D5.4 Lattice Energy
Refer back to Activity: Analyzing Formation of an Ion Pair. The third step involved bringing one Li+ ion close to one F− ion, which lowered the energy. When a large number of oppositely charged ions are brought close together to form a crystal lattice, the energy is lowered even more, because more ions are close together in a structure where attractive forces predominate over repulsive forces.
The lattice energy of an ionic compound is defined as the decrease in energy when the ionic crystal lattice forms from the separated ions. Lattice energy can be calculated using a modified form of Coulomb’s law; some calculated lattice energies are in the table below. (Note that because lattice energy is defined as a decrease in energy, a large positive lattice energy corresponds to a large negative ΔE, that is, a very stable (low energy) ionic solid.)
| Substance | Lattice Energy (kJ/mol) | ||||||
| NaI | 682 | ||||||
| CaI2 | 1971 | ||||||
| MgI2 | 2293 | ||||||
| NaOH | 887 | ||||||
| Na2O | 2481 | ||||||
| NaNO3 | 755 | ||||||
| Ca3(PO4)2 | 10,602 | ||||||
| CaCO3 | 2804 | ||||||
| Table: Calculated Lattice Energies. Representative values from CRC Handbook of Chemistry and Physics (2004). | |||||||
Lattice energies have a wide range of values depending on which ions make up a compound. Consider, for example, why the lattice energy increases as you go from NaI, to CaI2, to MgI2 (first three rows in Table: Calculated Lattice Energies).
According to Coulomb’s law, 
, the lattice energy is directly proportional to the sizes of the charges on the ions and inversely proportional to the distance between them (the sum of their ionic radii). Thus, we can compare NaI, CaI2, and MgI2 with respect to magnitudes of charges and sizes of ions.
Magnitudes of Charges: NaI consists of 1+ ions and 1− ions; CaI2 and MgI2 consist of 2+ ions and 1− ions.
Because the magnitude of Q1Q2 is larger, the lattice energies of CaI2 and MgI2 should be larger than for NaI.
Sizes of ions: All three compounds contain I− anions, so we only need to compare cation radii.
The radii of Ca2+ and Na+ are similar. This can be estimated from the periodic table: Na+ and Ca2+ are both smaller than K+, Na+ because it is above K+ in the periodic table, and Ca2+ because it is isoelectronic with K+ but has more protons in the nucleus. It is reasonable to assume that the radii are not very different, and the ionic-radius table confirms this: Na+ 116 pm; Ca2+ 114 pm. Thus, r is not a major factor affecting lattice energy for NaI and CaI2.
The radius of Mg2+ is significantly smaller than for Ca2+ (and Na+) because Mg is directly above Ca in the periodic table and the ions have the same charge. Thus, MgI2 should have a larger lattice energy than CaI2, which is consistent with the values in the table.
Based on what you have learned so far:
- Use the lattice energies to predict whether I– has a smaller or larger radius than OH– (you can approximate both as a sphere). Explain your reasoning.
- When an ionic compound dissolves in water, ions separate from the crystal lattice and move among the water molecules. Predict which of the substances in “Table: Calculated Lattice Energies” is least soluble in water. Explain your reasoning.
Write in your notebook, then left-click here for an explanation.
Lattice energy is greater (the crystal lattice is more stable) when the charges on the ions are larger and when the distance between them is smaller.
I– has a larger radius than OH–.
NaI and NaOH have the same cation but different anions, both of which have a charge of 1-. Hence, the difference in NaI and NaOH lattice energies is mostly due to difference in r. Because lattice energy decreases with larger distance between the ions, the smaller lattice energy of NaI compared to that of NaOH indicates that I– is larger than OH–.
Ca3(PO4)2 is the least water soluble compound.
The larger the lattice energy, the harder it is to separate ions from the crystal lattice. Because ions must separate, the substance with the largest lattice energy is likely to be least soluble. That substance in Table 1 is Ca3(PO4)2. (As a side note, to make phosphate fertilizer, Ca3(PO4)2 must be converted into a more soluble phosphate-containing compound so that plants can take it up from the soil.)
When looking at Table: Calculated Lattice Energies, you may have noticed that lattice energies for compounds containing 2+ and 2− ions are nearly quadruple those for similar compounds containing 1+ and 1− ions of similar size (compare NaNO3 and CaCO3). This observation is consistent with the general rule that lattice energies are highest for substances with small, highly charged ions.
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