Pseudo Order Conditions

If we run the same readion starting from a 200 1 mole/mole mixture of A and B, the change in [A] will never be more than 0.5%, because even at full conversion there will still be 199 equivalents of A left. This means that [A] = [A]0, giving a pseudo first-order readion profile that depends only on [B]. In the corresponding rate equation (Eq. (2.57)), the pseudo first-order constant k = k[A]0. Pseudo order conditions are very useful for isolating the contribution of a chemical species to the rate-determining step. 

Note that the definition of a large excess depends on your analytical method. The excess must be sufficiently large for the change in concentration to be within the experimental error range. For example, when using GC analysis, the total measurement error may be 1%. In this case, a 100-fold excess will work just as well as a 1000-fold excess. 

---

Use of the isolation or pseudo-order technique. This approach is discussed in Chapter 2, where it was shown how a second-order reaction could be converted to a pseudo-first-order reaction by maintaining one of the reactant concentrations at an essentially eonstant level. The same method may be usefully applied to eomplex reactions. In this way, for example. Scheme XI can be studied under conditions such that it functions as Scheme IX. A corollary that must be kept in mind is that a reaction system that is observed to behave in accordance with (as an example) Scheme IX may actually be more complex than it appears to be, if an unsuspected reactant is present under pseudo-order conditions. 

A study of this system often is carried out with pseudo-order conditions relative to D. Then the apparent second-order rate constant is given by Eq. (3-146). 

Orders with respect to two reactants are required. Look to see whether there are any experiments where one substance is at the same pressure, while the pressure of the other reactant is altered, i.e. look for pseudo-order conditions. 

The reaction is catalysed by acids, but during the experiment quoted [acid] remains constant, and reaction is being carried out under pseudo-order conditions. 

Toluene is both a reactant and the solvent, and so the toluene will always be in excess, and again reaction is carried out under pseudo-order conditions. 

In 1981, Fedotov et al. reported the observed rate constants for exchange of the different oxygens in PWi2O403- and PV v Wi2 V04(/3 V) (X 1 4) under pseudo-order conditions in H20 by O NMR at two different temperatures (20 °C and 70 °C). Unfortunately, neither the POM concentrations nor the pH values were stated, and the exchange rates could well vary with these parameters. Given this uncertainty, however, the following reactivity order and rates of... 

Initiation is generally determined by a kinetic measurement made under standard, pseudo-order conditions with a large excess of a reactive alkene. Ethyl vinyl ether (EVE) or butyl vinyl ether (BuVE) are widely used and acceptable for this purpose because there is no significant metathesis from the resultant stable, ruthenium Fischer-carbene complexes [13]. The initiation rate can be easily determined by NMR spectroscopy or by monitoring changes in the UV-vis spectrum. If analysis... 

Under pseudo first-order conditions (excess 2.5) k is given by d[2.Al... 

It may even be possible to adjust conditions such that measurements are made under pseudo-zero-order conditions where... 

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... 

A variation on the use of pseudo-ordered reactions is the initial rate method. In this approach to determining a reaction s rate law, a series of experiments is conducted in which the concentration of those species expected to affect the reaction s rate are changed one at a time. The initial rate of the reaction is determined for each set of conditions. Comparing the reaction s initial rate for two experiments in which the concentration of only a single species has been changed allows the reaction order for that species to be determined. The application of this method is outlined in the following example. 

Flooding and Pseudo-First-Order Conditions For an example, consider a reaction that is independent of product concentrations and has three reagents. If a large excess of [BJ and [CJ are used, and the disappearance of a lesser amount of A is measured, such flooding of the system with all components butM permits the rate law to be integrated with the assumption that all concentrations are constant except A. Consequentiy, simple expressions are derived for the time variation of A. Under flooding conditions and using equation 8, if x happens to be 1, the time-dependent concentration... 

Using pseudo-first order conditions with [SjO I ] = 1.8x10 and [Fe(CN)g ] = 6.5x10 M, the following absorbances were recorded at 25°C ... 

Table 2-4 gives data for the alkaline hydrolysis of phenyl cinnamate under pseudo-first-order conditions, with calculations made in order to apply the Guggenheim method. The plot according to Eq. (2-55) is shown in Fig. 2-9. From the slope the pseudo-first-order rate constant is 3.37 x 10 s . ... 

If pseudo-first-order conditions can be established, for example, by setting Cb Ca, then Scheme II collapses to Scheme III,... 

If pseudo-first-order conditions do not apply, the Scheme II rate equation is... 

Scheme VII constitutes an equivalent system if the concentration of reagent R is much larger than the reactant concentrations, so that we have pseudo-first-order conditions.

Any combination of first-order reactions can be simulated by extension of this procedure. Reversible reactions add only the feature that reacted species can be regenerated from their products. Second-order reactions introduce a new factor, for now two molecules must each be independently selected in order that reaction occur in the real situation the two molecules are in independent motion, and their collision must take place to cause reaction. We load the appropriate numbers of molecules into each of two grids. Now randomly select from the first grid, and then, separately, randomly select from the second grid. If in both selections a molecule exists at the respective selected sites, then reaction occurs and both are crossed out if only one of the two selections results in selection of a molecule, no reaction occurs. (Of course, if pseudo-first-order conditions apply, a second-order reaction can be handled just as is a first-order reaction.)... 

Considering the attention that we have given in this chapter to concentrationtime curves of complex reactions, it may seem remarkable that many kinetic studies never generate a comprehensive set of complicated concentration-time data. The reason for this is that complex reactions often can be studied under simplified conditions constituting important special cases for example, whenever feasible one chooses pseudo-first-order conditions, and then one studies the dependence of the pseudo-first-order rate constant on variables other than time. This approach is amplified below. 

First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu-... 

In some cases the alkoxide ions have been used in large excess under pseudo-first-order conditions. ... 

An interesting kinetic study was carried out under pseudo-first-order conditions for the base hydrolysis of the three isomeric N-methyl-cyanopyridinium salts, a reaction that leads partly to CN replacement and partly to the formation of a carboxamido derivative. ... 

Reactions with uncharged species such as amines, alcohols, and water offer frequent opportunities for investigations under pseudo-first-order conditions since many of these reagents are suitable solvents. However, the reactions with amines have often been investigated in alcohols and in non-hydroxylic solvents 27-29a have been found to follow second-order kinetics. 

Probably no reaction is truly zeroth-order. However, one might employ a very high concentration of the species on which the rate does depend to create pseudo-zeroth-order conditions. If the rate is independent of the limiting reagent, A, it is given by... 

Kinetic measurements were performed on a Hitachi 150-20 UV/VIS spectrophotometer. Dehydrobrominations were studied in DMF solution using cyclohexyl amine (CHA) as the base. Applied CHA concentrations were 2, 2.5, 3, 3.5, 4 and 5 10 3 mole.dm-3, initial concentration of 1 was 5 10 5 mole.dm-3 in every case (pseudo-first-order conditions). Ionic strength was adjusted to lO l mole.dm 3 with potassium nitrate. Kinetic curves / D(t) / were recorded at fix wavelength, X = 290 ran and the temperature was maintained at 30, 35.5, 40°C. Stock solutions were made daily for la and freshly for every measurement of Ih. The reaction was started by injection of solution of 1 to the thermostated solution of CHA. 

Kinetic studies of the hydride cluster [W3S4H3(dmpe)3] with acids in a non-coordinating solvent, i.e., dichloromethane, under the pseudo-first-order condition of acid excess, show a completely different mechanism with three kineti-cally distinguishable steps associated to the successive formal substitution of the coordinated hydrides by the anion of the acid, i.e., Ch in HCl [37]. The first two kinetic steps show a second-order dependence with the acid concentration. 

Figure A1.5 Concentration of [El] (A) and of free inhibitor, [/]f, (B) as a function of time for a binding reaction run under pseudo—first-order conditions.

---