Question

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55. # a first order reaction is 50% completed in 4 hr
then the time required for 90% completion of the
reaction will be
(1) 13.20 he (2) 7.25 hr
(3) 9.51 he
(4) 18.52 hr​

Answer 1

Answer:

The time required for 90% completion is 13.20 hr

Explanation:

The time required for 50% completion is the half life of the reaction.

The relation between half life and rate constant for first order reaction is:

$k=rateconstant=\frac{0.693}{t_{\frac{1}{2}}}$

putting values

$k=\frac{0.693}{4}=0.173hr^{-1}$

Now the rate law for first order reaction is:

$kt=ln(\frac{[A_{0}]}{[A_{t}]} )\\Where\\A_{0}=initial concentration\\A_{t}= concentration at time t$

given:

Initial concentration = 100

Final concentration = 10 [90% completion means 10% left]

putting values:

$0.173(time)=ln(\frac{100}{10})=2.302\\time=13.2hr$