Reactant zero-order

The ability to assign a group of resonance states, as required for mode-specific decomposition, implies that the complete Hamiltonian for these states is well approxmiated by a zero-order Hamiltonian with eigenfunctions [M]. The ( ). are product fiinctions of a zero-order orthogonal basis for the reactant molecule and the quantity m. represents the quantum numbers defining ( ).. The wavefimctions / for the compound state resonances are given by... 

The power to which the concentration of reactant A is raised in the rate expression is called the order of the reaction, m. If tn is 0, the reaction is said to be zero-order If m = 1, the reaction is first-order if mi = 2, it is second-order and so on. Ordinarily, the reaction order is integral (0,1,2,...), but fractional orders such as are possible. 

In a zero-order reaction, all the reactant is consumed in a finite time. 

Zero order reaction A reaction whose rate is independent of reactant concentration, 289,295-298, 317q Zinc, 86-87,550 Zn-Cn2+ voltaic cell, 481-485 Zwitterion Form of an amino acid in which there is a separation of charge between the nitrogen atom of the NH2 group (+) and one of the oxygen atoms of the COOH group (—), 623-624... 

Zero-order kinetic behaviour, in an unusual dehydration reaction [62], has been shown to be due to the constant area of reaction interface and this interface has been identified as original surfaces of the reactant crystallites which do not advance. Water molecules are mobile within the... 

Thus in Table 4.3 we add to Table 4.2 the last, but quite important, available piece of information, i.e. the observed kinetic order (positive order, negative order or zero order) of the catalytic reaction with respect to the electron donor (D) and the electron acceptor (A) reactant. We then invite the reader to share with us the joy of discovering the rules of electrochemical promotion (and as we will see in Chapter 6 the rules of promotion in general), i.e. the rules which enable one to predict the global r vs O dependence (purely electrophobic, purely electrophilic, volcano, inverted volcano) or the basis of the r vs pA and r vs pD dependencies. 

Inspection of Table 6.1 shows the following rule for electrophobic reactions Rule Gl A reaction exhibits purely electrophobic behaviour ((dr/dO)PA 0) when the kinetics are positive order in the electron donor (D) reactant and negative or zero order in the electron acceptor (A) reactant. 

FIGURE 13.9 (a) The concentration of the reactant in a zero-order reaction falls at a constant rate until the reactant is exhausted. 

The integrated rate law for a zero-order reaction is easy to find. Because the rate is constant (at k), the difference in concentration of a reactant from its initial value, [A]0, is proportional to the time for which the reaction is in progress, and we can write... 

More usually, the participation of adsorbed reactants and intermediates is inferred indirectly from kinetic data (Bockris, 1954). Thus the observation of reactions having a low or zero order with respect to the reactant concentration implies adsorption of the reactant. A reaction scheme... 

If the reaction order does not change, reactions with n < 1 wiU go to completion in finite time. This is sometimes observed. Solid rocket propellants or fuses used to detonate explosives can bum at an essentially constant rate (a zero-order reaction) until all reactants are consumed. These are multiphase reactions limited by heat transfer and are discussed in Chapter 11. For single phase systems, a zero-order reaction can be expected to slow and become first or second order in the limit of low concentration. 

Finally, although rare, we mention the occurrence of zero-order reactions. The special case of a pseudo-zero order reaction arises if a reactant is present in large excess, and the reaction does not noticeably change the concentration of the reactant. The differential and integral rate equations for a zero-order reaction R —> P are... 

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 ... 

Hatta number = (k DAlkuA) for first order reaction in the gaseous reactant and zero order in the liquid reactant... 

Most biological reactions fall into the categories of first-order or second-order reactions, and we will discuss these in more detail below. In certain situations the rate of reaction is independent of reaction concentration hence the rate equation is simply v = k. Such reactions are said to be zero order. Systems for which the reaction rate can reach a maximum value under saturating reactant conditions become zero ordered at high reactant concentrations. Examples of such systems include enzyme-catalyzed reactions, receptor-ligand induced signal transduction, and cellular activated transport systems. Recall from Chapter 2, for example, that when [S] Ku for an enzyme-catalyzed reaction, the velocity is essentially constant and close to the value of Vmax. Under these substrate concentration conditions the enzyme reaction will appear to be zero order in the substrate. 

Initially, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A and B. However, given that all the reaction stoichiometric coefficients are unity, and the initial reaction mixture has equimolar amounts of A and B, it seems sensible to first try to model the kinetics in terms of the concentration of A. This is because, in this case, the reaction proceeds with the same rate of change of moles for the two reactants. Thus, it could be postulated that the reaction could be zero order, first order or second order in the concentration of A. In principle, there are many other possibilities. Substituting the appropriate kinetic expression into Equation 5.47 and integrating gives the expressions in Table 5.5 ... 

The MO concentrations versus time profiles were fitted to second order polynomial equations and the parameters estimated by nonlinear regression analysis. The initial rates of reactions were obtained by taking the derivative at t=0. The reaction is first order with respect to hydrogen pressure changing to zero order dependence above about 3.45 MPa hydrogen pressure. This was attributed to saturation of the catalyst sites. Experiments were conducted in which HPLC grade MIBK was added to the initial reactant mixture, there was no evidence of product inhibition. 

Write a rate law equation for each of the following (a) A reaction first order with respect to A and second order with respect to B. (b) A reaction zero order with respect to A and second order with respect to B. (c) A reaction first order with respect to A and first order with respect to B. (d) A reaction second order with respect to B, its only reactant. 

Generally, however, it is the order with respect to a particular reactant (or reactants) that is of more interest and significance than the overall order, i.e. that the above reactions are first order, second order, and second order, respectively, with respect to A. Examples of both zero order, and non-integral orders, with respect to a particular reactant are also known. 

If the surface is nearly covered (0A 1) the reaction will be first-order in the gas phase reactant and zero-order in the adsorbed reactant. On the other hand, if the surface is sparsely covered (0A KAPA) the reaction will be first-order in each species or second-order overall. Since adsorption is virtually always exothermic, the first condition will correspond to low temperature and the second condition to high temperatures. This mechanism thus offers a ready explanation of a transition from first-to second-order reaction with increasing temperature. 

Fig. 16 (a) R (D + RX) and P (D,+ + R + X ) zero-order potential energy surfaces. Rc and Pc are the caged systems, (b) Projection of the steepest descent paths on the X-Y plane J, transition state of the photoinduced reaction j, transition state of the ground state reaction W, point where the photoinduced reaction path crosses the intersection between the R and P zero-order surfaces R ., caged reactant system, (c) Oscillatory descent from W to J on the upper first-order potential energy surface obtained from the R and P zero-order surfaces. 

In contrast to the other reaction orders, the velocity of a zero-order reaction does not change with the concentration of the substrate or with time (Fig. 24-6). The velocity (slope) is a constant and k has the units molar per minute (M/min, or M min ). Reactions that are zero-order in absolutely everything are rare. However, it is common to have reactions that may be zero-order in the reactant that you happen to be watching. Let s think of a two-step reaction. 

X-ray powder diffractometry can be used to study solid state reactions, provided the powder pattern of the reactant is different from that of the reaction product. The anhydrous and hydrated states of many pharmaceutical compounds exhibit pronounced differences in their powder x-ray diffraction patterns. Such differences were demonstrated earlier in the case of fluprednisolone and carbamazepine. Based on such differences, the dehydration kinetics of theophylline monohydrate (CvHgN H20) and ampicillin trihydrate (Ci6H19N304S 3H2O) were studied [66]. On heating, theophylline monohydrate dehydrated to a crystalline anhydrous phase, while the ampicillin trihydrate formed an amorphous anhydrate. In case of theophylline, simultaneous quantification of both the monohydrate and the anhydrate was possible. It was concluded that the initial rate of this reaction was zero order. By carrying out the reaction at several... 

Major differences were noted between the systems derived from Fe(CO)c and M(CO) (M = Cr, Mo, and W) with respect to the effect of the base concentration on the reaction rate. Thus in the case of the catalyst system derived from Fe(CO)5 tripling the amount of KOH while keeping constant the amounts of the other reactants had no significant effect on the rate of H2 production (11). However, in the case of the catalyst system derived from W(CO)g the rate of production increased as the amount of base was increased regardless of whether the base was KOH, sodium formate, or triethylamine (12). This increase may be interpreted as a first order dependence on base concentration provided some solution non-ideality is assumed at high base concentrations. Similar observations were made for the base dependence of H2 production in catalyst systems derived from the other metal hexacarbonyls Cr(CO) and Mo(CO) (12). Thus the water gas shift catalyst system derived from Fe(CO)5 has an apparent zero order base dependence whereas the water gas shift catalyst systems derived from M(CO)g (M - Cr, Mo, and W) have an approximate first order base dependence. Any serious mechanistic proposals must accommodate these observations. 

Studies analyzing the effects of the remaining reactants, H20 and C6HsCH0 indicate that the reaction appears to be zero order with respect to both reactants. It is interesting that in previous work we also found similar behavior for H20 in ruthenium catalyzed hydroformylation (12), as did Ungermann et al. with the WGSR (14). 

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