# Orders and Rate Equations

## 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.