For a first-order reaction,
t1/2 = 0.693/ K
K = rate constant
we know t1/2 = 200 sec
therefore; K = 0.693/t1/2 = 0.693/200 = 3.465 x
10-3 sec-1
(a) one-half;
t50% left = t1/2 = 200 sec
this is half life time = 200 secs
(b) one-sixteenth (1/16)
t6.25% left = t1/16 = 4 x t1/2 = 4
x 200 sec = 800 sec
(c) one-ninth (1/9)
[A] = [A]0 x e-kt
ln[A]/[A]0 = -KT
therefore;
ln(1/9) = - K x t1/9
t1/9 left = - ln(1/9)/ 3.465 x 10-3
sec-1 = 634 sec
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