Grade 12th · Chemistry · Chemical Kinetics
Master Rate Law and Rate Constant (k) for Class 12 Chemistry (NCERT Chapter 4: Chemical Kinetics). Complete formulas for reaction rate, order of reaction, integrated rate equations for zero and first order, and half-life derivations.
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For a general reaction aA + bB → Products, the Rate Law is an experimentally determined equation expressing reaction rate in terms of molar concentrations of reactants: Rate = k[A]^x[B]^y. Crucially, powers x and y are the orders with respect to A and B. They are determined experimentally and MAY NOT EQUAL the stoichiometric coefficients a and b. Overall order n = x + y can be zero, integer, or fractional.
A reaction is zero order when rate is independent of reactant concentration: -d[R]/dt = k[R]⁰ = k. Integrating from t = 0 ([R] = [R]₀) to time t: [R] = [R]₀ - kt. Slope of [R] vs t graph is -k. Setting [R] = [R]₀/2 gives half-life: t₁/₂ = [R]₀ / (2k). Characteristic: Half-life of a zero-order reaction is directly proportional to initial concentration [R]₀.
For a first-order reaction: -d[R]/dt = k[R]. Separating variables: d[R]/[R] = -k dt. Integrating both sides: ln[R] = -kt + C. At t = 0, [R] = [R]₀ ⇒ C = ln[R]₀. Therefore: ln([R]/[R]₀) = -kt, or k = (1/t)·ln([R]₀/[R]) = (2.303/t)·log([R]₀/[R]). When [R] = [R]₀/2: t₁/₂ = (2.303/k)·log(2) = (2.303 × 0.3010)/k = 0.693 / k. Hallmark: Half-life of a first-order reaction is completely INDEPENDENT of initial concentration.
Reaction rate approximately doubles for every 10°C rise in temperature (Temperature Coefficient ≈ 2 to 3). Arrhenius explained this via activation energy (Ea): k = A·e^(-Ea/RT), where A is the frequency factor and e^(-Ea/RT) represents the fraction of molecules with kinetic energy ≥ Ea. In logarithmic form: log(k) = log(A) - Ea / (2.303·R·T). A plot of log(k) vs 1/T gives a straight line with slope = -Ea / (2.303·R).
Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.
Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.
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Master Solutions: Raoult's Law & Colligative Properties for Grade 12th Chemistry. Includes verified formulas, core concepts, step-by-step checklists, and interactive solver tools.
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Rate law is the mathematically determined expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be equal to the stoichiometric coefficient in the balanced chemical equation: Rate = k[A]^x[B]^y.
Use the general formula for unit of k: (mol/L)¹⁻ⁿ · s⁻¹, where n is the reaction order. If unit is s⁻¹, 1 - n = 0 ⇒ n = 1 (First order). If unit is mol L⁻¹ s⁻¹, 1 - n = 1 ⇒ n = 0 (Zero order). If unit is L mol⁻¹ s⁻¹, 1 - n = -1 ⇒ n = 2 (Second order).
In the integrated rate expression k = (2.303/t)·log([R]₀/[R]), substituting [R] = [R]₀/2 cancels [R]₀ completely, yielding t₁/₂ = 0.693 / k, which contains no concentration term.