Problem 88 - Chemistry The Central Science In Si Units

Question

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\). (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

(a) ΔS > 0, ΔH > 0; (b) ΔS < 0, ΔH < 0; (c) ΔS > 0, ΔH > 0; (d) ΔS > 0, ΔH > 0; (e) ΔS > 0, ΔH < 0.

Step 1: Understand the concepts of ΔS and ΔH

ΔS represents the change in entropy (a measure of disorder or randomness), while ΔH represents the change in enthalpy (a measure of heat content). Positive ΔS indicates increased disorder, negative ΔS indicates a decrease in disorder. Positive ΔH indicates heat is absorbed (endothermic process), while negative ΔH indicates heat is released (exothermic process).

Step 2: Analyze process (a) - Sublimation of a solid

Sublimation is the phase transition from solid to gas. During sublimation, the substance becomes more disordered, increasing entropy (ΔS > 0). The process requires heat input, so it's an endothermic process with a positive ΔH (ΔH > 0).

Step 3: Analyze process (b) - Cooling of a solid

When a solid is cooled, the molecules move less and the disorder decreases, leading to a decrease in entropy (ΔS < 0). Since heat is being removed from the system, the process is exothermic and ΔH is negative (ΔH < 0).

Step 4: Analyze process (c) – Evaporation of ethyl alcohol

Evaporation involves a phase change from liquid to gas, where molecules gain freedom of movement and increase in disorder (ΔS > 0). It requires heat absorption from surroundings, making the process endothermic (ΔH > 0).

Step 5: Analyze process (d) – Dissociation of diatomic molecules

Dissociation of diatomic molecules into atoms increases disorder in the system (more particles), thus increasing entropy (ΔS > 0). Breaking chemical bonds requires energy, therefore it is typically endothermic (ΔH > 0).

Step 6: Analyze process (e) – Combustion of charcoal

Combustion is a reaction with oxygen releasing large amounts of energy in the form of heat. This process increases in disorder due to gas production (ΔS > 0) and is exothermic due to heat release (ΔH < 0).

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics, serving as a measure of a system's randomness or disorder. When a process leads to greater disorder, entropy increases, signified by a positive change in entropy, \( \Delta S > 0 \). On the other hand, when a system becomes more orderly, entropy decreases, leading to a negative \( \Delta S < 0 \). Let's consider how this concept applies to different processes:

1. **Sublimation of a solid** - As a solid transforms directly into gas, the molecules gain freedom, increasing randomness. Thus, \( \Delta S \) is positive.

• Greater freedom of molecules in gas phase
• Increased randomness

2. **Cooling of a solid** - Cooling reduces the motion of particles, thus decreases randomness, leading to a negative \( \Delta S \).

• Reduced thermal motion
• Lesser disorder

3. **Evaporation** - Transitioning from liquid to gas also increases randomness, therefore \( \Delta S \) is positive.

• Increased molecular freedom
• Greater disorder

4. **Dissociation** - Breaking a diatomic molecule into atoms increases randomness as more individual particles are formed, resulting in a positive \( \Delta S \).

• More particles formed
• Increased disorder

5. **Combustion** - Produces gas and energy, increasing randomness, giving a positive \( \Delta S \).

• Production of gases
• Increased system disorder

Enthalpy

Enthalpy represents the total heat content of a system. It indicates the exchange of heat during a process at constant pressure. A positive change in enthalpy, \( \Delta H > 0 \), marks an endothermic process where heat is absorbed. Conversely, a negative enthalpy change, \( \Delta H < 0 \), denotes an exothermic process where heat is released.

1. **Sublimation** - Moving from solid to gas requires heat, classifying it as endothermic, so \( \Delta H \) is positive.

• Heat needed for phase transition

2. **Cooling of a solid** - As heat is removed, it is exothermic, making \( \Delta H \) negative.

• Release of heat

3. **Evaporation** - Requires heat absorption from surroundings, thus it is endothermic with a positive \( \Delta H \).

• Heat absorption for phase change

4. **Dissociation** - Breaking bonds needs energy input, resulting in a positive \( \Delta H \) for this endothermic process.

• Energy needed to break bonds

5. **Combustion** - Releases a lot of heat, making it exothermic with a negative \( \Delta H \).

• Energy release through heat

Phase Transitions

Phase transitions are changes between different states of matter, such as solid, liquid, and gas. These transitions involve changes in energy and order and help illustrate concepts like entropy and enthalpy.

1. **Sublimation** - Transition from solid to gas bypassing the liquid state. During sublimation, entropy increases due to increased randomness of gas molecules.

• Direct solid to gas transition
• Large increase in disorder

2. **Evaporation** - Liquid to gas transition requiring energy, increasing system entropy as molecules disperse more freely.

• Heat absorption needed
• Increased freedom of molecules

3. **Cooling of solid** - Involves reducing temperature, solidifying that reduces entropy. It transfers energy to the surroundings.

• Decrease in molecular motion
• Lessened disorder

Chemical Reactions

Chemical reactions involve rearranging atomic structures to form new substances, accompanied by changes in energetics and entropy.

1. **Dissociation** - Breaking a diatomic molecule into atoms increases entropy by raising the number of particles, needing energy input.

• Separation of atoms
• Increased number of particles

2. **Combustion** - Combining a substance with oxygen, releasing energy. It increases entropy as more gas molecules and energy are produced.

• Oxidation releasing heat
• Production of gases

3. **Complex Reactions** - Often involve multiple steps, where products can have different entropy and enthalpy changes based on reaction conditions.

• Reactions can be exothermic or endothermic
• Entropy change depends on product formation