Kinetics Formulas

Understanding reaction rates is key in chemistry. Kinetics formulas help us analyze how reactant concentrations and temperature affect the speed of reactions, guiding us through concepts like rate laws, half-lives, and the impact of catalysts on reaction pathways.

1. Rate law equation: rate = k[A]^m[B]^n

   • The rate of a reaction depends on the concentration of reactants raised to a power.
   • The exponents (m and n) indicate the order of the reaction with respect to each reactant.
   • The rate constant (k) is specific to the reaction and varies with temperature.

2. Integrated rate law for zero-order reactions: [A] = -kt + [A]₀

   • The concentration of reactant decreases linearly over time.
   • The rate is constant and does not depend on the concentration of reactants.
   • The half-life is directly proportional to the initial concentration.

3. Integrated rate law for first-order reactions: ln[A] = -kt + ln[A]₀

   • The concentration of reactant decreases exponentially over time.
   • The rate depends linearly on the concentration of the reactant.
   • The half-life is constant and independent of the initial concentration.

4. Integrated rate law for second-order reactions: 1/[A] = kt + 1/[A]₀

   • The concentration of reactant decreases in a non-linear fashion over time.
   • The rate depends on the square of the concentration of the reactant.
   • The half-life is inversely proportional to the initial concentration.

5. Half-life formula for first-order reactions: t₁/₂ = ln(2)/k

   • The half-life is a constant value for first-order reactions.
   • It indicates the time required for half of the reactant to be consumed.
   • The value of k directly affects the duration of the half-life.

6. Arrhenius equation: k = Ae^(-Ea/RT)

   • The rate constant (k) increases with temperature and decreases with activation energy (Ea).
   • A is the pre-exponential factor, representing the frequency of collisions.
   • R is the universal gas constant, and T is the temperature in Kelvin.

7. Collision theory equation: k = pZe^(-Ea/RT)

   • The rate constant (k) is influenced by the frequency of effective collisions (p) and the orientation of molecules (Z).
   • Activation energy (Ea) must be overcome for a reaction to occur.
   • Higher temperatures increase the number of effective collisions.

8. Catalyst effect on activation energy: Ea(catalyst) < Ea(uncatalyzed)

   • Catalysts lower the activation energy, increasing the reaction rate.
   • They provide an alternative pathway for the reaction.
   • Catalysts are not consumed in the reaction and can be reused.

9. Relationship between rate constant and temperature: ln(k₂/k₁) = (Ea/R)(1/T₁ - 1/T₂)

   • This equation shows how the rate constant changes with temperature.
   • It allows for the comparison of rate constants at two different temperatures.
   • A higher temperature generally results in a higher rate constant.

10. Rate determining step in a multi-step reaction: overall rate = rate of slowest step

• The slowest step in a reaction mechanism controls the overall reaction rate.
• Identifying the rate-determining step is crucial for understanding reaction kinetics.
• The rate law can often be derived from the rate-determining step.