Question

\(t_{100\%}\) is the time required for 100% completion of a reaction, while \(t_{1/2}\) is the time required for 50% completion of the reaction. Which of the following correctly represents the relation between \(t_{100\%}\) and \(t_{1/2}\) for zero order and first order reactions respectively

• A. \(t_{100\%} = 2t_{1/2}, \quad t_{100\%} = \infty\)
• B. \(t_{100\%} = 2t_{1/2} \quad \text{and} \quad t_{100\%} = \infty\)
• C. \(t_{100\%} = 2t_{1/2} \quad \text{and} \quad t_{100\%} = (2t_{1/2})^2\)
• D. \(t_{100\%} = \infty \quad \text{and} \quad t_{100\%} = 2t_{1/2}\)

Answer 1

The Correct Option is B

Concept:

• Zero order reaction \[ t_{1/2} = \frac{[A]_0}{2k} \] \[ t_{100\%} = \frac{[A]_0}{k} \] Thus, \[ t_{100\%} = 2t_{1/2} \]
• First order reaction \[ t_{1/2} = \frac{0.693}{k} \] In first order reactions, reactant concentration approaches zero asymptotically, so the reaction never reaches exactly \(100\%\) completion. Thus, \[ t_{100\%} = \infty \]

\[ \boxed{t_{100\%} = 2t_{1/2} \text{ and } t_{100\%} = \infty} \]