Chemical Kinetics — NEET Notes

Rate of a chemical reaction

The rate of a reaction is the change in concentration of a reactant or product per unit time. NCERT defines it in two flavours. The average rate over an interval Δt is the total change in concentration divided by the interval — a coarse, finite-difference quantity. The instantaneous rate is the limit of the average rate as Δt approaches zero — the slope of the tangent to a concentration-time curve at a single instant. For a hypothetical reaction R → P, the two definitions write out as:

r_av = −Δ[R]/Δt = +Δ[P]/Δt   |   r_inst = −d[R]/dt = +d[P]/dt

Average vs instantaneous rate — NCERT Unit 3, Section 3.1

The negative sign attached to the reactant term keeps the rate positive — reactant concentration falls, so Δ[R] is negative. For a reaction with stoichiometric coefficients other than one, the rate must be expressed per unit coefficient. Consider 2N₂O₅ → 4NO₂ + O₂. The rate of the reaction is given by:

Rate = −½ · d[N₂O₅]/dt = +¼ · d[NO₂]/dt = +d[O₂]/dt

Rate written per unit stoichiometric coefficient

This convention guarantees a single, unambiguous rate for the whole reaction regardless of which species you choose to track. The units of rate are concentration · time⁻¹ — typically mol L⁻¹ s⁻¹ for solutions, or atm s⁻¹ for gaseous reactions where concentrations are expressed as partial pressures. The instantaneous rate is what enters every rate law and every Arrhenius calculation in this chapter.

Factors influencing the rate of a reaction

NCERT lists five external handles that can speed up or slow down a chemical reaction. They act through different mechanisms — concentration changes the number of collisions per unit time, temperature changes how many of those collisions have enough energy, a catalyst changes the activation energy of the path, surface area changes the available reaction interface, and light supplies activation energy to photochemical species. NEET examines each one in isolation and in combination.

Rate law and order of reaction

For a general reaction aA + bB → products, the experimental rate equation — the rate law — takes the form:

Rate = k · [A]^x · [B]^y

Rate law — exponents x and y must be determined experimentally

The exponents x and y are not the stoichiometric coefficients a and b — that is a textbook trap. They are determined by experiment, and they may be zero, fractional, or integer. The sum (x + y) is the overall order of the reaction; individual exponents are the order with respect to that reactant. The constant k is the rate constant (or specific reaction rate) — a temperature-dependent number that is independent of reactant concentration. NEET 2023 tested this directly: for rate = k[A]²[B], tripling [A] multiplies the rate by 3² = 9, not by 3.

The units of k depend on the order. For an overall order n, k has units of (concentration)¹⁻ⁿ · time⁻¹. Three to memorise:

A subtle point NCERT stresses: order can be fractional. Consider the reaction H₂ + Br₂ → 2HBr with experimental rate law Rate = k[H₂][Br₂]^½. The order with respect to H₂ is 1, with respect to Br₂ is ½, and the overall order is 1.5 — a non-integer. Such fractional orders signal that the reaction proceeds through a multi-step mechanism with one elementary step being rate-determining. NEET 2017 tested this exact pattern (X₂ + Y₂ → 2XY through a fast-slow-fast mechanism, overall order 1.5).

Molecularity vs order — the NEET trap

Of every concept in this chapter, the molecularity-vs-order distinction is the single biggest source of NEET errors. The two words sound similar; the concepts are different. Order is an empirical, experimental property of a reaction's rate law — the sum of exponents on concentration terms. Molecularity is a theoretical, mechanistic property of an elementary step — the number of reacting species that collide in that step. Order is what you measure; molecularity is what you propose. Confuse the two and you will lose marks every year.

One more clean distinction. Molecularity is sometimes called the "theoretical order" of an elementary step. If a reaction proceeds in a single elementary step, then order = molecularity automatically. But if it proceeds in multiple steps, the order is set by the rate-determining (slowest) step, and may equal the molecularity of that one step — but not of any other. Molecularity can never be zero or fractional; order can be both. That single asymmetry is enough to crack the trap every time.

Integrated rate equations

The rate law in differential form — Rate = −d[A]/dt = k[A]ⁿ — tells you the instantaneous rate, but to use it on lab data you must integrate it. The integrated form expresses concentration as a function of time directly, so you can plug in an initial concentration and get a final concentration after t seconds, or vice versa. NCERT derives the integrated rate equations for zero and first order only; second order is left to NIOS and competitive coaching.

Zero order integrated equation

For Rate = k[A]⁰ = k, integration gives:

[A] = [A]₀ − kt  ⇒  k = ([A]₀ − [A]) / t

Zero order — straight line with slope −k on a [A]-vs-t plot

The concentration of A falls linearly with time. A plot of [A] against t is a straight line; its slope equals −k, and the y-intercept equals [A]₀. Zero-order kinetics shows up in enzyme reactions at substrate saturation (the enzyme is rate-limited) and in surface-catalysed reactions where the catalyst surface is saturated with reactant — e.g. NH₃ decomposition on hot platinum at high pressure, or HI decomposition on gold. The rate is independent of [A] because adding more A does not change the saturated surface coverage.

First order integrated equation

For Rate = k[A], separation of variables and integration gives:

ln([A]₀/[A]) = kt  ⇒  k = (2.303/t) · log([A]₀/[A])

First order — NCERT's most-tested formula

The factor 2.303 appears because NCERT switches from natural log to common log. The equivalent exponential form is [A] = [A]₀ · e^−kt. Plotting log[A] against t gives a straight line of slope −k/2.303, and plotting ln[A] against t gives a slope of −k directly. This formula is the engine behind NEET 2017 (10⁻² s⁻¹ rate constant, 20 g → 5 g, find t = 138.6 s), NEET 2020 (k = 4.606 × 10⁻³ s⁻¹, 2.0 g → 0.2 g, find t = 500 s), and NEET 2022 (0.1 M → 0.001 M in 5 minutes, find k = 0.9212 min⁻¹). Memorise the formula; the numbers change every year.

Half-life of reactions

The half-life (t_½) of a reaction is the time required for the concentration of a reactant to fall to half its initial value. Its dependence on initial concentration is order-specific — and that dependence is the single most-tested distinguishing feature in NEET kinetics.

For a zero order reaction, setting [A] = [A]₀/2 in [A] = [A]₀ − kt gives t_½ = [A]₀/2k — directly proportional to the initial concentration. NEET 2018 tested this exactly: doubling [A]₀ of a zero-order reaction doubles its half-life. For a second order reaction, t_½ = 1/(k[A]₀) — inversely proportional to [A]₀. NEET 2018 also tested this in a head-to-head comparison (first vs second order). The pattern is so reliable that one of every three NEET kinetics PYQs reduces to "remember which order has which half-life dependence."

Pseudo first order reactions

Some reactions have a true overall order greater than one — yet behave kinetically like first order. The explanation is concentration imbalance: one reactant is present in such large excess that its concentration stays effectively constant over the course of the reaction, so it disappears from the experimentally observed rate law. Such reactions are called pseudo first order. The textbook example is the acid-catalysed hydrolysis of an ester:

CH₃COOC₂H₅ + H₂O  →  CH₃COOH + C₂H₅OH

Ester hydrolysis — pseudo first order in water

The true rate law is Rate = k′[ester][H₂O], a second-order expression. But in dilute aqueous solution, [H₂O] ≈ 55.5 mol L⁻¹ and barely changes as a tiny amount of ester hydrolyses. The product k′·[H₂O] is therefore effectively a constant — call it k — and the observed rate law collapses to Rate = k[ester], which is first order. A second classic example is the inversion of cane sugar: C₁₂H₂₂O₁₁ + H₂O → glucose + fructose, catalysed by dilute acid. Again [H₂O] is in vast excess, again the observed order is one.

Temperature dependence — the Arrhenius equation

Almost every reaction speeds up as temperature rises — a rough rule of thumb says the rate roughly doubles or triples for every 10 K rise. Svante Arrhenius (1889) formalised the dependence in a single equation that NEET tests almost every year:

k = A · e^−E_a/RT

The Arrhenius equation — rate constant vs absolute temperature

The four constants in this expression are: k the rate constant, A the Arrhenius pre-exponential or frequency factor (related to total collision frequency and an orientation/steric factor), E_a the activation energy (the minimum extra energy reactant molecules must have above their average to react), R the gas constant 8.314 J K⁻¹ mol⁻¹, and T the absolute temperature in kelvin. The exponential factor e^−E_a/RT is the Boltzmann fraction — the proportion of molecules with kinetic energy ≥ E_a. At higher T, more molecules clear the activation barrier; at higher E_a, fewer do.

Taking the natural log of both sides linearises the equation — and gives you the Arrhenius plot:

ln k = ln A − (E_a / R) · (1/T)

Logarithmic form — slope of ln k vs 1/T is −E_a/R

Plot ln k on the y-axis and 1/T on the x-axis: you get a straight line with slope = −E_a/R and y-intercept = ln A. This is the standard experimental method for extracting activation energy: measure k at several temperatures, plot ln k vs 1/T, multiply the slope by −R, and you have E_a. NEET 2021 Q.99 gave a slope of −5 × 10³ K and asked for E_a; multiplying by R gave 41.5 kJ mol⁻¹.

For two-point problems where you know k at two temperatures, NCERT also gives the integrated form:

log(k₂/k₁) = (E_a / 2.303 R) · (T₂ − T₁) / (T₁ T₂)

Two-point Arrhenius — solve for E_a, k₂, or any single unknown

One last NEET-favourite consequence: a catalyst lowers E_a, which raises k at any temperature. The frequency factor A and ΔH of the reaction remain unchanged — only the activation energy moves. NEET 2016 tested exactly this ("a catalyst alters which quantity?" — answer: activation energy). NEET 2023 added a delicate assertion-reason on whether a reaction can have zero activation energy — yes, certain radical reactions can — so do not absolutise the statement that "every reaction has a positive E_a".

Collision theory of reaction rates

The Arrhenius equation is empirical — it works, but it does not explain why. Collision theory, developed by Max Trautz and William Lewis in the 1910s for gas-phase bimolecular reactions, supplies the molecular picture. The theory rests on three postulates: (i) molecules must collide for a reaction to occur, (ii) only collisions with energy ≥ threshold are effective, and (iii) the colliding molecules must be in the correct orientation.

For a bimolecular reaction A + B → products, the theory writes the rate as:

Rate = P · Z_AB · e^−E_a/RT

Collision-theory rate — frequency × Boltzmann × steric factor

Here Z_AB is the collision frequency — number of A-B collisions per unit volume per unit time — proportional to the product of concentrations and to molecular speeds (and hence to √T). The Boltzmann factor e^−E_a/RT is the fraction of those collisions with enough energy to react. The steric factor P (or "probability factor") accounts for the geometric requirement that molecules must approach each other in the correct orientation — for many real reactions P ≪ 1, meaning most energy-sufficient collisions still fail because the molecules are wrongly aligned.

Three predictions from collision theory match NEET data exactly. First, raising concentration increases Z_AB — collision frequency — which is precisely what NEET 2020 Q.138 asked. Second, raising temperature increases both Z_AB (slightly, via √T) and far more importantly e^−E_a/RT (exponentially). Third, adding a catalyst lowers E_a, raising the Boltzmann fraction and therefore the rate — without changing Z_AB or P.

Collision theory's main limitation is its rigid-sphere assumption — it treats molecules as featureless billiard balls. For complex molecules, the steric factor P can be very small (10⁻⁵ or less), and a more refined treatment — transition state theory — is needed. NEET tests collision theory at the postulate level, not the transition-state level.