Half life of a first order reaction is 900 minute at 400 K , find its half life at 300 K ? ( Ea 2 303 R =1 3056 10^3 )

Step-by-step solution

For a first-order reaction, the half-life relates to the rate constant by t_ 1/2 = 0.693 k . The Arrhenius equation connects rate constants at two temperatures as ( k₂ k₁ ) = E_a 2.303R ( T₂ - T₁ T₁ T₂ ) . Given t_ 1/2,1 = 900 minutes at T₁ = 400 K, and E_a 2.303R = 1.3056 10^3 K, the half-life at T₂ = 300 K can be found by relating the ratios. Since t_ 1/2,2 t_ 1/2,1 = k₁ k₂ , ( t_ 1/2,2 900 ) = E_a 2.303R ( T₁ - T₂ T₁ T₂ ) . Substituting the values: ( t_ 1/2,2 900 ) = (1.3056 10^3) ( 400 - 300 400 300 ) = (1.3056