The rate constant for the decomposition of hydrocarbons is `2.418xx10^(-5)s^(-1)` as 546 K . If the energy of activation is 179.9 kJ.mol , what will be the value of pre-exponential factor ?

Explanation

Given: `k=2.418xx10^(-5)s^(-1),E_(a)=179kJ.mol^(-1)`
and T = 546K
According to Arrhenius equation,
`k=Ae^(-E_(a)//RT) " or, "Ink=InA -(E_(a))/(RT)`
or, `logk=logA-(E_(a))/(2.303RT)`
`thereforelogA=logk+(E_(a))/(2.303RT)`
`=log (2.418xx10^(-5))+(179.9xx10^(3))/(2.303xx8.314xx546)`
= 12.5916
`therefore A = "antilog"(12.5916)=3.905xx10^(12)s^(-1)`