Chemical KineticsJEE Main

Concept

The rate law says how fast a reaction goes as reactant is consumed: rate $= k[A]^n$. The order $n$ determines the shape of the concentration-vs-time curve and whether the half-life depends on concentration.

Key formula

Derivation

Integrating $-d[A]/dt = k[A]^n$ gives each form above. Half-lives differ sharply:

- Zero order: $t_{1/2} = [A]_0/2k$ (shrinks as it proceeds) - First order: $t_{1/2} = \ln2/k$ (constant — independent of concentration) - Second order: $t_{1/2} = 1/k[A]_0$ (grows as concentration falls)

Scenarios to explore

• Chemical Kinetics — Rate laws and half-lives for 0/1/2 order.

Real-world applications

• Drug metabolism and dosing intervals (often first order).
• Radioactive decay (first order) and enzyme kinetics.
• Reactor design and shelf-life prediction.

JEE exam tips

• A straight line of $\ln[A]$ vs $t$ ⇒ first order; $1/[A]$ vs $t$ ⇒ second order.
• Constant half-life is the fingerprint of a first-order reaction.

Common mistakes

• Assuming half-life is always constant — only true for first order.
• Mixing up the integrated forms for different orders.
• Reading order off stoichiometry — order is experimental, not from the balanced equation.

Exam traps to avoid

• Units of $k$ depend on order: 0th M/s, 1st 1/s, 2nd 1/(M·s).
• A zero-order reaction's rate is independent of concentration entirely.