Answer to Question #156466 in Physical Chemistry for Ra

Question

The half-life of a reaction, A Products, is independent of the initial concentration of A.

What is the order of the reaction?

If the concentration of A reduces to 50% of its initial value in 500 seconds, in how much time would it reduce to 12.5% of its initial concentration?

Answer 1

A $\to$ product

half life of reaction is indepedent initial onc. of A , so it is definitely a 1st order reaction

as t_1/2 prortional to [A₀]^(1-n) where [A₀] = initial concentration of A , n= order of reaction

so for n=1 the t_1/2 is independent of initial conc. of A.

from the defination of half life we can say that time required for 50% completion of reaction from the initial conc. of A is known as half life. so here t_1/2 = 500 sec

by simple analogy we can do it that after another half life it reduces to its half that is to 25 % then after another half life it reduces to 12.5 % .

so three half life needed to reduce the initail conc of A to 12.5 % of of its initial conc. of A

so 3 x 500 sec = 1500 sec (ans)

or we can do by using formula

% reduce to intitial conc of A = 12.5 = (1\2)ⁿ x 100 n = no of half life

or, 12.5\100 = (0.5)ⁿ

or, 0.125 = (0.5)ⁿ

or, (0.5)³ = (0.5)ⁿ so by compairing this we can write n=3

so for 3 half life that means 3 x 500 sec = 1500 sec time required to redue a 12.5 % of its inital conc.