Lattice enthalpy decreases as ions get larger, but I have found two explanations:

  1. The charge density is greater in smaller ions, so greater attraction
  2. The ions are themselves able to get closer together, so greater attraction

Do these two explanations relate in any way? What would be the best explanation?


Think about Coulomb's inverse-square law:

$$F = k\frac{q_1q_2}{r^2},$$

where $q$ is the magnitude of the charge, $r$ is the distance, and $k$ is the Coulomb’s constant.

Mathematically speaking, as $r$ increases, the magnitude of $F$ becomes smaller. As far as the charge density, as it increases, the magnitude of $F$ increases.

So both explanations are saying the same thing from different point of views. As ionic radii increases, charges are further apart so attraction decreases. As charge density increases, the attraction increases since the charges are increasing in magnitude.

Just as $\ce{MgO}$ is stronger then $\ce{NaCl}$ since $\ce{Mg}$ and $\ce{O}$ have smaller ionic radii and they both bare a $2+$ and $2-$ charge, respectively, making the lattice enthalpy greater.


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