Reaction Rates and Rate Laws

Learning Objectives

Define reaction rate and collision theory.

Explain how a rate law relates the reaction rate to reactant concentrations.

Determine the order of a reaction from experimental data.

Explain the role of activation energy in determining reaction rate.

The Speed of Chemical Change: Kinetics

Chemical kinetics is the study of the speed, or rate, of chemical reactions.

Reaction Rate: The change in concentration of a reactant or product per unit of time (e.g., in Molarity per second, M/s).

Collision Theory

For a reaction to occur, reactant particles must collide. The rate of the reaction depends on two factors:

1.Collision Frequency: The number of collisions per unit time.

2.Collision Effectiveness: Not all collisions lead to a reaction. A collision must have:

Sufficient Energy: The colliding particles must possess a minimum amount of kinetic energy, known as the activation energy (Ea), to break existing bonds.

Correct Orientation: The particles must collide in a specific orientation that allows the new bonds to form.

Rate Laws

A rate law is a mathematical expression that relates the rate of a reaction to the concentrations of the reactants. For a generic reaction A + B → Products, the rate law has the form:

Rate = k[A]ˣ[B]ʸ

k: The rate constant, a value that is specific to the reaction and its temperature.

[A] and [B]: The molar concentrations of reactants A and B.

x and y: The reaction orders. These are exponents that determine how the rate is affected by the concentration of each reactant. They must be determined experimentally and are not necessarily the stoichiometric coefficients.

Reaction Order:

If x=1, the reaction is 'first order' with respect to A. Doubling [A] doubles the rate.

If x=2, the reaction is 'second order' with respect to A. Doubling [A] quadruples the rate (2²=4).

If x=0, the reaction is 'zero order' with respect to A. Changing [A] has no effect on the rate.

The overall order of the reaction is the sum of the individual orders (x + y).

Determining the Rate Law from Data

By comparing the initial rates of a reaction in different experiments where the initial concentrations are varied, one can deduce the orders x and y.

Example:

| Exp. | [A] (M) | [B] (M) | Initial Rate (M/s) |

|---|---|---|---|

| 1 | 0.1 | 0.1 | 2 |

| 2 | 0.2 | 0.1 | 4 |

| 3 | 0.1 | 0.2 | 8 |

Compare Exp 1 and 2: [A] doubles, [B] is constant, Rate doubles. So, the reaction is first order in A (x=1).

Compare Exp 1 and 3: [B] doubles, [A] is constant, Rate quadruples. So, the reaction is second order in B (y=2).

Rate Law: Rate = k[A]¹[B]²

Key Terms

Rate Law: An equation that links the reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders).
Reaction Order: The exponent to which the concentration of a reactant is raised in the rate law. It defines how the rate is affected by the concentration of that reactant.
Activation Energy (Ea): The minimum amount of energy that must be provided for a chemical reaction to occur.
Collision Theory: A theory stating that for a chemical reaction to occur, the reacting particles must collide with sufficient energy and with the proper orientation.
Rate Constant (k): A coefficient of proportionality relating the rate of a chemical reaction at a given temperature to the concentration of the reactant or products.