# 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.