### Reaction Engineering

# Activation Energy

The decomposition of NO2 follows a second order rate equation. Data at different temperatures are as follows:

T (K) 592 603 627 651.5 656 k (cm^{3}/gmol.sec) 522 755 1700 4020 5030

Compute the energy of activation Energy from the data. The reaction is 2NO_{2} à 2NO + O_{2}

Calculations:

Activation energy is found from the Arrhenius' relation

k = k_{o} e^{-E/RT}

i.e.,

ln k vs. 1/T is a straight line with a slope of -E/R

where, E is the activation energy; and

R is the universal gas constant.

T (K) |
592 |
603 |
627 |
651.5 |
656 |

k (cm |
522 |
755 |
1700 |
4020 |
5030 |

1/T ( |
0.001689 |
0.001658 |
0.001595 |
0.001535 |
0.001524 |

ln k |
6.257668 |
6.626718 |
7.438384 |
8.299037 |
8.523175 |

From the above data, the following graph is drawn, and the slope is = -13622

Therefore,

E/R = 13622

**E **= 13622 x 8314 **= 113253.3 kJ/kmol **