Chemical Kinetics 

Chemical Kinetics – Basics

Chemical kinetics deals with the rate of chemical reactions, reaction mechanisms and the effect of factors such as concentration, temperature and catalysts on reaction rate.

Types of Chemical Reactions (Based on Rate)

• Very fast reactions: Instantaneous, usually ionic (e.g. AgNO₃ + NaCl → AgCl + NaNO₃)
• Moderate reactions: Measurable rates (e.g. ester hydrolysis, N₂O₅ decomposition)
• Very slow reactions: Extremely slow (e.g. rusting of iron)

Rate of Reaction

• Rate = change in concentration per unit time
• Average rate = Δx / Δt
• Instantaneous rate = dx / dt

For reaction: aA + bB → cC + dD

r = −(1/a)(d[A]/dt) = −(1/b)(d[B]/dt) = (1/c)(d[C]/dt) = (1/d)(d[D]/dt)

• Rate is always positive
• Unit: mol L⁻¹ time⁻¹
• For gases: atm time⁻¹

Factors Affecting Rate of Reaction

• Nature of reactants (state, size, chemical nature)
• Temperature (rate doubles/triples for 10°C rise)
• Concentration of reactants
• Catalyst (lowers activation energy)
• Sunlight (photochemical reactions)

Temperature Coefficient

Temperature coefficient = k_(t+10°C) / k_(t°C)

Rate Law & Rate Constant

Rate law: Rate = k[A]^m[B]ⁿ

• m + n = order of reaction
• k = rate constant (specific reaction rate)
• k is constant for a given reaction at fixed temperature

Molecularity vs Order of Reaction

Integrated Rate Laws & Half-Life

Zero Order Reaction

• k = x / t
• t_1/2 = a / (2k)
• Rate independent of concentration

First Order Reaction

• k = (2.303 / t) log (a / (a − x))
• t_1/2 = 0.693 / k
• Rate ∝ concentration

Second Order Reaction

• k = (1 / t) [ x / a(a − x) ]
• t_1/2 = 1 / (ka)
• Rate ∝ (concentration)²

Third Order Reaction

• t_1/2 = 3 / (2ka²)

Units of Rate Constant

• Zero order: mol L⁻¹ s⁻¹
• First order: s⁻¹
• Second order: L mol⁻¹ s⁻¹
• nth order: Lⁿ⁻¹ mol¹⁻ⁿ s⁻¹

Activation Energy (E_a)

• Minimum energy required for reaction to occur
• E_a = Threshold energy − Average kinetic energy
• Higher E_a → slower reaction

Arrhenius Equation

k = A e^−E_a/RT

• A = frequency factor
• E_a = activation energy
• R = gas constant
• T = absolute temperature

log k = log A − (E_a / 2.303RT)

From Arrhenius Equation

log(k₂/k₁) = (E_a/2.303R) (1/T₁ − 1/T₂)

Photochemical Reactions

Chemical reactions initiated by absorption of light.

Characteristics

• Each molecule absorbs one photon (E = hν = hc/λ)
• Do not occur in dark
• Require specific wavelength
• Rate depends on intensity of light absorbed
• ΔG may be positive or negative

Quantum Yield (φ)

φ = Number of molecules reacted / Number of photons absorbed