The rate constants k1 and k2 for two different reactions are 1016. 2000/T e and 1015. 1000/T e , respectively. The temperature at which k1 = k2 is: (AIPMT 2008)

Given, 2000 16 1 10 T k e x and 1000 15 2 10 T k e x When 1k and 2k are equal at any temperature T, we have 2000 1000 16 15 10 10 T T e e x x 000 1000 15 15 or 10 10 10 T T e e x x x 000 1000 or 10 T T e e x 2000 1000 or ln10 T T 2000 1000 or ln10 T T 1000 or 2.303log10 T or 2.303 1 1000 log10 1 T xx 1000 or 2.303 T K