R2.2.10 Order of a reaction (Higher Level Only) Notes

Reaction Order and Graphical Representations of Reaction Kinetics

The general form of the rate equation is:

$v = k[A]^n[B]^m$

Where:

1. $v$ is the rate of reaction,
2. $k$ is the rate constant (a value specific to the reaction and its temperature),
3. $[A]$ and $[B]$ are the concentrations of the reactants,
4. $n$ and $m$ are the reaction orders with respect to $A$ and $B$, respectively.

Examples of Reaction Orders

1. Zero Order ($n = 0$):
   1. The rate is independent of the concentration of the reactant.
   2. Doubling $[A]$ has no effect on $v$.
      $$v = k$$
2. First Order ($n = 1$):
   1. The rate is directly proportional to the concentration of the reactant.
   2. Doubling $[A]$ doubles $v$.
      $$v = k[A]$$
3. Second Order ($n = 2$):
   1. The rate is proportional to the square of the reactant concentration.
   2. Doubling $[A]$ increases $v$ by a factor of four.
      $$v = k[A]^2$$

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:

1. If a reaction is first order with respect to reactant $A$, the RDS likely involves a single molecule of $A$.
2. If it’s second order with respect to $A$, the RDS might involve the collision of two $A$ molecules.

Graphical Representations of Reaction Kinetics

1. Graphs are essential tools for analyzing reaction kinetics.
2. Two key types of graphs are rate–concentration graphs and concentration–time graphs, which help determine the reaction order and rate constant.

Rate–Concentration Graphs

1. These graphs plot the reaction rate ($v$) against the concentration of a reactant ($[A]$).
2. The shape of the graph reveals the reaction order:
   1. Zero Order: A horizontal line, because $v$ is constant and independent of $[A]$.
      $$v = k$$
   2. First Order: A straight line passing through the origin, as $v \propto [A]$.
      $$v = k[A]$$
   3. Second Order: A curve (parabola), since $v \propto [A]^2$.
      $$v = k[A]^2$$

Concentration–Time Graphs

1. These graphs show how the concentration of a reactant ($[A]$) changes over time.
2. The shape of the graph depends on the reaction order:
   1. Zero Order: A straight line with a negative slope. The rate of decrease in $[A]$ is constant.
      $$[A] = [A]_0 - kt$$
   2. First Order: An exponential decay curve, where the rate of decrease slows over time.
      $$[A] = [A]_0 e^{-kt}$$
   3. Second Order: A hyperbolic decay curve, steeper than that of a first-order reaction.
      $$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$$

Summary of Graphical Representations

Zero-order

First-order

Second-order

Experimental Determination of Reaction Order

To determine the order of a reaction experimentally:

1. Measure Initial Rates: Perform several experiments, varying the initial concentration of one reactant at a time, and record the initial rate of reaction.
2. Analyze Relationships: Use the data to determine how changes in concentration affect the rate.