Half-life a reaction is found to be inversely proportional to the cube of its initial concertration. — Chemical Kinetics Chemistry Question

💡 Solution & Explanation

# Solution: Determining Reaction Order from Half-Life Relationship **Given:** Half-life is inversely proportional to the cube of initial concentration $$t_{1/2} \propto \frac{1}{[A_0]^3}$$ **Step 1: Write the general half-life formula** For an nth-order reaction: $$t_{1/2} = \frac{k}{(n-1)[A_0]^{n-1}}$$ **Step 2: Compare with given relationship** From the given condition: $$t_{1/2} = \frac{C}{[A_0]^3}$$ where $C$ is a constant. **Step 3: Match the exponents** Comparing the two expressions: - Exponent of $[A_0]$ in denominator: $3$ - From the general formula: $n - 1 = 3$ Therefore: $$n = 4$$ **Answer: D (Fourth-order reaction)** The half-life being inversely proportional to the cube of initial concentration directly indicates that $(n-1) = 3$, giving us a **fourth-order reaction**.