In a first order reaction, The concentration of reactant is reduced to 1/8th of the initial concentration in 75 minutea at 298 K. What is the half period of the reaction in minutes?

Options

A. 50 min
B. 15 min
C. 30 min
D. 25 min

Answer

D

Explanation

Let a = 1, a - x = 1/8 th, t == 75 min
`k = (2.303)/(t) "log" (a)/(a - x) = (2.303)/(75) "log" (1)/(1//8) = (2.303 xx 0.903)/(75) "min"^(-1)`
for first order reaction,
`t_(1//2) = (0.693)/(k) = (0.693 xx 75)/(2.303 xx 0.903) = 25` min