The first order decomposition of `H_(2)O_(2)` in an appropriate medium is characterised by a rate constant of `0.2303min^(-1)`. What is the time (in min) required to complete `9//10` fraction of the reaction?

Options

A. 0.1
B. 10
C. 100
D. 0.01

Answer

B

Explanation

Given, rate constant (k) for first order ` = 0.2303 "min"^(-1)` .
For order reaction
Time `(t) = (2.303)/(k) "log" [(a)/(a-x)]` …(i)
where , a = initial concentration
(a-x) = concentration at time (t)
x = amount complete
Let , initial concentration (a) = 1
` x = (9)/(10)`
then , ` (a-x) = 1 -(9)/(10) = (1)/(10)`
From equation (i) ,
` t (2.303)/(02303) " log" (1)/(((1)/(10)))`
t = 10 log 10
` t = xx 10 xx 1 = 10 " min"^(-1)`
Hence , option (b) is correct .