reactant+orders

A rate law will typically be written as:

rate = k[A] x [B] y

where x and y are the orders of the reactants A and B, respectively.

Recall that in equilibrium, these exponents came from the coefficients of the balanced chemical equation. This is NOT the case in kinetics. In order to determine x and y, experimental data is required.

Changes in reactant concentrations may affect the rate at which a reaction occurs. These effects are called reaction orders.

There are three main orders (we will only focus on these, but be aware that orders can be more complicated than this):
 * zero-order: any change in reactant concentration will result in no change in reaction rate. Exponent = 0.
 * what this does mathematically: A 0 = 1. Therefore any reactant having a zero order would essentially remove it from the rate law equation.
 * first-order: any change in reactant concentration has a directly proportional effect on reaction rate. Exponent = 1.
 * example: if the concentration of a first-order reactant doubles, the rate will double. Tripling its concentration will triple the reaction rate.
 * second-order: any change in reactant concentration will have twice the effect on reaction rate. Exponent = 2.
 * if a second-order reactant's concentration is doubled, the rate will quadruple.

Typically, kinetics studies involve multiple trials of the same reaction, but with different reactant concentrations. Results are provided in tabular form, as this example will show.

Follow this link to an interactive spreadsheet that helps visualize orders.

__Example 1:__

Suppose a hypothetical reaction occurs between substance A and substance B:


 * A (aq) + B (aq) --> C (aq)**

And experiments are run to test the effects of changes in concentration on the reaction rate.


 * Experiment # || [A] 0, M || [B] 0 , M || Initial Rate, M/sec ||
 * 1 || 0.050 || 0.200 || 4.2 x 10 -5 ||
 * 2 || 0.10 || 0.200 || 8.4 x 10 -5 ||
 * 3 || 0.050 || 0.400 || 1..7 x 10 -4 ||

First, write the rate law for the reaction. Only reactants are involved:


 * rate law: rate = k[A] x [B] y **

The orders can then be determined using experimental data.

By keeping [B] constant (think experimental control), and doubling [A] (the variable), notice that the rate also doubled. This means the order for A is 1 (x = 1).

By keeping [A] constant (the control), and doubling [B] (the variable), notice that the rate increased by a factor of 4. This means the order for B is 2 (y = 2).

The rate law can then be written as:


 * rate = k[A] 1 [B] 2 **

Next, the data for a single experiment can be used to calculate the rate constant, k, using the rate law. Here it is calculated using the first experiment:

4.2 x 10 -5 = k(0.050) 1 (0.200) 2

After some math:


 * k = 0.021 M -2 sec -1 **

This rate constant will be the same no matter which experiment from the table is used. It can now be used to predict the reaction rates for any other combination of reactant concentrations.