Which compound in each of the following pairs of ionic...

Which compound in each of the following pairs of ionic substances has the most exothermic lattice energy? Justify your answers a. $\mathrm{LiF}, \mathrm{CsF} \quad$ d. $\mathrm{Na}_{2} \mathrm{SO}_{4}, \mathrm{CaSO}_{4}$ b. $\mathrm{NaBr}, \mathrm{Nal} \quad$ e. $\mathrm{KF}, \mathrm{K}_{2} \mathrm{O}$ c. $\mathrm{BaCl}_{2}, \mathrm{BaO} \quad$ f. $\mathrm{Li}_{2} \mathrm{O}, \mathrm{Na}_{2} \mathrm{S}$

Which compound in each of the following pairs of ionic substances has the most exothermic lattice energy? Justify your answers
a. $\mathrm{LiF}, \mathrm{CsF} \quad$ d. $\mathrm{Na}_{2} \mathrm{SO}_{4}, \mathrm{CaSO}_{4}$
b. $\mathrm{NaBr}, \mathrm{Nal} \quad$ e. $\mathrm{KF}, \mathrm{K}_{2} \mathrm{O}$
c. $\mathrm{BaCl}_{2}, \mathrm{BaO} \quad$ f. $\mathrm{Li}_{2} \mathrm{O}, \mathrm{Na}_{2} \mathrm{S}$

Key Concepts

Lattice Energy

Lattice energy is the energy released when oppositely charged ions in the gas phase come together to form an ionic solid. It is exothermic (negative), and its magnitude is directly influenced by the electrostatic forces between ions, meaning that a more exothermic lattice energy indicates stronger ionic bonds and a more stable ionic structure.

Ionic Charge

The magnitude of the charges on the ions plays a critical role in determining lattice energy. According to Coulomb’s law, the electrostatic attraction between ions is directly proportional to the product of their charges. A higher ionic charge leads to a stronger attraction and, consequently, a more exothermic (more negative) lattice energy.

Ionic Radii

The size of the ions affects the distance between the centers of the ions in the crystal lattice. Smaller ions allow for a shorter distance between charged centers, which results in stronger electrostatic attractions, as described by Coulomb’s law. Therefore, a decrease in ionic size leads to an increase in the magnitude of the lattice energy.

Coulomb’s Law

Coulomb’s law describes the force of attraction or repulsion between two charged particles. In the context of ionic solids, it explains how the force—and thus the lattice energy—increases with the magnitude of the charges and decreases with increasing distance between ion centers. This principle is crucial in predicting which ionic compound in a given pair will have the most exothermic lattice energy.

Transcript

00:01 So in this video we're going to talk about question 60 from chapter 8, which asks us which compound in each of the following pairs of ionic substances has the most exothermic lattice energy.

00:11 Justify your answers.

00:14 So the lattice energy is equal to a proportionality constant that corresponds to the arrangement of the solid times the charge of one of our ions times the charge of our other ion divided by the, distance between those charges.

00:35 So if we have larger charges like minus two and plus two instead of minus one and plus one, then our lattice energy will be larger.

00:46 It'll be more exothermic.

00:48 And if we have smaller distances between them, our lattice energy will be larger.

00:54 So as atomic radius increases, lattice energy decreases.

01:01 So in a, we have lithium fluoride and cesium fluoride.

01:05 So the difference is lithium and cesium.

01:07 So let's look at a periodic table.

01:09 So lithium is here.

01:11 It's one of our alkali metals and cesium is also an alkali metal, but it's way down here.

01:16 So cesium has a much larger atomic radius than lithium.

01:20 Just to refresh ourselves on the trends in atomic radius as we go down the periodic table and we add more shells of electrons, we are increasing our atomic radius.

01:30 Whereas if we go from left to right across the periodic table, we're increasing the number of protons, which are going to have a tighter pull on those outer electrons.

01:42 So we're actually decreasing atomic radius from left to right.

01:45 But in this case, we're comparing the atomic radius of lithium to the atomic radius of cesium because we know they're both going to have the same charge.

01:53 So the only difference is size.

01:55 And cesium is much larger than lithium.

01:57 So, so we said that as atomic radius increases, lattice energy decreases.

02:02 So the smaller atom, lithium, is going to be the one with the more exothermic lattice energy.

02:10 So a is lithium fluoride.

02:13 Then we have sodium bromide and sodium iodide...

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