Question

A supersaturated solution of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (a) After the excess sucrose has crystallized out, the remaining solution is saturated. (b) Alter the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium. (c) After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals.

Short answer

(a) True: After the excess sucrose has crystallized out, the remaining solution is saturated. (b) False: After the excess sucrose has crystallized out, the system is now stable and in equilibrium. (c) True: After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in water attaching to the surface of the crystals.

Step-by-step solution

Statement (a) Analysis

The first statement is about the state of the solution after the excess sucrose has crystallized out. We need to determine if the remaining solution is saturated.

Statement (a) Answer

After the excess sucrose has crystallized out, the remaining solution is saturated. This statement is True. When a supersaturated solution is cooled down, the excess solute will crystallize out, leaving a saturated solution behind.

Statement (b) Analysis

The second statement is about the stability and equilibrium of the system after the excess sucrose has crystallized out. We need to determine if the system is unstable and not in equilibrium.

Statement (b) Answer

After the excess sucrose has crystallized out, the system is now stable and in equilibrium. This statement is False. When excess sucrose crystallizes out of the supersaturated solution, it brings the solution to a state of equilibrium, and the system becomes stable.

Statement (c) Analysis

The third statement involves the rate of sucrose molecules leaving the surface of the crystals and being hydrated by water, compared to the rate of sucrose molecules in the water attaching to the surface of the crystals. We need to determine if these rates are equal after the excess sucrose has crystallized out.

Statement (c) Answer

After the excess sucrose has crystallized out, the rate of sucrose molecules leaving the surface of the crystals to be hydrated by water is equal to the rate of sucrose molecules in the water attaching to the surface of the crystals. This statement is True. When the solution reaches equilibrium, the rates of these two processes become equal. This is the definition of a dynamic equilibrium.

Key concepts

Dynamic Equilibrium

When we talk about a dynamic equilibrium in a chemical context, we are describing a situation where the rate of the forward process is exactly balanced by the rate of the reverse process. In our supersaturated sucrose example, this occurs when the rate at which sucrose molecules leave the surface of the crystals (crystallization) is precisely balanced by the rate at which they rejoin the crystals from the solution (dissolution).
This state of balance does not mean that the molecules have stopped moving. On the contrary, there is constant activity, but the overall concentrations of solutes and solvents remain constant over time. Dynamic equilibrium is crucial because it governs the stability of systems in chemistry, such as when chemicals are mixed together in a reaction and when solutes are dissolved in solvents.

Reaching Dynamic Equilibrium

In the case of our supersaturated sucrose solution, as it is cooled, the excess sucrose precipitates out. Once the rates of crystallization and dissolution equalize, the system has reached dynamic equilibrium. It is 'dynamic' because the exchange of sucrose molecules continues actively, and it is 'equilibrium' because there is no net change in the amount of sucrose within the solution and crystals.

Saturated Solutions

Saturated solutions represent a key concept in understanding solubility and concentration. In simple terms, a saturated solution is one that contains the maximum amount of solute that can dissolve in a solvent at a given temperature and pressure.
When additional solute is introduced to a saturated solution, it will not dissolve further; instead, it will remain in its solid form, possibly leading to crystallization at the bottom of the container. Saturated solutions are interesting because they represent the limit of a solvent's capacity to dissolve a specific solute.

Example: Sucrose in Water

Using our textbook problem as an example, when sucrose is added to hot water, it dissolves until reaching a saturation point. As the solution cools, its capacity to hold dissolved sucrose decreases, which means some of the dissolved sucrose reverts back to its solid form, leaving behind a saturated solution.

Crystallization of Solutes

Crystallization is the process where solute particles come out of solution and form a crystalline structure. It can occur naturally when a saturated solution loses solvent (through evaporation) or when the solution is cooled, as with our supersaturated sucrose solution.
During crystallization, solute molecules align themselves in a highly ordered structure, which often results in the formation of solid crystals that are visible to the naked eye. This process is significant in many fields, from making rock candy in the kitchen to purifying chemicals in a laboratory setting.

Significance of Temperature

Temperature plays a crucial role in crystallization. As we saw with the sucrose solution, cooling the solution can force solute molecules to leave the solution and form solid crystals. This is because cooler temperatures reduce the solubility of solutes in solvents, prompting crystallization. The fascinating process of solute molecules coming together in a precise pattern underscores the intricacy of chemical interactions and the delicate balance involved in saturation and supersaturation.