Problem 54 - Chemistry: An Atoms-Focused Approach

Question

The thermostat in a refrigerator filled with cans of soft drinks malfunctions and the temperature of the refrigerator drops below \(0^{\circ} \mathrm{C}\). The contents of the cans of diet soft drinks freeze, rupturing many of the cans and causing an awful mess. However, none of the cans containing regular, nondiet soft drinks freeze and rupture. Why?

Step-by-Step Solution

Answer

Answer: Diet soft drinks freeze and rupture because they have a higher freezing point than regular soft drinks due to their lower concentration of solutes (artificial sweeteners). When the temperature drops below 0°C, diet soft drinks freeze, while regular soft drinks, with a lower freezing point due to their higher solute concentration (sugar), remain unfrozen.

Step 1: Identify the main component difference between diet and regular soft drinks

The primary difference between diet and regular soft drinks is the sweetener used. Regular soft drinks are sweetened with sugar (sucrose), while diet soft drinks use artificial sweeteners (e.g., aspartame or sucralose) that provide a sweet taste without the calories.

Step 2: Examine the effect of solutes on freezing point

When solutes are dissolved in a liquid, they lower the freezing point of that liquid, a phenomenon known as freezing point depression. This occurs because solutes disrupt the formation of an organized lattice structure in the liquid as it freezes, making it more difficult for the liquid to become a solid. The greater the concentration of solute, the more the freezing point is depressed.

Step 3: Compare the concentration of solutes in diet and regular soft drinks

Regular soft drinks have a higher concentration of sucrose (sugar) than diet soft drinks, which have a lower concentration of artificial sweeteners. This is because artificial sweeteners are much sweeter than sugar, so a smaller amount is needed to achieve the desired sweetness.

Step 4: Relate the solute concentration to freezing point depression

Since regular soft drinks have a higher concentration of solutes (sugar) compared to diet soft drinks (artificial sweeteners), the freezing point of regular soft drinks is lower than that of diet soft drinks.

Step 5: Compare the freezing points of diet and regular soft drinks to the thermostat malfunction

When the thermostat malfunctions, the temperature of the refrigerator drops below \(0^{\circ} \mathrm{C}\). Since the freezing point of regular soft drinks is lower due to their higher solute concentration, they remain unfrozen at this temperature. However, the diet soft drinks, with a higher freezing point, freeze at this temperature, causing the cans to rupture and create a mess.

Key Concepts

Thermodynamics

Thermodynamics, the branch of physics that deals with the relationships between heat and other forms of energy, plays a crucial role in understanding why diet and regular soft drinks respond differently to changes in temperature. When the thermostat of the refrigerator malfunctions, it alters the energy balance within the system by reducing the temperature beyond the norm.

In simpler terms, thermodynamics helps explain how energy flow impacts the state of matter, such as turning a liquid into a solid. When solutes like sugar or artificial sweeteners are present, they influence the energy required for such phase changes. This is where the concept of freezing point depression becomes vital.

• Energy in this context is about moving particles and how they interact at different temperatures.
• When the refrigerator cools, the energy of the soft drink particles decreases, which can lead to freezing if the temperature gets too low.
• Solutes interfere with the energy interactions needed for the liquid to solidify, altering the freezing point.

Solubility

Solubility is a measure of how well a substance can dissolve in a liquid. For a soft drink, solubility pertains to how sugar or sweeteners dissolve within the liquid base. This characteristic affects the freezing point of a solution due to the way solutes interact with the liquid molecules.

In regular soft drinks, sugar (sucrose) readily dissolves, creating a solution with a large amount of dissolved solute. Diet sodas, on the other hand, contain artificial sweeteners which are required in smaller amounts due to their intense sweetness.

• High solubility increases solute particles in solution, leading to a larger effect on lowering the freezing point.
• The extent of how solutes can keep a liquid from freezing hinges on how dissolved and uniformly distributed those particles are.
• The sweeteners in diet drinks, being added in smaller quantities, offer less freezing point depression.

Phase Changes

Phase changes refer to the transition between solid, liquid, and gas states of a substance, such as the freezing (liquid to solid) of a soft drink. The key factor here is the freezing point — the temperature at which liquid begins to solidify.

For phase changes to occur, energy must be added or removed from a substance. During the malfunction of the refrigerator, energy is withdrawn from the liquid soft drinks, allowing them to transition to a solid state if conditions permit.

• The disruption of regular lattice formation by solutes makes freezing more challenging.
• A higher concentration of solutes, like sugar, means a lower tendency for the liquid to freeze at typical refrigerator temperatures.
• Diet sodas, with fewer solutes, reach their freezing points faster, resulting in ruptured cans when temperatures drop below freezing.