For reaction A P , rate constant k = 1.5 10^3 s ⁻¹ at 27° C. If activation energy for the above reaction is 60 kJ mol ⁻¹ , then the temperature (in ° C) at which rate constant, k = 4.5 10^3 s ⁻¹ is _______. (Nearest integer) Given : 2 = 0.30 , 3 = 0.48 , R = 8.3 J K ⁻¹ mol ⁻¹ , 10 = 2.3

Step-by-step solution

Using the Arrhenius equation: ( k₂ k₁ ) = E_a 2.3 R ( 1 T₁ - 1 T₂ ) Given: k₁ = 1.5 10^3 s ⁻¹ k₂ = 4.5 10^3 s ⁻¹ T₁ = 27^ C = 300 K E_a = 60 kJ mol ⁻¹ = 60000 J mol ⁻¹ R = 8.3 J K ⁻¹ mol ⁻¹ Substituting the values into the equation: ( 4.5 10^3 1.5 10^3 ) = 60000 2.3 8.3 ( 1 300 - 1 T₂ ) 3 = 60000 19.09 ( 1 300 - 1 T₂ ) 0.48 = 60000 19.09 ( 1 300 - 1 T₂ ) 1 300 - 1 T₂ = 0.48 19.09 60000 1 300 - 1 T₂ = 9.1632 60000 = 1.5272 10⁻⁴ 1 T₂ = 1 300 - 1.5272 10⁻⁴ 1 T₂ = 3.3333 10⁻³ - 0.1527 10⁻³ = 3.1806 10⁻³ K ⁻¹ T₂ = 1 3.1