For a first order reaction A B arrayll t/min & [A]/M \ 0 & 0.6500 \ x & 0.0650 \ 20 & 0.00065 array x = min. (Nearest integer)
Answer
7
Solution
First order: k = 2.303t [A]0[A]
From t = 20 min: k = 2.30320 0.65000.00065 = 2.30320 103 = 2.303 320 min-1
At t = x: x = 2.303k 0.65000.0650 = 2.303k 10
⇒ x = 2.303 202.303 3 = 203 = 6.67 min ≈ 7 min
(∵ For first order, time ∝ log of the fall: a 10-fold fall takes one-third of the time of a 1000-fold fall.)
Answer: 7