General Chemistry/Reaction Rates

Introduction
Reaction rates of a chemical system provide the underpinnings of many theories in thermodynamics and chemical equilibria.

Elementary reactions are one-step processes in which the reactants become the products without any intermediate steps. The reactions are unimolecular (A → products) or bimolecular (A + B → products). Very rarely, they could be trimolecular (A + B + C → products), but this is not common due to the rarity of three molecules colliding at the same time.

A complex reaction is made up of several elementary reactions, with the products of one reaction becoming the reactants of the next until the overall reaction is complete.

Rate Equation
Note [A] is raised to the power of m, its coefficient, just like an equilibrium expression. The rate of the reaction may rely on the molar coefficients of the reactant species, but it might not. However, for an elementary reaction, the concentrations of the species A and B are always raised to their molar coefficients. This only applies to elementary reactions, which is a very important distinction to make.

Order
The order of an equation is what the concentration of a substance is raised to in the rate equation. The greater the number, the greater effect it will have on rate. For example, zero order equations do not effect the rate. To find the order, you must alter one concentration and keep the rest the same, Dividing gives an equation which can be used to solve for the order. To find overall order, simply add all orders together.

Zero-Order Equations
Zero-order equations do not depend on the concentrations of the reactants.

First-Order Equations
First-order equations depend on the concentration of a unimolecular reaction.

Second-Order Equations
Second-order equations depend on the two concentrations of a bimolecular reaction.

Equilibrium
Equilibrium will occur when the forward and reverse rates are equal. As you may have already noticed, the equilibrium expression of a reaction is equal to the rate equations divided.

Understanding kinetics explains various concepts of equilibrium. Now it should make sense why increasing the reactant concentration will make more products. The forward rate increases, which uses up reactants, which decreases the forward rate. At the same time, products are made, which increases the reverse reaction, until both reaction rates are equal again.

Arrhenius Equation
The Arrhenius equation determines a rate coefficient based on temperature and activation energy. It is surprisingly accurate and very useful. The Arrhenius equation is:

$$k = Ae^{-E_a / RT}$$

$$E_a$$ is the activation energy for the reaction, in joules per mole. $$R$$ is the Universal Gas Constant, $$T$$ is the temperature (in kelvin), and $$A$$ is the prefactor. Prefactors are usually determined experimentally.