JEE Mains · Chemistry · STD 12 - 3. Chemical kinetics
\(t_{100\%}\) is the time required for the \(100\%\) completion of the reaction while \(t_{1/2}\) is the time required for \(50\%\) of the reaction to be completed. Which of the following option correctly represents the relation between \(t_{100\%}\) and \(t_{1/2}\) for zero and first order reactions respectively?
- A \(t_{100\%} = (t_{1/2})^2\) and \(t_{100\%} = (t_{1/2})^{-\infty}\)
- B \(t_{100\%} = 2t_{1/2}\) and \(t_{100\%} = (t_{1/2})^\infty\)
- C \(t_{100\%} = 2t_{1/2}\) and \(t_{100\%} = (2t_{1/2})^2\)
- D \(t_{100\%} = (t_{1/2})^\infty\) and \(t_{100\%} = 2t_{1/2}\)
Answer & Solution
Correct Answer
(B) \(t_{100\%} = 2t_{1/2}\) and \(t_{100\%} = (t_{1/2})^\infty\)
Step-by-step Solution
Detailed explanation
For a zero-order reaction: The integrated rate law is given by \(t = \dfrac{[A]_0 - [A]_t}{k}\). For \(50\%\) completion (\(t_{1/2}\)), \([A]_t = \dfrac{[A]_0}{2}\): \(t_{1/2} = \dfrac{[A]_0 - \dfrac{[A]_0}{2}}{k} = \dfrac{[A]_0}{2k}\) For \(100\%\) completion (\(t_{100\%}\)),…
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