The rate constant of a first order reaction increases from `4 xx 10 ^(-2)to 8xx10^(-2) ` when the temperatur changes from `27^(@) C` to `37 ^(@) C.` Calculate the energy of activation `(Ea ).Log 2= 0.301), log 3 = 0. 4771, log 4= 0. 6021`

Explanation

`log "" ( k _(2))/( k _(1)) = ( Ea )/( 2. 303 R) (( T _(2) - T _(1))/( T _(1) T _(2))), k _(1) = 4 xx 10 ^(-2) , k _(2) = 8 xx 10 ^(-2) , T _(1) = 273 + 27 = 300 K `
`T _(2) = 273 + 37 310 K , R = 8.314 J K ^(-1) mol ^(-1)`
`log "" ( 8 xx 10 ^(-2))/( 4 xx 10 ^(-2)) = ( Ea )/( 2. 303 xx 8. 314 ) (( 310 - 300)/( 300 xx 310)), log 2 = (Ea )/( 2. 303 xx 8. 314) xx (10)/( 300 xx 310)`
`Ea = ( 0. 301 xx 2. 303 xx 8. 314 xx 300 xx 310)/( 10) = 535 98 J mol ^(-1) = 53. 598 kJ mol ^(-1)`