For an elementary chemical reaction, the Arrhenius plot is given below. If the energy of activation is 6.64 kJ mol ⁻¹ and R =8.3 J K ⁻¹ mol ⁻¹ , the temperature at which the rate constant becomes e^2 min ⁻¹ , is

Step-by-step solution

According to the Arrhenius equation: k = A - E_a RT For a plot of k versus 1/T , the y-intercept corresponds to A . From the given graph, the line intersects the y-axis at 6 . Therefore, A = 6 . We are given: E_a = 6.64 kJ mol ⁻¹ = 6640 J mol ⁻¹ R = 8.3 J K ⁻¹ mol ⁻¹ k = e^2 min ⁻¹ , which gives k = (e^2) = 2 Substituting these values into the Arrhenius equation: 2 = 6 - 6640 8.3 T 6640 8.3 T = 6 - 2 6640 8.3 T = 4 T = 6640 4 8.3 T = 6640 33.2 T = 200 K Answer: 200 K