After 77.0 min, 44.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?
k = 2.303/t log [A]o/[A]t
where k = rate constant = ?
t = 77 min
[A]o = initial conc . = let it be a
[A]t = conc after time t ( 77 min) = since 44% of a has decomposed
...\
so 56% of a remain i.e. 56/100 X a = 0.56a
put the values...
k = 2.303/77 X log a/0.56a
k = 7.53 X 10^-3 min^-1
and
we know that
half life of a first order reaction = 0.693/k = 0.693/(7.53 X 10^-3 ) = 92.01 min
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