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) \(\mathrm{A}\) salt such as \(\mathrm{NaBr}\) 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 difference between NaBr and (CH3)4NBr in polar nonaqueous solvents can be explained using their lattice energies and solvation energies. NaBr has a high lattice energy due to the small size and charge of the Na+ and Br- ions, while polar nonaqueous solvents offer low solvation energy for these ions, leading to its insolubility. In contrast, (CH3)4NBr has a lower lattice energy because of its larger cation, which can better interact with polar nonaqueous solvents for a higher solvation energy. This allows (CH3)4NBr to be more soluble in these solvents compared to NaBr.

Step-by-step solution

Draw the energy diagram for the formation of a salt solution

To create the energy diagram, start by listing the following energy levels and associated processes from top to bottom: 1. Lattice energy of the crystalline solid: It is defined as the amount of energy required to separate one mole of a crystalline solid completely into its individual gaseous ions. 2. Heat of solution: This represents the energy change when one mole of salt dissolves in a solvent. 3. Solvation energy of the gaseous ions: The process of surrounding a solute particle by the solvent particles is called solvation. This energy is released when one mole of gaseous ions interacts with a solvent. The heat of solution can be calculated as the difference between the lattice energy of the crystalline solid and the solvation energy of the gaseous ions.

Understand the factors affecting lattice energy and solvation energy

Lattice energy is mainly determined by the following factors: 1. Charge of the ions: Higher charges of the ions result in stronger electrostatic forces between them, leading to a higher lattice energy. 2. Size of the ions: Smaller ions have a higher lattice energy due to a stronger interaction between them, as they are closer together. Solvation energy is affected by the following factors: 1. Polarity of the solvent: The more polar the solvent, the better its ability to stabilize the ions through solvophobic and solvophilic interactions. 2. Size of the ions: Smaller ions can more easily form interaction with the solvent molecules, leading to a higher solvation energy.

Explain the solubility of NaBr and (CH3)4NBr in polar nonaqueous solvents

Using the thermochemical cycle and the factors that determine the lattice energy and solvation energy, we can explain the different solubilities of NaBr and (CH3)4NBr in polar nonaqueous solvents as follows: For NaBr: 1. The lattice energy is high due to the small size and charge of the Na+ and Br- ions. 2. Polar nonaqueous solvents like acetonitrile or nitromethane are not very effective in stabilizing the Na+ and Br- ions, resulting in the lower solvation energy in these solvents. 3. The heat of solution is therefore not enough to compensate for the high lattice energy of NaBr, making it insoluble in these solvents. For (CH3)4NBr: 1. The lattice energy is lower because of a larger cation (tetramethylammonium) with a weaker electrostatic interaction with the anion (Br-). 2. The larger cation can better interact with polar nonaqueous solvents like acetonitrile or nitromethane, leading to a higher solvation energy. 3. The heat of solution in these solvents is enough to overcome the lower lattice energy of (CH3)4NBr, which makes it more soluble in such solvents compared to NaBr.

Key concepts

Lattice Energy

Lattice energy is a critical concept when studying the properties of ionic compounds. It is the energy released when ions bond to form a crystalline lattice, and conversely, it is the energy required to break a crystalline solid into its individual gaseous ions. A simple way to visualize this is to imagine the energy needed to pull apart the positive and negative ions in a salt, overcoming their attractive forces.

Importantly, the lattice energy depends on two main factors. Firstly, the charge of the ions: the higher the charge, the stronger the force of attraction between the ions, and thus, a higher lattice energy. Secondly, the size of the ions: smaller ions can pack closer together, leading to stronger interactions between them and, subsequently, a higher lattice energy.

In the context of the solubility of ionic compounds, knowing the amount of lattice energy can help us predict how readily a salt will dissolve in a particular solvent. For example, salts with high lattice energy will typically be less soluble, as it requires more energy to separate the ions and allow them to interact with the solvent.

Solvation Energy

Solvation energy plays a pivotal role in the dissolution process. When an ionic compound dissolves in a solvent, its ions are surrounded by solvent molecules, a process known as solvation. The energy change associated with this process is the solvation energy, which is often exothermic, meaning it releases energy.

The solvation energy is influenced by factors such as the solvent's polarity and the ion sizes. Polar solvents, such as water, are particularly efficient at solvating ions due to their ability to stabilize them with electrostatic interactions. In contrast, the size of the ions affects how closely the solvent molecules can approach and interact with them; smaller ions generally result in higher solvation energy due to better solvation.

When considering salt solubility, if the solvation energy is higher than the lattice energy, the process of dissolution is likely to be favorable, resulting in a soluble compound.

Thermochemical Cycle

The thermochemical cycle is a tool commonly used in chemistry to understand the energy changes that occur during the dissolution process of an ionic solid into a solvent. It's a diagrammatic representation that breaks down the steps of dissolution into smaller, more manageable processes for which energy changes can be measured or estimated.

In the case of salt dissolution, the thermochemical cycle typically involves three main stages: the separation of the ions from their crystal lattice (lattice energy), the introduction of ions into the solvent (solvation energy), and the overall energy change resulting from the formation of the solution (heat of solution). By considering these stages, chemists can evaluate the favorable and unfavorable steps in dissolving a salt in a specific solvent and predict the solubility of the compound.

Ionic Compound Solubility

Ionic compound solubility is a result of the interplay between lattice energy and solvation energy. When determining whether an ionic compound will dissolve in a particular solvent, chemists look at the balance between the energy needed to break the crystal lattice and the energy released upon solvation of the ions.

The solubility of an ionic compound is not a fixed value but varies with different solvents and environmental conditions. For example, factors such as temperature can influence solubility, often increasing solubility as the temperature rises. Additionally, the polarity of the solvent and the presence of other ionic species in solution can also affect solubility.

When considering salts like NaBr or tetramethylammonium bromide (CH3)4NBr, the solubility differences in polar nonaqueous solvents can be explained by these principles. The smaller sodium and bromide ions in NaBr have high lattice energy, making them less soluble. In contrast, the larger tetramethylammonium ions lower the lattice energy and enhance solvation, increasing the solubility of (CH3)4NBr.

Energy Diagram

An energy diagram is a visual representation of the energy changes occurring during chemical reactions or processes, such as the dissolution of an ionic compound. To illustrate the heat of solution, the diagram shows a comparison between the lattice energy and the solvation energy.

At the top, you would typically have the lattice energy, signaling the energy needed to separate the solid into ions. Below that is the heat of solution, indicating the overall energy change when the salt dissolves. Finally, at the lowest point, you find the solvation energy, which represents the released energy when the ions are solvated by the solvent molecules.

The energy diagram not only helps to visualize the energy profile of dissolution but also underscores the importance of both lattice energy and solvation energy in predicting and understanding the solubility of ionic compounds.