gib-co/BRL, New York, NY) on a shaker and a 0.2-ml aliquot was immediately sampled by a screen-protected pipette with further samples being taken over the next 700 s. The tracer quantity was assayed using the methods described below. A final sample was taken after the capsules has been in contact with the buffer for several hours (equilibrated tracer quantity) and the increment to the tracer concentration at each time was calculated. From the progress of tracer to equilibrium on a semilog plot a slope denoted as the zero -order rate flux constant was obtained and has been used as a measure of capsule permeability. [3H] -Glucose (580 daltons),insulin (6.2 kDa), and ovalbumin (45 kDa) have been used as tracers. Radioactivity was measured by means of a Packard 2000CA Liquid Scintillation Counter (Packard Instruments,... 

Derive an equation for calculating the outlet cA or fA for a zero-order reaction, if the inlet concentration IS cAo, and the mean residence time is t. 

If a reaction that must be investigated follows a reaction sequence as in Scheme 10.1, and if the reaction order for the substrate equals unity, it means that (with reference to Eq. (4 b)), the observed rate constant (k0bs) is a complex term. Without further information, a conclusion about the single constants k2 and fCM is not possible. Conversely, from the limiting case of a zero-order reaction, the Michaelis constant cannot be determined for the substrate. For particular questions such as the reliable comparison of activity of various catalytic systems, however, both parameters are necessary. If they are not known, the comparison of catalyst activities for given experimental conditions can produce totally false results. This problem is described in more detail for an example of asymmetric hydrogenation (see below). 

No general discussion of the multitude of behaviour patterns, especially as regards dependence on concentration of catalyst, or of components of a syncatalyst, can be profitable at this stage. As for the termination reactions - our special concern here - this kinetic pattern implies that Vt is of first order, Vt of zero order, with respect to monomer. This means that k3 or k4 contain a term k iplky, they may also contain one or more equilibrium constants - depending on the nature of the catalytic system. 

The rate of chemical attack will depend on the concentration according to the order of the reaction (i.e. in a zero-order reaction the rate is independent of concentration, in a first-order reaction the rate depends linearly on concentration, and in second-order reaction the rate depends on the square of concentration). Increasing the concentration, therefore, provides a means of acceleration. Remember, however, that chemical attack on plastics is a liquid-solid and not a liquid-liquid reaction, such that the reaction laws only hold if there is free movement of all chemical species with no limitations due to diffusion or transport and no barrier layers. Since this is rarely the case, temperature is preferred as a means of acceleration. 

In this expression, k is the rate constant—a constant for each chemical reaction at a given temperature. The exponents m and n, called the orders of reaction, indicate what effect a change in concentration of that reactant species will have on the reaction rate. Say, for example, m = 1 and n = 2. That means that if the concentration of reactant A is doubled, then the rate will also double ([2]1 = 2), and if the concentration of reactant B is doubled, then the rate will increase fourfold ([2]2 = 4). We say that it is first order with respect to A and second order with respect to B. If the concentration of a reactant is doubled and that has no effect on the rate of reaction, then the reaction is zero order with respect to that reactant ([2]° = 1). Many times the overall order of reaction is calculated it is simply the sum of the individual coefficients, third order in this example. The rate equation would then be shown as ... 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

If the total A+B component of the MQW is less than about 0.25 m, then the zero-order peak does not appear and dynamical-theory simulation must be used to determine the mean composition. 



---