For a hypothetical chemical reaction, the activation energy is zero. If k₁ and k₂ are the rate constants of this reaction at temperatures T₁ and T₂ respectively (where T₂ > T₁ ), which of the following relationships is correct?

Step-by-step solution

According to the Arrhenius equation, the relationship between rate constants at two different temperatures is given by: ( k₂ k₁ ) = E_a 2.303 R ( 1 T₁ - 1 T₂ ) Given that the activation energy ( E_a ) is zero, substituting E_a = 0 into the above equation yields: ( k₂ k₁ ) = 0 Taking the antilog on both sides gives: k₂ k₁ = 1 k₂ = k₁ Thus, for a reaction with zero activation energy, the rate constant is independent of temperature. Answer: k₂ = k₁