t100\% is the time required for the 100% completion of the reaction while t1/2 is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between t100\% and t1/2 for zero and first order reactions respectively ?
- t100\% = (t1/2)2 and t100\% = (t1/2)-
- t100\% = 2t1/2 and t100\% = (t1/2)
- t100\% = 2t1/2 and t100\% = (2t1/2)2
- t100\% = (t1/2) and t100\% = 2t1/2
Answer
(2) t100\% = 2t1/2 and t100\% = (t1/2)
Solution
Zero order: [A] = [A]0 - kt
For 100% completion, [A] = 0 ⇒ t100\% = [A]0k
Half-life: t1/2 = [A]02k
∴ t100\% = 2t1/2
First order: t = 2.303k [A]0[A]
For 100% completion, [A] → 0 ⇒ [A]00 ⇒ t100\%
(after every t1/2 only half of what is left reacts, so the reaction is never 100% complete)
∴ for first order t100\% is infinite, written as (t1/2) .
Answer: (2)