Chapter 3: Chemical Kinetics

Average & Instantaneous Rate

• Average Rate (r_av): Change in concentration over a long interval of time.
  r_av = - Δ[R]/Δt = + Δ[P]/Δt
• Instantaneous Rate (r_inst): Rate of reaction at a specific instant (when Δt → 0).
  r_inst = - d[R]/dt = + d[P]/dt

Rate Law & Rate Constant (k)

Mathematical expression correlating rate of reaction with molar concentration of reactants.

Rate = k[A]^x[B]^y

• Rate Constant (k): Rate of reaction when concentration of all reactants is unity. It depends heavily on Temperature.
• Units of k: (mol L⁻¹)^1-n s⁻¹ (where n = overall order).

Molecularity (Theoretical)

• Number of reacting species taking part in an elementary step that must collide simultaneously.
• It is always a whole number (1, 2, or 3). Cannot be zero or fractional.
• Has no meaning for complex (multi-step) reactions.

Order of Reaction (Experimental)

• Sum of the powers of concentration terms in the experimentally determined rate law. (n = x + y).
• It can be zero, fractional, or negative.
• In complex reactions, order is determined by the slowest step (Rate Determining Step).

Zero Order Reaction

Rate is independent of the concentration of reactants. (e.g., Decomposition of NH₃ on hot Pt surface).

[A] = [A]₀ - kt     OR     k = ([A]₀ - [A]) / t

Half-Life (t_1/2): Directly proportional to initial concentration.

t_1/2 = [A]₀ / 2k

First Order Reaction

Rate depends on the first power of reactant concentration. (e.g., All natural radioactive decays).

k = (2.303 / t) log([A]₀ / [A])    OR    [A] = [A]₀ e^-kt

Half-Life (t_1/2): Independent of initial concentration!

t_1/2 = 0.693 / k

Pseudo First Order Reaction

Reactions which are not truly first order but behave as first order because one reactant is present in large excess (so its concentration barely changes).

• Example: Acid hydrolysis of ethyl acetate (Water is in excess).
• Example: Inversion of cane sugar (Sucrose).

Collision Theory

• For a reaction to occur, molecules must collide with sufficient energy (Threshold Energy) and proper orientation.
• Activation Energy (E_a): The extra energy required by reactant molecules to reach the threshold energy.
  E_a = Threshold Energy - Average Kinetic Energy of reactants.

Arrhenius Equation

Shows exactly how Rate Constant (k) increases exponentially with Temperature.

k = A × e^-E_a/RT

Where 'A' is the Arrhenius (frequency) factor, R is gas constant, T is temp in Kelvin.

log k = log A - E_a / (2.303 RT)

Comparing at two different temperatures (T₁ and T₂):

log(k₂/k₁) = (E_a / 2.303 R) [ (T₂ - T₁) / (T₁T₂) ]