The first order rate constant for a certain reaction increases from 1.667 × 10–6 s–1 at 727ºC to1.667 × 10–4 s–1 at 1571ºC. The rate constant at 1150ºC, assuming constancy of activation energy over the given temperature range is [Given : log 19.9 = 1.299]

a 2 2 1 1 1 2 E k T T log k 2.303R T T a 2 2 1 1 1 2 4 a 6 a a 3 a 6 a E k T T or 2.303log k R T T E 1.667 10 1 1 2.303log R 1844 1000 1.667 10 E 844 2.303 2 ....(1) R 1844 1000 E 4.606 1844 1000 R 844 k E 1423 1000 2.303log R 1423 1000 1.667 10 E 423 R x x x x x x x x x x x ....(2) 1423 1000 x 3 6 3 6 3 6 5 1 3 Dividingequation (2)byequation 1 k log 1.667 10 2 423 1844 1000 1423 1000 844 k log 1.667 10 423 1844 2 1.299 1423 844 On taking Antilog,k 19.9 k 19.9 1.667 10 3.318 10 s x