The rate constants k₁ and k₂ for two different reactions are 10¹⁶ e^ -2000 / T and 10¹⁵ e^ -1000 / T , respectively. The temperature at which k₁=k₂ is

Step-by-step solution

Key Idea : The Arrhenius equation is represented as k=A e^ -E_a / R T In the given equations, first take log and then compare them. aligned & k₁=10¹⁶ e^ -2000 / T & k₂=10¹⁵ e^ -1000 / T aligned On taking log, we get aligned & k₁= 10¹⁶- 2000 2.303 T & k₂= 10¹⁵- 1000 2.303 T & k₁=k₂ aligned Hence, from Eqs (i) and (ii) T= 1000 2.303 ~K