Homogeneous Reactions

Abstract

We consider a one-phase system (so that the assumptions of invertibility discussed in the preceding chapter are justified) in which a single chemical reaction is taking place, say, e.g.,

$$\mathrm{CO+\frac{1}{2}O_{2}}\;=\;\mathrm{CO_{2}}$$

((3.1.1))

Equation (3.1.1) does not, of course, imply addition in the ordinary algebraic sense of the quantities CO and O₂. The meaning of equation (3.1.1) is to recall the experimentally observed fact that, when a given number of moles of CO is consumed by the reaction, the same number of moles of CO₂ is produced, and half as many moles of O₂ are consumed. Let the components appearing in the reaction be numbered consecutively, say CO is B ₁, O₂ is B ₂, and CO₂ is B ₃, and let σ _j be the corresponding stoichiometric coefficients, say σ₁ = −1, σ₂ = −1/2, and σ₃ = 1. We note that the stoichiometric coefficients of the species appearing on the left-hand side (the “reactants”) are assigned negative stoichiometric coefficients. Equation (3.1.1) can now be written as follows:

$$\underset{j}\sum\sigma_{j}B_{j}\;=\;0$$

((3.1.2))

It is very easy but perhaps impudent for me, an academic, an engineer on paper, to criticize those who have successfully created a large-scale commercial reactor, but I ask you to ponder on this point. This is a simple reaction between two molecules at 360 °C. Surely the chemical rate is not terribly small, and at 15 cm/sec in a 10 m deep bed the reactants are in contact for more than a minute. Surely you would be surprised if the reaction was not nearly complete in such a deep bed.

P. N. Rowe