Chemical reactions occur at vastly different speeds. The field of chemical kinetics studies and quantifies these reaction speeds. While factors like temperature and catalysts influence reaction speed, the most direct influence is the concentration of the starting materials, known as reactants. Understanding this relationship requires a mathematical framework that links the amount of substance present to the reaction rate. This mathematical expression, determined through experimentation, reveals the fundamental dynamics of the chemical change.
Defining the Rate Law and Reaction Order
The mathematical expression describing how the rate of a chemical reaction is affected by reactant concentrations is called the Rate Law. For a general reaction, the Rate Law is written as Rate = k[A]^x[B]^y. The variable k is the rate constant, a proportionality factor unique to that reaction at a specific temperature.
[A] and [B] represent the molar concentrations of the reactants. The exponents, x and y, are the reaction orders with respect to reactants A and B, respectively, and indicate the sensitivity of the reaction rate to concentration changes. The sum of all individual exponents (x + y + …) gives the overall reaction order.
Reaction orders must be determined through experimental observation. They are generally not the same as the stoichiometric coefficients, which only describe the final ratio of reactants and products.
Common Examples of Reaction Order
Reaction order is categorized by the value of the exponent, typically zero, one, or two.
Zero-Order Reactions
A zero-order reaction means the exponent for a reactant is zero, so its concentration term disappears from the Rate Law. The rate is simply equal to the rate constant (Rate = k), meaning the reaction speed does not change even if the reactant concentration is doubled or halved. This behavior often occurs when the process is limited by a factor other than concentration, such as when a catalyst surface is completely saturated with reactant molecules.
First-Order Reactions
A first-order reaction has an exponent of one for a reactant (Rate = k[A]). For this type of reaction, the speed is directly proportional to the reactant’s concentration. If the concentration is doubled, the reaction rate will also double. Radioactive decay is a classic example, where the rate of decay is proportional only to the amount of the isotope present.
Second-Order Reactions
In a second-order reaction, the rate is proportional to the square of a single reactant’s concentration (Rate = k[A]^2) or the product of two first-order reactant concentrations (Rate = k[A][B]). If a reaction is second-order with respect to reactant A, doubling the concentration of A will increase the reaction rate by a factor of four. This strong dependence suggests the chemical process involves the simultaneous collision of two molecules to initiate the reaction.
Determining Rate Order Experimentally
Since reaction orders cannot be predicted from a balanced chemical equation, scientists must use experimental methods to determine the exponents. The most straightforward technique is the Method of Initial Rates. This method involves conducting a series of experiments where the initial concentration of one reactant is systematically changed while the concentrations of all others are held constant.
The initial rate of the reaction is measured for each experiment. By comparing the results of two experiments, the effect of a specific reactant’s concentration change on the reaction rate can be isolated. For instance, if doubling the concentration of reactant A causes the initial rate to quadruple, the reaction is second-order with respect to A. Once the individual orders are determined for all reactants, they are substituted back into the general Rate Law expression to calculate the rate constant, k.
Rate Order and the Reaction Mechanism
The experimentally determined rate order provides insight into the actual sequence of molecular events during the reaction, known as the reaction mechanism. Most chemical changes proceed through a series of elementary steps, and the overall rate is governed by the speed of the slowest step, called the rate-determining step.
The exponents in the derived Rate Law reveal which reactants are involved in this rate-determining step. If a reactant’s concentration appears in the Rate Law, that molecule influences the speed of the slowest step. Conversely, if a reactant is zero-order, it is not involved in the rate-determining step, even if it appears in the overall balanced equation. The reaction order allows chemists to propose and test plausible step-by-step mechanisms. By matching the theoretical rate law derived from a proposed mechanism to the experimentally determined rate law, scientists can understand how atoms and molecules transform into products.