A chemical reaction transforms reactants into products, and its speed is the reaction rate. Reaction order quantifies how a reaction’s speed depends on reactant concentrations. This value is determined experimentally, not from a balanced chemical equation’s stoichiometric coefficients. Determining reaction order is important for understanding a reaction’s mechanism and predicting its behavior under different conditions.
Defining Reaction Order
Reaction order elucidates the relationship between reactant concentrations and the rate of a chemical reaction. This relationship is mathematically expressed through the “rate law”: Rate = k[A]$^x$[B]$^y$, where ‘k’ is the rate constant, and [A] and [B] represent reactant concentrations. The exponent for each reactant’s concentration is its “individual reaction order”. The “overall reaction order” is the sum of these individual orders (x + y). These orders are experimentally derived and do not necessarily correspond to stoichiometric coefficients. For example, a zero-order reaction’s rate is independent of that reactant’s concentration, while doubling a first-order reactant’s concentration doubles the rate, and a second-order reactant quadruples it.
The Initial Rates Approach
The initial rates method determines the rate law and reaction order for each reactant. This approach involves performing a series of experiments where one reactant’s initial concentration is systematically varied, while others are kept constant. The initial reaction rate is then measured for each experiment. By comparing initial rates, scientists deduce how the rate changes with specific reactant concentrations. For instance, if doubling a reactant’s concentration doubles the initial rate, the reaction is first order. If it quadruples the rate, it is second order. This systematic comparison allows for the determination of individual reaction orders, which are then used to formulate the complete rate law.
Using Integrated Rate Laws and Graphs
Integrated rate laws offer a method for determining reaction order by relating reactant concentrations directly to time. These mathematical expressions are derived from differential rate laws and allow chemists to predict reactant concentrations at any given time. For each common reaction order—zero, first, and second—a unique integrated rate law exists, which, when plotted appropriately, yields a linear relationship.
Zero-Order Reactions
For a zero-order reaction, plotting the reactant concentration, [A], against time results in a straight line with a negative slope equal to the rate constant.
First-Order Reactions
In a first-order reaction, a linear plot is obtained when the natural logarithm of the reactant concentration, ln[A], is plotted against time, with the slope being the negative of the rate constant.
Second-Order Reactions
For a second-order reaction, plotting the reciprocal of the reactant concentration, 1/[A], versus time produces a straight line, and its slope directly represents the rate constant.
Identifying which of these plots yields a linear relationship allows for the direct determination of the reaction order and the rate constant.
The Half-Life Method
The half-life (t$_{1/2}$) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. The utility of this method varies depending on the reaction order.
First-Order Reactions
For a first-order reaction, its half-life is constant and independent of the initial concentration. This constant half-life uniquely identifies first-order reactions.
Zero-Order Reactions
In contrast, the half-life of zero-order reactions is directly proportional to the initial concentration, decreasing as concentration decreases.
Second-Order Reactions
For second-order reactions, the half-life increases as the initial concentration decreases.
This varying dependence of half-life on concentration makes it a tool for confirming or suggesting a reaction’s order.