For a chemical reaction, the activation energy is 16.6 kJ mol ⁻¹ . When the temperature is increased from 200 K to T₂ , the rate constant increases by a factor of e^2 . The value of T₂ is ______ K . (Given R = 8.3 J K ⁻¹ mol ⁻¹ )

Step-by-step solution

According to the Arrhenius equation: ( k₂ k₁ ) = E_a R [ T₂ - T₁ T₁ T₂ ] Given that the rate constant increases by a factor of e^2 , we have k₂ k₁ = e^2 , which implies ( k₂ k₁ ) = 2 . Substitute the given values: E_a = 16.6 kJ mol ⁻¹ = 16600 J mol ⁻¹ T₁ = 200 K R = 8.3 J K ⁻¹ mol ⁻¹ The equation becomes: 2 = 16600 8.3 [ T₂ - 200 200 T₂ ] 2 = 2000 [ T₂ - 200 200 T₂ ] 2 = 10 ( T₂ - 200 T₂ ) 2 T₂ = 10 T₂ - 2000 8 T₂ = 2000 T₂ = 250 K Answer: 250