Reaction Order and Graphical Representations of Reaction Kinetics
Definition
Order of a reaction
The order of a reaction with respect to a reactant is the power to which the concentration of that reactant is raised in the rate equation.
The general form of the rate equation is:
$v = k[A]^n[B]^m$
Where:
- $v$ is the rate of reaction,
- $k$ is the rate constant (a value specific to the reaction and its temperature),
- $[A]$ and $[B]$ are the concentrations of the reactants,
- $n$ and $m$ are the reaction orders with respect to $A$ and $B$, respectively.
The overall reaction order is the sum of the individual orders: $n + m$.
Examples of Reaction Orders
- Zero Order ($n = 0$):
- The rate is independent of the concentration of the reactant.
- Doubling $[A]$ has no effect on $v$.
$$v = k$$
- First Order ($n = 1$):
- The rate is directly proportional to the concentration of the reactant.
- Doubling $[A]$ doubles $v$.
$$v = k[A]$$
- Second Order ($n = 2$):
- The rate is proportional to the square of the reactant concentration.
- Doubling $[A]$ increases $v$ by a factor of four.
$$v = k[A]^2$$
- Reaction orders cannot be deduced from the stoichiometric coefficients of the balanced chemical equation.
- They must be determined experimentally.
Reaction Mechanisms and the Rate-Determining Step
The reaction order provides critical clues about the rate-determining step (RDS), which is the slowest step in a reaction mechanism. For instance:
- If a reaction is first order with respect to reactant $A$, the RDS likely involves a single molecule of $A$.
- If it’s second order with respect to $A$, the RDS might involve the collision of two $A$ molecules.
Graphical Representations of Reaction Kinetics
- Graphs are essential tools for analyzing reaction kinetics.
- Two key types of graphs are rate–concentration graphs and concentration–time graphs, which help determine the reaction order and rate constant.
