Problem 24 - Chemistry The Molecular Science

Question

For each pair of items, predict which has the higher entropy, and explain why. (a) Item 1, a sample of pure silicon (to be used in a computer chip), or item 2 , a piece of silicon having the same mass but containing a trace of some other element, such as \(\mathrm{B}\) or \(\mathrm{P}\) (b) Item \(1,\) an ice cube at \(0^{\circ} \mathrm{C},\) or item \(2,\) the same mass of liquid water at \(0{ }^{\circ} \mathrm{C}\) (c) Item 1, a sample of pure \(\mathrm{I}_{2}\) solid at room temperature, or item \(2,\) the same mass of iodine vapor at room temperature

Step-by-Step Solution

Answer

(a) Impure silicon has higher entropy. (b) Liquid water has higher entropy. (c) Iodine vapor has higher entropy.

Step 1: Understanding Entropy

Entropy is a measure of disorder or randomness in a system. The higher the randomness, the higher the entropy.

Step 2: Analyze (a) Comparison

For part (a), we compare a pure silicon sample with another sample of silicon containing a trace element (such as B or P). The presence of an impurity increases the disorder of the atomic configuration, thus increasing the entropy. Therefore, the silicon containing a trace element has higher entropy than the pure silicon.

Step 3: Analyze (b) Comparison

For part (b), we compare an ice cube at 0°C with liquid water at 0°C. Solid ice has a regular crystal structure, leading to lower entropy. Liquid water, having a more random arrangement of molecules because it is not locked into a crystal structure, has higher entropy. Therefore, liquid water at 0°C has higher entropy than an ice cube at the same temperature.

Step 4: Analyze (c) Comparison

For part (c), we compare solid iodine with iodine vapor at room temperature. In solid form, iodine molecules are arranged in a more ordered structure compared to the gaseous state where molecules move freely and randomly. Therefore, iodine vapor has a higher entropy than solid iodine.

Key Concepts

Atomic Configuration

Atomic configuration refers to the specific arrangement of electrons within the orbitals of an atom. It greatly influences the entropy of a substance. When a trace element enters a pure substance, it disrupts the regular arrangement of atoms. This introduces more random factors into the atomic configuration, leading to an increase in entropy.

For example, when comparing pure silicon to silicon with a slight impurity, the impurity introduces irregularities in the highly structured silicon lattice. These irregularities enhance the disorder and randomness within the atomic structure. The introduction of such elements essentially creates a new microenvironment leading to varied atomic interactions, thus increasing the overall entropy of the material with the impurity.

It's important to remember:

• Purer configurations tend to have stricter atomic orders and thus, lower entropy.
• Impurities increase atomic disorder, raising entropy.

Crystal Structure

In solid states, atoms or molecules form ordered patterns known as crystal structures. This regular arrangement generally leads to lower entropy because of the predictability and order of the molecular positions.

However, when comparing solid and liquid forms, such as ice and liquid water, the difference is marked. Ice at 0°C is an example of a solid with a crystal structure, where water molecules maintain a fixed position, leading to lower entropy.

Upon melting, these water molecules break free from their structured positions, expanding into a liquid state. This state allows for random movement of molecules, significantly increasing entropy.

Key takeaways include:

• Crystalline solids have much more ordered structures.
• Liquids, due to their flow and lack of fixed positions, possess higher entropy.

Gaseous State

The gaseous state is characterized by high entropy due to the intrinsic randomness of molecules moving freely and independently. Compared to solids and liquids, gases have no definite shape or volume as intermolecular forces in a gas are minimal.

For instance, iodine can be seen both as a solid and as a vapor. In its solid state at room temperature, iodine molecules are closely packed and arranged in a structured, orderly manner. When iodine changes phase to a gaseous state, it forms a vapor where the molecules are widely separated and move chaotically.

It's essential to understand that:

• Gaseous states offer the highest entropy among the three states of matter.
• This high entropy results from the complete freedom of movement and minimal intermolecular interactions.