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[tex]4I^-(aq) + O_2 + 2H_2O \rightarrow 2I_2 + 4OH^-(aq)[/tex]
According to Atkins - Physical chemistry - fifth edition:
[tex]\Delta G^0_f(I^-aq)\ =\ -51.57\ kJmol^{-1}[/tex]
[tex]\Delta G^0_f(OH^-aq)\ =\ -157.24\ kJmol^{-1}[/tex]
So:
[tex]\Delta G^0_{reaction}\ =\ -105.67\ kJmol^{-1}[/tex]
and the reaction should really happen.
According to Atkins - Physical chemistry - fifth edition:
[tex]\Delta G^0_f(I^-aq)\ =\ -51.57\ kJmol^{-1}[/tex]
[tex]\Delta G^0_f(OH^-aq)\ =\ -157.24\ kJmol^{-1}[/tex]
So:
[tex]\Delta G^0_{reaction}\ =\ -105.67\ kJmol^{-1}[/tex]
and the reaction should really happen.