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 term describing this solution is "supersaturated solution." (b) To initiate crystallization, one can add a seed crystal or scratch the surface of the solution container. At the molecular level, this provides a surface for the supersaturated solute to adhere to and begin crystal formation.

Step-by-step solution

Determine the term describing the solution

To determine the term describing the solution, we need to compare the solubility at \(15^{\circ} \mathrm{C}\) to the amount of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\) dissolved in \(100 \mathrm{~g}\) of water at \(35^{\circ} \mathrm{C}\). If the amount of solute in the solution is greater than the solubility, the solution is called supersaturated. Solubility at \(15^{\circ} \mathrm{C}\): \(208 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water Amount of solute in the solution at \(35^{\circ} \mathrm{C}\): \(324 \mathrm{~g}\) per \(100 \mathrm{~g}\) of water Since \(324 \mathrm{~g} > 208 \mathrm{~g}\), the solution is a supersaturated solution. Answer (a): The term describing this solution is "supersaturated solution."

Suggest an action to initiate crystallization

A possible action to initiate crystallization would be to add a seed crystal or to scratch the surface of the container in which the solution is placed.

Explain the molecular-level processes behind the suggested action

When a seed crystal is added or the container's surface is scratched, it provides a surface on which the dissolved solute can begin to deposit and grow as crystals. In a supersaturated solution, the solute concentration is higher than its solubility. Hence, the solute particles have a higher probability of adhering to a surface and solidifying. This process lowers the concentration of the solute in the solution, eventually reaching the solubility equilibrium. Answer (b): To initiate crystallization, one can add a seed crystal or scratch the surface of the solution container. At the molecular level, this provides a surface for the supersaturated solute to adhere to and begin crystal formation.

Key concepts

Solubility

Solubility is a measure of how much of a solute can dissolve in a solvent at a specific temperature and pressure to form a solution. It's an important concept not just for classroom exercises, but in the formulation of medications, the creation of food products, and the field of environmental science where it helps predict the movement of pollutants.

In the classroom problem, the solubility of Chromium nitrate nonahydrate in water is given as 208 grams per 100 grams of water at 15°C. This numerical value indicates the maximum quantity of the salt that can dissolve in water at this temperature. If more solute is added beyond the solubility limit, it will not dissolve under normal circumstances and could form a precipitate.

Crystallization

Initiating Crystallization in a Supersaturated Solution

Crystallization is the process by which a solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. It is a critical process in different industries, such as pharmaceuticals and manufacturing. The exercise highlights a scenario where crystallization is not occurring naturally in a supersaturated solution and suggests two methods to induce the process: adding a seed crystal or scratching the container's surface.

This is akin to providing a template or a 'nucleation site' for the solute particles to latch onto, which can jump-start the formation of crystals. This procedure is encapsulated in various real-world applications where precise crystal formation is crucial, such as in the making of semiconductors and the sugar industry.

Solubility Equilibrium

Solubility equilibrium is the dynamic balance between the dissolution and precipitation processes of a solute in a solvent. It's an essential concept in understanding how solutions form and behave under different conditions.

When a solution reaches its solubility limit, it is saturated, and any additional solute will not dissolve. The classroom problem describes a situation where a solution at 35°C is slowly cooled to 15°C without forming a precipitate, signaling that the solute remains dissolved even beyond its usual solubility - thus, a supersaturated state.

At this point, the solution contains more solute than it would normally sustain at the lower temperature, creating a state of imbalance. By introducing a seed crystal or scratching the container's surface, as mentioned in the exercise, the excess solute can be coaxed out of the solution to re-establish the solubility equilibrium through crystallization.