Half-life Conceptual

Question

Which reaction order has half-life independent of initial concentration?

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1. **General Expression**: $t_{1/2} \propto [A]_0^{1-n}$, where $n$ is the reaction order.
2. **Zero Order ($n=0$)**: $t_{1/2} \propto [A]_0$. Half-life increases as concentration increases.
3. **First Order ($n=1$)**: $t_{1/2} \propto [A]_0^0$. This means $t_{1/2}$ is a **constant** ($0.693/k$), **independent** of how much reactant you start with.
4. **Second Order ($n=2$)**: $t_{1/2} \propto [A]_0^{-1}$. Half-life is inversely proportional to concentration.
5. **Summary**: First-order kinetics (like radioactive decay) are unique because they take the same time to reduce concentration from $100 	o 50$ as from $50 	o 25$.

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Half-life Conceptual

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