Question

The solubility of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water is \(208 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water at \(15^{\circ} \mathrm{C}\). A solution of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) in water at \(35^{\circ} \mathrm{C}\) is formed by dissolving \(324 \mathrm{~g}\) in \(100 \mathrm{~g}\) water. When this solution is slowly cooled to \(15^{\circ} \mathrm{C},\) no precipitate forms. (a) What term describes this solution? (b) What action might you take to initiate crystallization? Use molecular- level processes to explain how your suggested procedure works.

Short answer

(a) The given solution is a supersaturated solution since it contains more solute than the solubility limit at the given temperature. (b) To initiate crystallization, we can introduce seed crystals of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9\mathrm{H}_{2}\mathrm{O}\) into the solution or scratch the inner surface of the container. This provides a surface for the supersaturated solute particles to attach to and align themselves according to the crystal lattice, initiating the crystallization process.

Step-by-step solution

(a) Identify the term that describes the solution

Since the solubility of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9\mathrm{H}_{2}\mathrm{O}\) in water at \(15^{\circ}\mathrm{C}\) is \(208 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water, the maximum amount of solute that can dissolve in \(100 \mathrm{~g}\) of water at that temperature is \(208 \mathrm{~g}\). However, the given solution contains \(324 \mathrm{~g}\) of solute in \(100 \mathrm{~g}\) of water at \(35^{\circ}\mathrm{C}\), which is more than the solubility limit at \(15^{\circ}\mathrm{C}\). When this solution is cooled to \(15^{\circ}\mathrm{C}\), no precipitate forms. Therefore, the solution can be described as a #tag_bold#super#tag_end_bold#saturated solution as it contains more solute than the solubility limit at the given temperature.

(b) Suggest an action to initiate crystallization

To initiate crystallization, we can introduce a few seed crystals of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9\mathrm{H}_{2}\mathrm{O}\) into the solution. Alternatively, we can scratch the inner surface of the container in which the solution is kept.

(b) Explain the molecular-level process behind the suggested procedure

Crystallization requires a nucleus for the solute particles to attach to and start building the crystal lattice structure. By introducing seed crystals or scratching the inner surface of the container, we provide a surface for the supersaturated solute particles to attach to. As the solute particles come in contact with the seed crystal or the scratched surface, they can align themselves according to the crystal lattice and form a stable structure. This process reduces the amount of solute in the solution, causing further solute particles to come out of the solution and attach to the growing crystal lattice. As a result, the crystallization process is initiated.

Key concepts

Supersaturation and Solubility

Understanding the concept of solubility is essential when considering the formation of a supersaturated solution. Solubility refers to the maximum amount of solute that can be dissolved in a solvent at a specific temperature and pressure. When a solution exceeds this maximum solubility, it becomes supersaturated. This unusual state is achieved by dissolving more solute than normally allowed at an elevated temperature and then cooling the solution without forming a precipitate.

For example, when a solution of chromium nitrate nonahydrate is formed at 35°C with 324g of solute in 100g of water, its solubility at this higher temperature allows it to dissolve completely. Yet, when the solution is cooled back to 15°C, it doesn't immediately crystallize despite the solubility at this lower temperature being only 208g per 100g of water. This unique situation creates a supersaturated solution, teetering on the edge of crystallization, needing only a slight disturbance to trigger the release of excess solute.

Crystallization Process

The process of crystallization occurs when particles of the solute come out of solution and form a crystalline solid, a process that is central to the formation of many natural and synthetic materials. In a supersaturated solution, crystallization doesn't occur spontaneously due to the lack of a nucleus, which is essential to kick-start the organization of solute molecules into a defined crystal lattice.

Inducing crystallization can be done by implementing a site for nucleation, such as adding a small 'seed' crystal or mechanical disturbance like scratching the container's wall. With these actions, solute molecules begin to organize around the nucleation sites, and orderly crystal structures start to build. Crystallization is an exothermic process, which means that it releases heat as the solute molecules shift from a higher energy state in the solution to a lower energy state in the crystalline structure, stabilizing the system.

Role of Seed Crystals

Introducing seed crystals into a supersaturated solution is a crucial aspect of initiating crystallization. Seed crystals are small pieces of pure crystal that serve as a template for solute molecules to adhere to and grow upon. When a seed crystal is introduced to a supersaturated solution, it effectively breaks the solution’s metastable equilibrium state.

The solute molecules are attracted to the seed crystal's surface and begin to align themselves according to the crystal's existing lattice structure. This alignment encourages other solute molecules to likewise arrange themselves, a chain reaction that fuels the growth of the crystal. In the chromium nitrate nonahydrate example, the addition of chromium nitrate seed crystals provides the perfect arrangement to allow molecules from the supersaturated solution to escape the solution phase and crystallize in an orderly fashion. Having such a nucleus for crystal growth is critical to moving the crystallization process forward and can be utilized in processes ranging from rock candy creation to pharmaceutical development.