For a reaction A → 2B + C the half lives are 100 s and 50 s when the concentration of reactant A is — Chemical Kinetics Chemistry Question
Question
For a reaction A → 2B + C the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L respectively. The order of the reaction is ________. (Nearest Integer) –1
💡 Solution & Explanation
**Step 1: Use the half-life relationship for different reaction orders.** For a reaction of order n, the relationship between half-lives at different concentrations is: $$\frac{t_{1/2}^{(1)}}{t_{1/2}^{(2)}} = \left(\frac{[A]_2}{[A]_1}\right)^{n-1}$$ **Step 2: Identify given data.** - At [A]₁ = 0.5 mol/L: t₁/₂⁽¹⁾ = 100 s - At [A]₂ = 1.0 mol/L: t₁/₂⁽²⁾ = 50 s **Step 3: Substitute into the half-life formula.** $$\frac{100}{50} = \left(\frac{1.0}{0.5}\right)^{n-1}$$ **Step 4: Simplify both sides.** $$2 = (2)^{n-1}$$ **Step 5: Solve for n.** $$2^1 = 2^{n-1}$$ $$1 = n - 1$$ $$n = 2$$ **Step 6: Verify the relationship.** For a second-order reaction, half-life is inversely proportional to initial concentration. When concentration doubles (0.5 → 1.0), half-life should halve (100 → 50), which matches our data. Therefore, the answer is 2.