The temperature dependence of the rate constants for two different reactions is given by the following equations: k₁ = 10¹⁵ e^ -2000/T k₂ = 10¹⁴ e^ -1000/T The temperature at which both reactions have the same rate constant is:

Step-by-step solution

Given k₁ = k₂ 10¹⁵ e^ -2000/T = 10¹⁴ e^ -1000/T 10¹⁵ 10¹⁴ = e^ -1000/T e^ -2000/T 10 = e^ 1000/T Taking natural logarithm ( ) on both sides: (10) = 1000 T Since (10) = 2.303 ₁₀(10) = 2.303 1 = 2.303 2.303 = 1000 T T = 1000 2.303 K Answer: 1000 2.303 K