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Name: shifaan
Status: student
Age: 18
Location: N/A
Country: N/A
Date: 2000


Question:
I'm really confused about a concept. In chemical kinetics according to the maxwell-boltzmann distribution of energy, the activation energy for a reaction remain the same irrespective of the temperature. But on the other hand, according to the Arrhenius equation the activation energy of a reaction is dependant on temperature. Why do both of them say the totally opposite when talking of the same thing>?


Replies:
You are referring to approximations that focus on different aspects of the process. The Maxwell-Boltzmann distribution of energy does not require that activation energies be temperature-independent. It just tells you the occupancies of states at thermal equilibrium given the temperature and the energies of the states. (Even what I just wrote is an approximation - I'm neglecting degeneracies.) The discussion you encountered no doubt explained how the temperature accelerates the rate of a reaction by making the activation energy more accessible. If you allow the activation energy itself to change with temperature, the Maxwell-Boltzmann distribution of states still holds. The rate, however, becomes more complicated to calculate, because you need to also take the new activation energy into account.

Actually, the Arrhenius equation, k = A exp(-Ea/RT), does not require that the activation energy Ea changes with temperature. The rate certainly is temperature-dependent, but not tyhe activation energy. In fact, rates of a reaction at different temperatures are sometimes used, in concert with this equation, to determine the temperature-independent Ea. All you do is plot ln k against 1/T, giving a (hopefully) straight line with a slope of Ea/R.

Now, not all chemical reactions will give a straight line to such a plot. This means that the Ea changes with temperature. One way for this to occur is if Ea is actually a Gibbs free energy of activation, which can be broken down into an enthalpy and entropy of activation, G = H - TS. Then, even if H and S are temperature dependent (which they may not be), G (= Ea) will depend upon the temperature. In any event, as long as you know the Ea at a given temperature, you can calculate the rate (given some reasonable assumptions).

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois



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