A → B (first reaction) C → D (second reaction) Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hours. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 K of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at 300 K is 10-1 hour-1 (nearest integer).
Answer
5
Solution
First reaction at 500 K: t1/2 = 2 h
k1(500) = 0.6932 = 0.3465 h-1
Arrhenius equation: k500k300 = Ea2.303R ( 1300 - 1500 )
for the same two temperatures, k500k300 Ea
First reaction: k1(500)k1(300) = 2
Second reaction (Ea2 = Ea12): k2(500)k2(300) = 12 2
k2(500)k2(300) = 2
k2(500) = 2 k1(500) = 2 0.3465 = 0.693 h-1
k2(300) = 0.6931.414 = 0.49 h-1 = 4.9 10-1 h-1 5 10-1 h-1
Answer: 5