How would we prove that such a reaction is feasible at a particular temperature, by looking at quantities like enthalpy of formation, Gibbs free energy etc?
More or less.
The change in the gibbs free energy of a reaction determines whether a reaction is spontaneous or nonspontaneous. Negative values of indicate spontaneity, and positive values indicate nonspontaneity.
For a reaction to occur, the gibbs free energy must be negative at the specified conditions. You can find the molar gibbs free energies of substances in the standard state (25 C, 1 bar) from a table, usually found in the appendix of every quality chem textbook, and then find the change in gibb's free energy using Hess's Law.
There is a nice little equation relating values of gibbs free energy at different temperatures:
:delta: G
rxn = :delta: G
orxn + RTln(Q)
If you know the concentrations of the reactants and products, and the :delta: G
o of the reaction, you can determine the spontaneity of the reaction. Q is the reaction quotient.
If you can't obtain values for the gibbs free energy, you could always calculate them from the enthalpy and entropy changes using
:delta: G = :delta: H - T :delta: S
As for the spark, I would assume it raises the temperature so that the reactants can pass the activation energy barrier, but I am unsure.