Question

Decomposition of a hydrocarbon follows the equation} \[ k = (5.5 \times 10^{11}\, s^{-1})\, e^{\frac{-28000}{T}} \] The activation energy of reaction is _____ kJ mol\(^{-1}\). (Nearest Integer)} Given: \(R = 8.3\, J\,K^{-1}\,mol^{-1}\)}

Answer 1

Correct Answer: 233

Concept: Arrhenius equation: \[ k = A e^{-\frac{E_a}{RT}} \] Comparing with the given expression: \[ k = A e^{\frac{-28000}{T}} \] Thus: \[ \frac{E_a}{R} = 28000 \] Step 1: {Calculate activation energy} \[ E_a = 28000 \times R \] \[ E_a = 28000 \times 8.3 \] \[ E_a = 232400 \, J\,mol^{-1} \] Step 2: {Convert to kJ mol\(^{-1}\)} \[ E_a = 232.4 \, kJ\,mol^{-1} \] Nearest integer: \[ E_a = 233 \, kJ\,mol^{-1} \]