Question

A textbook on chemical thermodynamics states, "The heat of solution represents the difference between the lattice energy of the crystalline solid and the solvation energy of the gaseous ions." (a) Draw a simple energy diagram to illustrate this statement. (b) A salt such as NaBr is insoluble in most polar nonaqueous solvents such as acetonitrile $\left({\mathrm{CH}}_3\mathrm{CN}\right)$ or nitromethane $\left({\mathrm{CH}}_3{\mathrm{NO}}_2\right)$, but salts of large cations, such as tetramethylammonium bromide $\left[{\left({\mathrm{CH}}_3\right)}_4\mathrm{NBr}\right]$, are generally more soluble. Use the thermochemical cycle you drew in part (a) and the factors that determine the lattice energy (Section 8.2) to explain this fact.

Short answer

The solubility of a salt in a solvent is determined by comparing lattice energy and solvation energy. NaBr has high lattice energy due to small, highly charged ions and is insoluble in polar nonaqueous solvents, as their solvation energy is not enough to overcome the lattice energy. In contrast, tetramethylammonium bromide has a larger cation, resulting in lower lattice energy, which allows for greater solubility as solvation energy can compensate for the lattice energy.

Step-by-step solution

Draw the energy diagram

To draw the energy diagram, we need to take into consideration the two factors that constitute the heat of solution: lattice energy and solvation energy. We can represent these on the y-axis, with lattice energy being positive (as it takes energy to break the bonds in the crystal lattice) whereas solvation energy is negative (energy is released when the ions interact with the solvent). The heat of solution is the difference between these two energies.

Identify factors that determine the lattice energy

According to section 8.2 of the textbook, there are two main factors that determine the lattice energy of a compound: ion size and ion charge. Larger ions have weaker electrostatic interactions with their neighbors and thus have lower lattice energies. Similarly, ions with lower charges will have weaker interactions and lower lattice energies.

Relate lattice energy factors to solubility

The solubility of a salt in a solvent can be determined by comparing the lattice energy and the solvation energy. If the solvation energy is higher (more negative) than the lattice energy, then the salt will dissolve since the energy released upon solvation will compensate for the energy needed to break the lattice bonds.

Explain the solubility of NaBr and tetramethylammonium bromide

NaBr has relatively small, highly charged ions (Na${}^{+}$ and Br${}^{-}$), which results in a high lattice energy. In contrast, tetramethylammonium bromide has a large, bulkier cation (tetramethylammonium, ${\left({\mathrm{CH}}_3\right)}_4{\mathrm{N}}^{+}$) which results in a lower lattice energy. When comparing these two salts, the solvation energy of polar nonaqueous solvents (like ${\mathrm{CH}}_3\mathrm{CN}$ and ${\mathrm{CH}}_3{\mathrm{NO}}_2$) is not enough to overcome the lattice energy of NaBr, and hence it is insoluble. On the other hand, the lower lattice energy of tetramethylammonium bromide can be compensated by the solvation energy, leading to greater solubility in these solvents.

Key concepts

Lattice Energy

Lattice energy is a term used in chemistry to describe the amount of energy that is required to separate a crystal into its individual gaseous ions. It essentially measures the strength of the bonds between ions in an ionic compound. The higher the lattice energy, the more stable the crystal structure and, consequently, the more energy it takes to break it apart.

When we look at ionic compounds, several factors influence their lattice energy. The foremost factors include the charge on the ions and their radii. Ions with higher charges will attract each other more strongly, resulting in higher lattice energy. In contrast, larger ions have more diffused charges, leading to weaker attractions and lower lattice energy.

The concept of lattice energy helps us understand why certain salts, such as sodium bromide (NaBr), can be difficult to dissolve. These salts have high lattice energies due to their small, highly charged ions.

Solvation Energy

Solvation energy, sometimes also referred to as hydration energy when water is the solvent, is the energy released when ions are surrounded by solvent molecules. This process, known as solvation, is crucial for understanding dissolving processes in chemistry.

When an ionic compound dissolves in a solvent, the ions are separated and each ion becomes surrounded by solvent molecules. This interaction is energetically favorable and releases energy. The amount of solvation energy is influenced by the nature of both the solute ions and the solvent. A good solvent is one that has a high affinity for the ions, which is often the case for polar solvents with ionic solutes.

Generally, the higher the charge and the smaller the radius of the ion, the greater the solvation energy. This concept explains why some compounds, like tetramethylammonium bromide with its large cation, have lower lattice energy and can be more easily solvated, increasing their solubility.

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that deals with the relationship between heat and other forms of energy in chemical processes. It provides a framework for understanding how energy is transferred in reactions and the direction in which reactions will proceed.

One of the important principles in chemical thermodynamics is the conservation of energy, which states that energy cannot be created or destroyed. During solvation, for example, the energy needed to break the lattice (lattice energy) and the energy released when solute ions interact with the solvent (solvation energy) must balance out. The heat of solution is thus a direct manifestation of these thermodynamic principles, representing the net energy change when a solid dissolves to form a solution.

This approach helps us understand the energetic factors that influence solubility and why certain salts, despite having similar chemical structures, may dissolve differently in solvents.

Ionic Solubility

Ionic solubility is a term referring to the extent to which an ionic compound can dissolve in a solvent to form a homogeneous solution. This property is particularly important in fields such as pharmaceuticals, where the solubility of a compound can affect the efficiency of a drug.

The solubility of an ionic compound is governed by a balance between lattice energy and solvation energy. If the solvation energy is sufficient to overcome the lattice energy, the compound will likely dissolve; otherwise, it may remain insoluble. Factors such as temperature and solvent polarity also play significant roles in ionic solubility.

In the case of large cation salts like tetramethylammonium bromide, their lower lattice energy compared to small cation salts like NaBr means they are more likely to dissolve in polar solvents. This characteristic is crucial for chemists when selecting solvents for various applications or predicting the behavior of compounds in different environments.