Rate Law, Order & Molecularity Why this matters When a reaction speeds up or slows down as you change concentration, that behaviour holds the mechanism’s clues. The experimental rate law tells you exactly how rate depends on concentrations. From it, you get the order of reaction, identify pseudo-first-order tricks, and pick correct units for the rate constant k. This is the language used in pharma kinetics, radiochemistry, and industrial process control. Rate law at a glance: Rate = k[A] x[B] y. The exponents x and y come from experiments, not just from the balanced equation. Rate law: the experimental rule For a reaction A + B → Products, experiments show how the initial rate changes when you change [A] or [B]. We capture that in a rate law. Think of x and y as sensitivity powers: how strongly rate responds to each reactant’s concentration. You can’t read these powers from overall stoichiometry (except for a single elementary step). The experimental rate law fits Rate = k[A] x[B] y. The exponents x and y are the (partial) orders in A and B. General rate law (preserve) Overall order (preserve) Overall order = x + y (sum of exponents in the rate law). Rate law An experimentally determined mathematical relation between the reaction rate and the concentrations of reactants (and sometimes catalysts). Order of reaction Sum of the concentration exponents in the rate law. Can be zero, integer, fractional, or negative. Rate constant (k) Proportionality constant in the rate law. For a given reaction at a fixed temperature, k is constant; its units depend on overall order. neet-alert Do not assume order from stoichiometric coefficients. Except for a single elementary step, stoichiometry ≠ rate exponents. Always use experimental data. Units of k and quick identification Because rate has units of concentration per time, the units of k must balance the rate law. Spotting the units is a fast NEET skill: once you know the overall order n, you know the units of k right away. Units of k for overall order n. Common concentration unit for NEET: mol L -1 ; time: s. Overall order (n) Rate law (one-reactant form) Typical units of k (mol, L, s) Units of k by overall order n Rate = k mol L -1 s -1 Rate = k[A] s -1 Rate = k[A] 2 (or k[A][B]) L mol -1 s -1 Rate = k[A] 3 (rare overall order) L 2 mol -2 s -1 How rate responds to concentration: 0, 1st, 2nd order Visualise three simple patterns for a single-reactant case (A → Products): - Zero order: rate is flat (independent of [A]); often due to saturated surface or constant light intensity in photochemical steps. - First order: rate ∝ [A]; many decompositions, radioactive decay, and hydrolyses in excess solvent. - Second order: rate ∝ [A] 2 or [A][B]; bimolecular collisions control rate. Rate vs [A] trends: zero order (horizontal), first order (straight line through origin), second order (curve upward). Fractional order (e.g., 1/2) can arise from multi-step mechanisms or adsorption equilibria. Negative order can appear when a reactant inhibits the rate (rate decreases as its concentration increases). Overall third order is rare; example: oxidation of NO, where experiments give Rate = k[NO] 2[O2] (overall order 3). Order can be unusual too Molecularity: only for a single elementary step Molecularity counts how many species collide in one elementary step of a mechanism: unimolecular (1), bimolecular (2), very rarely termolecular (3). It cannot be zero, fractional, or negative. Molecularity is a theoretical/mechanistic concept tied to a single step, whereas order is an experimental result for the overall reaction. Aspect Order vs Molecularity — crisp comparison Basis Order of reaction Molecularity Definition Sum of exponents in experimental rate law No. of species colliding in one elementary step Possible values 0, integer, fractional, or negative Positive integers only: 1, 2 (rarely 3) How determined Experimentally (initial rates, half-life, isolation) From mechanism’s elementary step Applies to Overall reaction behaviour A single mechanistic step Equality? Equals molecularity only if the reaction is a single elementary step Not defined for complex overall reactions tip Quick check: If you need experiments to find it → that’s order. If you can count colliding molecules in a proposed single step → that’s molecularity. Finding order from data: initial rates, isolation, half-life method Initial-rates method is the workhorse for NEET data questions. You run the reaction multiple times, changing initial concentrations, and measure the initial rate each time. Then compare how rate scales with each reactant. Initial-rates method — steps Hold [B]0 constant; vary [A]0 between trials and measure initial rates. If doubling [A]0 doubles the rate, order in A is 1; if it quadruples, order in A is 2; if rate doesn’t change, order in A is 0; in general, rate ratio = ([A] ratio) x . Repeat by holding [A]0 constant and varying [B]0 to find order in B. Sum partial orders for overall order and solve for k from any trial. Flowchart of the initial-rates method to extract partial orders and k from a set of trials. gpt-image-2 2026-05-26T17:04:43.966Z Flowchart for determining rate law by initial rates: Start node (Collect trials with varying initial concentrations) → Branch 1: Hold [B] constant, vary [A], compute rate ratios → Determine order in A (slope in log–log or integer inference) → Branch 2: Hold [A] constant, vary [B], compute rate ratios → Determine order in B → Sum to overall order → Compute k. Clean vector, boxes with arrows, neutral palette, no in-image text other than labels A, B, rate. Orders x and y come from experiments with varying initial concentrations and measuring initial rates — not from the balanced equation. Isolation method (to simplify multi-reactant rate laws) Keep one reactant in large excess so its concentration stays ~constant. Its factor merges into k, giving an apparent rate law in the other reactant(s) only. Example: If Rate = k[A][B] and [B] ≫ [A], then Rate ≈ k′[A] with k′ = k[B] (pseudo-first-order in A). Half-life method: Often, first-order reactions show concentration-independent half-life; this clue helps assign first order quickly. The actual integrated equations and t 1/2 expressions are covered in the next concept (NTCH08/03). Pseudo-first-order: classic ester hydrolysis Acid-catalysed hydrolysis of an ester such as ethyl acetate (IUPAC: ethyl ethanoate; SMILES: CCOC(=O)C) by water (SMILES: O) produces acetic acid (ethanoic acid; SMILES: CC(=O)O) and ethanol (SMILES: CCO). True rate law depends on both ester and water, but in aqueous solution [H2O] is huge and effectively constant, so the reaction appears first order in ester. Overall: CH3COOC2H5 + H2O → CH3COOH + C2H5OH (acid catalysed). Apparent Rate = k′[ester], where k′ = k[H2O]. Protonation of the ester carbonyl activates it; water attacks; proton transfers and C–O bond cleavage yield acetic acid and ethanol; acid is regenerated. Protonation of the carbonyl oxygen in ethyl ethanoate to enhance electrophilicity. C=O → C=OH+ dilute acid, aqueous; [H2O] large room temperature (typical lab conditions) H2O lone pair attacks C=O+ Water attacks the carbonyl carbon to form a tetrahedral intermediate. Proton shuffle Proton transfers within the intermediate set up the leaving group. Break C–O(Et); H+ restored C–O bond cleavage expels ethanol; acetic acid formed; catalyst regenerated. Acid-catalysed hydrolysis of ethyl ethanoate (pseudo-first-order in excess water) ethyl acetate ethyl ethanoate substrate (appears first-order under excess water) oxidane water nucleophile; large excess → pseudo-first-order oxonium ion (catalyst) hydronium/acid catalyst (regenerated) gpt-image-2 Pseudo-first-order setup: ester in large volume of water so [H2O] is effectively constant; apparent first-order decay of ester. 2026-05-26T17:04:44.611Z Schematic beaker with a small number of ester molecules and a dense background of water molecules; label [H2O] ≫ [ester]. Show rate law box: true rate k[ester][H2O] → apparent k′[ester] where k′ = k[H2O]. Clean 2D vector, red arrows for logic, no extra text. Common rate-law patterns and examples Type Rate-law form (single key species) Units of k Typical contexts/examples Zero-, first-, second-order: rate-law forms and typical contexts Order Zero order Rate = k mol L -1 s -1 Surface-catalysed steps at saturation; photochemical steps at constant light intensity First order Rate = k[A] s -1 Radioactive decay; inversion of sucrose; hydrolysis of esters in large excess water (pseudo-first-order in ester) Second order Rate = k[A] 2 or k[A][B] L mol -1 s -1 Bimolecular reactions where collision frequency controls rate clinical Pharmacokinetics: Many drugs are eliminated by first-order kinetics — rate of elimination ∝ plasma concentration. Dose schedules use this to maintain therapeutic levels. If elimination becomes zero order (enzyme saturation), elimination rate becomes constant, risking accumulation and toxicity if dosing isn’t adjusted. False. Orders are determined experimentally and reflect the mechanism, not overall stoichiometry. Example: a reaction might be 2A → products but have Rate = k[A] 1 or k[A] 2 depending on mechanism and experiments. The exponents (orders) in the rate law equal the stoichiometric coefficients from the balanced equation. For a given reaction at a fixed temperature, k is constant and independent of concentrations. k changes with temperature, catalyst, or if the reaction itself changes. The rate constant k changes when reactant concentrations change. Order always equals molecularity. They can match only for a single elementary step. For most overall (multi-step) reactions, order is experimental while molecularity is defined only for individual elementary steps and must be a positive integer. High-yield traps: (1) Reading order from the balanced equation, (2) forgetting that overall order can be zero/fractional/negative, (3) misidentifying k units. Always confirm with data and the units rule [k] = (concentration) (1−n) time −1 . neet-alert Core terms — quick recap Experimental relation between rate and concentrations; e.g., Rate = k[A] x[B] y Rate law Sum of exponents in the rate law (overall order = x + y) Order of reaction Proportionality constant in the rate law; depends on temperature and catalyst, not on concentrations Rate constant (k) A single mechanistic step with defined molecularity Elementary reaction Overall reaction comprising multiple elementary steps Complex reaction Number of species colliding in an elementary step; allowed values: 1, 2, rarely 3 Molecularity Apparent first-order kinetics when one reactant is in large, effectively constant excess Pseudo-first-order Find partial orders by comparing initial rate changes when varying one reactant at a time Initial-rates method Use the [A]-independence of t1/2 for first-order (and other t1/2 trends) to suggest order (details in NTCH08/03) Half-life method Keep one reactant in large excess to reduce a multi-reactant rate law to an apparent simpler order Isolation method