Chemical Kinetics revision notes

Key Concepts & Definitions

Chemical Kinetics:

The branch of chemistry that deals with the study of reaction rates and their mechanisms. The word "kinetics" is derived from the Greek word 'kinesis', meaning movement.

Thermodynamics vs. Kinetics:

Thermodynamics predicts the feasibility of a reaction (ΔG<0\Delta G < 0ΔG<0) and its extent (equilibrium), but chemical kinetics determines the speed.JEE TIPThermodynamic data may indicate a reaction is feasible (e.g., diamond converting to graphite), but kinetic data shows the rate is so slow that it is imperceptible.

Classification of Reaction Rates:

Very Fast (Instantaneous): Ionic reactions, such as the precipitation of silver chloride (AgClAgClAgCl) upon mixing aqueous silver nitrate (AgNO3AgNO_3AgNO3​) and sodium chloride (NaClNaClNaCl). Very Slow: Rusting of iron in the presence of air and moisture. Moderate Speed: Inversion of cane sugar and hydrolysis of starch.

Average Rate (ravr_{av}rav​):

The change in concentration of a reactant or product over a macroscopic time interval (Δt\Delta tΔt).

Instantaneous Rate (rinstr_{inst}rinst​):

The rate of a reaction at a specific instant of time, determined mathematically when Δt\Delta tΔt approaches zero (dtdtdt), or graphically by drawing a tangent to the concentration vs. time curve.

Rate Law (Rate Expression):

The mathematical expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power (which may or may not match the stoichiometric coefficients).

Rate Constant (kkk):

The proportionality constant in the rate law. Also known as specific reaction rate.

Order of Reaction:

The sum of powers of the concentration of the reactants in the rate law expression.

Elementary Reactions:

Reactions that take place in a single step.

Complex Reactions:

Reactions that take place in a sequence of elementary steps (a mechanism).

Molecularity:

The number of reacting species (atoms, ions, or molecules) taking part in an elementary reaction that must collide simultaneously to bring about the reaction.

Intermediate:

A species formed during the course of a complex reaction but does not appear in the overall balanced equation. In the bimolecular collision of H2H_2H2​ and I2I_2I2​, an unstable intermediate (activated complex) is temporarily formed before breaking up into two molecules of HIHIHI.

Rate of Reaction & Stoichiometry

• Expressing Rate: For a hypothetical reaction $R \rightarrow P$, the rate is expressed as $-\frac{\Delta[R]}{\Delta t}$ (rate of disappearance) or $+\frac{\Delta[P]}{\Delta t}$ (rate of appearance). The negative sign ensures the rate value remains a positive quantity.
• Units of Rate: Concentration time$^{-1}$ (e.g., $\text{mol L}^{-1}\text{s}^{-1}$). For gaseous reactions using partial pressures, the unit is $\text{atm s}^{-1}$.
• Stoichiometric adjustments: For reactions where stoichiometric coefficients are not equal to 1, the rate of disappearance/appearance is divided by the respective coefficient to equate the overall rate of reaction.
  • Example 1: $2HI(g) \rightarrow H_2(g) + I_2(g)$ $\Rightarrow$ $\text{Rate} = -\frac{1}{2}\frac{\Delta[HI]}{\Delta t} = \frac{\Delta[H_2]}{\Delta t} = \frac{\Delta[I_2]}{\Delta t}$.
  • Example 2: $5Br^-(aq) + BrO_3^-(aq) + 6H^+(aq) \rightarrow 3Br_2(aq) + 3H_2O(l)$ $\Rightarrow$ $\text{Rate} = -\frac{1}{5}\frac{\Delta[Br^-]}{\Delta t} = -\frac{\Delta[BrO_3^-]}{\Delta t} = -\frac{1}{6}\frac{\Delta[H^+]}{\Delta t} = +\frac{1}{3}\frac{\Delta[Br_2]}{\Delta t} = +\frac{1}{3}\frac{\Delta[H_2O]}{\Delta t}$.

Rate Law, Order & Molecularity

• Rate Law Dependence: Rate depends on reactant concentrations, temperature, and catalysts. For $aA + bB \rightarrow cC + dD$, Rate = $k[A]^x[B]^y$.
  • The exponents $x$ and $y$ must be determined experimentally.
  • Overall Order $= x + y$. Order can be 0, 1, 2, 3, or fractional.
• Examples of Rate Laws:
  • $2NO(g) + O_2(g) \rightarrow 2NO_2(g) \Rightarrow \text{Rate} = k[NO]^2[O_2]$ (Matches stoichiometry).
  • $CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl \Rightarrow \text{Rate} = k[CHCl_3][Cl_2]^{1/2}$ (Fractional order = 1.5).
  • $CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH \Rightarrow \text{Rate} = k[CH_3COOC_2H_5]^1[H_2O]^0$ (Order = 1).
• Determining Units of Rate Constant ($k$): $k = (\text{concentration})^{1-n}\text{time}^{-1}$ where $n$ is the reaction order.
  • Zero order ($n=0$): $\text{mol L}^{-1}\text{s}^{-1}$.
  • First order ($n=1$): $\text{s}^{-1}$.
  • Second order ($n=2$): $\text{mol}^{-1}\text{L s}^{-1}$.
  • JEE TIPYou can identify the order of an unknown reaction directly by looking at the units of its rate constant $k$.
• Molecularity vs. Order:
  • Order is experimental; molecularity is theoretical.
  • Molecularity strictly applies to elementary steps. For complex reactions, molecularity of the overall reaction has no meaning.
  • Molecularity must be an integer (1, 2, 3) and cannot be zero or fractional.
  • Specific Examples of Molecularity:
    • Unimolecular (1 reacting species): Decomposition of ammonium nitrite: $NH_4NO_2 \rightarrow N_2 + 2H_2O$.
    • Bimolecular (2 reacting species): Dissociation of hydrogen iodide: $2HI \rightarrow H_2 + I_2$.
    • Termolecular (3 reacting species): Oxidation of nitric oxide: $2NO + O_2 \rightarrow 2NO_2$.
  • Probability of termolecular collisions ($>3$ molecules colliding simultaneously) is extremely low. Thus, reactions of higher order generally occur in multiple steps. Example: $KClO_3 + 6FeSO_4 + 3H_2SO_4 \rightarrow KCl + 3Fe_2(SO_4)_3 + 3H_2O$ appears to be 10th order but is actually 2nd order experimentally.

Integrated Rate Equations & Graphs

• 1. Zero Order Reactions: Rate is independent of reactant concentration.
  • Equation: $[R] = -kt + [R]_0$.
  • Graph: $[R]$ vs $t$ yields a straight line with slope $= -k$ and y-intercept $= [R]_0$.
  • Examples: Decomposition of gaseous ammonia ($NH_3$) on a hot platinum catalyst at high pressure. (At high pressure, the metal surface saturates, making rate independent of concentration). Thermal decomposition of $HI$ on a gold surface. Certain enzyme-catalyzed reactions.
• 2. First Order Reactions: Rate is proportional to the first power of concentration.
  • Equations: $\ln[R] = -kt + \ln[R]_0$ OR $[R] = [R]_0 e^{-kt}$ OR $k = \frac{2.303}{t} \log\frac{[R]_0}{[R]}$.
  • Graphs: $\ln[R]$ vs $t$ $\rightarrow$ slope $= -k$, intercept $= \ln[R]_0$. $\log([R]_0/[R])$ vs $t$ $\rightarrow$ straight line through origin, slope $= k/2.303$.
  • Examples: Hydrogenation of ethene ($C_2H_4 + H_2 \rightarrow C_2H_6$). All natural and artificial radioactive decays. Example: $^{226}_{88}Ra \rightarrow ^{222}_{86}Rn + ^{4}_{2}He$. Decomposition of $N_2O_5$ and $N_2O$.
• 3. First Order Gas Phase Reactions: For a typical reaction: $A(g) \rightarrow B(g) + C(g)$.
  • Let $p_i$ be initial pressure of A. Total pressure at time $t$ is $p_t$.
  • $p_t = (p_i - x) + x + x = p_i + x \Rightarrow x = p_t - p_i$.
  • Pressure of A at time $t$: $p_A = p_i - x = 2p_i - p_t$.
  • Equation: $k = \frac{2.303}{t} \log\left(\frac{p_i}{2p_i - p_t}\right)$.

Half-Life of a Reaction ($t_{1/2}$)

The time in which reactant concentration is reduced to half its initial value.

• Zero Order: $t_{1/2} = \frac{[R]_0}{2k}$. Directly proportional to initial concentration.
• First Order: $t_{1/2} = \frac{0.693}{k}$. Independent of initial concentration.
• JEE TIPFor a first-order reaction, the time required for 99.9% completion is exactly 10 times its half-life ($t_{99.9\%} \approx 10 \times t_{1/2}$).

Pseudo First Order Reactions

Reactions that are functionally first order but involve more than one reactant (higher molecularity). Occurs when one reactant is present in such large excess that its concentration change is negligible.

• Examples:
  • Acid-catalyzed Hydrolysis of Ethyl Acetate: $CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$. (Water is in massive excess).
  • Inversion of Cane Sugar (Sucrose): $C_{12}H_{22}O_{11} + H_2O \xrightarrow{H^+} C_6H_{12}O_6 (\text{Glucose}) + C_6H_{12}O_6 (\text{Fructose})$. Rate $= k[C_{12}H_{22}O_{11}]$.

Temperature Dependence & Arrhenius Equation

• Rule of Thumb: A 10°C rise in temperature nearly doubles the rate constant.
• Arrhenius Equation: $k = A e^{-E_a/RT}$.
  • $A =$ Arrhenius factor (pre-exponential factor / frequency factor).
  • $E_a =$ Activation energy (J/mol).
  • $e^{-E_a/RT} =$ The fraction of molecules having kinetic energy equal to or greater than $E_a$.
• Reaction Coordinate & Energy: When reactants convert to products, they pass through an unstable intermediate called an "activated complex". The energy required to reach this state is the activation energy ($E_a$).
• Maxwell-Boltzmann Distribution:
  • Plots the fraction of molecules ($N_E/N_T$) vs kinetic energy.
  • The peak is the "most probable kinetic energy".
  • Increasing temperature flattens and shifts the curve rightwards. The area under the curve beyond $E_a$ (which represents the fraction of effective molecules) effectively doubles for a 10-degree rise.
• Linearized Arrhenius Equation & Graph:
  • $\ln k = -\frac{E_a}{RT} + \ln A$.
  • Plot of $\ln k$ vs $1/T$ is a straight line.
  • Slope $= -E_a/R$, Y-intercept $= \ln A$.
• Comparing Two Temperatures: $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$.

Collision Theory of Chemical Reactions

Proposed by Max Trautz and William Lewis. Assumes molecules are hard spheres.

• Collision frequency ($Z$): Number of collisions per second per unit volume.
• Rate Equation (Basic): $\text{Rate} = Z_{AB} e^{-E_a/RT}$.
• Threshold Energy: The minimum kinetic energy molecules must possess for a collision to be effective. (Threshold Energy = Activation Energy + energy already possessed by reacting species).
• Steric Factor / Probability Factor ($P$): Not all collisions with sufficient energy yield products. Proper spatial orientation is required. For example, in the formation of methanol from bromoethane, improper orientation causes molecules to bounce back without reacting.
• Modified Rate Equation: $\text{Rate} = P \cdot Z_{AB} \cdot e^{-E_a/RT}$.
• Drawback: It ignores the structural aspect of molecules by treating them as rigid hard spheres.

Catalysis

• A catalyst accelerates the reaction by providing an alternate pathway or mechanism with a lower activation energy ($E_a$), thus reducing the potential energy barrier.
• Specific Catalyst Example: Addition of Manganese dioxide ($MnO_2$) considerably increases the rate of decomposition of Potassium chlorate ($KClO_3$): $2KClO_3 \xrightarrow{MnO_2} 2KCl + 3O_2$.
• Key Traits of a Catalyst:
  • Does NOT alter the Gibbs free energy ($\Delta G$) of the reaction.
  • Catalyzes spontaneous reactions, but CANNOT catalyze non-spontaneous reactions.
  • Does NOT change the equilibrium constant ($K_{eq}$). It catalyzes the forward and backward reactions to the exact same extent, helping equilibrium to be attained faster.
  • "Inhibitor" is the correct term for a substance that reduces the reaction rate (do not use "negative catalyst").

Reactions & Mechanisms

• Decomposition of Hydrogen Peroxide: $2H_2O_2 \xrightarrow{I^-, \text{ Alkaline medium}} 2H_2O + O_2$. Rate $= k[H_2O_2][I^-]$. (Overall 1st order in reactant, 1st order in catalyst $\Rightarrow$ 2nd order overall). Mechanism: Step 1 (Slow, RDS): $H_2O_2 + I^- \rightarrow H_2O + IO^-$. Step 2 (Fast): $H_2O_2 + IO^- \rightarrow H_2O + I^- + O_2$. Note: $IO^-$ (hypoiodite) is the reaction intermediate.

Formulae & Equations

1. Average Rate: $r_{av} = \frac{-\Delta[Reactant]}{\Delta t} = \frac{+\Delta[Product]}{\Delta t}$.
2. General Rate Law: For $aA + bB \rightarrow cC$, $Rate = k[A]^x[B]^y$.
3. Units of $k$: $mol^{1-n} L^{n-1} s^{-1}$ (where $n$ is order).
4. Zero Order Kinetics:
   • $k = \frac{[R]_0 - [R]}{t}$
   • $t_{1/2} = \frac{[R]_0}{2k}$
5. First Order Kinetics:
   • $k = \frac{2.303}{t} \log\frac{[R]_0}{[R]}$
   • $[R] = [R]_0 e^{-kt}$
   • $t_{1/2} = \frac{0.693}{k}$
6. Arrhenius Equation: $k = A e^{-E_a/RT}$
   • $\ln k = -\frac{E_a}{RT} + \ln A$
   • $\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]$
7. Collision Theory Equation: $\text{Rate} = P \cdot Z_{AB} \cdot e^{-E_a/RT}$.

⚠️ EXCEPTIONS & ANOMALIES

• Zero Order Reactions & Concentration: While normally reaction rates decrease as reactants are consumed, zero-order reactions maintain a completely constant rate regardless of how much reactant is left, up until the reactant is completely exhausted. Why? They occur under special conditions (like metal surface catalysis at high pressure) where the surface is saturated. The reaction rate is limited by the available surface area, not the bulk gas concentration.
• Pseudo First-Order Concentration Anomaly: In reactions like the hydrolysis of ethyl acetate ($CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$), the reaction is bimolecular but behaves as first-order. Why? Water is present in such massive stoichiometric excess (e.g., 10 moles vs 0.01 moles) that its concentration is virtually unchanged during the reaction, rendering the rate independent of it.
• Fractional Order: $CHCl_3 + Cl_2 \rightarrow CCl_4 + HCl$ has an order of 1.5 ($[Cl_2]^{1/2}$). Why? It proceeds via a complex mechanism resulting in a fractional power dependence.
• The "Termolecular" Limit Anomaly: While we can write balanced equations with 4, 5, or even 10 reactants, reactions with a molecularity greater than 3 are exceedingly rare and do not proceed in a single step. Why? The statistical probability of more than three molecules colliding simultaneously with proper orientation and sufficient kinetic energy is practically zero.
• The Complex Reaction Molecularity Exception: Molecularity is rigorously defined for elementary steps, but the overall molecularity of a complex (multi-step) reaction has absolutely no meaning.
• "Negative Catalyst" Terminology Error: It is a common misnomer to call a substance that reduces the rate of a reaction a "negative catalyst". The word catalyst must not be used in this context; the correct and only term is inhibitor.
• Thermodynamic Feasibility vs. Kinetic Deadlock: A reaction can be highly thermodynamically spontaneous ($\Delta G < 0$) but functionally never occur. Why? The activation energy is so high that the reaction rate is imperceptible. Example: The conversion of diamond to graphite is thermodynamically favored, but kinetically "frozen" at room temperature.
• Catalysts and Equilibrium: A catalyst lowers the activation energy and speeds up the reaction, but it does not alter the Gibbs free energy ($\Delta G$) or the equilibrium constant ($K_{eq}$). Why? It lowers the activation energy of both the forward and backward reactions by the exact same amount, merely helping the system reach the exact same equilibrium state faster.
• Catalysts and Non-Spontaneous Reactions: A catalyst can only accelerate spontaneous reactions; it cannot catalyze or force a non-spontaneous reaction to occur.

Previous Year JEE Topics

• Integrated Rate Equation Graphs: Determining order and $k$ from plots of $[R]$ vs $t$, $\ln[R]$ vs $t$, and the slope/intercept values.
• Arrhenius Parameter Calculations: Using two-point temperatures ($T_1, T_2$) and $k_1, k_2$ values to solve for $E_a$ or plotting $\ln k$ vs $1/T$ to match linear formats.
• Catalyst Thermodynamics: True/False questions verifying that catalysts do NOT shift equilibrium ($K_{eq}$) or alter $\Delta H$, $\Delta G$.
• Gas Phase First Order Kinetics: Calculating total pressure $p_t$ or $k$ after time $t$ using variable substitution (the ICE table method).
• Decomposition Mechanisms: Identifying intermediates ($IO^-$) and the rate determining step in reactions like the $I^-$ catalyzed $H_2O_2$ decomposition.

Memory Aids & JEE Traps

• [JEE TIP] Trap 1 - Coefficient Blindness:

  • Misconception: The rate of disappearance of reactant $A$ in the reaction $2A \rightarrow B$ is calculated as $-\frac{1}{2}\frac{\Delta[A]}{\Delta t}$.
  • Correct Understanding: The rate of disappearance or consumption of a specific species is simply $-\frac{\Delta[A]}{\Delta t}$, completely ignoring its coefficient. The stoichiometric divisor $\frac{1}{2}$ is strictly used only when equating it to the overall, unified "Rate of Reaction" ($\text{Rate} = -\frac{1}{2}\frac{\Delta[A]}{\Delta t} = +\frac{\Delta[B]}{\Delta t}$).

• [JEE TIP] Trap 2 - Molecularity vs Order Limits:

  • Misconception: The molecularity of a reaction can be zero, negative, or a fractional number, matching the flexible mathematical behavior of reaction order.
  • Correct Understanding: Order is an experimental quantity that can comfortably be zero, fractional, or negative. Conversely, Molecularity is a theoretical concept representing the exact number of reactant molecules colliding simultaneously in an elementary step; it must strictly be a positive integer ($1$, $2$, or $3$). It can never be zero or non-integer.

• [JEE TIP] Trap 3 - Complex Reaction Molecularity:

  • Misconception: The overall molecularity of a multi-step (complex) reaction is determined by adding up all the stoichiometric coefficients in the final balanced chemical equation.
  • Correct Understanding: Molecularity has absolutely no meaning for a complex reaction. It is mathematically and conceptually restricted to individual, discrete elementary steps. For a multi-step mechanism, the slowest step acts as the Rate Determining Step (RDS) and dictates the overall kinetic order, but the full complex reaction cannot be assigned a total molecularity value.

• [JEE TIP] Trap 4 - Catalyst Thermodynamic Barrier:

  • Misconception: Adding an efficient chemical catalyst to a reaction shifts the equilibrium position forward, maximizing the equilibrium constant ($K_{eq}$) and altering the standard enthalpy ($\Delta H$) of the reaction.
  • Correct Understanding: A catalyst never alters state functions like $K_{eq}$, $\Delta G$, or $\Delta H$. It merely provides an alternate, lower-energy reaction pathway. Because it lowers the activation energy ($E_a$) equally for both the forward and backward reactions, it only accelerates the speed at which equilibrium is reached, without changing the final equilibrium concentrations.

• [JEE TIP] Trap 5 - First-Order Half-Life Invariance:

  • Misconception: The half-life ($t_{1/2}$) of a first-order reaction progressively shrinks as the reactant is continuously consumed over time.
  • Correct Understanding: For a first-order process, the half-life expression is $t_{1/2} = \frac{0.693}{k}$. Because this formula is entirely independent of the initial concentration ($[R]_0$), the time required to consume exactly $50\%$ of the remaining reactant remains perfectly constant at every stage of the reaction.

• [JEE TIP] Trap 6 - Zero-Order Half-Life Decay:

  • Misconception: The half-life of a zero-order reaction remains constant throughout the course of the chemical reaction.
  • Correct Understanding: The half-life of a zero-order reaction is expressed as $t_{1/2} = \frac{[R]_0}{2k}$, making it directly proportional to the starting concentration. As the reaction progresses and the concentration of reactants steadily drops, the remaining half-life gets progressively shorter.

• [JEE TIP] Trap 7 - Arrhenius Logarithmic Slope Switch:

  • Misconception: The slope of an Arrhenius plot of $\log k$ versus $\frac{1}{T}$ is universally equal to $-\frac{E_a}{R}$.
  • Correct Understanding: The slope is exactly $-\frac{E_a}{R}$ only when plotting the natural logarithm ($\ln k$) against $\frac{1}{T}$. If the graph uses the common base-10 logarithm ($\log_{10} k$) vs $\frac{1}{T}$, the conversion factor changes the slope value to exactly $-\frac{E_a}{2.303R}$. Failing to check the log base leads to fatal calculation errors.

• [JEE TIP] Trap 8 - Gas Phase Kinetics Stoichiometric Lock:

  • Misconception: The integrated first-order gas phase rate formula $k = \frac{2.303}{t} \log\left(\frac{p_i}{2p_i - p_t}\right)$ applies perfectly to all first-order gaseous decomposition reactions.
  • Correct Understanding: This specific mathematical expression only works for reactions matching the precise stoichiometry $A(g) \rightarrow B(g) + C(g)$ (where 1 mole of gas splits into exactly 2 moles of gas). If the problem involves a different ratio (e.g., $2A(g) \rightarrow 3B(g) + C(g)$), you must manually construct a custom ICE table using partial pressures to derive the correct variable relationship for $Q$.

• [JEE TIP] Trap 9 - The Catalyst Energy Illusion:

  • Misconception: A catalyst accelerates a chemical reaction by directly transferring energy to the reactant molecules to increase their average kinetic energy.
  • Correct Understanding: A catalyst has zero effect on the kinetic energy of molecules; only an increase in temperature can shift the Maxwell-Boltzmann kinetic energy distribution. A catalyst works exclusively by introducing a completely different, lower-energy transition state pathway, thereby reducing the activation energy ($E_a$) hurdle that the existing molecules must cross.

• [JEE TIP] Trap 10 - Activation Energy Inverse Speed:

  • Misconception: Reactions that possess a highly demanding, large activation energy ($E_a$) will inherently result in a larger rate constant ($k$).
  • Correct Understanding: According to the Arrhenius equation ($k = A e^{-E_a/RT}$), the rate constant and activation energy share an inverse exponential relationship. A smaller activation energy ($E_a$) allows a larger fraction of molecular collisions to be effective, which exponentially increases the rate constant ($k$) and accelerates the reaction.