Question

Consider yourself a research scholar in the forensic science department studying the age of a dead biological sample. During one of the studies, you found that the sample decomposed by following first order kinetics. 

If 50% of the sample is decomposed in 120 minutes, how long will it take for 90% of the sample to decompose?

Answer 1

Given: `t_(1//2)` = 120 min

For a first-order reaction:

`t_(1//2) = 0.693/k`   ....(where 0.693 = ln⁡ 2)

k = `(0.693)/120`

= 0.005775 min⁻¹

For 90% decomposition, 10% of the sample remains.

a = 100

⇒ (a − x)

= (100 − 90)

= 10

Using the first-order rate equation:

`t = 2.303/k log  a/((a - x))` 

= `2.303/0.005775 log  100/10`

= 398.79 log 10

= 398.79 × 1 

= 398.79 minutes