Question

What is the explanation for the following trends in lattice energies? \(\mathrm{NaF} \quad-260 \mathrm{Kcal} / \mathrm{mole} \quad \mathrm{NaCl}-186 \mathrm{Kcal} / \mathrm{mole}\) \(\mathrm{NaCl}-186 \mathrm{Kcal} / \mathrm{mole} \quad \mathrm{KCl}-169 \mathrm{Kcal} / \mathrm{mole}\) \(\mathrm{NaBr}-177 \mathrm{Kcal} / \mathrm{mole} \quad \mathrm{CsCl}-156 \mathrm{Kcal} / \mathrm{mole}\)

Short answer

The trends in lattice energy for the given alkali metal halides can be explained by the ion sizes and charges. Smaller ions and higher charges result in stronger ionic bonds and hence higher lattice energies. For instance, NaF has a higher lattice energy compared to NaCl due to the smaller fluoride ion, and KCl has a lower lattice energy than NaCl due to the larger potassium ion. In the case of NaBr and CsCl, the larger ion sizes in CsCl result in weaker ionic bonds and a lower lattice energy compared to NaBr.

Step-by-step solution

Understand lattice energy

Lattice energy is the energy required to separate one mole of a solid ionic compound into its gaseous ions. The lattice energy is a measure of the strength of the ionic bonds within the lattice. A higher lattice energy indicates stronger ionic bonds within the compound.

Discuss the relationship between ion size and lattice energy

According to Coulomb's law, the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In the case of an ionic bond, this force (or attraction) between the positive and negative ions depends on the sizes of the ions and the charges on them. Smaller ions with higher charges will typically have stronger attractions and thus, higher lattice energies.

Identify the trend in lattice energy between NaF and NaCl

In the case of NaF (-260 Kcal/mole) and NaCl (-186 Kcal/mole), both compounds have the same cation, Na⁺, but different anions (F⁻ and Cl⁻). Fluoride (F⁻) is a smaller ion than chloride (Cl⁻), and the ionic bond between Na⁺ and F⁻ will be stronger due to the smaller distance between the ions. Therefore, NaF has a higher lattice energy compared to NaCl.

Identify the trend in lattice energy between NaCl and KCl

In the case of NaCl (-186 Kcal/mole) and KCl (-169 Kcal/mole), both compounds have the same anion, Cl⁻, but different cations (Na⁺ and K⁺). The potassium ion (K⁺) is larger than the sodium ion (Na⁺). As a result, the distance between K⁺ and Cl⁻ is greater, leading to weaker ionic bonds and a lower lattice energy for KCl than NaCl.

Identify the trend in lattice energy between NaBr and CsCl

In the case of NaBr (-177 Kcal/mole) and CsCl (-156 Kcal/mole), we have different cations (Na⁺ and Cs⁺) and different anions (Br⁻ and Cl⁻). The cesium ion (Cs⁺) is larger than the sodium ion (Na⁺), and the bromide ion (Br⁻) is larger than the chloride ion (Cl⁻). The larger ion sizes in CsCl result in a greater interionic distance and weaker ionic bonds, leading to a lower lattice energy compared to NaBr. In summary, the trends in lattice energy can be explained by the ion sizes and charges of the alkali metal halides. Smaller ions and higher charges result in stronger ionic bonds and higher lattice energies.

Key concepts

Ionic Bonds

Ionic bonds are a type of chemical bond formed between two atoms with a large difference in electronegativity, leading to the transfer of electrons and the creation of ions. The atom that loses an electron becomes a positively charged cation, while the atom that gains an electron becomes a negatively charged anion. These oppositely charged ions attract each other through electrostatic forces to form a crystal lattice structure.

For students trying to grasp this concept, imagine ionic bonds as a strong magnetic attraction between two opposite poles. Just as a magnet with a strong pull will hold its opposite pole tighter, similarly, the stronger the attraction between ions (due to their charges and sizes), the stronger their ionic bond will be. This is crucial in understanding why certain compounds, such as alkali metal halides, form resilient lattice structures.

Coulomb's Law

Coulomb's law states that the force between two charged particles, like ions in an ionic compound, is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:
\( F = k\frac{ q_1 q_2}{r^2} \) where \(F\) is the force, \(k\) is the Coulomb's constant, \(q_1\) and \(q_2\) are the charges on the ions, and \(r\) is the distance between the centers of the two ions.

Illustrating Coulomb's law in simple terms:

Think of this law similar to how a magnet's pull might feel to metal objects at different distances. When closer together, the pull is stronger—just as the attraction between ions is stronger when they are closer (a smaller r value), leading to a higher lattice energy.

Ion Size and Charge

The ion size and charge are significant factors that affect the strength of the ionic bonds as per Coulomb's law. Larger ions have more diffuse electron clouds, leading to an increased distance between the centers of positive and negative charges, while smaller ions are able to come closer together. Similarly, the greater the charge on an ion, the stronger the electrostatic attraction between ions.

Visualizing ion size and charge:

Imagine two magnets, one much larger than the other. Although both may have the same strength, the larger one has its magnetic force spread over a larger area, so at the same distance, its pull feels weaker. Ion size works in a similar manner; larger ions result in weaker interactions and hence lower lattice energies. Now, if you increase the strength of the magnet (analogous to ion charge), its pull becomes stronger, irrespective of size.

Alkali Metal Halides

Alkali metal halides are a group of ionic compounds composed of alkali metal ions (like Na⁺, K⁺, and Cs⁺) and halide ions (like Cl⁻, Br⁻, and F⁻). The trends in their lattice energies can be predicted based on the concepts of ionic bonds, Coulomb's law, and the influence of ion size and charge.

Understanding alkali metal halides:

An easy way to picture alkali metal halides is to think of them as organized dancers at a ball, where each dancer (ion) has a partner (counterion). The closeness of the partners (ion size) and the intensity of their embrace (charge) influences the energy of their dance (lattice energy). When dancers are smaller and embrace each other tightly (small ions with high charges), the dance is more energetically intense, resulting in higher lattice energies.