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The reduction potential for $\ce{AgI}$ is $-0.15\ \mathrm{V}$ and for $\ce{AgCl}$ it’s $0.22\ \mathrm{V}$. As $nFE =-\Delta{G} = T\Delta{S} - \Delta{H}$ this must imply that $\ce{AgI}$ is a stronger bond in order for it to be negative.

I would think $\ce{AgI}$ is weaker due to having a much larger ionic radii for $\ce{I-}$ than $\ce{Cl-}$ and the lack of covalence due to a smaller $\Delta\chi$

I think that it must be something to do with the size of the $\ce{I-}$ mean that it causes significant ordering of the water molecules in the solution and it's this entropic effect that is actually the key idea as otherwize I can't rationalise it at all.

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    $\begingroup$ "lack of covalence due to a smaller Δχ" - I'm afraid it's the other way round. $\endgroup$
    – Mithoron
    Jun 1 '15 at 11:31
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The answer is hard-soft acid/base theory (or HSAB theory). Essentially, some Lewis acids and bases are hard and some are soft, with a few borderline cases.

Hard acids and bases tend to have

  • Small atomic/ionic radius
  • Highly charges (or highly positive/negative oxidation state)
  • High electronegativity for bases and low electronegativity for acids
  • Low polarizability

Soft acids and bases tend to have

  • Large atomic/ionic radius
  • Low or zero charge / oxidation state
  • Moderate electronegativity
  • High polarizability

According to HSAB theory, matches that are hard-hard and soft-soft form strong interactions, where hard-soft matches are weaker interactions.

$\ce{Ag+}$ is a soft Lewis acid. $\ce{Cl-}$ is a hard Lewis base, while $\ce{I-}$ is a soft Lewis base. Therefore, we would predict that $\ce{Ag+}$ and $\ce{I-}$ will have have a stronger attraction than than $\ce{Ag+}$ and $\ce{Cl-}$.

We can see this difference in attraction in the solubilities of $\ce{AgCl}$ and $\ce{AgI}$ in water. $\ce{AgCl}$ is much more soluble in water than $\ce{AgI}$ (realizing that both are nearly insoluble). See the solubility constant data:

  • $\ce{AgCl}\ \ \ k_{\text{sp}}=1.8\times 10^{-10}$
  • $\ce{AgI}\ \ \ \ \ \ k_{\text{sp}}=8.5\times 10^{-17}$
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