Problem 7 - Chemistry: Principles and Reactions

Question

In each of the following pairs, choose the substance with a lower entropy. (a) \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}, \mathrm{H}_{2} \mathrm{O}(l)\) at \(30^{\circ} \mathrm{C}\) (b) C (graphite), \(\mathrm{C}\) (diamond) (c) \(\mathrm{Cl}_{2}(l), \mathrm{Cl}_{2}(g)\), both at room temperature

Step-by-Step Solution

Answer

a) \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}\), \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(30^{\circ} \mathrm{C}\) b) C (graphite), C (diamond) c) \(\mathrm{Cl}_{2}(l)\), \(\mathrm{Cl}_{2}(g)\), both at room temperature Answer: a) \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}\) b) C (diamond) c) \(\mathrm{Cl}_{2}(l)\)

Step 1: Compare the temperature-related entropy

Consider the entropy of water at different temperatures. (a) \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}\), \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(30^{\circ} \mathrm{C}\) Entropy increases with an increase in temperature as the particles gain more kinetic energy, which results in increased randomness. Therefore, the water at a lower temperature will have lower entropy. Answer: \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(10^{\circ} \mathrm{C}\)

Step 2: Compare the entropy of different allotropes

Consider the entropy of two allotropes of carbon. (b) C (graphite), C (diamond) Graphite and diamond are both forms of carbon, but they have different structures. Graphite has a layered structure with weakly bonded layers, where the carbon atoms can move relatively freely. In contrast, diamond has a strong, rigid covalent bonding structure, with a higher degree of order. Thus, diamond will have a lower entropy compared to graphite. Answer: C (diamond)

Step 3: Compare the entropy of different phases

Consider the entropy of chlorine in different phases. (c) \(\mathrm{Cl}_{2}(l)\), \(\mathrm{Cl}_{2}(g)\), both at room temperature As we move from a liquid phase to a gaseous phase, the particles get more freedom to move around, leading to higher randomness and higher entropy. As a result, the liquid phase of chlorine at room temperature will have lower entropy compared to the gaseous phase. Answer: \(\mathrm{Cl}_{2}(l)\)

Key Concepts

Temperature-Related Entropy

Entropy, a measure of disorder or randomness in a system, is a fundamental aspect of chemistry that plays a vital role in understanding how substances behave under different conditions.

When we talk about temperature-related entropy, we deal with the fact that as temperature increases, the kinetic energy of particles in a substance also increases. This results in higher entropy because the particles move more rapidly and are less likely to be in a structured arrangement.

Illustrating Entropy with Water

For instance, when comparing the entropy of water at two different temperatures, we can confidently say that water at a higher temperature has greater entropy. This is because water molecules at higher temperatures have more energy and thus greater freedom of movement, leading to a more disordered state.

Importance in Chemical Reactions

The concept of temperature-related entropy is critical when examining chemical reactions. Reactions tend to occur more readily when the outcome is an increase in entropy, and understanding how temperature affects entropy can provide insight into reaction conditions and spontaneity.

Allotropes of Carbon

Carbon is unique among elements in its ability to form a wide array of structures, known as allotropes. Each allotrope of carbon has distinct physical and chemical properties that arise from the different ways carbon atoms can bond together.

Graphite vs. Diamond

In the case of graphite and diamond, we have two allotropes that are as different as can be while still being pure carbon.

• Graphite has a layer structure with weak forces between layers, allowing layers to slide over one another and giving graphite its lubricating properties and high entropy.
• Diamond, on the other hand, has each carbon atom strongly bonded to four others in a tetrahedral structure, making it incredibly hard and with lower entropy due to its ordered nature.

Understanding the differences in entropy among allotropes helps to explain their different properties and behaviors, such as electrical conductivity and hardness—a key concept for students and researchers in material science.

Phases of Matter

The phases of matter—solid, liquid, and gas—each have characteristic levels of entropy. Entropy is least in solids, where particles are closely packed in a regular arrangement with minimal movement.

From Solid to Gas

As we move from solid to liquid, and then to gas, particles obtain progressively more freedom to move. This increased freedom results in a corresponding increase in entropy. Liquids, being more fluid than solids, allow their molecules to rearrange and flow past one another, leading to medium entropy. Gases have the highest entropy because their molecules move freely and occupy the entire volume of their container.

Understanding Phase Changes

This hierarchy of entropy among the phases is essential when studying phase changes. It explains why certain processes, like the evaporation of a liquid into a gas, involve an increase in entropy and why, conversely, condensation—a gas turning into a liquid—exhibits a decrease in entropy. Knowing how phase transitions affect entropy helps in various fields, from designing cooling systems to understanding atmospheric phenomena.