Question

The half-life for the first-order decomposition of a is 355 s. how much time must elapse for the concentration of a to decrease to
a.one-fourth

Answer 1

Given the half life of the first order decomposition reaction is 355 s

Rate constant of the first order reaction is related to the half life by the equation,

$k = \frac{0.693}{t_{\frac{1}{2}}}$

$k = \frac{0.693}{355 s}$

k = 0.00195 $s^{-1}$

The concentration of the substance is decreased to 1/4 th.

If we start with 1 M solution, after time t the concentration becomes 1/4th = 0.25 M

First order rate law:

$[A] = [A]_{0} e^{-kt}$

$[A] = 0.25 M$

$[A]_{0} = 1 M$

$k = 0.00195 s^{-1}$

Plugging in the values to solve for t,

$0.25 M = 1 M (e^{-(0.00195s^{-1})t})$

$ln(\frac{0.25}{1}) = - (0.00195 s^{-1})(t)$

$t = \frac{ln(0.25)}{0.00195} s$

t = 710 s