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:
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).
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.
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.
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.
Presence of Light/Radiation: Some reactions (photochemical reactions) occur or are accelerated in the presence of light (e.g., photosynthesis, H2+Cl2hv2HCl).
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 NH4NO2→N2+2H2O)
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).
CH3COOC2H5+H2OH+CH3COOH+C2H5OH
Rate =k′[CH3COOC2H5], where k′=k[H2O] (as H2O 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−k0t
[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−k1t
Or k1=t2.303log[R]t[R]0
k1 = first-order rate constant
Half-life (t1/2):
t1/2=k10.693
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:
Reactant molecules must collide with each other to react.
Not all collisions lead to a reaction. Only effective collisions result in product formation.
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:
Increased collision frequency (minor effect on rate).
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:
logk1k2=2.303REa(T11−T21)
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).