In a first order reaction, `75%` of the reactants disappeared in `1.386 hr`. What is the rate constant ?

Options

A. `3.6 xx 10^(-3)s^(-1)`
B. `7.2 xx 10^(-3)s^(-1)`
C. `2.7 xx 10^(-4)s^(-1)`
D. `1.8 xx 10^(-3)s^(-1)`

Answer

C

Explanation

Let original amount `N_(0) = 100`
Since, disappeared amount `= 75%`
`:.` left amount, `N = 100 - 75 = 25`
`:.` Since, `(N_(0))/(N) = 2^(n)` where `n =` no. of hlaf lives
or, `(100)/(25) = 2^(n)`
or, `2^(2) = 2^(2)`, here `n = 2`
`because` Total time `= n xx t_(1//2)`
`1.386` hours `= 2 xx t_(1//2)`,
`t_(1//2) = 0.693` hours
`= 2494.8 sec`.
`k = (0.693)/(2494.8) = 2.7 xx 10^(-4) sec^(-1)`