Question

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

Answer 1

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