The first-order reaction 2 N 2 O ( g ) → 2 N 2 ( g ) + O 2 ( g ) Has a rate constant of 1.3 × 1 0 - 11 s - 1 at 270 o C and 4.5 × 1 0 - 10 s - 1 at 350 o C . What is the activation energy for this reaction?

Step-by-step solution

l o g 10 k 2 k 1 = E a 2.303 R 1 T 1 - 1 T 2 R = 8.314 J K - 1 m o l - 1 T 1 = ( 273 + 270 ) K = 543 K T 2 = ( 273 + 350 ) K = 623 K k 2 = 4.5 × 1 0 - 10 s - 1 , k 1 = 1.3 × 1 0 - 11 s - 1 log 10 4.5 × 10 − 10 1.3 × 10 − 11 = E a 2.303 × 8.314 1 543 − 1 623 1.534 = E a 19.1471 80 543 × 623 E a = 1.534 × 19.1471 2.364 × 1 0 - 4 = 124.6 k J