Chemical kinetics investigates the speed at which chemical reactions occur. It examines factors influencing reaction velocity and the step-by-step processes (mechanisms) by which reactants transform into products. To quantify this speed, scientists rely on a mathematical construct called the Rate Expression, or Rate Law. The expression relates reactant concentration to the observed reaction speed, typically measured in Molarity per second (M/s). Understanding this relationship helps predict how quickly a chemical process will proceed under various conditions.
Defining the Rate Expression and Its Variables
The Rate Expression is formulated as an equation where the reaction speed equals a constant multiplied by the concentrations of the reactants, each raised to an exponential power: Rate = \(k\)[A]\(^x\)[B]\(^y\). [A] and [B] represent the molar concentrations of the chemical species influencing the speed. The term “Rate” represents the change in concentration of a reactant or product over time.
The concentrations, represented by the terms in square brackets, are the variables that can be directly changed. For instance, increasing the concentration of reactant [A] leads to more frequent molecular collisions, which accelerates the reaction speed. These concentration terms reflect the immediate availability of the molecules needed for the reaction.
The letter \(k\) is the rate constant, a proportionality factor linking the concentration terms to the actual rate. This constant is unique to every specific reaction and is dependent on temperature. The value of \(k\) determines the inherent speed capability of the reaction, which only changes if the temperature is adjusted. The units for the rate constant vary depending on the rate law’s form, ensuring the final rate is expressed in concentration per unit time.
The exponents, labeled \(x\) and \(y\), are the reaction orders with respect to the individual reactants. They indicate how sensitive the reaction rate is to a change in that specific reactant’s concentration.
Reaction Order
The reaction order dictates the mathematical relationship between a reactant’s concentration and the resulting speed of the reaction. If the reaction order \(x\) is 1 (first-order), doubling the concentration of reactant A causes the reaction rate to double proportionally. This suggests a direct, linear dependence, such as in processes like radioactive decay.
If the reaction order \(x\) is 2 (second-order), the dependence is quadratic; doubling the concentration of A results in the reaction speed quadrupling (\(2^2\)). This higher order indicates that the concentration has a greater influence on the overall reaction velocity, as seen in reactions that require two molecules to collide effectively. Some reactions may exhibit a zero-order dependence, meaning that changing the concentration of that reactant has no measurable effect on the reaction speed, provided some is present.
The overall reaction order is the sum of all individual orders in the rate expression, calculated as \(x + y + …\). This combined value characterizes the total sensitivity of the reaction rate to changes in the concentrations of all reactants. These orders can be whole numbers, zero, or fractions, reflecting the complexity of the reaction mechanism. They are not necessarily related to the coefficients found in the balanced chemical equation.
Experimental Determination
The reaction orders, \(x\) and \(y\), cannot be reliably predicted by simply looking at the balanced chemical equation. The coefficients in a balanced equation, known as stoichiometric coefficients, represent the overall mass balance but rarely reflect the reaction’s actual molecular pathway. This is because most chemical transformations occur as a sequence of simpler steps.
Only in the rare case of an elementary reaction, which proceeds in a single, simultaneous step, do the experimentally determined orders match the stoichiometric coefficients. For multi-step reactions, the rate expression is governed by the slowest step in the sequence, known as the rate-determining step. The rate expression only includes the species involved up to and including this slowest step, which dictates the overall speed of the process.
Therefore, the rate expression and its orders must be determined through experimentation. The most common technique for this is the Method of Initial Rates. This involves performing a series of experiments where the initial concentration of one reactant is varied while the concentrations of all other reactants are held constant.
By observing how the initial speed of the reaction changes in response to the concentration variation, scientists can algebraically solve for the value of the exponent, \(x\) or \(y\). For example, if doubling the concentration of A quadruples the rate, the order for A must be 2. This systematic experimental approach is the only way to accurately establish the true mathematical description of a reaction’s speed and understand its underlying mechanism.