Chapter 3: Chemical Kinetics

Average Rate (r_av)

Change in concentration of reactants or products over a specific time interval.

r_av = - Δ[R]/Δt = + Δ[P]/Δt

Instantaneous Rate (r_inst)

Rate of reaction at a particular instant of time (when Δt → 0).

r_inst = - d[R]/dt = + d[P]/dt

General Reaction Expression

For reaction: aA + bB → cC + dD

Rate = - (1/a)d[A]/dt = - (1/b)d[B]/dt = + (1/c)d[C]/dt = + (1/d)d[D]/dt

Factors Affecting Rate

• Concentration: Rate usually increases with an increase in reactant concentration.
• Temperature: Rate increases with temperature (rule of thumb: rate doubles for every 10°C rise).
• Catalyst: Increases rate by providing an alternate path with lower activation energy.
• Surface Area: Greater surface area of solid reactants increases the rate.

Rate Law

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

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

Rate Constant (k)

Also known as specific reaction rate. It is the rate of reaction when the concentration of all reactants is unity (1 mol/L).

• Independent of initial concentration.
• Depends heavily on Temperature.

Units of Rate Constant (k)

General formula for unit: (mol L^-1)^1-n s^-1 (where n is the order)

• Zero Order: mol L^-1 s^-1
• First Order: s^-1
• Second Order: mol^-1 L s^-1

Molecularity

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

Order of Reaction

• Sum of the powers of concentration terms in the experimentally determined rate law. (n = x + y).
• It is an Experimental value.
• Can be zero, fractional, or negative.
• Assigned for both elementary and complex reactions (determined by the slowest step).

Zero Order Reactions

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

k = ([R]₀ - [R]) / t

Half-Life (t½): Time taken for concentration to reduce to half.

t½ = [R]₀ / 2k

First Order Reactions

Rate depends on the first power of reactant concentration. (e.g., Natural radioactive decay).

k = (2.303 / t) log([R]₀ / [R])

Half-Life (t½): Independent of initial concentration.

t½ = 0.693 / k

Pseudo First Order Reaction

Reactions which are actually of higher order but behave as first order due to one reactant being present in large excess.

• Example 1: Acid hydrolysis of ethyl acetate (Water is in excess).
• Example 2: Inversion of cane sugar.

Collision Theory

• Reactant molecules are assumed to be hard spheres. Reaction occurs only when they collide.
• Effective Collisions: Must possess sufficient energy (Threshold energy) and proper orientation.
• Formula: Rate = P × Z_ab × e^-Ea/RT
• (P = Steric/Probability factor, Z_ab = Collision frequency)

Activation Energy (Ea)

The extra energy required by reactant molecules to reach the threshold energy.

Threshold Energy = Ea + Average kinetic energy of reactants

Arrhenius Equation

Gives the exact dependence of rate constant on temperature.

k = A × e^-Ea/RT

Logarithmic form:

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

Comparing at two different temperatures (T1 and T2):

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