3.1.1 Relative Rates of Reaction

The relative rates of reaction of the various species involved in a reaction can be obtained from the ratio of the stoichiometric coefficients. For Reaction (2-2),

2-2

we see that for every mole of A that is consumed, c/a moles of C appear. In other words,

Rate of formation of (Rate of disappearance of A)

Similarly, the relationship between the rates of formation of C and D is

The relationship can be expressed directly from the stoichiometry of the reaction,

2-1

for which

3-1

or

For example, in the reaction

we have

If NO₂ is being formed at a rate of 4 mol/m³/s, i.e.,

r_NO2 = 4 mol/m³/s

then the rate of formation of NO is

the rate of disappearance of NO is

–r_NO = 4 mol/m³/s

and the rate of disappearance of oxygen, O₂, is

3.2 The Reaction Order and the Rate Law

In the chemical reactions considered in the following paragraphs, we take as the basis of calculation a species A, which is one of the reactants that is disappearing as a result of the reaction. The limiting reactant is usually chosen as our basis for calculation. The rate of disappearance of A, –r_A, depends on temperature and composition. For many reactions, it can be written as the product of a reaction rate constant, k_A, and a function of the concentrations (activities) of the various species involved in the reaction:

3-2

The algebraic equation that relates –r_A to the species concentrations is called the kinetic expression or rate law. The specific rate of reaction (also called the rate constant), k_A, like the reaction rate, –r_A, always refers to a particular species in the reaction and normally should be subscripted with respect to that species. However, for reactions in which the stoichiometric coefficient is 1 for all species involved in the reaction, for example,

1NaOH + 1HC1 → 1NaC1 + 1 H₂O

we shall delete the subscript on the specific reaction rate, (e.g., A in k_A), to let

k = k_NaOH = k_HC1 = k_NaC1 = k_H2O