Chemistry · Physical Chemistry

Chemical Kinetics formulas for JEE

Every Chemical Kinetics formula you need for JEE, grouped by concept.

FormulasRevision notes
26 formulas3 concepts
01Rate of Reaction and Order02Collision Theory and Activation Energy03Integrated Rate Equations and Half-Life
01

Rate of Reaction and Order

6 formulas

Rate Law

Rate=k[A]x[B]yRate = k[A]^x[B]^y

Expression relating reaction rate to the molar concentration of reactants.

applies whenx and y are experimentally determined orders.
kineticsrate_laworder

Rate Law for H2O2 Decomposition

Rate=k[H2O2][I−]Rate = k[H_2O_2][I^-]

Specific experimental rate law for the iodide-catalyzed decomposition of hydrogen peroxide.

applies whenAlkaline medium, iodide acting as a catalyst.
kineticsrate_lawcatalyst

Units of Rate Constant

k=(mol L−1)1−ns−1k = (\text{mol L}^{-1})^{1-n} s^{-1}

General formula to deduce the unit of the specific rate constant based on reaction order.

applies whenWhere n is the overall order of the reaction.
kineticsrate_constantunits

Average Rate of Reaction

rav=−Δ[R]Δt=+Δ[P]Δtr_{av} = -\frac{\Delta[R]}{\Delta t} = +\frac{\Delta[P]}{\Delta t}

Change in concentration of reactant or product over a macroscopic time interval.

applies whenApplicable for finite time intervals.
kineticsrateaverage

Instantaneous Rate of Reaction

rinst=−d[R]dt=+d[P]dtr_{inst} = -\frac{d[R]}{dt} = +\frac{d[P]}{dt}

Rate of reaction at a specific instant of time.

applies whenAs Δt approaches zero.
kineticsrateinstantaneous

Rate of Reaction with Stoichiometry

Rate=−1ad[A]dt=−1bd[B]dt=1cd[C]dt=1dd[D]dtRate = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}

Equating the overall rate of reaction using stoichiometric coefficients.

applies whenFor a general reaction aA + bB -> cC + dD
kineticsratestoichiometry
02

Collision Theory and Activation Energy

7 formulas

Arrhenius Equation

k=Ae−Ea/RTk = A e^{-E_a/RT}

Equation relating the rate constant to absolute temperature and activation energy.

applies whenApplicable across a wide range of standard chemical reactions.
kineticsarrheniustemperature

Arrhenius Equation (Logarithmic)

ln⁡k=−EaRT+ln⁡A\ln k = -\frac{E_a}{RT} + \ln A

Linearized form of the Arrhenius equation for graphing.

applies whenUsed for straight-line plot of ln k vs 1/T.
kineticsarrheniuslogarithm

Arrhenius Equation (Two Temperatures)

log⁡k2k1=Ea2.303R[T2−T1T1T2]\log \frac{k_2}{k_1} = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right]

Formula for comparing rate constants at two different temperatures.

applies whenActivation energy must remain constant over the temperature range.
kineticsarrheniustemperature_comparison

Collision Theory Equation (Basic)

Rate=ZABe−Ea/RTRate = Z_{AB} e^{-E_a/RT}

Rate equation based on collision frequency and activation energy.

applies whenAssumes reactant molecules are hard spheres.
kineticscollisionbasic

Collision Theory Equation (With Steric Factor)

Rate=PZABe−Ea/RTRate = P Z_{AB} e^{-E_a/RT}

Modified collision theory rate equation accounting for proper spatial orientation.

applies whenP is the steric or probability factor.
kineticscollisionsteric_factor

Fraction of Effective Molecules

x=e−Ea/RTx = e^{-E_a/RT}

Fraction of molecules having energy equal to or greater than the activation energy.

applies whenFollows Maxwell-Boltzmann distribution.
kineticsarrheniusprobability

Temperature Coefficient

μ=kT+10kT\mu = \frac{k_{T+10}}{k_T}

Ratio of specific reaction rates at two temperatures separated by 10 K.

applies whenTypically between 2 and 3 for most thermal reactions.
kineticstemperature_coefficientjee-advanced
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03

Integrated Rate Equations and Half-Life

13 formulas

First Order Integrated Rate Equation

k=2.303tlog⁡[R]0[R]k = \frac{2.303}{t} \log\frac{[R]_0}{[R]}

Concentration of reactant at time t for a first-order reaction.

applies whenReaction order n = 1.
kineticsintegratedfirst_order

First Order Half-Life

t1/2=0.693kt_{1/2} = \frac{0.693}{k}

Time required for the reactant concentration to reach half its initial value in a first-order reaction.

applies whenReaction order n = 1; independent of initial concentration.
kineticshalf_lifefirst_order

Zero Order Half-Life

t1/2=[R]02kt_{1/2} = \frac{[R]_0}{2k}

Time required for the reactant concentration to reach half its initial value in a zero-order reaction.

applies whenReaction order n = 0.
kineticshalf_lifezero_order

Zero Order Integrated Rate Equation

[R]=−kt+[R]0[R] = -kt + [R]_0

Concentration of reactant at time t for a zero-order reaction.

applies whenReaction order n = 0.
kineticsintegratedzero_order

Consecutive Reactions Maximum Concentration Time

tmax=ln⁡(k1/k2)k1−k2t_{max} = \frac{\ln(k_1/k_2)}{k_1 - k_2}

Time at which the intermediate species reaches its maximum concentration in consecutive first-order reactions.

applies whenFor series reaction A -> B (k1) -> C (k2).
kineticsconsecutive_reactionsjee-advanced

First Order Gas Phase Reaction

k=2.303tlog⁡(pi2pi−pt)k = \frac{2.303}{t} \log\left(\frac{p_i}{2p_i - p_t}\right)

Integrated rate equation for gas-phase reactions using partial pressures.

applies whenSpecifically for stoichiometry A(g) -> B(g) + C(g).
kineticsintegratedfirst_ordergas

First Order Integrated Rate (Exponential)

[R]=[R]0e−kt[R] = [R]_0 e^{-kt}

Exponential decay form of the first-order rate equation.

applies whenReaction order n = 1.
kineticsintegratedfirst_orderexponential

First Order 99.9% Completion Time

t99.9%≈10t1/2t_{99.9\%} \approx 10 t_{1/2}

Identity relating the time required for 99.9% completion to the half-life.

applies whenReaction order n = 1.
kineticsintegratedfirst_ordercompletion

n-th Order Half-Life General Rule

t1/2∝1[R]0n−1t_{1/2} \propto \frac{1}{[R]_0^{n-1}}

Proportionality relating half-life to initial concentration for any n-th order reaction.

applies whenValid for any order n ≠ 1.
kineticshalf_lifenth_orderjee-advanced

Second Order Half-Life

t1/2=1k[R]0t_{1/2} = \frac{1}{k[R]_0}

Time required for the reactant concentration to reach half its initial value in a second-order reaction.

applies whenReaction order n = 2.
kineticshalf_lifesecond_orderjee-advanced

Parallel Reactions Rate Constant

keff=k1+k2k_{eff} = k_1 + k_2

Effective rate constant for competitive parallel first-order reactions.

applies whenFor A -> B (k1) and A -> C (k2). The ratio of products is [B]/[C] = k1/k2.
kineticsparallel_reactionsjee-advanced

Reversible First Order Reactions

kf+kb=1tln⁡(xexe−x)k_f + k_b = \frac{1}{t} \ln \left(\frac{x_e}{x_e - x}\right)

Integrated equation for opposing/reversible first-order reactions.

applies whenWhere x is dissociation at time t, x_e is dissociation at equilibrium.
kineticsreversible_reactionsjee-advanced

Second Order Integrated Rate Equation

1[R]−1[R]0=kt\frac{1}{[R]} - \frac{1}{[R]_0} = kt

Integrated rate law for a second order reaction with equal initial reactant concentrations.

applies whenFor rate = k[R]^2 or k[A][B] where [A]_0 = [B]_0.
kineticsintegratedsecond_orderjee-advanced
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