Chemical Kinetics – Detailed Notes for NEET/JEE Mains

1. Introduction to Chemical Kinetics

• Chemical Kinetics: The branch of physical chemistry that deals with the study of the rates of chemical reactions, the factors affecting these rates, and the mechanism by which the reactions occur.
• Reaction Rate: The change in concentration of a reactant or product per unit time.

2. Rate of a Chemical Reaction

• Average Rate of Reaction: The change in concentration of reactants or products over a measurable time interval.
  • For a reaction R→P:
    • Average rate =−ΔtΔ[R]​=+ΔtΔ[P]​
    • The negative sign indicates a decrease in reactant concentration over time.
    • Units: mol L−1s−1 or atm s−1 (for gases).
• Instantaneous Rate of Reaction: The rate of reaction at a particular instant of time.
  • Instantaneous rate =−dtd[R]​=+dtd[P]​
  • Represented by the slope of the tangent to the concentration vs. time curve at that instant.
• Stoichiometry and Rate: For a general reaction aA+bB→cC+dD:
  • Rate =−a1​dtd[A]​=−b1​dtd[B]​=+c1​dtd[C]​=+d1​dtd[D]​

3. Factors Affecting Rate of Reaction

1. Concentration of Reactants: Generally, the rate of reaction increases with an increase in the concentration of reactants. This is explained by collision theory (more particles, more collisions).
2. Temperature: The rate of most reactions increases with an increase in temperature. For many reactions, the rate roughly doubles for every 10∘C rise in temperature (temperature coefficient). This is due to an increase in the kinetic energy of molecules, leading to more effective collisions.
3. Nature of Reactants:
   • Physical state: Gaseous reactions are generally faster than liquid reactions, which are faster than solid reactions.
   • Surface area: For reactions involving solids, increasing the surface area increases the rate.
   • Strength of bonds: Reactions involving weaker bonds are faster.
4. Catalyst: A substance that alters (usually increases) the rate of a reaction without being consumed in the reaction. Catalysts provide an alternative reaction path with a lower activation energy.
5. Presence of Light/Radiation: Some reactions (photochemical reactions) occur or are accelerated in the presence of light (e.g., photosynthesis, H2​+Cl2​hv​2HCl).

4. Molecularity of a Reaction

• Definition: The number of reacting species (atoms, ions, or molecules) that collide simultaneously in an elementary reaction to bring about a chemical reaction.
• Characteristics:
  • It is always a whole number (1, 2, 3).
  • It can be defined only for elementary reactions (single-step reactions).
  • It cannot be more than three, as the probability of simultaneous collision of more than three particles is very low.
  • Molecularity is a theoretical concept.
• Types:
  • Unimolecular: Molecularity = 1 (e.g., decomposition of NH4​NO2​→N2​+2H2​O)
  • Bimolecular: Molecularity = 2 (e.g., 2HI→H2​+I2​)
  • Trimolecular: Molecularity = 3 (e.g., 2NO+O2​→2NO2​)
• Complex Reactions: Occur in a sequence of elementary steps. The molecularity of each elementary step is defined, but not for the overall complex reaction. The slowest step in a complex reaction is called the rate-determining step.

5. Order of Reaction

• Definition: The sum of the powers of the concentration terms of the reactants in the experimentally determined rate law expression.
• Characteristics:
  • It can be a whole number, fraction, or even zero.
  • It is determined experimentally (cannot be predicted from the balanced equation unless it’s an elementary reaction).
  • It can be defined for elementary as well as complex reactions.
  • It is equal to the molecularity only for elementary reactions.
• Rate Law Expression: For a general reaction aA+bB→cC+dD, the rate law is given by:
  • Rate =k[A]x[B]y
  • Order of reaction with respect to A is x.
  • Order of reaction with respect to B is y.
  • Overall order of reaction =x+y.
  • k is the rate constant or specific reaction rate. It is constant at a given temperature.
  • Units of k: Depends on the order of reaction. General formula: (mol L−1)1−ns−1 or atm1−ns−1 (where n is the order).
    • Zero order: mol L−1s−1
    • First order: s−1
    • Second order: L mol−1s−1
• Zero Order Reaction (n=0):
  • Rate does not depend on the concentration of reactants.
  • Example: Photochemical reactions, enzyme-catalyzed reactions when enzyme is saturated, decomposition of NH3​ on hot platinum surface.
• First Order Reaction (n=1):
  • Rate is directly proportional to the first power of the concentration of one reactant (or sum of concentrations of multiple reactants each raised to power one).
  • Example: Radioactive decay, hydrolysis of ester in acidic medium.
• Pseudo First Order Reaction:
  • A reaction that appears to be second order but behaves as first order because one of the reactants is present in large excess (its concentration remains effectively constant).
  • Example: Hydrolysis of ester in acidic/basic medium or sucrose (inversion of cane sugar).
    • CH3​COOC2​H5​+H2​OH+​CH3​COOH+C2​H5​OH
    • Rate =k′[CH3​COOC2​H5​], where k′=k[H2​O] (as H2​O is in large excess).

6. Integrated Rate Equations

• Used to determine the concentration of reactants/products at any given time or to find the time required for a certain change in concentration.

A. Zero Order Reaction

• Rate =−dtd[R]​=k0​
• Integrated rate law: [R]t​=[R]0​−k0​t
  • [R]t​ = concentration at time t
  • [R]0​ = initial concentration
  • k0​ = zero-order rate constant
• Half-life (t1/2​): Time required for the concentration of reactant to reduce to half of its initial value.
  • t1/2​=2k0​[R]0​​
  • For a zero-order reaction, half-life is directly proportional to the initial concentration.
• Graphical Representation: Plot of [R] vs t is a straight line with a negative slope equal to −k0​.

B. First Order Reaction

• Rate =−dtd[R]​=k1​[R]
• Integrated rate law: ln[R]t​=ln[R]0​−k1​t
  • Or k1​=t2.303​log[R]t​[R]0​​
  • k1​ = first-order rate constant
• Half-life (t1/2​):
  • t1/2​=k1​0.693​
  • For a first-order reaction, half-life is independent of the initial concentration.
• Graphical Representation:
  • Plot of ln[R] vs t is a straight line with a negative slope equal to −k1​.
  • Plot of log[R] vs t is a straight line with a negative slope equal to −2.303k1​​.

7. Collision Theory of Chemical Reactions

• Based on kinetic theory of gases. Explains reaction rates in terms of collisions between reacting molecules.
• Postulates:
  1. Reactant molecules must collide with each other to react.
  2. Not all collisions lead to a reaction. Only effective collisions result in product formation.
  3. For a collision to be effective, molecules must possess:
     • Activation Energy (Ea​): The minimum extra energy that reacting molecules must possess to undergo effective collisions.
     • Proper Orientation: Molecules must collide in a specific orientation for bonds to break and new bonds to form.
• Threshold Energy: The minimum energy that the reacting molecules must possess for a collision to be effective.
  • Threshold Energy = Activation Energy + Average Kinetic Energy of Reactants.
• Potential Energy Barrier: The energy barrier that reactants must overcome to form products. The peak of this barrier represents the activated complex (transition state), an unstable intermediate formed during an effective collision.
• Effect of Temperature: Increasing temperature increases the kinetic energy of molecules, leading to:
  1. Increased collision frequency (minor effect on rate).
  2. Significantly increased fraction of molecules with energy greater than or equal to activation energy (major effect on rate).

8. Arrhenius Equation

• Quantitatively describes the effect of temperature on the rate constant (k) of a reaction.
• Equation: k=Ae−Ea​/RT
  • k = rate constant
  • A = Arrhenius factor or pre-exponential factor or frequency factor (related to collision frequency and orientation).
  • Ea​ = Activation energy (in J mol−1)
  • R = Gas constant (8.314 J K−1 mol−1)
  • T = Temperature (in Kelvin)
• Logarithmic form: lnk=lnA−RTEa​​
  • Or, logk=logA−2.303RTEa​​
• Graphical Representation: A plot of lnk vs 1/T (or logk vs 1/T) gives a straight line.
  • Slope =−REa​​ (or −2.303REa​​)
  • Y-intercept =lnA (or logA)
• For rate constants at two different temperatures:
  • logk1​k2​​=2.303REa​​(T1​1​−T2​1​)

9. Catalysis

• Catalyst: A substance that changes the rate of a chemical reaction without being consumed in the reaction.
• Mechanism of Catalysis: A catalyst provides an alternative reaction pathway (mechanism) with a lower activation energy, thereby increasing the rate of reaction. It does not change ΔG or the equilibrium constant (Kc​). It only helps the reaction reach equilibrium faster.
• Types of Catalysis:
  • Homogeneous Catalysis: Reactants and catalyst are in the same phase (e.g., decomposition of SO2​ to SO3​ with NO as catalyst in gaseous phase).
  • Heterogeneous Catalysis: Reactants and catalyst are in different phases (e.g., Haber’s process for NH3​ synthesis with solid Fe catalyst and gaseous reactants).