Orders and Rate Equations

Fractional Orders and Complex Mechanisms

The order of reaction is determined experimentally and reflects the relationship between the rate of reaction and the concentration of reactants.
Zero order reactions occur at a constant rate, regardless of the concentration of reactants.
First order reactions have a rate that’s directly proportional to the concentration of one reactant.
Second order reactions have a rate proportional to the square of the concentration of one reactant, or to the product of the concentrations of two reactants.
Fractional orders of reaction are less common but can occur, suggesting a complex reaction mechanism.

Rate Equation and Determining Orders of Reaction

The rate equation provides a mathematical representation of the relationship between the rate of a reaction and the concentrations of the reactants.
Rate constant (k) is a proportionality factor in the rate equation. Its value depends on temperature and the presence of a catalyst.
The rate equation can only be determined through experimental measurements.
Graphical methods, such as plotting concentration against time for zero and first order reactions, can help identify the order with respect to a single reactant.

Rate Determining Step and Molecularity

The slowest step in a series of reaction steps is the rate determining step. It dictates the overall rate of the reaction.
The molecularity of a reaction step is the number of particles colliding in a single step.
The molecularity of the rate determining step provides an upper limit to the overall order of the reaction.
The experimental rate equation can provide information on the mechanism of reaction and the possible rate determining step.

Half-life and First Order Reactions

Half-life (t½) is the time taken for the concentration of a reactant to decrease to half of its initial value.
In a first order reaction, the half-life is constant and is independent of the initial concentration of reactants.
The concept of half-lives is useful for managing the risk associated with hazardous chemical reactions.
The equation for the half-life of a first-order reaction is t½ = 0.693 / k, where k is the rate constant.

The Arrhenius Equation

The Arrhenius equation describes the temperature dependence of reaction rates.
The equation is k = Ae^(-Ea/RT), where A is the pre-exponential factor (frequency of successful collisions), Ea is the activation energy, R is the gas constant, T is the temperature, and k is the rate constant.
Plotting the logarithm of the rate constant against the reciprocal of the absolute temperature provides a straight line as per the Arrhenius plot.
The activation energy and the pre-exponential factor can be determined from the Arrhenius plot.
The Arrhenius equation is key in industrial chemistry where controlling reaction rates is often essential.