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 rate constant

Explanation

Let the original material be .a., t = 15 minutes Amount decomposed
` =x= ( a xx 20 )/(100 ) = 0.2 a`
Calculation of rate constant, k
For a first order,
` k=( 2.303 )/(t) log ""(a)/((a-x)) = ( 2.303 )/( 15 min ) log"" (a)/(a-0.2 a)`
`=( 2.303 )/( 15 min) log "" (a)/( 0.8 a) = ( 2.303)/( 15 min ) log 1.25`
`= 0.1535 xx 0.0969 min""^(-1) = 0.0149 min""^(-1)`