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MHT CET202525 Apr 2025Morning ShiftChemistryChemical KineticsActual

The rate constant is doubled when temperature increases from 27^ C to 37^ C . What is activation energy in kJ ?

Options

  1. A21.32
  2. B34.12
  3. C53.60
  4. D43.54

Correct answer

C. 53.60

Step-by-step solution

The activation energy E_a can be determined using the integrated Arrhenius equation for two temperature conditions: ( k₂ k₁ ) = E_a R ( 1 T₁ - 1 T₂ ) Given T₁ = 27^ C = 300 , K , T₂ = 37^ C = 310 , K , and k₂ k₁ = 2 , with R = 8.314 , J , mol ⁻¹ , K ⁻¹ . Substituting values yields: (2) = E_a 8.314 ( 1 300 - 1 310 ) Evaluating the temperature term: 1 300 - 1 310 = 310 - 300 300 310 = 10 93000 Using (2) 0.693 , the equation becomes: 0.693 = E_a 8.314 10 93000 Solving for E_a : E_a = 0.693 8.314 93000 10 = 53600.6 , J

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