Question

In a zero order reaction, it takes 342 seconds for 75% of a hypothetical reaction to decompose. Determine the half-life t1/2} in units of seconds. Do not enter units with your numerical answer.

Answer 1

Answer : The half-life is, $1.17\times 10^4s$

Explanation :

First we have to calculate the rate constant for zero order reaction.

The expression used is:

$\ln [A]=-kt+\ln [A_o]$

where,

$[A_o]$ = let initial concentration = 100

$[A]$ = final concentration = 25

t = time = 324 s

k = rate constant = ?

Now put all the given values in the above expression, we get:

$\ln (25)=-k\times 324+\ln (100)$

$k=4.28\times 10^{-3}Ms^{-1}$

Now we have to calculate the half-life.

The expression used is:

$t_{1/2}=\frac{[A_o]}{2k}$

$t_{1/2}=\frac{100}{2\times 4.28\times 10^{-3}}$

$t_{1/2}=11682.24s=1.17\times 10^4s$

Thus, the half-life is, $1.17\times 10^4s$