Consider the two different first order reactions given below A + B C (Reaction 1) P Q (Reaction 2) The ratio of the half life of Reaction 1 : Reaction 2 is 5 : 2. If t1 and t2 represent the time taken to complete 2/3rd and 4/5th of Reaction 1 and Reaction 2, respectively, then the value of the ratio t1 : t2 is 10-1 (nearest integer). [Given : 10(3) = 0.477 and 10(5) = 0.699]
Answer
17
Solution
First order: t = 2.303k [R]0[R] and t1/2 = 0.693k
(t1/2)1(t1/2)2 = k2k1 = 52
2/3 complete ⇒ [R]0[R] = 3 ⇒ t1 = 2.303k1 3
4/5 complete ⇒ [R]0[R] = 5 ⇒ t2 = 2.303k2 5
∴ t1t2 = k2k1 3 5 = 52 0.4770.699
= 1.71 17 10-1
Answer: 17