COMEDK2023Morning ShiftChemistryChemical KineticsActual
How much faster would a reaction proceed at 25^ C than at 0^ C if the activation energy is 65 ~kJ ?
Options
- A11 times
- B12 times
- C4 times
- D6 times
Correct answer
A. 11 times
Step-by-step solution
The Arrhenius equation relates the rate constants k₁ and k₂ at temperatures T₁ and T₂ as follows: ( k₂ k₁ ) = E_a R ( 1 T₁ - 1 T₂ ) Given E_a = 65000 J/mol , T₁ = 273 K , T₂ = 298 K , and R = 8.314 J/(mol K) . Substituting the values: ( k₂ k₁ ) = 65000 8.314 ( 1 273 - 1 298 ) ( k₂ k₁ ) = 7818.14 ( 298 - 273 273 298 ) ( k₂ k₁ ) = 7818.14 ( 25 81354 ) ( k₂ k₁ ) = 7818.14 0.00030729 2.4025 Taking the exponential of both sides: k₂ k₁ = e^ 2.4025 11.05 The reaction proceeds approximately 11 times faster. Answer: 11 time