CBSE · Class 12 · Chemistry · Chapter 3

Chemical Kinetics — Formula Sheet

Board Formulas

9 formulas

1.Rate of Reaction
$Rate = - \frac{1}{a} \frac{d [ A ]}{d t} = + \frac{1}{b} \frac{d [ B ]}{d t}$
$[A], [B]$ : Molar concentrations (mol/L) · $a, b$ : Stoichiometric coefficients · $t$ : Time (s)
For aA → bB, rate expressed with negative sign for reactants (disappearing) and positive for products, divided by stoichiometric coefficients.
2.Rate Law and Order★
$Rate = k [A]^{m} [B]^{n}, Order = m + n$
Powers m, n are EXPERIMENTAL (not stoichiometric). Overall order = m + n. Units of k depend on total order.
3.Zero-Order Integrated Rate Law
$[A]_{t} = [A]_{0} - k t, t_{1/2} = \frac{[ A ] _{0}}{2 k}$
$[A]_{t}$ : Concentration at time t · $[A]_{0}$ : Initial concentration · $k$ : Zero-order rate constant
Concentration decreases LINEARLY with time. Half-life ∝ [A]₀. Rate independent of [A]. Units of k: mol L⁻¹ s⁻¹.
4.First-Order Integrated Rate Law★
$k = \frac{2.303}{t} lo g \frac{[ A ] _{0}}{[ A ] _{t}}$
Working equation for most numericals. Also written as ln([A]₀/[A]_t) = kt or [A]_t = [A]₀ e^(−kt). Units of k: s⁻¹.
5.Half-Life of First-Order Reaction★
$t_{1/2} = \frac{0.693}{k}$
INDEPENDENT of initial concentration. Fundamental property of first-order kinetics (used in radioactive decay).
6.Half-Life of Second-Order Reaction
$t_{1/2} = \frac{1}{k [ A ] _{0}}$
Depends INVERSELY on initial concentration. Units of k: L mol⁻¹ s⁻¹.
7.Arrhenius Equation★
$k = A e^{- E_{a} / R T}$
$A$ : Frequency factor (same units as k) · $E_{a}$ : Activation energy (J/mol) · $R$ : 8.314 J·mol⁻¹·K⁻¹ · $T$ : Absolute temperature (K)
Rate constant rises exponentially with temperature. A = frequency factor (collisions per second, correct orientation). E_a = activation energy.
8.Arrhenius Two-Temperature Form★
$lo g \frac{k _{2}}{k _{1}} = \frac{E _{a}}{2.303 R} (\frac{1}{T _{1}} - \frac{1}{T _{2}})$
Direct application: given k at two temperatures, find Ea, or vice versa.
9.Temperature Coefficient (rule of thumb)
$μ = \frac{k _{T + 10}}{k _{T}} \approx 2 to 3$
For a 10 °C rise in temperature the rate typically 2-3 fold. Used in qualitative reasoning.