A substance decomposes by following first order kinetics. If 50% of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose ?

Explanation

Since 50% of the compound decomposes in 120 minutes,`t_(1//2)`= 120 min
For a first order reaction,
` k= ( 0.693 )/(t_(1//2)) = ( 0.693)/( 120 min) = 5.775 xx 10^(-3) min""^(-1)`
` t= ( 2.303 )/(k) log ""(a)/((a-x))`
` = ( 2.303)/( 5.775 xx 10^(-3) min""^(-1)) log "" (100)/( ( 100-90)) = 398 .78 min`