Question

What is the half life of a compound if 75% of a given sampleof

Answer 1

Answer:

$t_{1/2}=30.14\ min$

Explanation:

Using integrated rate law for first order kinetics as:

$[A_t]=[A_0]e^{-kt}$

Where,  

$[A_t]$ is the concentration at time t

$[A_0]$ is the initial concentration

Given:

75 % is decomposed which means that 0.75 of $[A_0]$ is decomposed. So,

$\frac {[A_t]}{[A_0]}$ = 1 - 0.75 = 0.25

t = 60 min

$\frac {[A_t]}{[A_0]}=e^{-k\times t}$

$0.25=e^{-k\times 60}$

k = 0.023 min⁻¹

Considering the expression for half life as:-

$t_{1/2}=\frac {ln\ 2}{k}$

Where, k is rate constant

So,  

$t_{1/2}=\frac{\ln 2}{0.023}\ min$

$t_{1/2}=30.14\ min$