Chemical Kinetics formulas for JEE Main & Advanced

18 formula entries for Chemical Kinetics, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Rate of Reaction

Rate = - \frac{1}{a} \frac{d [A]}{d t} = \frac{1}{b} \frac{d [B]}{d t}

When to use. Use to define and calculate the speed of a chemical reaction in terms of concentration changes.

Trap. Forgetting to divide by stoichiometric coefficients when comparing rates of different species.

Rate Law and Order of Reaction

Rate = k [A]^{m} [B]^{n}

When to use. Use to mathematically describe how concentration of reactants affects reaction rate.

Trap. Assuming order equals stoichiometric coefficients; order is experimental, not from balanced equation.

Integrated Rate Law: Zero Order

[A] = [A]_{0} - k t

;

t_{1 / 2} = \frac{[A]_{0}}{2 k}

When to use. Use for reactions where rate is independent of concentration (e.g., some photochemical or surface reactions).

Trap. Forgetting that half-life depends on initial concentration for zero order (unlike first order).

Integrated Rate Law: First Order

[A] = [A]_{0} e^{- k t}

;

t_{1 / 2} = \frac{\ln 2}{k}

When to use. Use for reactions like radioactive decay, decomposition of N $_{2}$ O $_{5}$ , or any reaction with rate proportional to one reactant.

Trap. Using natural log (ln) instead of log base 10; the formula $\log [A] = \log [A]_{0} - \frac{k t}{2.303}$ is common.

Integrated Rate Law: Second Order

\frac{1}{[A]} = \frac{1}{[A]_{0}} + k t

;

t_{1 / 2} = \frac{1}{k [A]_{0}}

When to use. Use for reactions like 2A → products or A + B → products when [A] = [B] initially.

Trap. Confusing with first order; second order half-life depends on initial concentration.

Determining Order from Experimental Data

Rate = k [A]^{m} \Rightarrow \log (Rate) = \log k + m \log [A]

When to use. Use when given a table of initial concentrations and initial rates to find the rate law.

Trap. Assuming order from stoichiometry; always use experimental data.

Pseudo-First Order Reaction

Rate = k^{'} [ester]

where

k^{'} = k [H_{2} O]

When to use. Use when one reactant is present in much higher concentration than others, simplifying kinetics.

Trap. Forgetting that the excess reactant's concentration is absorbed into the rate constant.

Arrhenius Equation

k = A e^{- E_{a} / R T}

;

\ln k = \ln A - \frac{E_{a}}{R T}

When to use. Use to calculate activation energy, rate constant at different temperatures, or predict temperature dependence.

Trap. Using log base 10 instead of natural log; the formula $\log k = \log A - \frac{E_{a}}{2.303 R T}$ is common.

Arrhenius Equation: Two-Point Form

\ln \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})

When to use. Use when given k at two temperatures to find E $_{a}$ , or to find k at another temperature.

Trap. Using Celsius instead of Kelvin for temperature.

Effect of Temperature on Rate

k \propto e^{- E_{a} / R T}

When to use. Use to predict how rate changes with temperature.

Trap. Assuming the 10°C rule is universal; it's an approximation and depends on E $_{a}$ .

Collision Theory

f = e^{- E_{a} / R T}

When to use. Use to understand the molecular basis of reaction rates and the Arrhenius pre-exponential factor.

Trap. Thinking all collisions lead to reaction; only effective collisions do.

Half-Life Method to Determine Order

t_{1 / 2} \propto [A]_{0}^{1 - n}

When to use. Use when given half-life data at different initial concentrations to find order.

Trap. Forgetting that this method works only for reactions with a single reactant or when other reactants are in excess.

Deriving Rate Law from Mechanism

Example:

A ⇌ B

(fast),

B \to C

(slow) gives rate =

k K [A]

When to use. Use when a reaction mechanism is given and you need to find the overall rate law.

Trap. Forgetting to use equilibrium constant to express intermediate concentration.

Catalysis and Activation Energy

k_{catalyzed} = A e^{- E_{a}^{'} / R T}

with

E_{a}^{'} < E_{a}

When to use. Use to explain how catalysts increase reaction rates.

Trap. Thinking a catalyst changes the equilibrium constant; it speeds up both forward and reverse equally.

Temperature Coefficient (Q $_{10}$ )

Q_{10} = \frac{k_{T + 10}}{k_{T}}

When to use. Use as a rough estimate of temperature effect on rate.

Trap. Assuming Q $_{10}$ is always 2; it's an approximation.

Radioactive Decay as First Order

N = N_{0} e^{- λ t}

;

t_{1 / 2} = \frac{0.693}{λ}

When to use. Use for any radioactive decay problem.

Trap. Using mass instead of number of atoms; they are proportional but careful with units.

Using Initial Rates to Find Rate Constant

k = \frac{Rate}{[A]^{m} [B]^{n}}

When to use. Use when given initial rates at various concentrations.

Trap. Using concentrations from later times instead of initial rates.

Units of Rate Constant

Units of k = M^{1 - n} s^{- 1}

When to use. Use to verify the order from given k units or to determine k units from order.

Trap. Forgetting that for gas-phase reactions, concentration can be in atm or mol/L; units adjust accordingly.

Values to remember

$\ln 2 \approx 0.693$ Integrated Rate Law: First Order
$2.303$ Integrated Rate Law: First Order
$R = 8.314 {J mol}^{- 1} K^{- 1}$ Arrhenius Equation

Read the full chapter: Chemical Kinetics for JEE, with what JEE asks and the common traps.