Given two ionic compounds, for instance:

$$\ce{CaS} \quad \mathrm{or} \quad \ce{KCl}$$

What is the procedure to predict which of the two have the highest lattice energy (in absolute value)?

(Suppose that I do not know the values of radii of the atoms but I can only look at the periodic table).

I know that I must look at the ratio

$$\frac{Z_1 Z_2}{r_1 + r_2} \propto E_\text{lattice},$$

where $r_1 + r_2$ is the distance between the two atoms in each molecule of the compound, $Z_1 Z_2$ is the product of atomic numbers of each element in the molecule.

But, for example, in the case above I have both $r_1 + r_2$ and $Z_1 Z_2$ bigger for $\ce{KCl}$ then $\ce{CaS}$, so I cannot say (without knowing the numerical values) if one of the two ratios would be higher.

Am I missing something?

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    $\begingroup$ The lattice energy is proportional to the charges of the atoms in the formula, not their atomic number! (There are no molecules in such simple ionic substances, btw.) $\endgroup$ – Karl Jul 24 '17 at 0:48

The Lattice Energy of Ionic Compounds is directly proportion to the Charge Density. As Ca, S have 2 units of charge while K, Cl have one and there is not much of a difference in size ( atleast not enough to overcome the doubling of the charge), the charge density of Ca and S ions would be more. Consequently, the lattice strength of CaS would be more.

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  • $\begingroup$ So it depends mainly on how many electrons are exchanged! Thanks a lot! But, for istance, if I take $MgO$ and $MgS$, there are two electron exchanged in both, nevertheless the same problem showed in question remains, so is there a "secondary" criterium to select one of the two? $\endgroup$ – Sørën Jul 24 '17 at 8:38
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    $\begingroup$ @Sørën As the no. of e- exchanged are the same, we now have to focus on the size of the receiving atom (which will give us an idea about the strength of the electrostatic forces). $\endgroup$ – Ayushmaan Jul 24 '17 at 8:49

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