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 \(\mathrm{H}_{2} \mathrm{O}(g)\).

Short answer

(a) ∆S: positive, ∆H: positive; (b) ∆S: negative, ∆H: negative; (c) ∆S: positive, ∆H: positive; (d) ∆S: positive, ∆H: positive; (e) ∆S: positive, ∆H: negative.

Step-by-step solution

(a) A solid sublimes

The entropy change (∆S) should be positive due to the increase in randomness as the solid turns into gas. The enthalpy change (∆H) should also be positive since heat is absorbed to break the bonds in the solid.

(b) The temperature of a sample of Co(s) is lowered from 60°C to 25°C

The entropy change (∆S) should be negative due to the decrease in randomness as the solid cools down. The enthalpy change (∆H) should be negative as well since heat is removed from the solid during cooling.

(c) Ethyl alcohol evaporates from a beaker

The entropy change (∆S) should be positive due to the increase in randomness as the liquid turns into gas. The enthalpy change (∆H) should be positive since heat is absorbed to break the intermolecular forces in the liquid.

(d) A diatomic molecule dissociates into atoms

The entropy change (∆S) should be positive due to the increase in randomness as the molecule dissociates into individual atoms. The enthalpy change (∆H) should be positive since energy is required to break the molecular bonds.

(e) A piece of charcoal is combusted to form CO₂(g) and H₂O(g)

The entropy change (∆S) should be positive due to the increase in randomness with the formation of gaseous products. The enthalpy change (∆H) should be negative since the combustion process releases energy (exothermic reaction).

Key concepts

Entropy

Entropy is a measure of disorder or randomness in a system. In thermodynamics, it helps predict the direction of spontaneous processes. When a system's entropy increases, it means there's more molecular disorder.

Consider the example of solid sublimation: when a solid changes directly into a gas, it moves from an ordered state to a more disordered state. This means the entropy change (\(\Delta S\) ) is positive, as gas particles have more freedom to move around compared to solids.

Whenever substances change phase from solid to liquid or liquid to gas, entropy also increases due to greater molecular movement. During chemical reactions like dissociation or combustion involving gaseous products, \(\Delta S\) is often positive too, indicative of the increase in disorder.

Enthalpy

Enthalpy is a concept in thermodynamics that represents the total heat content of a system. It's often associated with heat changes during phase transitions and chemical reactions.

For endothermic processes, where heat is absorbed, \(\Delta H\) is positive. This occurs when phase changes require breaking of bonds, such as in sublimation and evaporation. Energy input is necessary to overcome the attractive forces between molecules, thus absorbing heat.

On the contrary, in exothermic processes like combustion, \(\Delta H\) is negative since energy is released as heat. The formation of products requires less energy than is released, making it energetically favorable. Understanding whether \(\Delta H\) is positive or negative helps in predicting whether a reaction absorbs or releases energy.

Phase Changes

Phase changes refer to the transformation of a substance from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. Each phase change involves energy exchange and changes in entropy.

During phase changes like melting, vaporization, and sublimation, energy is absorbed to break bonds, leading to an increase in disorder. Therefore, processes like evaporation and sublimation are associated with positive entropy (\(\Delta S\) ) and enthalpy (\(\Delta H\) ) changes.

Conversely, when substances move from higher to lower energy states, such as freezing or condensation, the process releases energy while decreasing randomness, resulting in negative \(\Delta S\) and \(\Delta H\) . Phase transitions are crucial to understanding energy flow in matter.

Dissociation Reactions

Dissociation reactions occur when molecules break apart into smaller entities such as ions or atoms. This process is significant, especially in chemistry, for understanding reaction pathways and energy dynamics.

During dissociation, entropy (\(\Delta S\) ) increases as a single entity separates into multiple parts, leading to increased randomness or disorder in the system. This is why dissociating diatomic molecules into individual atoms results in a positive \(\Delta S\) .

The enthalpy (\(\Delta H\) ) during such reactions is positive, because breaking chemical bonds requires an input of energy. Recognizing how dissociation impacts \(\Delta H\) and \(\Delta S\) aids in predicting the spontaneity and energy requirements of chemical reactions.