Determining the order of a chemical reaction is fundamental to chemical kinetics, the field that examines reaction speed. The reaction order describes how reactant concentration influences the speed, or rate, at which the reaction proceeds. Understanding this relationship provides insight into the exact molecular mechanism by which reactants transform into products. By monitoring reactant concentration over time, graphical methods can identify the reaction order, revealing a key characteristic of the chemical process.
Understanding Integrated Rate Laws
The differential rate law relates the instantaneous reaction rate directly to reactant concentrations, but it is impractical for analyzing experimental data taken over time. The integrated rate law offers a practical solution by mathematically transforming the rate law to connect reactant concentration directly to time. This transformation is necessary because the reaction rate constantly changes as reactants are consumed. Integrated rate laws for zero, first, and second-order reactions result in equations that resemble the algebraic form of a straight line: \(y = mx + b\). By plotting concentration data in three specific ways, we can identify which plot yields a straight line, indicating the true reaction order.
Graphical Identification of Zero-Order Reactions
For a zero-order reaction, the rate of consumption of a reactant is constant and does not depend on its concentration. The integrated rate law for reactant A is \([\text{A}]_t = -kt + [\text{A}]_0\), matching the \(y = mx + b\) form. To test this graphically, plot the concentration of the reactant, \([\text{A}]\), on the \(y\)-axis against time, \(t\). If the reaction is zero-order, this plot will produce a straight line. Since concentration decreases over time, the line will have a negative slope, and the \(y\)-intercept corresponds to the initial concentration, \([\text{A}]_0\).
Graphical Identification of First-Order Reactions
First-order reactions are common, where the rate is directly proportional to the concentration of a single reactant. As the reactant is consumed, the reaction rate slows down exponentially. The integrated rate law uses a natural logarithm to linearize this decay: \(\ln[\text{A}]_t = -kt + \ln[\text{A}]_0\). To test this order, plot the natural logarithm of the concentration, \(\ln[\text{A}]\), versus time, \(t\). If the data is first-order, this plot yields a straight line with a negative slope, and the \(y\)-intercept corresponds to \(\ln[\text{A}]_0\).
Graphical Identification of Second-Order Reactions
A second-order reaction rate is proportional to the square of one reactant’s concentration, making the rate highly sensitive to concentration changes. The integrated rate law for a single reactant is \(\frac{1}{[\text{A}]_t} = kt + \frac{1}{[\text{A}]_0}\). To identify this order graphically, plot the inverse of the reactant’s concentration, \(\frac{1}{[\text{A}]}\), versus time, \(t\). This transformation is unique because while \([\text{A}]\) decreases over time, its inverse increases. Consequently, a straight line on this plot will have a positive slope, and the \(y\)-intercept corresponds to \(\frac{1}{[\text{A}]_0}\).
Determining the Reaction Rate Constant
Once the correct linear plot is identified, the next step is quantifying the reaction’s speed using the reaction rate constant, \(k\). The constant \(k\) reflects the intrinsic speed of the reaction at a given temperature and is derived directly from the slope of the linearized graph. For zero-order and first-order reactions, the slope equals the negative rate constant (\(-k\)). For a second-order reaction, the slope equals the positive rate constant (\(k\)). Determining the slope thus provides the value of \(k\), allowing for predictions about future reactant concentrations.