Reaction kinetics is the branch of chemistry that studies the speed, or rate, at which a chemical reaction occurs. Understanding how fast a reaction proceeds involves determining its dependence on the concentrations of the reacting substances. The reaction order is a value, determined only through experimentation, that describes how a change in a reactant’s concentration affects the overall reaction rate. Knowing this order allows chemists to predict a reaction’s behavior and is foundational for controlling and optimizing chemical processes.
The Mathematical Framework of the Rate Law
The relationship between reactant concentrations and the reaction rate is formalized by the rate law, a mathematical expression written as \(Rate = k[A]^x[B]^y\). This equation defines the speed of a reaction at a specific temperature.
The symbol \(k\) is the rate constant, a proportionality factor unique to each reaction and temperature. The bracketed terms, \([A]\) and \([B]\), represent the molar concentrations of the reactants. The exponents, \(x\) and \(y\), are the individual reaction orders for reactants A and B. These exponents must be determined through a systematic experimental approach, as they are not necessarily equal to the stoichiometric coefficients from the balanced chemical equation.
Analyzing the Experimental Data Table
To find the unknown exponents in the rate law, chemists use the “method of initial rates,” which requires an experimental data table. This table organizes the results from multiple trials of the same reaction, usually conducted at the same temperature. The table consists of columns listing the experiment number, the initial concentrations of each reactant, and the corresponding initial reaction rate.
The experimental design is structured to isolate the effect of each reactant. Between any two selected experiments, the concentration of one reactant is varied while the concentrations of all other reactants are kept constant. By comparing the resulting change in the initial rate between those two trials, the effect of the varied reactant can be isolated and quantified. This systematic variation is the foundation for calculating the individual reaction orders.
The Method of Isolation: Finding Individual Reaction Orders
The method of isolation provides a structured way to solve for the individual exponents, \(x\) and \(y\), by comparing the experimental data. The goal is to find experiments where only one reactant’s concentration changes, allowing its contribution to the rate to be determined. To find the order \(x\) for reactant A, two experiments must be selected where the concentration of A changes, but the concentration of B remains the same.
The mathematical approach involves setting up a ratio of the rate laws for the two chosen experiments. By dividing the rate law for Experiment 2 by the rate law for Experiment 1, the terms for the constant reactant B and the rate constant \(k\) mathematically cancel out. This simplification leaves an expression where the ratio of rates equals the ratio of concentrations, both raised to the power of the unknown order \(x\). The equation is \(\frac{Rate_2}{Rate_1} = (\frac{[A]_2}{[A]_1})^x\).
A simplified example illustrates this concept. If the concentration of reactant A is doubled while B is held constant, and the initial rate quadruples, the relationship is \(4 = 2^x\). This reveals that \(x\) must equal 2, meaning the reaction is second order with respect to reactant A.
If the concentration of A is doubled and the rate only doubles, the relationship is \(2 = 2^x\), meaning \(x=1\) (first order). If doubling the concentration of A results in no change to the rate, the relationship is \(1 = 2^x\), meaning \(x=0\) (zero order). This procedure is repeated by selecting experiments where the concentration of reactant B is varied while A is held constant, to solve for the exponent \(y\). This systematic comparison determines the partial order for each reactant.
Determining the Rate Constant and Overall Order
Once the individual reaction orders, \(x\) and \(y\), have been determined, the complete rate law is known except for the numerical value of the rate constant, \(k\). This constant is calculated by substituting the values for \(x\) and \(y\), along with the rate and concentrations from any single experiment, back into the rate law equation. This calculation should be performed using multiple trials to ensure consistency in the determined value for \(k\).
The units of the rate constant are not fixed and depend directly on the overall reaction order, which is the sum of all the individual orders (\(x+y\)). For example, if a reaction is second order overall, the units for \(k\) will be \(M^{-1}s^{-1}\). The overall order of the reaction is calculated by adding the determined exponents together. The result is the complete rate law, which summarizes the reaction’s speed dependence on all its reactants.