# Which of the following has the most exothermic lattice energy: Ca_3N_2, CaO, SrF_2, Sr_3N_2, Ca_3P_2?

Oct 7, 2016

${\text{Ca"_3"N}}_{2}$ has the most exothermic lattice energy.

#### Explanation:

Lattice energy is the energy released when oppositely charged ions in the gas phase come together to form a solid.

According to Coulomb's Law, the force of attraction between oppositely charged particles is directly proportional to the product of the charges of the particles (${q}_{1}$ and ${q}_{2}$) and inversely proportional to the square of the distance between the particles.

$F = \frac{{q}_{1} {q}_{2}}{r} ^ 2$

1. Lattice energy decreases as you move down a group.

The atomic radius increases as you move down a group.

The force of attraction is inversely proportional to the square of the distance, so lattice energy decreases as the atomic radius increases.

2. Lattice energy increases as the magnitude of the charge increases.

The force of attraction is directly proportional to the product of the charges of the particles.

Therefore, lattice energy increases as the charges increase.

Conclusion: the salts with the largest ionization energies will be at the top of the Periodic Table and will have ions with the greatest charges.

Let's assemble the ions in a mini-Periodic Table.

$\text{Ca"^"2+"color(white)(m)"N"^"3-"color(white)(m)"O"^"2-"color(white)(m)"F"^"-}$
$\text{Sr"^"2+"color(white)(ml)"P"^"3-}$

The cation with the smallest ionic radius is $\text{Ca"^"2+}$.

The anion with the greatest charge is $\text{N"^"3-}$.

Thus, the salt with the most exothermic lattice energy is ${\text{Ca"_3"N}}_{2}$.