Reaction Order - Chemistry

1. Fundamental Concepts

Definition: Reaction order describes how the rate of a reaction depends on the concentration of the reactants. It is determined experimentally and is not related to the stoichiometric coefficients in the balanced equation.

Rate Law Equation:

: Rate constant (temperature dependent).

: Molar concentrations of reactants.

: Orders with respect to reactants A and B (must be determined by experiment).

Overall Order: The sum of the individual orders ( ).

2. Key Concepts

Zero Order: Rate is independent of concentration ( ). Concentration decreases linearly with time.

First Order: Rate is directly proportional to concentration ( ). Concentration decays exponentially. Half-life ( ) is constant.

Second Order: Rate is proportional to the square of the concentration ( ). Rate is very sensitive to concentration changes.

Units of k:

0th Order:

1st Order:

2nd Order:

Integrated Rate Laws (Linear Plots):

0th: ( vs is linear)

1st: ( vs is linear)

2nd: ( vs is linear)

3. Examples

Easy

Question: Given the rate law , what is the overall order of the reaction?

Answer: 3rd Order.

Explanation: Sum the exponents: .

Medium

Question: A first-order reaction has a rate constant . Calculate the half-life ( ) of the reaction.

Answer: 34.7 seconds.

Explanation: Use the first-order half-life formula:

Hard

Question: Determine the order of the reaction using the following experimental data.

Answer: The reaction is second order with respect to A, zero order with respect to B, and second order overall.

Explanation:

1. Compare Exp 1 and 2: [A] doubles ( ), [B] stays same. Rate quadruples ( ). Since , . (Order in A is 2).

2. Compare Exp 1 and 3: [B] doubles ( ), [A] stays same. Rate stays same ( ). Since , . (Order in B is 0).

3. Overall: .

4. Problem-Solving Techniques

Method of Initial Rates:

Find two experiments where only one reactant's concentration changes.

Use the ratio: .

If Rate when Conc 1st Order.

If Rate when Conc 2nd Order.

If Rate when Conc 0th Order.

Graphical Analysis:

Plot the data. If the y-axis creates a straight line, that defines the order.

Y-axis = 0th Order.

Y-axis = 1st Order.

Y-axis = 2nd Order.

Half-life Trend:

If is constant 1st Order.

If doubles as concentration halves 2nd Order.