Order the following solids according to increasing lattice energy.

HgI2, CdCl2, ZnCl2

Now I get how to sort of do it, but I do not get how to do it if I'm looking at its radius if they do not provide it in the question.

As one goes DOWN the periodic table in the same column, the size increases. As one goes across the table in the same row, the size generally decreases.

To order solids according to increasing lattice energy, you need to consider several factors, such as the charges of the ions, the distances between them, and the arrangement of ions in the crystal lattice. While the size (radius) of the ions can have an influence on lattice energy, it is not always explicitly provided in the question. In such cases, you can make an educated assumption based on general trends.

Typically, the lattice energy increases with decreasing ionic size and increasing ionic charge. Smaller ions can get closer to each other, resulting in stronger electrostatic interactions and higher lattice energy.

Here's how you can approach ordering the given solids based on lattice energy without explicit information about the radius:

1. Analyze the charges of the ions:
- HgI2: Hg2+ and I^- ions
- CdCl2: Cd2+ and Cl^- ions
- ZnCl2: Zn2+ and Cl^- ions

2. Compare the charges of the cations:
- Cd2+ > Zn2+ > Hg2+

3. Compare the charges of the anions:
- Cl^- < I^-

Based on these comparisons, we can assume that Hg2+ has the largest radius, while Cd2+ has the smallest radius, since an increase in charge often corresponds to a decrease in ionic size.

Now, considering the anions, we know that I^- is larger than Cl^- because chloride is a smaller ion compared to iodide.

Combining the information, we can tentatively order the solids as follows, starting with the one with the lowest lattice energy:

CdCl2 < ZnCl2 < HgI2

Please note that this is an assumption based on trends and not definitive. To obtain a more accurate ordering, it would be ideal to have explicit information about the ionic radii, which you can find in reference tables or through experimental data.