[Mr.A]

In my last kinetics lecture, we were teached that arrhenius constant does not depend on the temperature , but answering sumones's question, the lecturer told that theres a negligible variation of arrhenius constant with temperature.

Is it possible? as i got find in Atkin's that , the arrhenius constant is taken by the intercept of the graph of ln k = ln A - (Ea/RT) . so the arrhenius constant is taken when the  temperature is at infinity (1/T = 0 when T = infinity )

so in the case what i think is arrhenius constant cannot be variate with the temperature.

And i got to know that theres a relationship between the speed of molecules and the arrhenius constant. Is that true? if it how? in which theory is it said so?

[curiouscat]

In my last kinetics lecture, we were teached that arrhenius constant does not depend on the temperature , but answering sumones's question, the lecturer told that theres a negligible variation of arrhenius constant with temperature.

Is it possible?

AFAIK there is no fundamental law that forces it to be temp. independent strictly. Yes, it can have a weak T dependence sometimes. Often this is much smaller than other uncertainties so can be ignored.

[Mr.A]

more explanation please ! anyone?

[Corribus]

As the previous poster mentioned, and as your teacher specified, the pre-exponential factor is generally taken to be temperature independent.  Non-Arrhenius behavior (nonlinear plots of ln k vs. 1/T) are usually explained by a temperature dependence of the activation energy E_a, not a temperature dependence of A.  Temperature dependence of E_a can happen in, for example, proton transfer reactions, where quantum tunnelling is expected to be an important mechanistic factor.  In cases where A might be temperature dependent, usually the effect is expected to be small, and it would be hard to dissociate it from any effect of temperature on E_a.  In such complex reactions, the Arrhenius expression is probably not the best way to model the reaction dynamics, anyway.

Generally speaking, the exponential portion of the Arrhenius equation represents the fraction of molecules that have enough kinetic (or other) energy to react.  This portion of the equation is temperature dependent because mean kinetic energy is directly related to temperature.  From a statistical mechanics point of view, the Arrhenius equation can be easily expressed in terms of the Boltzmann constant, which relates the probability of reactants having enough kinetic energy to react to the activation energy, mediated by the temperature.  (I.e., there is a statistical distribution of molecular kinetic energies, the mean of which is related to the temperature.  Some fraction of those will have an energy that surpasses the energy difference between the isolated reactants and activation complex or transition state.  This will govern the rate of reaction.)

However before reactants can react, they must collide.  Even if two reactants have enough kinetic energy to react, no reaction takes place if they don't hit each other.  Here is where A comes in.  The likelihood of collision is generally assumed to be temperature independent or to have weak temperature dependence.  For exampe, two reactants not only have to hit each other, but they often have to have the right mutual orientations when they collide.  The relative orientation is not temperature dependent.  To determine A, the y-intercept of the Arrhenius plot (ln k vs. 1/T) is calculated.  What this means is that A is determined by measuring the rate in the limit of infinite temperature - in other words, when every molecule in the sample has enough energy to react.  This is basically saying that even if all molecules could react, they only can react if they collide.  This is why A is usually interpreted as being related to the frequency of "reactable collisions".

Keep in mind though that A is semiempirical and includes both the collision frequency AND steric factors (mutual orientation of reactants).  For this reason it is a significantly more complex factor than activation energy to understand conceptually as well as calculate by other means.  This is why, though it's usually understood to be temperature independent, it's possible there might be some weak temperature dependence to it in some situations, but this temperature dependence would probably be overshadowed by the temperature dependence of the activation energy, if applicable, or the overall rate, which is already exponentially related to temperature.

Does this help? 

[curiouscat]

I'll add that in my experience it is much easier to predict Ea from first principles than it is to predict A.

OTOH, accuracy in Ea matters more than accuracy in A anyways.

[Mr.A]

thanks alot , CORRIBUS and CURIOUSCAT. specially i must say that CORRIBUS's explanation not just cleared my mind but gave me new points too.. thanks a lot both of you anyways 

[kelvinLTR]

it has the term u (relative velocity of a particle) inside the Arhenious constant and that depends on temperature.

It's funny cz we learned about this last week and I asked the same question from the lecturer.

He went on to say that the variation of rate due to change in the speed of the molecule is negligible compared to the change in the molar fraction of the number of molecules with the necessary activation energy