The rate constant for the reaction, A₂B₄O → AB₄ + AO, is described as,

log k = 14.1 - \(\frac{{10000K}}{T}\).

The activation energy for this reaction (in kJ mol^-1) is closest to

Concept:

• According to Arrhenius equation, the rate constant k at temperature T is related to the activation energy E_a  by the equation:

  \(k\, =\, A\, e^{-\frac{E_{a}}{RT}}\) ---------(1)

• Where, A is pre-exponential factor or frequency factor, R is universal gas constant, 8.314 J K^-1mol^-1
• Taking log on both sides of equation (1) we get,\(log\, k\, =\, log\, A\, -\, \frac{E_{a}}{2.303RT}\)----------(2)

Explanation:

Given,

log k = 14.1 - \(\frac{{10000K}}{T}\)

We know from equation (2),  \(log\, k\, =\, log\, A\, -\, \frac{E_{a}}{2.303RT}\)

Comparing above two relations, we get

\(\frac{E_{a}}{2.303RT}\) = \(\frac{{10000K}}{T}\)

\(\therefore\)  E_a = 2.303R \(\times\) 10000K

= 2.303 \(\times\) 8.314 J K^-1 mol^-1 \(\times\) 10000 K 

= 191.47 kJ

Conclusion: -

Therefore, the activation energy for this reaction (in kJ mol-1) is closest to 191.4