The decomposition of a compound is found to follow a first order rate law. If it takes 15 minutes for 20 per cent of original material to react, calculate.
the time at which 10% of the original material remains unreacted.

Explanation

Let the original material be .a., t = 15 minutes Amount decomposed
` =x= ( a xx 20 )/(100 ) = 0.2 a`
Calculation of time for 100-10 = 90% decomposition,
` k= 0.0149 min""^(-1)`
` ( a-x) = 10 % = 0.1 a`
` t=( 2.303 )/(k ) log "" (a)/((a-x)) = ( 2.303 )/( 0.0149 min""^(-1)) log ""(a)/( 0.1 a)`
` =( 2.303 )/( 0.0149 min""^(-1)) log 10 = ( 2.303 )/( 0.0149 ) min `
` = 154 .56 min`