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 \(25^{\circ} \mathrm{C}\) . ( ) 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 \(\mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

(a) \(\Delta S > 0\), \(\Delta H > 0\). (b) \(\Delta S < 0\), \(\Delta H < 0\). (c) \(\Delta S > 0\), \(\Delta H > 0\). (d) \(\Delta S > 0\), \(\Delta H > 0\). (e) \(\Delta S > 0\), \(\Delta H < 0\).

Step-by-step solution

(a) A solid sublimes.

In the process of sublimation, a solid directly turns into a gas, without passing through the liquid phase. This process results in an increase in disorder, as the substance moves from a more ordered solid state to a less ordered gas state. Hence, the entropy change \(\Delta S\) is expected to be positive. Sublimation is an endothermic process, meaning that the system absorbs energy from its surroundings. This absorbed energy increases the heat content of the system. Therefore, the enthalpy change \(\Delta H\) is expected to be positive.

(b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\).

Lowering the temperature of a system leads to a decrease in its molecular motion or the kinetic energy, which results in a decrease in disorder. Therefore, \(\Delta S\) is expected to be negative in this case. Lowering the temperature of a substance decreases its energy content as heat is released into the surroundings. Hence, the enthalpy change \(\Delta H\) is expected to be negative in this case.

(c) Ethyl alcohol evaporates from a beaker.

When a liquid evaporates, it turns into a gas. This process increases the disorder or randomness of the molecules, as they move from a more ordered liquid phase to a less ordered gas phase. Therefore, the entropy change \(\Delta S\) is expected to be positive. Evaporation is an endothermic process, as the liquid absorbs energy from its surroundings to change into a gas. Thus, the enthalpy change \(\Delta H\) is expected to be positive in this case.

(d) A diatomic molecule dissociates into atoms.

When a diatomic molecule dissociates into atoms, it breaks a chemical bond, which increases the disorder of the system. Therefore, the entropy change \(\Delta S\) is expected to be positive. Dissociation requires energy to break the chemical bond between the atoms, making it an endothermic process. Thus, the enthalpy change \(\Delta H\) is expected to be positive in this case.

(e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2}\mathrm{O}(g)\).

Combustion is an exothermic process, meaning that heat is released into the surroundings. In this process, the piece of charcoal undergoes a chemical reaction, and as a result, the change in entropy depends on the balance between the decrease in entropy due to the combustion reaction and the increase in entropy as the products are formed in the gas phase. Overall, the entropy change \(\Delta S\) is positive due to the greater number of gas product molecules compared to the solid reactants. Because the combustion process releases heat into the surroundings, the enthalpy change \(\Delta H\) is expected to be negative.

Key concepts

Sublimation

Sublimation is the process where a solid transforms directly into a gas without passing through the liquid phase. This transformation is fascinating because it exemplifies a significant change in energy and structure. During sublimation, the particles in a solid, which are closely packed together, become far apart as they transition into a gaseous state. This transition causes a significant increase in disorder or randomness.

• The entropy change \(\Delta S\) is positive because disorder increases.
• Sublimation is an endothermic process, absorbing heat from the surroundings.
• Therefore, the enthalpy change \(\Delta H\) is also positive due to energy absorption.

Sublimation is observed in everyday life, such as when dry ice (solid CO2) sublimes and disappears without melting.

Entropy change (ΔS)

Entropy is a measure of disorder or randomness in a system. When analyzing physical or chemical changes, entropy change \(\Delta S\) provides valuable insights into the movement of particles and energy within the system.

• A positive \(\Delta S\) indicates an increase in disorder, for example, when a solid turns into a liquid or gas.
• A negative \(\Delta S\) suggests a system becoming more ordered, such as when cooling a gas into a liquid or solid.
• Processes with small or negligible changes in particle distribution may have \(\Delta S \approx 0\).

Considering entropy is crucial for understanding why certain processes occur spontaneously, as systems tend to favor increasing entropy.

Enthalpy change (ΔH)

Enthalpy \(\Delta H\) refers to the total heat content in a system. It helps determine whether a process absorbs or releases heat and occurs whether in a physical phase change or chemical reaction.

• A positive \(\Delta H\) indicates an endothermic process, which requires energy absorption, such as melting or vaporization.
• A negative \(\Delta H\) characterizes exothermic processes, where energy is released, like freezing and combustion.

Understanding \(\Delta H\) is essential for predicting whether a reaction or change will occur under given conditions and aids in evaluating energy requirements and heat exchange.

Endothermic and exothermic processes

The classification of processes as either endothermic or exothermic helps us understand how energy flows within a system. Each type demonstrates how energy affects temperature and phase changes.

Endothermic Processes:

• Absorb heat from surroundings, causing the surroundings to cool down.
• Include processes like sublimation, melting, and vaporization.

Exothermic Processes:

• Release heat, warming the surroundings.
• Common examples include freezing, condensation, and combustion.

The distinction between these processes helps determine energy changes involved and their implications on equilibrium, spontaneity, and system behavior.

Phase transitions

Phase transitions are processes where a substance changes from one state of matter to another, such as from solid to liquid, liquid to gas, and so on. These changes are fundamental to thermodynamics and involve both enthalpy and entropy shifts.

• When a solid melts to a liquid, both \(\Delta H\) and \(\Delta S\) tend to be positive.
• Condensation of a gas into a liquid typically results in negative \(\Delta H\) and \(\Delta S\).
• Sublimation involves significant \(\Delta S\) and \(\Delta H\) due to directly transitioning to gaseous state.

By exploring phase transitions, one understands the energy required and how molecules behave as external conditions change.