Reactions involving a single reactant

For a second-order reaction involving a single reactant, such as acetaldehyde (recall Example 11.1),... 

We start with an ideal, porous, spherical catalyst particle of radius R. The catalyst is isothermal and we consider a reaction involving a single reactant. Diffusion is described macroscopically by the first and second laws of Pick, stating that... 

A test of the Lindemann mechanism is normally applied to observed apparent first-order kinetics for a reaction involving a single reactant, as in A - P. The test may be used in either a differential or an integral manner, most conveniently by using results obtained by varying the initial concentration, cAo (or partial pressure for a gas-phase reaction). In the differential test, from equations 6.4-20 and -20a, we obtain, for an initial concentration cAo = cM, corresponding to the initial rate rPo,... 

Compared with the previous example involving Rh-catalysed phenylation of cyclohexenone, the mechanistic investigation presented in this section involves a much less direct approach. This arises from the nature of the cyclo-isomerisation reaction, involving a single reactant and rather unstable intermediates. It is thus hard to manipulate the resting state of the catalytic cycle in order to facilitate direct study, e.g. by NMR, although Widenhoefer has... 

Most reactions involving a single reactant show either first-order or second-order kinetics. However, sometimes such a reaction can be a zero-order reaction. The rate law for a zero-order reaction is... 

General Case. The general rate equation for a reaction involving a single reactant is... 

The implication is that this is an elementary reaction involving a single reactant molecule. No other species appear to take part, which would seem to rule out the possibilities of collisions, and yet energy will certainly be required to break the C—Cl bond the reactant molecule will not simply fall apart of its own volition. 

Reactions involving a single reactant, say A, can be written in the general form uA = products... 

The half-life for a chemical reaction involving a single reactant can be defined as the time it takes for the concentration of the reactant to fall to one-half of its initial value. (It is important to note that it is not equivalent to one-half the time required for the reaction to go to completion.)... 

As an example of a reaction involving a single reactant, we can consider the gas-phase decomposition of NO2 at 300 °C which we have already discussed in Section 3.3, Equation 3.4... 

The crucial point about this equation is that the rate of reaction now depends only on the concentration of Br in other words the kinetic contribution of this reactant has been isolated by arranging for the concentration of CIO" to be in large excess. The form of the expression is exactly the same as that which would be proposed for a reaction involving a single reactant. Hence, the various methods available for determining the partial order for a single-reactant process (Section 5.3) can be applied in an identical way in order to determine p. 

Understand how integrated rate equations can be used either to determine, or confirm, whether a reaction involving a single reactant is first- or second-order overall. (Question 5.2 and Exereise 5.2)... 

For a reaction involving a single reactant, the rate, R, can generally be written as... 

Indeed, according to the general equation of transition-state theory (2.4.26) adapted to the case of a homogeneous reaction involving a single reactant A, we can write ... 

In Section 3.1.5 we explored the thermodynamics of a simple reaction involving a single reactant A going to a single product B. The ratio of A and B at equilibrium reflects their intrinsic stabilities at their standard states. The intrinsic stabilities are expressed as AG° values, which are indicative of the energy it would take to convert one mole of A to B if A started at its standard state and B ended at its standard state. The ratio of A to B at equilibrium is constant for any initial concentration of the reactant ([A]o). For example, for a reaction with an equilibrium constant K of 10 and an initial concentration [A]o of 11 mM, at equilibrium there will be lOmMB and 1 mM A, because 10/1 = 10. If the initial concentration of A was 2.2 xM, then at equilbrium there will be 2 )jlM B and 0.2 xM A, because 2/0.2 = 10. We now explore how a reaction such as that given in Eq. 4.1 differs. 

Table 13.1. Specific solutions for reactions involving a single reactant...

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