Partial orders of reaction

A mathematical expression (usually in the form of a differential rate equation) showing how the rate of the reaction depends on the concentrations of chemical entities and rate constants (and/or equilibrium constants) and any partial orders of reactions. See Chemical Kinetics... 

Order of reaction, n (SI unit 1) — If the macroscopic (observed, empirical, or phenomenological) - reaction rate, v, for any reaction can be expressed by an empirical differential rate equation, which contains a factor of the form k[A] [B]. .. (expressing in full the dependence of the rate of reaction on the concentrations [A], [B]. ..), where a and /3 are constant exponents (independent of concentration and time) and k is the rate constant (rate coefficient) independent of [A] and [B] etc., then the reaction is said to be of order a with respect to A, of order f3 with respect to B, etc., and of (total or overall) order n = a + 13 +. .. The exponents a, /3, etc. can be positive or negative integral or rational nonintegral numbers. They are the reaction orders with respect to A, B, etc., and are sometimes called partial orders of reaction. Orders of reaction deduced from the dependence of initial rates of reaction on concentration are called orders of reaction with respect to concentration orders of reaction deduced from the dependence of the rate of reaction on time of reaction are called orders of reaction with respect to time . 

For a simple (elementary) reaction, a partial order of reaction is the same as the -> stoichiometric number of the reactant concerned and must, therefore, be a positive integer (see - reaction rate). The overall order is then the same as the molecularity. For stepwise reactions there is no general connection between stoichiometric numbers and partial orders. Such reactions may have more complex rate laws, so that an apparent order of reaction may vary with the concentrations of the chemical species involved and with the progress of the reaction in such cases it is not useful to use the orders of reaction terms, although apparent orders of reaction may be deducible from initial rates. In a stepwise reaction, orders of reaction may in principle always be assigned to the elementary steps. 

We remember that these equations are valid if 3 < Ha . To determine the interfacial area in a gas-liquid reactor, it is necessary to know the partial orders of reaction m, n, and q in the range of the operating conditions. Values of these orders from the literature, given in Table XVI, show large discrepancies for closely similar experimental conditions. For example, the value of n may be 1 or 2, or may vary continuously from 1 to 2. 

In the relation (8.19) a, p,. .. are partial orders of reaction. Their sum gives the global order of reaction n = a + P +. If the reference component is A then the reaction rate is expressed in general by the following relation ... 

Note that the partial orders of reaction a, p,. .. correspond to the stoichiometric coefficients only for elementary reactions. In the case of non-elementary reactions the apparent orders of reactions are different from stoichiometric coefficients, and more than one reaction step must be considered to explain the reaction mechanism. 

The powers to which the concentration terms are raised in Equation 4.8 are known as partial orders of reaction. Thus a is the partial order of reaction with respect to reactant A, p is the partial order of reaction with respect to reactant B, yis the partial order of reaction with respect to reactant C, and so on. The overall order of reaction (n) is defined by the sum of the partial orders... 

It is often, but not always, the case that the partial orders of reaction turn out to be small integers. If the partial order for a reactant is either 1 or 2, then the reaction is referred to as being first-order or second-order in that particular reactant. The most frequently observed values of overall order n are also 1 and 2 and the corresponding reactions are then referred to as being, respectively, first- and second-order processes. An overall order of reaction can only be defined for a reaction that has an experimental rate equation corresponding to the general form given in Equation 4.8. 

It is very important to recognize in this example that there is no simple link between the stoichiometry of the reaction and the form of the experimental rate equation. Trying to equate the partial orders of reaction for S20 and I to their balancing coefficients in the chemical equation would be similar to trying to relate apples to pears. It cannot he overemphasized that partial orders of reaction can be determined only from experimental measurements of the kinetics of a process. In the case of SiOs" turns out by coincidence, and no more than this, that the partial order has the same value as the balancing coefficient. For I , the partial order and the balancing coefficient (equal to 3) are very different. 

For reactions (b) and (c) in Table 4.2 what are the partial orders of reaction with respect to the individual reactants and the overall order of reaction in each case ... 

Reaction (e) in Table 4.2 demonstrates that a partial order of reaction may be fractional, the partial order with respect to CI2 is 1.5. This type of behaviour is often found for gas-phase reactions which have a particular type of mechanism. 

There is no systematic relationship between the stoichiometry of a reaction and the partial orders of reaction that are determined by experiment. 

The rate equation for a chemical reaction, which provides information on the partial orders of reaction and the rate constant, has to be determined experimentally. 

Partial orders of reaction are of more interest than the overall order. Essentially, the overall order of reaction provides a convenient means of categorizing reactions, but otherwise is of little importance. 

In the next two sections we shall look in some detail at how experiments can be designed, and how the resulting data can be analysed, to obtain the form of a rate equation for a chemical reaction under a given set of experimental conditions. In subsequent sections we shall see that it is the values of partial orders of reaction, together with the value of the rate constant and the way in which it varies with temperature, that enable us to propose detailed mechanisms for reactions such as those in Table 4.2, among many others. 

Partial orders of reaction are experimental quantities and often turn out to have small integer values. If the partial order is 1 for a particular reactant, then the reaction is first-order with respect to that reactant. If the partial order is 2 the reaction is second-order with respect to that reactant. 

To establish the form of an experimental rate equation it is necessary to determine the values of both the partial orders of reaction and the experimental rate constant. There is no definitive set of rules for carrying out this process and, for example, a particular approach may be influenced by knowledge gained about the kinetic behaviour of similar reactions. In any approach, however, there are common steps and one strategy based on these steps is shown as a flow diagram in Figure 5.1. 

Check for second-order behaviour, or use a general approach for determining die partial order of reaction (Section 5.3.2)... 

This prediction is also borne out experimentally (cf. Table 4.1) since the experimental rate equation is of exactly the same form in other words the partial order of reaction with respect to each reactant is 1 and overall the reaction is second-order. In the case of a unimolecular reaction, the situation is more complicated since a single reactant particle has to become energized or activated by collisions, either with other reactant particles or other bodies that are present, in order for reaction to occur. However, although we shall not go into detail, a theoretical treatment shows that under most circumstances the rate of reaction will be directly proportional to the concentration of the single reactant species so that the theoretical rate equation can be written... 

Thus, with Step 2 rate-limiting and Step 1 a rapidly established pre-equilibrium, the proposed reaction mechanism predicts that the experimental rate equation will be second-order overall with the partial order of reaction with respect to each reactant equal to 1. Furthermore on comparison with an experimental rate equation of the form... 

Since the reaction involves only a single reactant, the partial order of reaction with respect to this reactant is the same as the overall order of reaction. 

Table Q.2 Data for using the differential method to determine the partial order of reaction with respect to NO2 for the gas-phase thermal decomposition of this compound at300°C...

The plot in Figure E.6, which is a very good straight line, extends to well over 50% of the complete reaction. There is thus no doubt that partial order of reaction with respect to CH3N2CH3 is 1 and that the decomposition reaction is first-order overall. 

Pa being the partial pressure of gaseous reactant A, and a its partial order of reaction and... 

And is called kinetic equation or reaction rate law. Here r. is rate of reactions normalized over volume, C.,. is molar concentrations of reac-tants, k. is constant value characterizing the rate reactions at reactants concentration equal to 1, which is called reaction rate constant or intrinsic reaction rate, v.. is stoichiometric coefficient of the component i usually called partial order of reaction. Sum of one reaction partial order determines order of the reaction overall or order of its rate law. Elementary reactions (acts) dominate, which are subject to the rate law of zero, first and second order. For instance, for an elementary direct reaction... 

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