Class 12 Chemistry · Chapter 3 NotesChemical Kinetics

The rate of a reaction is the change in concentration of a reactant or product per unit time. For a reaction R → P, the rate of disappearance of R is given by the decrease in concentration of R divided by the time interval, and the rate of appearance of P is the increase in concentration of P divided by the same interval. Because reactant concentration decreases, a negative sign is used to make the rate positive. The average rate is measured over a time interval, while the instantaneous rate is the rate at a specific moment, obtained as the limit when the time interval approaches zero. Graphically, the instantaneous rate is the slope of the tangent to the concentration versus time curve at that time.

• Average rate = –Δ[R]/Δt = +Δ[P]/Δt
• Instantaneous rate = –d[R]/dt = +d[P]/dt
• Units of ratemol L⁻¹ s⁻¹ (or atm s⁻¹ for gases)

The rate law expresses the rate of a reaction in terms of the molar concentrations of reactants, each raised to a power that may or may not equal its stoichiometric coefficient. For a general reaction aA + bB → cC + dD, the rate law is often written as Rate = k[A]ˣ[B]ʸ, where x and y are determined experimentally. The sum x + y is the overall order of the reaction. The constant k is the rate constant, which is independent of concentration but depends on temperature. The order can be zero, a whole number, or even a fraction. The rate law cannot be predicted from the balanced equation alone; it must be determined by experiment.

• Rate = k[A]ˣ[B]ʸ; order = x + y
• Rate constant k = Rate / ([A]ˣ[B]ʸ)
• Units of k depend on the overall orderfor zero order, mol L⁻¹ s⁻¹; for first order, s⁻¹; for second order, L mol⁻¹ s⁻¹

Molecularity is the number of reacting species that collide simultaneously in an elementary reaction. It is a theoretical concept applicable only to elementary steps and can be 1 (unimolecular), 2 (bimolecular), or rarely 3 (termolecular). Complex reactions proceed through a series of elementary steps, and the overall rate is governed by the slowest step, called the rate-determining step. Unlike order, molecularity cannot be zero or fractional. For an elementary reaction, the order and molecularity are the same. Intermediates are species formed in one step and consumed in another, and they do not appear in the overall balanced equation.

• Unimolecularone species, e.g., NH₄NO₂ → N₂ + 2H₂O
• Bimoleculartwo species, e.g., 2HI → H₂ + I₂
• Termolecularthree species, e.g., 2NO + O₂ → 2NO₂ (rare)

The integrated rate equation relates concentration to time. For a zero order reaction, Rate = k, and integration gives [R] = –kt + [R]₀. A plot of [R] versus t is a straight line with slope –k. For a first order reaction, Rate = k[R], and integration gives ln[R] = –kt + ln[R]₀ or k = (2.303/t) log([R]₀/[R]). A plot of ln[R] versus t is a straight line with slope –k. The integrated equations allow determination of k from concentration-time data without drawing tangents.

• Zero orderk = ([R]₀ – [R]) / t
• First orderk = (2.303/t) log([R]₀/[R])
• First order in gas phasek = (2.303/t) log(pᵢ / (2pᵢ – pₜ))

The half-life (t₁/₂) is the time required for the concentration of a reactant to fall to half of its initial value. For a zero order reaction, t₁/₂ = [R]₀ / (2k), which depends on the initial concentration. For a first order reaction, t₁/₂ = 0.693 / k, which is independent of initial concentration. This means that for a first order reaction, the time taken to reduce the concentration by half is always the same, regardless of how much reactant is present initially. Half-life is a useful parameter for comparing reaction rates and for radioactive decay calculations.

• Zero ordert₁/₂ = [R]₀ / 2k
• First ordert₁/₂ = 0.693 / k
• For first order, t₁/₂ is constant

The rate of most reactions increases with temperature. Quantitatively, this is described by the Arrhenius equation: k = A e^(–Ea/RT), where A is the pre-exponential factor (frequency factor), Ea is the activation energy, R is the gas constant, and T is the absolute temperature. Taking natural logarithm gives ln k = ln A – Ea/RT. A plot of ln k versus 1/T is a straight line with slope –Ea/R and intercept ln A. The equation shows that a lower activation energy or higher temperature leads to a larger rate constant. The activation energy is the minimum energy that colliding molecules must possess to form products.

• k = A e^(–Ea/RT)
• ln k = ln A – Ea/RT
• log(k₂/k₁) = (Ea/2.303R) (1/T₁ – 1/T₂)

A catalyst is a substance that increases the rate of a reaction without being consumed in the overall reaction. It provides an alternative pathway with a lower activation energy, thereby increasing the fraction of molecules that can overcome the energy barrier. A catalyst does not change the Gibbs energy change (ΔG) or the equilibrium constant of a reaction; it only helps the system reach equilibrium faster. Catalysts are highly specific in their action. Substances that decrease the rate of a reaction are called inhibitors. In some reactions, the catalyst may form an intermediate complex with reactants, which then decomposes to give products and regenerate the catalyst.

• Catalyst lowers activation energy
• Does not alter ΔG or equilibrium constant
• Inhibitor decreases reaction rate

Collision theory explains reaction rates based on the frequency and energy of collisions between reactant molecules. For a bimolecular reaction A + B → Products, the rate is given by Rate = Z_AB e^(–Ea/RT), where Z_AB is the collision frequency. However, not all collisions lead to products; only those with sufficient energy (greater than or equal to activation energy) and proper orientation are effective. To account for orientation, a steric factor P is introduced: Rate = P Z_AB e^(–Ea/RT). The theory assumes molecules behave as hard spheres, which is a simplification, but it successfully explains many features of reaction rates.

• Rate = P Z_AB e^(–Ea/RT)
• Effective collisions require proper orientation and sufficient energy
• Steric factor P accounts for orientation probability