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A single reactant A undergoes two competing first-order paths to give two different products: A ─k₁→ B, with activation energy Eₐ₁ A ─k₂→ C, with activation energy Eₐ₂ If Eₐ₂ = 2Eₐ₁, the relation between k₁ and k₂ is:
- k₂ = k₁e^{Eₐ₁/RT}
- k₂ = k₁e^{Eₐ₂/RT}
- k₁ = Ak₂e^{Eₐ₁/RT}
- k₁ = 2k₂e^{Eₐ₂/RT}
Correct answer: k₁ = Ak₂e^{Eₐ₁/RT}
Solution
The correct option relates the rate constants k₁ and k₂ through the Arrhenius equation, which shows how the rate constant depends on activation energy. Since Eₐ₂ is twice Eₐ₁, the relationship indicates that k₁ is proportional to k₂ adjusted by the exponential factor involving Eₐ₁, reflecting the influence of activation energy on reaction rates.
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