Half life of a first order chemical reaction is 69 hr at 300 K. Also , rate of this reaction is doubled as temperature is increased from 300 K to 310 K. Determine activation energy and pre - exponential factor for this reaction.

Explanation

`k_(310)/k_(300)=2`
`log=.k_2/k_1=E_a/(2.303R)((T_2-T_1)/(T_1T_2))`
`log2=E_a/(2.303R)((310-300)/(310xx300))=(10E_a)/(300xx310Rxx2.303)`
`E_a=53.60 "kJ mol"^(-1)`
At 300 K:
`t_(1//2)=69`hr
`k=(0.693)/69=0.01"hr"^(-1)`
Now applying the Arrhenius equation:
Ink = InA `-E_a/(RT)`
In (0.01)=InA = `-(53600)/(8.314xx300)`
A `=2.15xx10^(7)hr^(-1)`