[kirushanth]

Can we compare, in a reaction, the reaction enthalpy and the activation energy?

I guess we should have Activation energy>=Reaction enthalpy always...

[Schrödinger]

I guess we should have Activation energy>=Reaction enthalpy always...

Yes. You could say that.

E_act is almost always positive. ( I do remember someone telling me that negative E_act has been reported)

In the case of exothermic reactions, enthalpy < 0 and E_act obviously is > enthalpy.

In the case of endothermic reactions, the transition state is at a higher level than the products. Hence once again, E_act > enthalpy

[Enthalpy]

Puzzling! I had always imagined an activation energy as positive.

I sniff a hidden question in the question:

The produced energy does not need to exceed the activation energy, because the reaction energy is measured between the initial and the final state, not from the energy peak.

And: you don't need the products to provide more than the activation energy to the reactants, because heat is a statistical value. If the activation energy is 1000K, the reaction can proceed at 300K - just at some lucky molecules at a time. Additionally, this energy can be provided by the initial temperature.

Think of an equilibrium: even with an activation energy, both reaction directions (hence H>0 and H<0) will proceed provided the hill isn't too high.

But a relation with the initial conditions, sure.

[jaspevacek]

A negative E_act can occur in dilute gas phase. By lowering the temperature, you slow the molecules down so that when they contact, they stick and react rather than fly apart.

[Stepan]

As far as I remember the negative activation energy is usually an artifact of some secondary processes, like: mass transfer, or reactor configuration or experiment setup. for a particular chemical reaction it is generally positive.

There is no simple way to estimate activation energy from enthalpy.  But is you study several similar reactions measured under the same conditions, let say:
Ethylene+H2
Propylene+H2
Butene+H2
..
you almost for sure can discover  some sort of empirical correlation between  activation energy and enthalpy: Ea=Constant+alpha*Delta(H). Often alpha is about 0.5. To observe this effect you need to be sure that the reaction is not affect by mass transfer of reagents (slow reaction, low conversion). 

Not sure what is the explanation of this correlation.

[juanrga]

Can we compare, in a reaction, the reaction enthalpy and the activation energy?

I guess we should have Activation energy>=Reaction enthalpy always...

Interesting question. I cannot think of a counterexample and agree.