Rate constant k for first order reaction has been found to be `2.54 xx 10^(-3) s^(-1)`. Calculate its three-fourth life.

Explanation

For a first order reaction,
` k=( 2.303 )/(t) log "" (a)/((a-x))`
Let .a. be 100 , `t=t_(0.75 ) = ?`
`(a - x) = 100 - 75 = 25,k= 2.54 xx 10^(-3) s^(-1)`
Substituting the values in equation (1),
`2.54 xx 10^(-3) s^(-1) = ( 2.303 )/( t_(0.75 )) log"" (100)/(25 )`
` t_(0.75 )=( 2.303 )/(2.54 xx 10^(-3) s^(-1) ) log "" 4`
` or t_(0.75 ) = 0.9066 xx 10^3 xx 0.6021 s = 5.46 xx 10^2 s`