Question

Relation between $t_{1/2}$ & $t_{100\%}$ for zero order & Ist order reaction respectively is:

• A. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = 2 \times t_{1/2}$
• B. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = t_{1/2}$
• C. $t_{100\%} = 2 \times t_{1/2} : t_{100\%} = \infty$
• D. $t_{100\%} = \infty : t_{100\%} = 2 \times t_{1/2}$

Answer 1

The Correct Option is C

Chemical kinetics defines the time taken for a reaction to reach certain stages of completion ($t_{1/2}$ is 50% completion, $t_{100\%}$ is full completion).
1. For Zero Order Reaction:
Rate equation: $[A]_0 - [A]_t = kt$
At $t_{1/2}$, $[A]_t = [A]_0/2 \Rightarrow t_{1/2} = \frac{[A]_0}{2k}$
At $t_{100\%}$, $[A]_t = 0 \Rightarrow t_{100\%} = \frac{[A]_0}{k}$
Clearly, $t_{100\%} = 2 \times t_{1/2}$.

2. For First Order Reaction:
Rate equation: $[A]_t = [A]_0 e^{-kt}$
At $t_{1/2}$, $t_{1/2} = \frac{\ln 2}{k}$
At $t_{100\%}$, the concentration $[A]_t$ must reach zero. Looking at the equation, $[A]_0 e^{-kt} = 0$ is only possible as $t \rightarrow \infty$.
Therefore, for first-order reactions, completion theoretically takes infinite time ($t_{100\%} = \infty$).

3. Conclusion:
The respective relations are $t_{100\%} = 2 \times t_{1/2}$ for zero order and $t_{100\%} = \infty$ for first order. This matches option (3).