Problem 92 - Chemistry The Central Science In Si Units

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.

Step-by-Step Solution

Answer

(a) True, (b) False, (c) True.

Step 1: Understand Supersaturation and Crystallization

A supersaturated solution is one that contains more solute than it can theoretically hold at a given temperature. When it cools, the excess solute tends to crystallize out. After crystallization, the solution returns to its saturation limit, meaning it is now saturated but no longer supersaturated.

Step 2: Evaluate Statement (a)

After the excess sucrose crystallizes out, the remaining solution reaches a point where it has an equilibrium amount of sucrose for the given temperature, becoming saturated. Thus, statement (a) is true.

Step 3: Evaluate Statement (b)

Once the excess sucrose has crystallized out and the solution is saturated, the system is in a stable condition and at equilibrium between the dissolved sucrose and the solid form. Therefore, statement (b) is false, as the system is stable and in equilibrium.

Step 4: Evaluate Statement (c)

At equilibrium, the dynamic balance between sucrose molecules moving from the solid to the solution and vice versa is maintained, meaning the rate of molecules dissolving equals the rate of molecules crystallizing. Therefore, statement (c) is true.

Key Concepts

Crystallization Process

Crystallization is a fascinating process where a solute turns from a liquid solution to a solid form. Imagine a crowded dance floor, which is our supersaturated solution, packed with more dancers (solute particles) than it can reasonably accommodate.
You might have noticed that when you dissolve a lot of sugar in hot water and let it cool, crystals begin to form. This happens because the solution can no longer hold the excess sugar as it gets cooler. Crystallization occurs because the solution was initially over-saturated, like how once the dance floor gets too crowded, some people might have to step off.
Once the crystallization process starts, the solute molecules, such as sucrose, come together to form a solid, and slowly drift out of the solution forming a regular pattern. With time, the excess solute that was dissolved beyond the saturation point precipitates out as crystals.

Saturation and Equilibrium

In chemistry, saturation refers to the maximum amount of solute that a solvent can dissolve at a given temperature. Once this point is reached, the solution is said to be saturated. Think of it like a sponge that has soaked up all the water it can and cannot hold anymore.
At this stage, equilibrium is achieved. Saturation and equilibrium go hand-in-hand. Equilibrium in a saturated solution is a dynamic state. Even though it may seem like nothing is happening, at a microscopic level, there's a constant exchange of solute molecules between the dissolved state and the crystallized state.

• Solute molecules continuously leave the solvent to join the crystal.
• At the same time, molecules from the crystal dissolve back into the solvent.

This exchange maintains the equilibrium, with the concentration of dissolved solute remaining constant under steady conditions.

Chemical Equilibrium

Chemical equilibrium is when the rate of the forward reaction equals the rate of the backward reaction. In the context of our crystallization example, it means the rate at which sucrose dissolves back into the solution is equal to the rate at which sucrose crystallizes out.
This balance ensures the system does not change over time. It's a bit like a two-way street where cars (solute molecules) are moving in both directions at the same rate.
Importantly, this doesn't mean that all movement stops. Instead, it is a dynamic process where molecules are continuously moving, yet the overall concentration remains unchanged.

• Equilibrium ensures the solution remains stable.
• Even if crystallization initially seems to make things unbalanced, equilibrium is quickly restored.

This dynamic stability is a hallmark of chemical equilibrium in solutions.

Solubility and Temperature

Solubility tells us how much solute can dissolve in a solvent at a specific temperature. Typically, higher temperatures increase solubility because molecules move faster and can hold more solute, similar to how warm air can hold more moisture.
However, when you cool a hot saturated solution, solubility decreases, leading to crystallization as we've seen in our sucrose example. It's like cooling a mug of tea whereby the excess sugar that couldn't dissolve at the cooler temperature drops out of the solution.

• The solubility of a substance is crucial for determining how much solute can be dissolved.
• Temperature changes can quickly alter the solubility and thus the state of the solution.

Understanding these concepts helps explain why a supersaturated solution can form crystals when cooled, as the solution can no longer sustain the same concentration of solute.