Question

Does entropy increase or decrease in the following processes? (a) Polymeric complex carbohydrates are metabolized by the body, converted into smaller simple sugars. (b) Steam condenses on a glass surface. (c) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\)

Short answer

(a) Entropy increases; (b) entropy decreases; (c) entropy decreases.

Step-by-step solution

Analyze process (a)

Entopy is a measure of disorder. When polymeric carbohydrates are broken down into simpler sugars, the structure becomes more disordered. This conversion involves breaking larger molecules into smaller ones, which leads to an increase in entropy. Hence, the entropy increases.

Analyze process (b)

In the condensation process, water molecules transition from being widely spaced apart in gaseous form to being more closely packed in liquid form. This transition results in a decrease in disorder, as the molecules are more ordered in liquid form than in gaseous form. Therefore, the entropy decreases.

Analyze process (c)

In the given chemical reaction, gases are reacting to form a new gas. The reactants have more moles of gas (3 moles) compared to the product (2 moles). A reduction in the number of gas molecules suggests a decrease in randomness or disorder. Hence, the entropy decreases.

Key concepts

Disorder

Entropy is deeply linked to the concept of disorder, representing the randomness and chaos present in a system. When considering chemical processes, such as the breakdown of complex carbohydrates into simple sugars, the increase in disorder is evident. Large, organized molecules are converted into smaller, more numerous pieces. This leads to more available configurations and, consequently, an increase in entropy. Disorder is an essential concept because it helps to explain why certain processes occur spontaneously—they favor the direction where disorder increased and so does entropy.

Chemical Reactions

Chemical reactions often involve changes in entropy as substances transform into different chemical entities. For instance, in the reaction where sulfur dioxide (\(\text{SO}_2\)) and oxygen (\(\text{O}_2\)) combine to form sulfur trioxide (\(\text{SO}_3\)), several factors affect entropy.

• The main aspect is the change in the number of gas molecules, and consequently the change in disorder.
• A decrease in the number of gas molecules, from three moles to two, reduces the available freedom of movement. The chemical system becomes slightly more ordered.

This results in a decrease in entropy. Thus, in chemical reactions, the change in entropy plays a crucial role in determining the feasibility and spontaneity of the reaction.

Phase Transitions

Phase transitions involve changes in the physical state of matter and its associated entropy. A classic example is the condensation of steam into water. In steam, water molecules are scattered and move freely, reflecting a high level of disorder. When steam condenses on a cool surface, it transforms into liquid water, where molecules are closer together and more arranged. This transition from gas to liquid signifies a decrease in entropy—or, a gain in order—as the freedom of movement for molecules reduces. Understanding entropy in phase transitions is key to comprehending phenomena like weather patterns and refrigeration processes.

Molecular Structure

Molecular structure has a significant impact on the entropy of a system. Entropy not only depends on the physical state but also on the arrangement and complexity of molecules. For example, when complex carbohydrates are metabolized, their structural complexity decreases as they break down into simpler sugars.

• This process increases entropy because simpler molecules can adopt more orientations and positions compared to the more restrictive large molecules.
• Entropy generally increases when structures are simplified or energy is added, as it releases constraints on particles' positions.

Thus, understanding molecular structure helps predict how energetic and structural changes influence entropy in chemical and biological systems.