Chemical kinetics is the area of chemistry dedicated to studying the speed, or rate, at which a chemical reaction occurs. A rate law is a mathematical equation that precisely links the speed of this chemical change to the amounts of the starting materials, known as reactants. Understanding a reaction’s rate law is important for predicting how quickly products will form, which is useful in both laboratory research and industrial processes, such as controlling manufacturing output or determining product shelf life.
Defining the Rate Law Equation
The rate law is expressed as an equation that shows a direct relationship between the reaction rate and the concentration of the reactants. For a general reaction involving two reactants, A and B, the rate law takes the form: \(\text{Rate} = k[\text{A}]^x[\text{B}]^y\). In this expression, “Rate” quantifies the speed at which the concentration of reactants decreases or products increases, typically measured in units like moles per liter per second.
The terms \([\text{A}]\) and \([\text{B}]\) represent the molar concentrations of the reactants. The symbol \(k\) is the rate constant, which acts as a proportionality factor that converts the concentrations into the reaction rate. The exponents, \(x\) and \(y\), are whole numbers, fractions, or zero, and they indicate how sensitive the reaction rate is to a change in the concentration of that specific reactant.
This equation allows chemists to predict how manipulating the amount of a starting material will affect the overall speed of the reaction. For instance, if the exponent \(x\) is 2, doubling the concentration of reactant A will quadruple the rate.
Understanding Reaction Order
Reaction order describes the sensitivity of the reaction rate to changes in reactant concentration, determined by the exponents in the rate law. The individual order with respect to a reactant is simply its exponent, while the overall reaction order is the sum of all the exponents (\(x + y\)).
Zero-Order Reactions
A zero-order reaction is one where the rate is completely independent of the reactant’s concentration, meaning the exponent is zero. For example, in some reactions that occur on a metal surface, the rate is constant because the surface area is the limiting factor. The rate stays the same until the reactant is completely used up.
First-Order Reactions
A first-order reaction is where the reaction rate is directly proportional to the concentration of a single reactant, meaning its exponent is one. Doubling the concentration of a first-order reactant will exactly double the reaction rate. A common example of this behavior is radioactive decay, where the rate of decay is proportional only to the amount of the radioactive material present.
Second-Order Reactions
A second-order reaction depends on the concentration of a reactant raised to the power of two, or on the product of two first-order reactant concentrations. If a reaction is second-order with respect to reactant A, doubling \([\text{A}]\) will increase the reaction rate by a factor of four (\(2^2=4\)). Reactions of third order or higher are possible, but are very rare because they require three or more molecules to collide simultaneously.
The Significance of the Rate Constant (k)
The rate constant, \(k\), is a numerical value that provides a measure of the reaction’s intrinsic speed under a specific set of conditions. It acts as the bridge in the rate law equation, linking the concentrations of the reactants to the calculated reaction rate. A higher value of \(k\) signifies a faster reaction, while a lower value indicates a slower one.
The rate constant is unique to every chemical reaction and is not influenced by changes in reactant concentration. However, the value of \(k\) is highly dependent on temperature, which is the most significant factor affecting it. As temperature increases, the value of the rate constant almost always increases, resulting in a faster overall reaction rate.
This temperature dependence is explained by the fact that heating a substance increases the kinetic energy of the molecules. Higher energy causes more frequent and more forceful collisions between reactant molecules. Crucially, a greater fraction of these molecules will possess the minimum energy, known as the activation energy, required to successfully transform into products, thereby increasing \(k\).
How Rate Laws are Determined
A rate law cannot be reliably predicted by simply looking at the coefficients in the balanced chemical equation. The stoichiometry, which describes the ratio of reactants and products, does not necessarily correspond to the exponents in the rate law. Therefore, the rate law and the reaction orders must be determined strictly through experimentation.
The most common laboratory technique for this determination is the Method of Initial Rates. This process involves running a series of experiments where the initial concentration of one reactant is systematically changed while the concentrations of all other reactants are held constant. The instantaneous rate of the reaction is measured immediately after mixing the reactants for each trial.
By comparing the change in the initial rate to the change in the concentration of the varied reactant, chemists can calculate the exponent, or reaction order, for that specific reactant. Once the individual orders for all reactants have been determined, they are combined with the experimental rates and concentrations to calculate the numerical value of the rate constant, \(k\).