Physical ChemistryHigh Yield (2-3 Qs in JEE)

Chemical Kinetics Formulas

Rate laws, order and molecularity, integrated rate equations for zero and first order, half-life, and Arrhenius equation.

8 Formulas•464+ Questions in Bank•

Concept Diagram

Reaction Coordinate & Activation Energy

Potential energy profile showing reactant ground state, transition state, forward activation energy Ea, and enthalpy change ΔH.

\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = k [A]^x [B]^y, \quad \text{Order} = x + y

Stoichiometric rate definition and experimental power dependence.

Examiner Tip: Order can be zero, fractional, or negative; molecularity is always integer.

[A]_t = [A]_0 - kt \; (\text{Zero Order}), \quad \ln\frac{[A]_0}{[A]_t} = kt \iff [A]_t = [A]_0 e^{-kt} \; (\text{First Order})

Concentration-time profiles for fundamental reaction mechanisms.

Examiner Tip: First-order equation in log10: k = (2.303/t) * log10([A]₀ / [A]_t).

t_{1/2} = \frac{[A]_0}{2k} \; (\text{Zero Order}), \quad t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k} \; (\text{First Order}), \quad t_{1/2} \propto \frac{1}{[A]_0^{n-1}}

Time required for reactant concentration to reduce to half its initial value.

Examiner Tip: For first-order: t_75% = 2 * t_50%, and t_99.9% ≈ 10 * t_50%.

k = A e^{-E_a / RT} \iff \log_{10}\frac{k_2}{k_1} = \frac{E_a}{2.303 R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Temperature dependence of rate constant governed by activation energy barrier E_a.

Examiner Tip: Plot of ln k vs 1/T has slope -E_a / R.

\Delta E_a = E_a - E_a', \quad \frac{k_{\text{cat}}}{k_{\text{uncat}}} = e^{\Delta E_a / RT}

A catalyst provides an alternate pathway with lower activation energy, accelerating both forward and backward rates equally.

Examiner Tip: A catalyst does NOT change equilibrium constant K or ΔG.

\text{2nd Order: } \frac{1}{[A]_t} - \frac{1}{[A]_0} = kt \implies t_{1/2} = \frac{1}{k [A]_0}, \quad n\text{-th Order: } \frac{1}{n-1}\left(\frac{1}{[A]_t^{n-1}} - \frac{1}{[A]_0^{n-1}}\right) = kt

Integrated rate law and half-life for second-order and general n-th order reactions (n ≠ 1).

Examiner Tip: Plot of 1/[A]_t versus t for a second-order reaction yields a straight line with slope +k.

k_{\text{eff}} = k_1 + k_2, \quad \frac{[B]_t}{[C]_t} = \frac{k_1}{k_2}, \quad \% \text{ Yield of } B = \frac{k_1}{k_1 + k_2} \times 100\%, \quad E_{a,\text{eff}} = \frac{k_1 E_{a1} + k_2 E_{a2}}{k_1 + k_2}

Kinetics where reactant A decomposes simultaneously into two distinct products B and C.

Examiner Tip: Product ratio [B]/[C] is constant and equal to k₁/k₂ at all times throughout the reaction.

A \xrightarrow{k_1} B \xrightarrow{k_2} C \implies t_{\text{max}} = \frac{\ln(k_2 / k_1)}{k_2 - k_1}, \quad [B]_{\text{max}} = [A]_0 \left(\frac{k_1}{k_2}\right)^{\frac{k_2}{k_2 - k_1}}

Sequential first-order decay. Intermediate concentration [B] rises to a peak and then decays to zero.

Examiner Tip: If k₂ >> k₁, intermediate B reacts immediately upon formation, validating the Steady State Approximation: d[B]/dt ≈ 0.

Frequently tested misconceptions in Chemical Kinetics

•Units of rate constant k change with reaction order: k = (mol/L)^(1-n) s^(-1).
•Half-life of first order reaction is independent of initial concentration, but for zero order t_1/2 ∝ [A]₀.