#Chemical Kinetics: Rate Laws and Integrated Rate Laws

#Introduction to Reaction Orders and Rate Laws

This section is crucial for understanding how reaction rates change with reactant concentrations. Expect to see these concepts in both multiple-choice and free-response questions.

#Reaction Order (n)

• The reaction order, denoted by n, describes how the concentration of a reactant affects the reaction rate.
• While n is often an integer (0, 1, or 2), it can be a fraction in complex reactions.
• For the AP exam, focus on integer orders (0, 1, and 2).

#Rate Law

• A rate law expresses the relationship between the rate of a reaction and the concentrations of the reactants.

• General form: Rate = k[A]ⁿ

• k is the rate constant (temperature-dependent)

• [A] is the concentration of reactant A

• n is the order of the reaction with respect to reactant A

#Analogies to Understand Rate Laws

• Think of population dynamics:

  • In a crisis, population decay is exponential.
  • The rate of decay is proportional to the current population.

• Similarly, in chemical reactions: - As reactants are consumed, the reaction rate typically decreases. - The rate depends on the concentration of reactants.

#Deriving Integrated Rate Laws

#The Math Behind Rate Laws

• For a simple reaction A → B, the rate of reaction can be expressed as:
  • Rate = k[A]ⁿ
• Using calculus, we can derive the integrated rate laws, which relate reactant concentration to time.

#General Derivation (Calculus-Based)

• Differential rate law:
  $$-\frac{d[A]}{dt} = k[A]^n$$
• Separating variables and integrating (if you're comfortable with calculus): $$\int_{[A]_0}^{[A]} \frac{d[A]}{[A]^n} = -k \int_{0}^{t} dt$$ -...