First order reaction is found to have rate constant, `k= 5.5xx 10^(-14) s^-1`. Find the half life to the reaction.

Explanation

We are given that
`k = 45. 48 xx 10 ^(-14) s ^(-1)`
We are to fine out `t _(2//3)`
We know that : For first order reaction, `t = ( 2. 303 )/( k ) log "" (a)/( a -x)`
`therefore t _(2//3)= (2. 303)/( k ) log "" (a)/( a - (2)/(3)a ) = ( 2. 303 )/( 5. 48 xx 10 ^(-14)) log"" ^(a)/( a//3) = ( 2. 303 xx 10 ^(14))/( 5. 48) xx 0. 47 71`
`= 2 xx 10 ^( 14) = 2 xx 10 ^(13)s.`