For a certain process, δg is large and negative. does this mean that the process necessarily has a low activation barrier?

yes
no

No!

Explanation:

In thermodynamics, Gibbs free energy (ΔG) is a thermodynamic potential, a function of extensive state (depends on the amount of matter) with units of energy, which gives the condition of balance and spontaneity for a chemical reaction at constant pressure and temperature. A process is spontaneous when its Gibbs energy is negative and it is not when this quantity has a positive value.

The activation energy is the minimum energy necessary for a given chemical reaction to occur. This energy is what is required so that two molecules that are going to react overcome the repulsion of their electronic clouds and can get close enough for the reaction to occur. In this way, the lower the activation energy, the less energy is required for the molecules to overcome the repulsion and the reaction will be faster. The activation energy is related to the speed of the reaction through the Arrhenius equation and, therefore, is a magnitude related to the kinetics of a reaction.

As you can see, the ΔG is a thermodynamic function while the activation energy is a kinetic parameter. The kinetics and thermodynamics of a reaction do not necessarily go hand in hand. You can not study the thermodynamics of a reaction from its kinetic and vice versa.

An example of this is the transformation of diamond into graphite. Pure carbon can occur in two different crystalline forms: diamond and graphite. In the diamond, the carbon atoms are arranged in a highly ordered cubic crystal structure.

At ambient temperature and pressure, the transformation of diamond into graphite is a spontaneous process, since it is a process associated with a decrease in the Gibbs free energy. Therefore, one might be tempted to say that diamonds, over time, will inevitably transform into graphite. However, this reaction is extremely slow (it can take thousands of years) since it involves the migration of atoms that have very little mobility because they are rigidly linked. In this way, the transformation of diamond into graphite has an extremely high activation energy despite being a spontaneous reaction with a negative Gibbs energy.

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