The rate constant of a first order reaction is 3.46 10⁻² ~s ⁻¹ at 298 K . What is the rate constant of the reaction at 350 K if its activation energy is 50.1 ~kJ ~mol ⁻¹ ?( R =8.314 ~J K ⁻¹ ~mol ⁻¹ ) ( 2=0.3010)

Step-by-step solution

aligned & K ₁=3.46 10⁻² & ~T ₁=298 ~K & ~K ₂=? & ~T ₂=350 ~K & E _ a =50.1 ~kJ ~mol ⁻¹ & R =8.314 JK ⁻¹ ~mol ⁻¹ aligned According to Arrhenius theory, aligned & K ₂ ~K ₁ = E _ a 2.303 R [ 1 ~T ₁ - 1 ~T ₂ ] & K ₂ 3.46 10⁻² = 50.1 10^3 2.303 8.314 [ 1 298 - 1 350 ] & K ₂ 3.46 10⁻² =1.30 & ~K ₂ 3.46 10⁻² =10^ 1.30 =20 aligned aligned K ₂ & =3.46 10⁻² 20 ~K ₂ & =69.03 10⁻² aligned K ₂=0.69 ~s ⁻¹