Introduction to Chemical Kinetics
Chemical Kinetics is the branch of physical chemistry which deals with the rate at which chemical reactions occur, the mechanism by which chemical reactions take place, and the influence of various factors such as concentration, temperature, pressure, catalyst, etc., on the reaction rates.
Types of Chemical Reactions
On the basis of reaction rates, chemical reactions have been classified into three types:
Very Fast or Instantaneous Reactions
Occur at very fast rate
Involve ionic species
Known as ionic reactions
Almost impossible to determine rates
Examples:
AgNO₃ + NaCl → AgCl + NaNO₃ (Precipitation)
HCl + NaOH → NaCl + H₂O (Neutralization)
Moderate Reactions
Proceed with measurable rates at normal temperature
Studied in chemical kinetics
Mostly molecular in nature
Examples:
2H₂O₂ → 2H₂O + O₂ (Decomposition)
2N₂O₅ → 2N₂O₄ + O₂ (Decomposition)
Very Slow Reactions
Extremely slow
Take months to show measurable change
Examples:
Fe₂O₃ + xH₂O → Fe₂O₃·xH₂O (Rusting of iron)
2H₂ + O₂ → 2H₂O (At room temperature)
Rate of a Reaction
The rate (speed or velocity) of a reaction is the change in concentration per unit time.
Rate = Δx/Δt or dx/dt = (x₂ - x₁)/(t₂ - t₁)
where Δx or dx is the concentration change in the time interval Δt or dt.
Concentration is generally expressed in active mass, i.e., mole L⁻¹. The rate measured over a long time interval is called average rate and the rate measured for an infinitesimally small time interval is called instantaneous rate.
Rate Expressions for Reactions
For the reaction: aA + bB → cC + dD
-d[A]/dt = Rate of disappearance of A
-d[B]/dt = Rate of disappearance of B
d[C]/dt = Rate of formation of C
d[D]/dt = Rate of formation of D
-d[B]/dt = Rate of disappearance of B
d[C]/dt = Rate of formation of C
d[D]/dt = Rate of formation of D
dx/dt = -1/a · d[A]/dt = -1/b · d[B]/dt = 1/c · d[C]/dt = 1/d · d[D]/dt
Important Points
- The rate of reaction is always positive
- The rate of chemical reaction decreases as the reaction proceeds
- Unit of rate = mole L⁻¹ time⁻¹ (for gaseous reactions: atm time⁻¹)
- Rate in atm time⁻¹ = Rate in mole L⁻¹ × RT
Factors Affecting Rate of a Reaction
Nature of Reactants
Physical state: Gaseous > Liquid > Solid
Physical size: Rate increases with decrease in particle size
Chemical nature: Ionic reactions are fast, bond rearrangement reactions are slow
Effect of Temperature
Rate generally increases with temperature
Rate doubles or triples for every 10°C rise
Temperature coefficient μ = k(t+10°C)/kt°C
Concentration of Reactants
Rate is directly proportional to concentration
Rate decreases with decrease in concentration
Presence of Catalyst
Lowers activation energy
Greater decrease in Ea → higher reaction rate
Effect of Sunlight
Photochemical reactions influenced by UV/visible light
Examples: Photosynthesis, Photography
Radiant energy supplies activation energy
Law of Mass Action and Rate Constant
The rate at which a substance reacts is directly proportional to its active mass and the rate at which a reaction proceeds is proportional to the product of the active masses of the reacting substances.
For aA + bB → product: Rate = dx/dt = k[A]ᵃ[B]ᵇ
When [A] = [B] = 1 mol/litre, then dx/dt = k. Thus, rate constant k is also called specific reaction rate.
Important Points
- Value of k depends on nature of reactant, temperature, and catalyst
- k is independent of concentration of reactants
- Unit of k = [mol/litre]¹⁻ⁿ × sec⁻¹ where n = order of reaction
Rate Law: Molecularity and Order of Reaction
Molecularity
Sum of molecules of reactants in balanced equation
Derived from reaction mechanism
Cannot be zero, negative, or fractional
Cannot be greater than 3
Examples:
NH₄NO₂ → N₂ + 2H₂O (Unimolecular)
NO + O₃ → NO₂ + O₂ (Bimolecular)
2NO + O₂ → 2NO₂ (Trimolecular)
Order of Reaction
Sum of exponents in rate law
Determined by slowest step in mechanism
Can be zero, negative, positive, fractional
Can be greater than 3
Example:
For Rate = k[A]ˣ[B]ʸ
Overall order = x + y
Order and Molecularity of Some Reactions
| S.No. | Chemical Equation | Molecularity | Rate Law | Order |
|---|---|---|---|---|
| 1 | aA + bB → product | a + b | dx/dt = k[A]ᵃ[B]ᵇ | a + b |
| 3 | 2H₂O₂ → 2H₂O + O₂ | 2 (Bimolecular) | dx/dt = k[H₂O₂] | 1 |
| 7 | CH₃Cl + OH⁻ → CH₃OH + Cl⁻ | 2 (Bimolecular) | dx/dt = k[CH₃Cl][OH⁻] | 2 |
| 9 | CH₃CHO → CH₄ + CO | 1 (Unimolecular) | dx/dt = k[CH₃CHO]³/² | 1.5 |
| 11 | 2O₃ → 3O₂ | 2 | dx/dt = k[O₃]²[O₂]⁻¹ | 1 |
Rate Constants and Half-Life Periods
| Order | Rate Constant | Unit | Effect on Rate (m times conc.) | Half-Life (T₅₀) |
|---|---|---|---|---|
| 0 | k₀ = x/t | conc. time⁻¹ | No change | a/(2k₀) |
| 1 | k₁ = (2.303/t) log(a/(a-x)) | time⁻¹ (s⁻¹) | m times | 0.693/k₁ |
| 2 | k₂ = (1/t)[1/(a-x) - 1/a] | conc⁻¹ time⁻¹ | m² times | 1/(k₂a) |
| 3 | k₃ = (1/2t)[1/(a-x)² - 1/a²] | conc⁻² time⁻¹ | m³ times | 3/(2k₃a²) |
| n | kₙ = 1/((n-1)t)[1/(a-x)ⁿ⁻¹ - 1/aⁿ⁻¹] | conc¹⁻ⁿ time⁻¹ | mⁿ times | (2ⁿ⁻¹ - 1)/((n-1)kₙaⁿ⁻¹) |
Methods for Determination of Order
Integration Method
Uses integrated rate equations
Value of k determined for all sets
Constant k value gives order
Half-Life Method
t₁/₂ ∝ a¹⁻ⁿ
Plot log t₁/₂ vs log a gives slope (1-n)
n = 1 + [log(t₁/₂)₁ - log(t₁/₂)₂] / [log a₂ - log a₁]
Graphical Method
Plot log(a-x) vs t → straight line for 1st order
Plot 1/(a-x) vs t → straight line for 2nd order
Plot 1/(a-x)² vs t → straight line for 3rd order
Van't Hoff Differential Method
Rate = kCⁿ
n = [log(-dC₁/dt) - log(-dC₂/dt)] / [log C₁ - log C₂]
Ostwald's Isolation Method
Initial rate method
Vary one reactant at a time
Determine order with respect to each reactant
Theories of Reaction Rate
Collision Theory
Basic requirement: collision between reacting species
Collision frequency (Z): collisions per second per unit volume
Effective collisions produce chemical change
Two barriers: Energy barrier and Orientation barrier
Rate = f × Z (f = fraction of effective collisions)
k = PZABe⁻ᴱᵃ/ᴿᵀ (P = orientation factor)
Activation Energy (Eₐ) = Threshold Energy - Average Kinetic Energy of Reacting Molecules
Transition State Theory
Activated complex in equilibrium with reactants
Transition state can form products or return to reactants
Rate ∝ concentration of transition state
ΔH = Eₐ(forward) - Eₐ(reverse)
Endothermic: Eₐ(forward) < Eₐ(reverse)
Exothermic: Eₐ(forward) > Eₐ(reverse)
Arrhenius Equation
k = Ae⁻ᴱᵃ/ᴿᵀ
log k = log A - Eₐ/(2.303RT)
log(k₂/k₁) = Eₐ/(2.303R) × [1/T₁ - 1/T₂]
Important Points
- A = frequency factor, Eₐ = activation energy
- Plot of log k vs 1/T gives straight line
- Slope = -Eₐ/(2.303R)
- Intercept = log A
Mechanism of Reactions
First Order Consecutive Reactions
R → I → P (two steps, both first order)
I produced by step I, consumed by step II
Each stage has own rate and rate constant
Reactions with Slow Step
Rate determined by slowest step
If k₁ << k₂: -d[R]/dt = d[P]/dt = k₁[R]
Parallel Reactions
Reactants consumed in multiple reactions
Rate of disappearance = sum of rates of all reactions
Photochemical Reactions
Chemical reactions initiated by absorption of light. Absorbed energy activates reactant molecules to cross energy barrier.
Characteristics
Each molecule absorbs only one photon (Einstein's law)
Do not occur in dark
Require definite energy (specific wavelength)
Rate depends on intensity of radiation
ΔG may or may not be negative
Temperature has little effect on rate
Mechanism of H₂ + Cl₂ Reaction
Chain reaction producing 10⁶-10⁸ HCl molecules per photon
Light absorption: Cl₂ + hν → Cl₂*
Chain initiation: Cl₂* → Cl• + Cl•
Chain propagation: Cl• + H₂ → HCl + H•; H• + Cl₂ → HCl + Cl•
Chain termination: Cl• + Cl• → Cl₂
Quantum Yield (φ)
φ = (Number of molecules reacted or product formed) / (Number of photons absorbed)
Applications of Photochemistry
- Photosynthesis in plants
- Photography
- Formation and destruction of ozone layer
- Photoetching in electronic industry
- Polymerization reactions
- Modern printing technology
- Free radical combinations
Tips & Tricks
Key Points for JEE Main
- Different reactions have different rates due to different activation energies
- Reaction NO + ½O₂ → NO₂ has negative temperature coefficient
- Fuels need activation energy (provided by flame) to initiate reaction
- Quantum efficiency: H₂ + Cl₂ → 2HCl (φ = 10⁶-10⁸); H₂ + Br₂ → 2HBr (φ = 0.01)
- For zero order: t₀.₇₅ = 1.5 × t₀.₅; t₀.₅₀ = 2 × t₀.₂₅
- For first order: t₀.₇₅ = 2 × t₀.₅; t₀.₅₀ = 2 × t₀.₂₅
- For second order: t₀.₇₅ = 3 × t₀.₅; t₀.₅₀ = 3 × t₀.₂₅
Do's
Understand difference between order and molecularity
Practice integrated rate equations
Learn to determine order from experimental data
Remember Arrhenius equation applications
Don'ts
Don't confuse order with molecularity
Don't forget units of rate constants
Don't mix up half-life formulas
Don't ignore temperature effects on rate
JEE Main Weightage
This chapter typically carries 2-3 questions in JEE Main, covering rate laws, order of reactions, Arrhenius equation, and reaction mechanisms.
Chapter Weightage in JEE Main
Weightage
Medium (2-3 questions)