Given below are two statements: R=8.314 J K ⁻¹ mol ⁻¹ and 1 cal =4.2 J Statement I: When E_a=12.6 kcal/mol, the room temperature rate constant is doubled by a 10 ,^ C increase in temperature ( 298 K to 308 K) Statement II: For a first order reactions A B, Here [A]_o is the initial concentration of A and t_ 1/2 is half life of reaction. In the light of the above statements, choose the correct answer from the options g

Step-by-step solution

For Statement I: According to the Arrhenius equation: ( k₂ k₁ ) = E_a 2.303 R ( T₂ - T₁ T₁ T₂ ) Given that the rate constant doubles, k₂ = 2k₁ . The temperatures are T₁ = 298 K and T₂ = 308 K. The gas constant R = 8.314 J K ⁻¹ mol ⁻¹ = 8.314 4.2 cal K ⁻¹ mol ⁻¹ 1.98 cal K ⁻¹ mol ⁻¹ . Substituting the values: (2) = E_a 2.303 1.98 ( 308 - 298 298 308 ) 0.301 = E_a 4.56 ( 10 91784 ) E_a = 0.301 4.56 91784 10 12598 cal/mol 12.6 kcal/mol. Thus, Statement I is true. For Statement II: For a first order reaction, the half-