A first-order reaction has an activation energy of 22.98 kJ mol ⁻¹ . If the rate constant of the reaction at 300 K is k , at what temperature will the rate constant become 10k ? (Given: 2.303 R = 19.15 J K ⁻¹ mol ⁻¹ )

Step-by-step solution

According to the Arrhenius equation: k₂ k₁ = E_a 2.303 R [ T₂ - T₁ T₁ T₂ ] Given: k₁ = k k₂ = 10k T₁ = 300 K E_a = 22.98 kJ mol ⁻¹ = 22980 J mol ⁻¹ 2.303 R = 19.15 J K ⁻¹ mol ⁻¹ Substituting the values: ( 10k k ) = 22980 19.15 [ T₂ - 300 300 T₂ ] (10) = 1200 [ T₂ - 300 300 T₂ ] 1 = 1200 [ T₂ - 300 300 T₂ ] 300 T₂ = 1200 T₂ - 360000 900 T₂ = 360000 T₂ = 400 K Answer: 400 K