Rate constants of a reaction at 500 K and 700 K are 0.04 ~s ^ -1 and 0.14 ~s ^ -1 , respectively; then, activation energy of the reaction is : (Given: 3.5=0.5441, R =8.31 ~J ~K ^ -1 ~mol ^ -1

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Correct answer: C. 18219 J

K =A e^ -E_a / R T After taking In both side K= A- E_a R T In K _1= A - E _ a RT _1 at temp. T _1...(i) In K _2= A - E _ a RT _2 at temp. T _2,,(ii) (ii) - (i) In K_2- InK K_1= E_a R [ 1 T_1 - 1 T_2 ] K _2 ~K _1 = E _ a R [ 1 500 - 1 700 ] 0.14 0.04 = E_a R [ 700-500 500 700 ] 14 4 = E_a R [ 200 500 700 ] 3.5= E_a 2.303 R [ 1 250 7 ] 0.5441= E_a 2.303 8.31 [ 1 250 7 ] E_a=0.5441 8.31 250 7 2.303 =0.5441 83.1 25 7 2.303 =18222.65 18219 ~J

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