Example 1 · level 1
A first-order reaction has rate constant k = 0.025 s⁻¹. Find its half-life in s, correct to 2 decimal places. (Use t½ = 0.693 ÷ k.)
Show solution
- t½ = 0.693 ÷ 0.025 = 27.72 s.
Answer: 27.72 s
CLASS 11–12 CHEMISTRY · CHEMICAL KINETICS
Rate laws and first-order half-life
For a first-order reaction t½ = 0.693 ÷ k, independent of starting concentration. Find the order for a reactant by seeing how the rate changes when only its concentration changes.
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Worked examples
Example 2 · level 2
A first-order decomposition has a half-life of 40 min. Starting with 160 g of reactant, what mass (in g) remains after 160 min?
Show solution
- Number of half-lives = 160 ÷ 40 = 4.
- Remaining = 160 × (1/2)⁴ = 10 g.
Answer: 10 g
Example 3 · level 3
For A + B → products, initial-rate data (concentrations in mol/L, rate in 10⁻³ mol L⁻¹ s⁻¹): Exp 1: [A] = 0.1, [B] = 0.3, rate = 2. Exp 2: [A] = 0.3, [B] = 0.3, rate = 6. Exp 3: [A] = 0.1, [B] = 0.6, rate = 2. Which rate law fits the data?
- rate = k[B]
- rate = k[A]²[B]
- rate = k[A]
- rate = k[A][B]
Show solution
- Exp 1 → 2: [A] × 3 ⇒ rate × 3 = 3, so order in [A] is first (1).
- Exp 1 → 3: [B] × 2 ⇒ rate × 1 = 2⁰, so order in [B] is zero (0).
- So rate = k[A]; overall order = 1.
Answer: rate = k[A]