For a reaction, activation energy E _ a =0 and the rate constant at 200 ~K is 1.6 10^6 ~s ⁻¹ . The rate constant at 400 ~K will be [Given that gas constant R =8.314 JK ⁻¹ ~mol ⁻¹ ]

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Correct answer: B. 1.6 10^6 ~s ⁻¹

Key Idea Rate constants at two different temperatures is given by Arrhenius equation as follows: k₂ k₁ = E_a 2.303 R [ 1 T₁ - 1 T₂ ], T₂>T₁ Given, E _ a =0, ~T ₁=200 ~K , k ₁=1.6 10^6 ~s ⁻¹ T ₂=400 ~K , R =8.314 JK ⁻¹ ~mol ⁻¹ According to Arrhenius equation, k ₂ k ₁ = E _ a 2.303 R [ 1 ~T ₁ - 1 ~T ₂ ] On substituting the given values in above equation, we get aligned & k ₂ 1.6 10^6 = 0 2.303 8.314 [ l 200 - l 400 ] & ( k ₂ 1.6 10^6 )=0 & k ₂ 1.6 10^6 =10^0=1 & k ₂=1.6 10^6 ~s ⁻¹ at 400 ~K aligned Thus, option (2) i

For a reaction, activation energy E _ a =0 and the rate constant at 200 ~K is 1.6 10^6 ~s ⁻¹ . The rate constant at 400 ~K will be [Given that gas constant R =8.314 JK ⁻¹ ~mol ⁻¹ ]

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