Question

For each of the following processes, indicate whether the signs of $\mathrm{\Delta }S$ and $\mathrm{\Delta }H$ 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) $\mathrm{A}$ diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form ${\mathrm{CO}}_2(\mathrm{g})$ and ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$.

Short answer

(a) $\mathrm{\Delta }S>0$, $\mathrm{\Delta }H>0$ (b) $\mathrm{\Delta }S<0$, $\mathrm{\Delta }H<0$ (c) $\mathrm{\Delta }S>0$, $\mathrm{\Delta }H>0$ (d) $\mathrm{\Delta }S>0$, $\mathrm{\Delta }H>0$ (e) $\mathrm{\Delta }S>0$, $\mathrm{\Delta }H<0$

Step-by-step solution

Entropy Change (

As the solid sublimes directly into gas, the particles become more dispersed and disordered. Therefore, the entropy change $\mathrm{\Delta }S$ is positive.

Enthalpy Change (

During sublimation, the solid absorbs heat from its surroundings to convert into the gaseous state. This implies that the enthalpy change $\mathrm{\Delta }H$ is positive. (b) The temperature of a sample of $\mathrm{Co}(s)$ is lowered from ${60}^{\circ }\mathrm{C}$ to ${25}^{\circ }\mathrm{C}$.

Entropy Change (

As the temperature decreases, the movement of the atoms decreases and the system becomes more ordered. Thus, the entropy change $\mathrm{\Delta }S$ is negative.

Enthalpy Change (

During the cooling process, the sample of $\mathrm{Co}(s)$ releases heat to its surroundings. This results in a negative enthalpy change $\mathrm{\Delta }H$. (c) Ethyl alcohol evaporates from a beaker.

Entropy Change (

In the evaporation process, the ethyl alcohol converts from liquid to vapor, increasing the disorder in the system. The entropy change $\mathrm{\Delta }S$ is positive.

Enthalpy Change (

To evaporate, the ethyl alcohol absorbs heat from its surroundings. As a result, the enthalpy change $\mathrm{\Delta }H$ is positive. (d) A diatomic molecule dissociates into atoms.

Entropy Change (

Upon dissociation, the system becomes more disordered as the atoms spread out more freely. The entropy change $\mathrm{\Delta }S$ is positive.

Enthalpy Change (

Dissociation requires the absorption of energy to break the bond between the two atoms. Thus, the enthalpy change $\mathrm{\Delta }H$ is positive. (e) A piece of charcoal is combusted to form ${\mathrm{CO}}_2(\mathrm{g})$ and ${\mathrm{H}}_2\mathrm{O}(\mathrm{g})$.

Entropy Change (

Combustion causes the formation of gaseous products from the solid and gaseous reactants. As gases are more disorderly than solids, the entropy change $\mathrm{\Delta }S$ is positive.

Enthalpy Change (

During combustion, heat is released as the charcoal reacts with oxygen. This exothermic process results in a negative enthalpy change $\mathrm{\Delta }H$.

Key concepts

Entropy Change

Entropy change, denoted as $\mathrm{\Delta }S$, is a measure that gives us insight into the disorder or randomness of a system. In thermodynamics, when a process leads to a more disordered state, $\mathrm{\Delta }S$ is considered positive. For instance, during sublimation, the transformation of a solid directly into a gas significantly increases the disorder, as the particles are free to move about much more than in the solid state. This concept helps us understand phenomena like the solid subliming in our exercise, where the entropy definitely increases, signifying a positive $\mathrm{\Delta }S$.

Conversely, when a system becomes more ordered, as seen when a substance cools down and its particles slow their movement, $\mathrm{\Delta }S$ is negative. This reflection of nature's tendency to move towards disorder is encapsulated in the second law of thermodynamics, which suggests that the total entropy of an isolated system can never decrease over time.

Enthalpy Change

Enthalpy change, $\mathrm{\Delta }H$, represents the heat content change within a system under constant pressure. It's a central topic in chemical thermodynamics that can tell us if a process is endothermic (absorbing heat, positive $\mathrm{\Delta }H$ such as in sublimation or evaporation) or exothermic (releasing heat, negative $\mathrm{\Delta }H$ as in combustion).

Simply put, if you consider a beaker of ethyl alcohol, when it evaporates, it absorbs heat from the surroundings because the liquid molecules need energy to overcome intermolecular forces and transition into the vapor phase. This energy uptake is a hallmark of a positive enthalpy change. On the other hand, cooling a substance generally releases heat to the surroundings, as seen with the sample of $\mathrm{Co}(s)$ in the exercise, hence a negative $\mathrm{\Delta }H$.

Sublimation

Sublimation is a fascinating phase transition in which a solid turns directly into a gas without passing through a liquid state. This process, common in substances like dry ice (solid ${\mathrm{CO}}_2$ ), involves both an increase in entropy (positive $\mathrm{\Delta }S$ ) because of the resulting higher disorder, and absorption of heat, shown as a positive enthalpy change (positive $\mathrm{\Delta }H$ ).

This phase change is not only a captivating demonstration of chemical thermodynamics but also has practical applications in freeze-drying food and manufacturing electronics, where removal of certain materials without passing through a liquid stage is desirable.

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that deals with the energy changes during chemical reactions and phase changes. Core to this study are the laws of thermodynamics, which describe the principles governing energy transformations in chemical systems.

The concepts of enthalpy and entropy are instrumental in predicting the spontaneity and equilibrium of chemical processes. For example, during a diatomic molecule's dissociation into individual atoms, thermodynamics can help us understand the energy requirement for the process and the resulting increase in the system's disorder.

Enthalpy of Vaporization

The enthalpy of vaporization, symbolized as $\mathrm{\Delta }{H}_{vap}$, is the amount of heat required to convert a unit mass of a liquid into a gas at constant pressure. This concept is crucial when discussing the evaporation of ethyl alcohol, as featured in the exercise.

During evaporation, molecules must absorb sufficient energy to escape the liquid's surface and disperse into the atmosphere as a vapor. This absorbed energy is what we quantify as $\mathrm{\Delta }{H}_{vap}$ and is positive since the process is endothermic, requiring heat from the surroundings.

Enthalpy of Combustion

Combustion is an exothermic reaction where a substance reacts with oxygen, releasing energy in the form of heat and light. The enthalpy of combustion, $\mathrm{\Delta }{H}_{comb}$, is thus negative because the system releases energy to the surroundings.

Considering the combustion of charcoal into ${\mathrm{CO}}_2(g)$ and ${\mathrm{H}}_2\mathrm{O}(g)$ from the exercise, the negative enthalpy change indicates that less energy is present in the chemical bonds of the products than was in the reactants. This release of energy is what we experience as heat during combustion.