MP Board Class 12 Chemistry Chapter 4: Chemical Kinetics Notes (रासायनिक बलगतिकी)

MP Board Class 12 Chemistry Chapter 4: Chemical Kinetics (रासायनिक बलगतिकी) — This chapter covers the rate of chemical reactions, factors affecting reaction rates, rate laws, order of reactions, integrated rate equations, half-life, collision theory, and Arrhenius equation. In MP Board Class 12 Chemistry exams, this chapter typically carries 4–6 marks including numericals on rate constant calculation, half-life determination, and temperature dependence of reaction rates.

⚡ Rate of Chemical Reaction (अभिक्रिया की दर)

Chemical kinetics is the branch of chemistry that deals with the speed or rate of chemical reactions and the mechanism by which they occur. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time.

📐 Average Rate vs Instantaneous Rate

Property Average Rate Instantaneous Rate
Definition Rate over a finite time interval Rate at a particular instant
Formula r_avg = −Δ[R]/Δt = +Δ[P]/Δt r_inst = −d[R]/dt = +d[P]/dt
Time interval Large (seconds to hours) Infinitesimally small (dt)
Use General rate description True rate at a specific moment

Units of rate: mol L⁻¹ s⁻¹ or atm s⁻¹ (for gaseous reactions)
For a general reaction: aA + bB → cC + dD, the rate is expressed as:

📐 Rate Expression

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

🧪 Expressing Rate of Reaction — Example

For the reaction: 2N₂O₅(g) → 4NO₂(g) + O₂(g), the rate can be written as:

  • Rate = −½ d[N₂O₅]/dt = +¼ d[NO₂]/dt = +d[O₂]/dt
  • The negative sign indicates decrease in concentration of reactant N₂O₅
  • The positive sign indicates increase in concentration of products NO₂ and O₂
🎯 Exam Tip: In MP Board 2027 exams, questions on rate expression are frequently asked as 2-mark very short answer questions. Practice writing rate expressions for at least 5 different reactions with their stoichiometric coefficients.

📊 Rate Law and Order of Reaction (दर नियम एवं अभिक्रिया कोटि)

📌 Rate Law

The rate law (or rate equation) expresses the rate of a reaction as a function of the concentration of reactants. For a reaction A + B → Products, the rate law is:

📐 Rate Law Expression

Rate = k [A]ˣ [B]ʸ

where k = rate constant (specific rate), x = order w.r.t A, y = order w.r.t B

🔄 Order of Reaction

The order of a reaction is the sum of the powers of concentration terms in the rate law expression. It is determined experimentally, NOT from the balanced chemical equation.

Order Rate Law Example Rate = k
Zero Order Rate ∝ [A]⁰ Photochemical HCl formation k
First Order Rate ∝ [A]¹ N₂O₅ decomposition k[A]
Second Order Rate ∝ [A]² or [A][B] 2HI → H₂ + I₂ k[A]²
Pseudo First Order One reactant in large excess Acid catalysed hydrolysis of ester k[ester]

📏 Molecularity vs Order of Reaction

Parameter Order of Reaction Molecularity
Definition Sum of powers in rate law Number of reacting species in elementary step
Determined by Experiment Balanced equation (for elementary reactions)
Values Can be zero, fractional, negative Always a positive integer (1, 2, 3)
Example Thermal decomposition of HI: Order = 2 Same reaction: Molecularity = 2
🎯 Exam Tip: MP Board frequently asks to distinguish between order and molecularity (3 marks). Also, pseudo-first-order reactions like hydrolysis of methyl acetate in excess water are favourite topics. Remember: molecularity is always a whole number; order can be fractional.

📐 Integrated Rate Equations (समाकलित दर समीकरण)

Integrated rate equations express the concentration of reactants as a function of time. They are used to determine the order of a reaction and to calculate the rate constant.

📘 Zero Order Reaction (शून्य कोटि अभिक्रिया)

A + B → Products; Rate = k[A]⁰ = k

  • Integrated equation: [A] = [A]₀ − kt
  • k = ([A]₀ − [A]) / t
  • Units of k: mol L⁻¹ s⁻¹
  • Plot of [A] vs t gives a straight line with slope = −k

📗 First Order Reaction (प्रथम कोटि अभिक्रिया)

Rate = k[A]¹ = k[A]

  • Integrated equation: k = (2.303/t) log₁₀([A]₀/[A])
  • or [A] = [A]₀e^(−kt)
  • Units of k: s⁻¹ (or time⁻¹)
  • Plot of log[A] vs t gives a straight line with slope = −k/2.303
  • Examples: Radioactive decay, N₂O₅ decomposition, hydrolysis of sugar

📕 Second Order Reaction (द्वितीय कोटि अभिक्रिया)

For same initial concentration of both reactants: Rate = k[A]²

  • Integrated equation: k = (1/t)(1/[A] − 1/[A]₀)
  • Units of k: L mol⁻¹ s⁻¹
  • Plot of 1/[A] vs t gives a straight line with slope = k

⏱️ Half-Life of a Reaction (अर्धायु काल)

The half-life (t½) of a reaction is the time required for the concentration of a reactant to reduce to half of its initial value.

Order Half-Life Formula Dependence on [A]₀
Zero Order t½ = [A]₀ / 2k Directly proportional
First Order t½ = 0.693/k Independent of [A]₀
Second Order t½ = 1/(k[A]₀) Inversely proportional

📘 Key Concept

For first-order reactions, the half-life is constant and independent of initial concentration. After n half-lives, the fraction remaining = (½)ⁿ. For example, after 3 half-lives, ⅛ of the initial concentration remains.

🎯 Exam Tip: Half-life numerical problems are almost guaranteed in MP Board exams — typically 3 marks. Remember the three formulas and practice at least 5 numericals. The first-order half-life formula t½ = 0.693/k is the most commonly asked.

🔬 Arrhenius Equation & Activation Energy (आरहीनियस समीकरण एवं सक्रियण ऊर्जा)

📌 Arrhenius Equation

The Arrhenius equation shows the temperature dependence of the rate constant:

📐 Arrhenius Equation

k = A e^(−Ea/RT)

Logarithmic form: log k = log A − Ea/(2.303 RT)

where Ea = activation energy (J/mol), R = 8.314 J/K·mol, T = temperature (K), A = frequency factor

📊 Two-Point Form

To compare rate constants at two different temperatures T₁ and T₂:

📐 Two-Point Arrhenius Equation

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

⚡ Activation Energy (Ea)

  • Activation energy is the minimum energy that reacting molecules must possess for a reaction to occur
  • Lower Ea → faster reaction (more molecules have enough energy)
  • Catalysts lower activation energy, providing an alternative pathway
  • Threshold energy = Activation energy + Energy of reactants
🎯 Exam Tip: Arrhenius equation numericals are very common in MP Board 12th Chemistry — typically 3–5 marks. Practice calculating Ea² from given k values at two temperatures using the two-point form. The logarithmic form (log k vs 1/T plot giving a straight line with slope = −Ea/2.303R) is also frequently asked as a theory question.

🔧 Factors Affecting Reaction Rate (अभिक्रिया दर को प्रभावित करने वाले कारक)

Factor Effect on Rate Explanation
Concentration Increases rate More molecules → more collisions
Temperature Strong increase Rate typically doubles for every 10°C rise (Arrhenius equation)
Catalyst Increases rate Lowers activation energy, not consumed in reaction
Surface Area Increases rate More active sites for reaction (heterogeneous)
Nature of Reactants Varies by reaction Ionic reactions are fast; covalent bond breaking is slow
Pressure (Gases) Increases rate Higher pressure = higher concentration of gases

📘 Temperature Coefficient (θ)

The temperature coefficient is the ratio of rate constants at two temperatures differing by 10°C:

θ = k_(T+10) / k_T ≈ 2 to 3

This means the rate of reaction approximately doubles for every 10°C rise in temperature.

🔄 Collision Theory of Chemical Reactions (टक्कर सिद्धांत)

The collision theory explains reaction rates based on the frequency and effectiveness of molecular collisions. According to this theory:

  • For a reaction to occur, reactant molecules must collide with each other
  • Not all collisions lead to a reaction — only effective collisions do
  • An effective collision requires:
Condition Explanation
1. Sufficient Energy Molecules must have at least activation energy (Ea) to break existing bonds
2. Proper Orientation Molecules must collide in correct spatial orientation for bond formation

Rate according to collision theory: Rate = Z_AB × f × p

  • Z_AB = collision frequency (total collisions per unit volume per unit time)
  • f = fraction of molecules with energy ≥ Ea (from Maxwell-Boltzmann distribution)
  • p = orientation factor (steric factor), between 0 and 1

📝 MP Board Previous Year Questions (पूर्व वर्षों के प्रश्न)

✅ 2 Mark Questions

  1. What is the difference between average rate and instantaneous rate of a reaction? (2020, 2022)
  2. Define half-life of a reaction. Write the half-life expression for a first-order reaction. (2021, 2023)
  3. What is a pseudo-first-order reaction? Give an example. (2019, 2022, 2024)
  4. Define activation energy. How does a catalyst affect activation energy? (2020, 2023)
  5. State the units of rate constant for zero-order and first-order reactions. (2021)

✅ 3 Mark Questions

  1. Derive the integrated rate equation for a first-order reaction. (2020, 2022, 2024)
  2. Explain the effect of temperature on reaction rate using the Arrhenius equation. (2021, 2023)
  3. Differentiate between order of reaction and molecularity. (2019, 2022)
  4. A first-order reaction has k = 2.0 × 10⁻³ s⁻¹. Calculate its half-life. (2023, 2024)
  5. Explain collision theory of chemical reactions. What conditions are necessary for effective collisions? (2021)

✅ 5 Mark Questions (Numericals)

  1. The rate constant for a first-order reaction is 2.3 × 10⁻⁴ s⁻¹. Calculate the time required for the concentration to reduce to 25% of its initial value. [log 4 = 0.6020] (2020, 2023)
  2. For a reaction, k = 3.0 × 10⁻³ s⁻¹ at 300K and k = 8.0 × 10⁻³ s⁻¹ at 320K. Calculate the activation energy (Ea). [R = 8.314 J/K·mol, log 2.67 = 0.426] (2022, 2024)
  3. The half-life of a first-order reaction is 500 seconds. Find the time required for 90% completion of the reaction. [log 10 = 1] (2021)
📘 Key Points for Revision: Focus on deriving integrated rate equations for first-order reactions, understanding the Arrhenius equation (both forms), collision theory conditions, and practising half-life numericals. The formula k = 0.693/t½ for first-order reactions is almost guaranteed in the MP Board 2027 exam.

📘 Important Formulas — Quick Revision

• Rate = −d[R]/dt = k[R]ⁿ (general rate law)

• Zero order: [R] = [R]₀ − kt; t½ = [R]₀/2k

• First order: k = (2.303/t) log[R]₀/[R]; t½ = 0.693/k

• Second order: 1/[R] − 1/[R]₀ = kt; t½ = 1/k[R]₀

• Arrhenius: k = Ae^(−Ea/RT); log k = log A − Ea/2.303RT

• Two-point: log(k₂/k₁) = Ea(T₂−T₁)/(2.303R × T₁T₂)

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