To determine the favourable redox reaction in the given solution, we need to compare the standard electrode potentials (E^{\circ}) of the reactions involved. The reactions provided are:
The standard electrode potential for this half-reaction is given as E^{\circ}_{Fe^{3+}/Fe^{2+}} = +0.77 \, V.
The standard electrode potential for this half-reaction is given as E^{\circ}_{I_2/2I^-} = +0.536 \, V.
The tendency of the reaction to occur is determined by the reduction potential. Higher reduction potential means a higher tendency for reduction to occur. However, since both reactions given are in standard reduction potential form, we will consider them as is:
For both an oxidation and reduction reaction to occur simultaneously (redox), one must act as an oxidizing agent and the other as a reducing agent. The reaction with the higher E^{\circ} value acts as the cathode (reduction), and the one with the lower value acts as the anode (oxidation).
Since E^{\circ}_{Fe^{3+}/Fe^{2+}} = +0.77 \, V is higher, Fe^{3+} would potentially be reduced, but since the solution also contains I^-\, it acts as a reducing agent.
The correct favourable reaction, considering E^{\circ} values, is:
This is because Fe^{3+} has a higher tendency to be reduced more than I_2 at 35^{\circ} C.