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# Reaction Order

The relationship between the concentrations of species to the rate of a reaction is the reaction order.

### Introduction

Once the rate law of a reaction has been determined, that same law can be used to understand more fully the composition of the reaction mixture. More specifically, the reaction order is the power to which the concentration of that species is raised to. It tells you to what extent the concentration of a species affects the rate of a reaction, as well as which species affects the rate the most.

### Relation to Rate Law

For the reaction:
$aA + bB \longrightarrow P$
rate=k[A]x[B]y
where [A] is the concentration of species A, x is the order with respect to species A. [B] is the concentration of species B, y is the order with respect to species B, and k is the rate constant.

n, is the reaction order for the whole chemical reaction. This can be found by adding the reaction orders with respect to the reactants. In this case, n = x + y.

### Simple Rules

The order of a reaction does NOT need to be an integer. The following orders are possible:

• Zero: A zero order tells you that the concentration of that species does NOT affect the rate of a reaction
• Negative integer: A negative order tells you that the concentration of that species INVERSELY affects the rate of a reaction
• Positive integer: A positive order tells you that the concentration of that species DIRECTLY affects the rate of a reaction
• Non-Integer: Non-integer orders, both positive and negative, represent more intricate relationships between concentrations and rate in more complex reactions.

### Methods to Determining Reaction Order

For chemical reactions that require only one elementary step, the values of x and y are equal to the stoichiometric coefficients in front of the reactant. For other chemical reactions that require more than one elementary state, this may not always be the case. In saying this, there are many simple ways of determining the order of a reaction. One very popular method is known as the differential method.

#### The Differential Method

The Differential Method, also known as the Initial Rates Method, uses an experimental data table to determine the order of a reaction with respect to the reactions that were used. Below is an example of a table that can be looked at from the following chemical reaction:

$A + B \longrightarrow P$

 Experiment [A] M [B] M Rate M Min-1 1 0.100 0.100 1.0 x 10-3 2 0.200 0.100 1.0 X 10-3 3 0.100 0.200 2.0 x 10-3

When looking at the experiments in the table above, what needs to be noticed are factors that are changing in each experiment. So, in order to determine the reaction order with respect to A, you need to find where A is changing. That is between experiments 1 and 2. Write a rate law equation based on the chemical reaction above (can be seen below)

Rate = k[A]x[B]y

Once this is done, you must divide the rate law equation from experiment 2 by the rate law equation for experiment 1. You will notice that the [B]y will cancel out and you are left with "x" being the unknown variable. By doing simple algebra, you can determine through the steps that x = 0.

The same steps must be taken for determining the reaction order with respect to B. Instead, however, you will use experiment 1 and 3 for this process. After working through the problem and canceling out [A]x from the equation, you should find that y = 1.

Finding the reaction order for the whole process is the easy addition of x and y, n = 0 + 1. Therefore n = 1

After finding your reaction order, several pieces of information can be solved for, such as half-life for example.

#### Other methods

Other methods that can be used to solve for reaction order are: The Integration Method, The Half-Life Method, and The Isolation Method.

### Problems

1. Define Reaction Order

Use the following information to solve questions 2 and 3:

Given the rate law equation: Rate = k[A]1[B]2

2. Determine: a) the reaction order with respect to A, b) the reaction order with respect to B, and c) the total reaction order for the equation.

3. Assuming the reaction occurs in one elementary step, propose a chemical equation using P as the symbol for your product.

Use the data table below to answer questions 4 and 5

 Experiment [A] M [B] M Rate M Min-1 1 0.100 0.100 1.0 x 10-3 2 0.400 0.100 2.0 X 10-3 3 0.100 0.150 2.0 x 10-3

4.  Use The Differential Method to determine the reaction order with respect to A (x) and B (y). What is the total reaction order (n)?

5. What is the rate constant k?

1. The relationship between the concentrations of species to the rate of a reaction
2. a) x = 1, b) y = 2, and c) n = 3
3. $$A + 2B \longrightarrow P$$
4. x = 0.5 and y = 1.7. n = 2.2
5. k = 0.10 M min-1

### References

• Chang, Raymond. (2005). Physical Chemistry for the Biosciences. Sausalito,CA: University Science Books.
• Shagoury, Richard.  Chemistry 1A Lecture Book. 4th Ed.  Custom Publishing. 2006. Print

### Contributors

• Sevini Shahbaz, Andrew Iskandar (University of California, Davis)