Inverse first order

The oxidation of mercurous ions by thallium (3+) ion shows an inverse first-order dependence on [Hg2+], which means that one Hg2+ ion must be subtracted out in figuring the composition.3 Thus, we have... 

The actual result is this The chains are broken when Cu24 is added. The reaction slows considerably but does not come to a halt. Kinetic studies show that the order with respect to [RM] drops from f to 1 with Cu2+ added and that the order with respect to [02] rises from 0 to 1. One term shows an inverse first-order dependence on [Cu2+], The rate under these conditions became... 

Stability constants as a function of temperature and the calculated complexation enthalpies and entropies of the associated reactions are given in Table II. The results of duplicate experiments at 2.0 M acidity and ionic strength are shown as the last entry in the table. Comparison of the results at 25°C, and 1.0 and 2.0 M acidity indicate an approximate inverse first order stoichiometry in [IT "] for the Kj and acid independence for K2. 

C15-0102. What happens to the rate of a reaction involving CO if the concentration is doubled and the reaction Is (a) first order in CO (b) half order in CO and (c) inverse first order in CO ... 

Extraction rates of zinc (II) and nickel (II) with ethyldithizone, butyldithizone, or hexyldithizone in an organic phase (chloroform, CCI4, w-heptane, or benzene) showed a first-order dependence on the ligand and metal ion concentration and an inverse-first-order dependence on the proton concentration. The results were explained by chelate formation in the interfacial region [59]. The effects of stirring on the distribution equili-... 

The decomposition of ammonia on platinum has a rate expression of this form. The reaction is first order in ammonia and inverse first order in hydrogen. 

The initial concentrations of A and B in the feedstream are each 10 moles/m3. The remainder of the stream consists of inerts at a concentration of 30 moles/m3. The reaction is reversible and substantial amounts of all species exist at equilibrium under the pressure and temperature conditions employed. The forward reaction is first-order with respect to A and first-order with respect to B. At 120 °C the rate constant for the forward reaction is 1.4 m3/ mole-ksec. The reverse reaction is first-order in C, first-order in D, and inverse first-order in B. The rate constant for the reverse reaction is 0.6 ksec-1. 

Rate dependence on carbon monoxide pressure. zero order inverse first order inverse first order inverse first order... 

This mechanistic scheme agrees with the experimental observations of the first order dependences on M(CO)fi and formate concentrations and the inverse first order dependence on CO pressure for the rate of production in the water gas shift reaction catalyzed by M(CO (M = Cr, Mo and W) in the presence of a base sufficiently strong to generate formate from CO by equation 2. 

In the case of M(CO)6 catalysts, where M = Cr, Mo, or W, the kinetics were quite different than observed for Fe(CO)5, exhibiting an important approximately first order rate dependency on the concentration of base, relative to the zero order in concentration of base observed for the Fe(CO)5 system. Furthermore, instead of a zero order rate dependency for Pco, as observed for Fe(CO)5, the M(CO)6 catalysts displayed an inverse first order dependency (/.< ., inhibiting effect). 

Scheme 22. The rate equation for this mechanism is described in (1). The authors determined that the reaction is first-order in allylic carbonate, aniline and catalyst, and inverse first-order in allylamine product. These results are consistent with the proposed mechanism. Thus, iridium-catalyzed allylic substitution is inhibited by product. In addition, the formation of the allyliridium intermediate is disfavored.

Figures 3-21 and 3-22 show results in the ATRP polymerization of styrene using 1-phenylethyl bromide as the initiator, CuBr as catalyst (activator), and 4,4-di-5-nonyl-2,2 -bipyridine as ligand [Matyjaszewski et al., 1997]. Figure 3-21 shows the decrease in monomer concentration to be first-order in monomer, as required by Eq. 3-223. The linearity over time indicates that the concentration of propagating radicals is constant throughout the polymerization. The first-order dependencies of Rp on monomer, activator, and initiator and the inverse first-order dependence on deactivator have been verified in many ATRP reactions [Davis et al., 1999 Patten and Matyjaszewski, 1998 Wang et al., 1997].

Compare Eq. 3-229 with 3-224. The decay in monomer concentration depends on the orders of both initiator and activator initial concentrations with no dependence on deactivator concentration and varies with t2/3 under non-steady-state conditions. For steady-state conditions, there are first-order dependencies on initiator and activator and inverse first-order dependence on deactivator and the time dependence is linear. Note that Eq. 3-229 describes the non-steady-state polymerization rate in terms of initial concentrations of initiator and activator. Equation 3-224 describes the steady-state polymerization rate in terms of concentrations at any point in the reaction as long as only short reaction intervals are considered so that concentration changes are small. 

It follows that the equilibrium constant K is given by kf/kr. The reverse reaction is inverse second order in iodide, and inverse first-order in H+. This means that the transition state for the reverse reaction contains the elements of arsenious acid and triiodide ion less two iodides and one hydrogen ion, namely, H2As03I. This is the same as that for the forward reaction, except for the elements of one molecule of water, the solvent, the participation of which cannot be determined experimentally. The concept of a common transition state for the forward and reverse reactions is called the principle of microscopic reversibility. 

The basic steps in the hydroformylation mechanism do not change in the presence of ligand-modified cobalt, but the kinetics of the reaction is affected.30 First-order dependence of the rate on hydrogen partial pressure and an inverse first-order dependence on CO partial pressure were observed in the unmodified system.36 At high CO pressures the rate is first-order in both alkene and cobalt concentrations. The last, product-forming, step—the cleavage of the acylcobalt... 

A number of striking similarities were observed in the kinetics of Ag11 decomposition in these mineral acids. (1) The rate laws showed second order dependence on Agu and inverse first order dependence on Ag1 concentration. (2) Arrhenius activation energies were all about 46 kj mol-1. (3) Measured rate constants taken under similar conditions of temperature and ionic strength were comparable from one medium to another. 

Although it is clear from Figure 3 that ortAo-hydroxyoximes are able to extract nickel under mildly acidic conditions (a pH value of 4 to 5), the attainment of equilibrium is slow, at least 1 h of phase contacting being required at moderate stirring speeds. The extraction rate shows an inverse first-order dependence on the hydrogen ion concentration,165 however, hence much shorter mixing times are adequate under the ammoniacal conditions used in commercial processes. 

In the unmodified catalyst system (Scheme 1), the rate shows a first-order dependence on hydrogen pressure and an inverse first-order dependence on carbon monoxide pressure, so that the rate is nearly independent of total pressure. The reaction is first order in alkene and first order in cobalt at higher CO pressures. With phosphine-modified cobalt catalysts, the rate-determining step depends on the ligand and the alkene. 

The Ru(III)-catalysed oxidation of o-, m-, and p- hydroxybenzoic acids156-158 with bromamine-B (BAB) in acidic solution showed a first-order dependence on the reductant, BAB, and Ru(III). An inverse first-order dependence with respect to acidity has been observed. Mechanistic aspects have been discussed. 

Rate data for the iodination of pyrazole in aqueous solution showed the reaction to be first-order in both iodine and heterocycle and an inverse first-order [H+] dependence was found over the pH range 5.96-6.74 (64JA2857). A kinetic study of the aqueous iodination of pyrazole coordinated to Ni2+ showed the coordinated ligand to react more rapidly, and a [H+] dependence that differed from that of the free ligand (82JA2460). However, the results of this study should be viewed with caution, as the presence of several nickel-pyrazole complexes in solution necessarily leads to uncertainties about the exact nature of the reactive species. 

Reduction of Ferric Chelates by HSO3 and Formation of Dithionate. FeJ+(EDTA) is reduced by HSO3, producing dithionate and a small amount of S0/2 (24). The rate of reduction of Fe +(EDTA) is first order in [HSO3] and [Fe +(EDTA)], and inversely first order in [Fe2+(EDTA)]. 

Coke formation is inverse first order in H2, 0.75 order in feedstock pressure, and inverse first order in coke already present Ea = 37 kcal/mole. Coking is more pronounced with heavier feedstocks, especially polycyclic hydrocarbons.69 ... 

The mechanism of the oxidative addition of aryl bromides to the bis-P(o-tolyl)3 Pd(0) complex 3 was surprising [196]. It has been well established that aryl halides undergo oxidative addition to L2Pd fragments [197 -200] thus, one would expect oxidative addition of the aryl halide to occur directly to 3 and ligand dissociation and dimerization to occur subsequently. Instead, the addition of aryl halide to [Pd[P(o-tolyl)3]2] occurs after phosphine dissociation, as shown by an inverse first-order dependence of the reaction rate on phosphine concentration and the absence of any tris-phosphine complex in solution [196]. 

The mechanisms of the reductive eliminations in Scheme 5 were studied [49,83], and potential pathways for these reactions are shown in Scheme 6. The reductive eliminations from the monomeric diarylamido aryl complex 20 illustrate two important points in the elimination reactions. First, these reactions were first order, demonstrating that the actual C-N bond formation occurred from a monomeric complex. Second, the observed rate constant for the elimination reaction contained two terms (Eq. (49)). One of these terms was inverse first order in PPh3 concentration, and the other was zero order in PPh3. These results were consistent with two competing mechanisms, Path B and Path C in Scheme 6, occurring simultaneously. One of these mechanisms involves initial, reversible phosphine dissociation followed by C-N bond formation in the resulting 14-electron, three-coordinate intermediate. The second mechanism involves reductive elimination from a 16-electron four-coordinate intermediate, presumably after trans-to-cis isomerization. 

Equation (28) has been called the Langmuir rate law [5], Certain special cases of this equation lead to a variety of different kinetic forms. For example, if all species are only slightly adsorbed, the denominator tends to unity and the reaction becomes simply first-order in each of A and B. On the other hand, if A (and P and Q) is weakly adsorbed and B strongly, the denominator reduces to K cB which converts the reaction into one that is first order in A but inverse first order in B. Strong adsorption of one of the reactants thus denies surface sites to the other reactant and effectively stifles the catalytic process. 

Ruthenium has been investigated by many laboratories as a possible catalyst for ammonia synthesis. Recently, Becue et al. [T. Becue, R. J. Davis, and J. M. Garces, J. Catal., 179 (1998) 129] reported that the forward rate (far from equilibrium) of ammonia synthesis at 20 bar total pressure and 623 K over base-promoted ruthenium metal is first order in dinitrogen and inverse first order in dihydrogen. The rate is very weakly inhibited by ammonia. Propose a plausible sequence of steps for the catalytic reaction and derive a rate equation consistent with experimental observation. 

The oxidation of carbon monoxide on palladium single crystals at low pressures (between 10 and 10 torr) and temperatures ranging from about 450 to 550 K follows a rate law that is first order in O2 and inverse first order in CO. An appropriate sequence of elementary... 

Nitronium ion has been found to catalyse decomposition in strong sulphuric acid solutions . The reaction is found to be first-order in peroxomonosulphuric acid above 95 % sulphuric acid and inverse first-order below 91 %, in addition to second-order dependence, over the whole region, on nitric acid. A mechanism has been proposed. 

The rate is first-order in [I ], first-order in [OCP], and inverse first-order in 10H ]. The inverse dependence on hydroxide suggests a rapid equilibrium preceding a slow step, namely,... 

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