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) After 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

\( \textbf{Short Answer:} \) Statement (a): True Statement (b): False Statement (c): True

Step-by-step solution

(Statement (a) Analysis)

Let's analyze statement (a): "After the excess sucrose has crystallized out, the remaining solution is saturated". A saturated solution is one in which the maximum amount of solute has been dissolved in the solvent; if any more solute were to be added, it would not dissolve. After the excess sucrose crystallizes, the maximum amount of sucrose that can dissolve in the water at room temperature has been achieved. The remaining solution is indeed saturated. Therefore, statement (a) is true.

(Statement (b) Analysis)

Now, let's analyze statement (b): "After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium". A system at equilibrium is one in which the forward and reverse reactions are occurring at the same rate. In this case, after the excess sucrose has crystallized, there is no further change in the system unless external factors (like temperature or pressure) change again. At this point, the solution is saturated and the system is in equilibrium. Therefore, statement (b) is false.

(Statement (c) Analysis)

Finally, let's analyze statement (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". This statement is actually describing a system in equilibrium, where the rate of dissolution (sucrose molecules leaving the surface of the crystals and getting dissolved in water) is equal to the rate of crystallization (sucrose molecules in water attaching to the surface of the crystals). As explained earlier, at this point, the system is in equilibrium. Hence, statement (c) is true. In conclusion, the answers are: Statement (a): True Statement (b): False Statement (c): True

Key concepts

Crystallization

Crystallization occurs when the dissolved particles in a solution come together to form solid crystals. In a supersaturated solution, more solute is dissolved than under normal circumstances, usually by heating the solvent and then cooling the solution slowly. This excess solute, which cannot remain in solution, eventually begins to crystallize. This process is orderly and is essential in many natural and industrial processes.

• Crystals form when there is an excess of solute in the solution, and conditions favor the formation of solid particles.
• This often happens when a hot saturated solution is cooled, causing solute molecules to aggregate and form solid crystals.
• The process can be harnessed to purify substances, as it often yields very pure crystalline form compounds.

Crystallization helps remove excess solute, leading directly to a saturated solution, ready for chemical or physical explorations.

Saturated Solution

A saturated solution is a state where the maximum possible amount of solute is dissolved in a solvent at a given temperature. No additional solute can dissolve in the solution because it has reached its full capacity. This is an important concept for understanding the behavior of solutions, especially in chemistry.

• In a saturated solution, the addition of more solute will result in no further dissolution, and the excess solute may precipitate or crystallize out.
• It represents a state of balance between the dissolved solute particles and those that are undissolved.
• The amount of solute needed to reach saturation varies with temperature; warmer solutions can usually dissolve more solute.

Understanding saturation is crucial when working with chemical reactions and solutions to predict substances' behaviors under various conditions.

Equilibrium

Equilibrium in a solution means that the rate at which solute dissolves and solvents saturate is equal to the rate at which solute crystallizes out. This equilibrium state signifies a balance in dynamic processes, where two opposing processes occur simultaneously.

• In a crystallization scenario, equilibrium is reached when the rate of dissolution equals the rate of crystallization.
• At equilibrium, the concentration of solute in the solution remains constant over time.
• Changing conditions like temperature or pressure can disrupt equilibrium, favoring either dissolution or crystallization.

Achieving equilibrium is essential in many industrial processes, ensuring consistency and predictability in chemical manufacturing.

Dissolution

Dissolution is the process through which a solute dissolves in a solvent, forming a homogeneous solution. It involves the interaction between solute particles and solvent molecules, often facilitated by stirring and temperature changes.

• The dissolution process allows solute particles to disperse and become part of the solvent medium.
• Temperature increases generally enhance dissolution as they provide energy to overcome solute particles' attraction forces.
• Proper dissolution is necessary for achieving uniform reactions and outcomes in chemical experiments.

Dissolution drives many natural and human-made processes, enabling the formation of vital solutions in various chemical and biological applications.