The rate constant for a firstorder reaction is 18 102 s1 at

The rate constant for a first-order reaction is 1.8 × 10-2 s-1 at 654 K and 3.5 x 10-2 s-1 at 878 K. What is the activation energy? (R = 8.3145 J/mol K) 6 kJ/mol O 6.1 kJ/mol O 13 kJ/mol O1700 kJ/mol O 14 kJ/mol

Solution

According to collision theory, a reaction takes place when the molecules collide. Every collision is not an effective collision i.e does not result into reaction. A collision is effective only if the colliding molecules have energy greater than a particular value called the Thresold energy. As a result , the no: of effective collisions increases & so does the rate of reaction.

Activation energy is the difference between the threshold energy & average energy of the reacting molecules.

Formula is

logk2/k1= Ea/2.303R(T2-T1/T1T2)

k1= rate const at temp T1 , k1= 1.8x10-2s-1 , T1= 654K

k2 = rate const at temp T2 , k2 = 3.5x 10-2s-1 , T2= 878K , R= 8.314J/mol .K

log(3.5/1.8) = Ea/2.303x8.314(878-654)/(878x654)

log(2) = Ea(224)/10980081.8 , log2= 0.3010

Ea= 14754.48J/mol = 14754.48/1000= 14kJ/mol

(e) 14kJ/mol