5.1 Reaction Rates and Rate Laws

Reaction kinetics is all about understanding how fast chemical reactions happen. It's like tracking a race between molecules, measuring how quickly they transform into new substances. This knowledge helps us predict and control reactions in everything from industrial processes to drug metabolism.

The key players in reaction kinetics are reaction rate, rate laws, and half-life. By studying these, we can figure out how different factors affect reaction speed and even peek into the hidden steps of complex reactions.

Reaction Kinetics Fundamentals

Definition of reaction rate

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• Reaction rate measures how quickly reactants are consumed or products are formed over time, typically expressed in mol/L·s
• Provides insight into reaction mechanisms allowing prediction of reaction progress and optimization of industrial processes
• Influenced by concentration of reactants, temperature, catalysts, and surface area of solid reactants (heterogeneous catalysis)

Derivation of rate laws

• Rate law mathematically relates reaction rate to reactant concentrations: Rate = $k[A]^m[B]^n$, k is rate constant
• Determined experimentally through method of initial rates or integrated rate law method
• Reaction order (m + n) indicates rate dependence on concentration
  • Zero-order: rate independent of concentration
  • First-order: rate directly proportional to concentration
  • Second-order: rate proportional to square of concentration or product of two concentrations
• Order determined graphically by plotting concentration vs. time or analyzing half-life changes with initial concentration

Half-life calculation and significance

• Half-life measures time for reactant concentration to halve
• Formulas vary by reaction order:
  1. Zero-order: $t_{1/2} = \frac{[A]_0}{2k}$
  2. First-order: $t_{1/2} = \frac{\ln(2)}{k}$
  3. Second-order: $t_{1/2} = \frac{1}{k[A]_0}$
• Inversely related to rate constant, larger k leads to shorter half-life
• Applied in radioactive decay and drug metabolism studies (pharmacokinetics)

Elementary vs complex reactions

• Elementary reactions occur in single step, rate law derived directly from balanced equation
• Complex reactions involve multiple elementary steps, overall rate law may not match balanced equation
• Types of complex reactions include consecutive, parallel, and chain reactions
• Reaction mechanisms propose sequence of elementary steps, must align with overall balanced equation and experimental rate law