Chemical Kinetics and Rate Laws

In chemical engineering, while thermodynamics determines if and to what extent a reaction will occur, Chemical kinetics determines how fast the reaction will occur. Understanding the rate at which chemicals are produced or consumed is essential for reactor design and scaling up chemical processes.

Reaction Rate

The Reaction rate ($-r_A$) refers to the number of moles of substance A reacting (disappearing) per unit time per unit volume. For homogeneous reactions, the unit of rate is typically $\text{mol} / (\text{m}^3 \cdot \text{s})$ or $\text{mol} / (\text{L} \cdot \text{s})$.

By convention, $-r_A$ is positive when reactant A is consumed.

The Rate Law

The rate law (or rate equation) is an algebraic equation that relates the reaction rate to the concentration of reacting substances and temperature. The rate law must be determined purely from experiments; it generally cannot be deduced directly from the overall stoichiometric equation.

A common form of the rate law is the power law model:

The Overall order of reaction is the sum of the individual orders: $n = \alpha + \beta$

Elementary Reactions

An Elementary reaction is a reaction that occurs in a single step exactly as written in the equation. For elementary reactions only, the reaction orders ($\alpha, \beta$) correspond directly to the stoichiometric coefficients in the balanced chemical equation.

The Arrhenius Equation

The specific reaction rate constant ($k$) is highly dependent on temperature. This relationship is described by the Arrhenius Equation:

Activation energy ($E_a$) represents the minimum energy barrier that reacting molecules must overcome for a reaction to occur. As temperature increases, the proportion of molecules with energy higher than $E_a$ increases exponentially, causing the reaction rate to rise rapidly.

Engineering Check

Assuming a reaction is elementary just by looking at its stoichiometric equation is a very common engineering mistake. A reaction like $2A + B \rightarrow C$ might look like a third-order reaction overall, but experimentally, it may proceed through a complex multi-step mechanism that yields a first-order or even fractional-order rate law. Therefore, engineers must always rely on empirical kinetic data for reactor design.