Rate of Reaction, Rate Law and Order

• Define rate of reaction in terms of concentration change per unit time
• Write and interpret the rate law: rate = k[A]^m[B]^n
• Determine order of reaction from initial rate experiments
• Distinguish between order (experimental) and molecularity (theoretical)
• Calculate units of rate constant k for any order reaction
• Identify and handle pseudo-first-order reactions

Level 1 — Foundations

Rate of Reaction
For aA + bB → cC + dD: $\text{rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = +\frac{1}{c}\frac{\Delta[C]}{\Delta t} = +\frac{1}{d}\frac{\Delta[D]}{\Delta t}$

• Negative sign for reactants (concentration decreasing), positive for products.
• Units: mol L⁻¹ s⁻¹ (or mol L⁻¹ min⁻¹ etc.)
• Instantaneous rate = −d[A]/dt (slope of tangent to [A] vs t curve)

Rate Law
rate = k[A]^m[B]^n

• k = rate constant (depends on T, not concentration)
• m = order w.r.t. A, n = order w.r.t. B
• Overall order = m + n
• Orders must be determined experimentally; they need NOT equal stoichiometric coefficients

Molecularity
Number of molecules (atoms/ions) taking part in an elementary step.

• Always a positive integer (1, 2, or 3)
• Applies only to elementary reactions; complex reactions have no molecularity as a whole

Level 2 — JEE Depth

Units of Rate Constant k
From rate = k[A]^n: $k = \frac{\text{rate}}{[\text{conc}]^n} \Rightarrow \text{units} = \frac{\text{mol L}^{-1}\text{s}^{-1}}{(\text{mol L}^{-1})^n} = (\text{mol L}^{-1})^{1-n}\text{s}^{-1}$

Initial Rate Method (Finding Orders Experimentally)
Keep [B] constant, vary [A]: $\frac{r_2}{r_1} = \left(\frac{[A]_2}{[A]_1}\right)^m \Rightarrow m = \frac{\log(r_2/r_1)}{\log([A]_2/[A]_1)}$

Pseudo-First-Order Reactions
When one reactant is in large excess (e.g., hydrolysis of ester in excess water):
rate = k[ester][H₂O] → rate ≈ k'[ester] where k' = k[H₂O] (pseudo-first-order)
Allows simpler experimental analysis.

Temperature Dependence (Preview)
k increases with T; quantified by Arrhenius equation k = Ae^(−Ea/RT) (covered in Arrhenius note).

JEE Traps

• Order can be zero, fractional, or negative — molecularity cannot
• Molecularity is defined only for elementary steps
• Rate law is not derived from balanced equation for multi-step mechanisms
• Units of k change with order — always re-derive rather than memorise

Example 1: Finding Order from Initial Rate Data

Experiment data:
Exp  [A] (M)  [B] (M)  Rate (mol/L/s)
 1    0.1      0.1      2×10⁻⁴
 2    0.2      0.1      4×10⁻⁴   (rate doubled, [A] doubled, [B] same)
 3    0.1      0.2      8×10⁻⁴   (rate quadrupled, [B] doubled, [A] same)

Step 1: Order w.r.t. A
  r₂/r₁ = (0.2/0.1)^m → 4×10⁻⁴ / 2×10⁻⁴ = 2^m → 2 = 2^m → m = 1

Step 2: Order w.r.t. B
  r₃/r₁ = (0.2/0.1)^n → 8×10⁻⁴ / 2×10⁻⁴ = 2^n → 4 = 2^n → n = 2

Step 3: Overall order = m + n = 1 + 2 = 3 (third order)

Step 4: Find k from Experiment 1
  rate = k[A]¹[B]²
  2×10⁻⁴ = k × (0.1) × (0.1)²
  2×10⁻⁴ = k × 0.001
  k = 0.2 L² mol⁻² s⁻¹

Answer: rate = k[A][B]², overall order = 3, k = 0.2 L² mol⁻² s⁻¹

Example 2: Calculating Rate from Rate Law

Given: rate = k[A][B]², k = 2×10⁻³ L² mol⁻² s⁻¹, [A] = 0.1 M, [B] = 0.2 M

Step 1: Substitute values
  rate = (2×10⁻³) × (0.1) × (0.2)²

Step 2: Calculate [B]² = (0.2)² = 0.04

Step 3: rate = 2×10⁻³ × 0.1 × 0.04
             = 2×10⁻³ × 4×10⁻³
             = 8×10⁻⁶ mol L⁻¹ s⁻¹

Answer: rate = 8×10⁻⁶ mol L⁻¹ s⁻¹

Check units: (L² mol⁻² s⁻¹)(mol L⁻¹)(mol L⁻¹)² = mol L⁻¹ s⁻¹ ✓

• Q1: For 2NO(g) + O₂(g) → 2NO₂(g), if rate = k[NO]²[O₂], what is the overall order?
• Q2: The rate doubles when [A] is doubled (B constant) and is unaffected by [B]. Write the rate law.
• Q3: What are the units of k for a zero-order reaction?
• Q4: In hydrolysis of sucrose (excess water), rate = k'[sucrose]. What is this type of kinetics called?
• Stretch: Q5: A reaction has rate = k[A]^(1/2). What happens to the rate when [A] is increased 4-fold? What does a fractional order suggest about the mechanism?

NCERT Chapter 3 link: Chapter 3 "Chemical Kinetics" Class 12 — covers rate expression, factors affecting rate, rate law, order, molecularity, and units of k. NCERT Table 3.1 gives experimental data for rate determination.

Exam connections: JEE often gives a 3-row data table and asks to find m, n, k, and units. Multi-step mechanism questions ask which step is rate-determining. Pseudo-first-order appears in hydrolysis MCQs. Negative/fractional orders appear in JEE Advanced.

Study strategy: Master the ratio method (r₂/r₁) for finding orders — it is faster than logarithms for integer orders. Practice unit analysis for k as a standalone skill. Distinguish the vocabulary: rate (has units mol/L/s), rate constant k (units depend on order), rate law (mathematical expression).

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• Mirror / body / home activity: physically do the concept and photograph or describe for portfolio.
• Voice or text reflection with AI Mentor: explain the concept to a younger student or family member.

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• One hands-on project or measurement using the Drishti kit or household items that makes the concept physical.
• Direct link to at least one Future Skill track (Money Management, Green Tech, Cyber Defenders, Micro-Entrepreneurship, AI Mastery, Sustainable Living, Personality Development).
• Coding extension where relevant (simple script, simulation, or data logging).

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