chemical_kinetics_introduction

Introduction:

A popular and proper use of the word “chemistry” is to imply a chemical reaction. In that context, chemistry occurs when molecules or atoms collide and combine or are ripped asunder. The science of chemical kinetics is all about describing the collisions and departures in the language of mathematics and making measurements to verify the description. A chemical mechanism is a dissected multi-part picture of the reactive events. The mechanism can have as many steps as can be measured or imagined. Every step can have a forward and reverse rate, with no limitation other than the practical one about whether the step can be detected in some experiment. There have been many mechanisms put forth with theoretical and not measurable intermediate molecules.

Extent of Reaction, ξ (xi)

The progress of a chemical reaction can be quantified as the number of molecular transformations divided by Avogadro's number.

The change in the extent of reaction is given by dx = dn_i/v_i , where v_i is the stoichiometric number associated with each reactant or product and ni is the number of moles of each. If the stoichiometric coefficients are deemed to be positive for products and negative for reactants, then 0 = Σ v_in_i .

where C_i represents the concentration of individual reactants and products. In this discussion, chemical entities will be labeled A, B, C . . . and most often stoichiometric coefficients, v_i , will be unity. That is, the mechanism will be implied by the reaction equation. As an example, consider a reaction in which species A collides with another of its own kind to produce an intermediate A-A, which then reacts to form product B. Rather than confuse the issue with 2A => AA* => B,
we will write A + A => A-A => B. Each reactant, A, is shown with unity as the stoichiometric coefficient.

From an appropriate table of data, varying only one reactant at a time, one can sometimes derive values for x and y and thus permit the calculation of k. x and y may not have integer or rational fraction values, at which time, the units of k are not meaningful and the exercise is not very beneficial. The order of a reaction is its dependence on the concentration of a specific reactant. For the example given, one may use data to discover that

While the order of the reaction is most often addressed in the context of each reactant or product, some authors refer to an overall reaction order, which is taken to be the sum of the reaction order for each entity. When observing graphed data for the change of a reactant versus time, it is the total order of the reaction that is being followed. However, the data are often misleading and difficult to interpret. It is most useful to first model the supposed reaction mechanism and then try to isolate and observe elementary steps.

First Order Reactions (Unimolecular)

Suppose we know that a reaction is first order in one of the reactants. What does that imply? Specifically, it suggests that whenever that reactant (the one that is 1st order) has sufficient energy to react, then no other reactant is interfering. The classic example of a first order process is radioactive decay. Each atom in a uranium-238 sample will at some time give up an alpha particle and the overall sample will decrease in its radiation measurement following a mathematical model that is first order. Again, by first order, it is meant that the rate of change is proportional (or apparently so) to the concentration of only one reactant. From careful observation and theoretical analysis we learn that the time course of the reaction is a single exponential curve.