The decomposition of `H_(2)O_(2)` is a first order reaction. Calculate the half life time and rate constant for the decomposition from the fact that the fraction decomposed in 50 minutes is 0.75

Explanation

Step I. Calculation of rate constant(k)
Let the initial conc. A, Final conc. = a-0.75a=0.25a, t=50min.
For the first order reaction,
`k=2.303/t log (a)/(a-x) = (2.303)/(50"min")log a/(0.25a)`
`=(2.303)/(50 "min") log 4 = (2.303 xx 0.6020)/(50"min") = 0.02773 min^(-1)`
Step II. Calculation of half life period `(t_(1//2))`
`t_(1//2) = 0.693/k = 0.6930/(0.2773 min^(-1)) = 24.99` min