Rate law

Consider the general reaction

The rate of the reaction at a given time is proportional to the molar concentrations of the reactants at that time raised to simple powers:

where the proportionality constant $k$ is called the rate constant, which is independent of concentration and varies with temperature. For unit concentrations of A and B, $k$ is equal to the rate of the reaction. Equation (6.2) is called the differential rate law.

The powers $x$ and $y$ of the concentration terms A and B in the rate law are not necessarily equal to the stoichiometric coefficients ($a$ and $b$) appearing in Eq. (6.1). Thus $x$ and $y$ may be simple whole numbers, zero or a fraction, and they are experimentally determined. The rate law in Eq. (6.2) is determined experimentally and expresses the rate of a chemical reaction in terms of the molar concentrations of the reactants — it is not predicted from the stoichiometry of the reactants.

The exponents $x$ and $y$ appearing in the rate law tell us how the concentration change affects the rate of the reaction:

(i) For $x = y = 1$, Eq. (6.2) gives rate $= k\mathrm{[A][B]}$. The equation implies that the rate of the reaction depends linearly on the concentrations of A and B: if the concentration of either A or B is doubled, the rate would be doubled. …