In this video, at 1:30, the presenter remarks that the charge of $\mathrm{Na}$ is $1^{+}$ and that the charge of $\mathrm{Cl}$ is $1^{-}$. Then, at 2:00, he remarks that the charge of $\mathrm{Fe}$ is $3^{+}$ and that the charge of $\mathrm{O}$ is $2^{-}$. Finally, he remarks that the result of substituting $3^{+}$ and $2^{-}$ for $q_1$ and $q_2$ in $ E_{\mathrm{latice}} =\frac{Kq_1q_2}{r}$ is six times the result of substituting $1^{+}$ and $1^{-}$ in the same equation. Hence he assumes that the value of $r$ is the same for both compounds, and concludes that the lattice energy of $\mathrm{Fe_2O_3}$ is six tiems greater than the lattice energy of $\mathrm{NaCl}$.
I thought that the fact that $\mathrm{Fe_2O_3}$ comprises more charged atoms than $\mathrm{NaCl}$ comprises would affect the differences between their lattice energies. Accordingly, I thought that the presenter should have multiplied the charge of $\mathrm{Fe}$ by $2$ and multiplied the charge of $\mathrm{O}$ by $3$, and then substituted those two products into $q_\mathrm{1}q_\mathrm{2}$ respectively? Evidently, I was wrong about that.
In estimating the relative lattice energies, should the estimator consider the number of each kind of atom in the compounds?
