How to calculate which ionic compound has the highest melting point?

Question

Which of the following compounds has the highest melting point: $\ce{PCl5}$, $\ce{H2O}$, $\ce{NaCl}$, $\ce{SrCl2}$, $\ce{CaF2}$?

In general, ionic compounds will have higher boiling points than those of dipole-dipole interaction compounds.

So, the compound above that will have the highest melting point will certainly be an ionic compound, either $\ce{NaCl}$, $\ce{CaF2}$ or $\ce{SrCl2}$.

I thought that I should calculate the molar weight but that won't work, because the correct answer is $\ce{CaF2}$, and $\ce{SrCl2}$ has a greater molar weight.

Between ionic compounds, how can the one with the highest boiling point be predicted?

Answer 1

The strength of the ionic bond depends on Coulomb's law for the force acting between two charged particles where larger force translates to a stronger ionic bond. The equation is

$$F = \frac{-k\cdot q_1 \cdot q_2}{r^2}$$

$k$ is a constant; $q_1$ and $q_2$ are the charges on the ions and $r$ is the distance between the ions.

So the larger the charge the greater the force, and the smaller the radius the smaller the distance between the ions (smaller $r$ in the equation) again leading to a stronger force.

So, first you should calculate the charge on each ion in a molecule. As can see, the charge on strontium ($\ce{Sr^2+}$) and calcium ($\ce{Ca^2+}$) ions is more than the charge on sodium ions ($\ce{Na+}$). Also, calcium ions are smaller than strontium ions. Fluorine ions are also smaller than Chlorine ions. So $\ce{CaF2}$ will have higher bond strength which means it will have higher boiling point since stronger bonds need more energy to break.

Answer 2

You can deduce it from the Coulomb law. As you can see, the bigger the charge of the respective ions, the electrostatic interaction between them is stronger. The charge of calcium and strontium cations is twice as that of sodium. r is the distance between the charges, so for smaller ions the distance would be smaller i.e. the interaction would be greater. Calcium cation is smaller than strontium cation, therefore the correct answer is indeed calcium fluoride.

It can also be explained with more sophisticated equations: Kapustinskii equation or Born-Lande equation. I will let you analyze them.