# Why does silver (I) have a larger lattice enthalpy and hydration enthalpy than sodium?

The ionic radius of the $$\ce{Ag^+}$$ ion is $$129$$ pm, and that of the $$\ce{Na^+}$$ ion is $$116$$ pm.

Since the sodium ion is smaller than the silver ion, it makes sense that it has a stronger polarizing power than the silver ion. Due to the higher charge density, the lattice energy of $$\ce{NaX}$$ compounds is predicted to be larger than those of $$\ce{AgX}$$ compounds. However, that is not the case, as shown here:

Furthermore, the enthalpy of hydration of $$\ce{Na^+}$$ is expected to be more exothermic than that of $$\ce{Ag^+}$$, because $$\ce{Na^+}$$ is more polarizing than $$\ce{Ag^+}$$. However, that is not the case:

Why are the lattice enthalpies of silver compounds larger than those of sodium compounds, and why are hydration enthalpies of silver compounds more exothermic than those of sodium compounds, despite the silver ion being larger than the sodium ion?

Sources:

R. D. Shannon (1976). "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides". Acta Crystallogr A. 32: 751–767. Bibcode:1976AcCrA..32..751S. doi:10.1107/S0567739476001551.

Atkin's Physical Chemistry

• Partly at least because ionic radii are not as uniquely or strictly defined as you would seem to believe. And, partly because lattice enthalpies vs ionic radii is a very tenuous connection. – Jon Custer Jul 9 at 18:51
• The silver ion is larger and can have more interactions at the same time. – Karl Jul 9 at 20:00
• ... and because it's relatively larger, it forms a different crystal structure, and then quantitative comparison of molar properties becomes very questionable – Karl Jul 9 at 20:52
• Crystal structure shouldn't affect enthalpy of hydration, right? – DrPepper Jul 9 at 20:56
• not "crystal", but (statistically) more water molecules fit around a larger ion – Karl Jul 9 at 21:12