COMEDK2024ChemistryChemical KineticsActual
The temperature ( T ) and rate constant ( k ) for a first order reaction R P , was found to follow the equation k =-(2000) 1 ~T +8.0 . The pre-exponential factor ' A ' and activation energy E _ a , respectively are: [Given: R =8.314 ~J ~K ⁻¹ ~mol ⁻¹ ]
Options
- A6.0 ~s ⁻¹ and 10^8 ~kJ ~mol ⁻¹
- B1 10^8 ~s ⁻¹ and 38.3 ~kJ ~mol ⁻¹
- C1 10⁻⁸ ~s ⁻¹ and 16.6 ~kJ ~mol ⁻¹
- D8.0 ~s ⁻¹ and 16.6 ~kJ ~mol ⁻¹
Correct answer
B. 1 10^8 ~s ⁻¹ and 38.3 ~kJ ~mol ⁻¹
Step-by-step solution
The Arrhenius equation is given by k = A e^ -E_a / (RT) . Taking the logarithm on both sides, we get k = A - E_a 2.303 RT . Comparing this with the given equation k = -2000 ( 1 T ) + 8.0 , we identify the slope and the intercept. The slope is - E_a 2.303 R = -2000 . Therefore, E_a = 2000 2.303 R = 2000 2.303 8.314 J mol ⁻¹ . E_a = 4606 8.314 38294 J mol ⁻¹ = 38.3 kJ mol ⁻¹ . The intercept is A = 8.0 . Therefore, A = 10^8 s ⁻¹ . Answer: 1 10^8 ~s ⁻¹ and 38.3 ~kJ ~mol ⁻¹