Question

Predict whether each of the following processes results in an increase in entropy in the system. (Define reactants and products as the system.) (a) Water vapor condenses as dew (liquid water) at \(0^{\circ} \mathrm{C}\) and 1 atm pressure. (b) An exothermic reaction of \(\mathrm{Al}(\mathrm{s})\) and \(\mathrm{Br}_{2}(\ell)\) forms \(\mathrm{Al}_{2} \mathrm{Br}_{6}(\mathrm{s})\) (c) The endothermic decomposition of solid \(\mathrm{CaCO}_{3}\) at \(800^{\circ} \mathrm{C}\) to produce an equilibrium mixture containing solid \(\mathrm{CaCO}_{3},\) solid \(\mathrm{CaO}\) and gaseous \(\mathrm{CO}_{2}\) (d) One mol of AgCl(s) decomposes, forming 1.0 mole of \(\mathrm{Ag}(\mathrm{s})\) and \(0.5 \mathrm{mol} \mathrm{Cl}_{2}(\mathrm{g})\)

Short answer

(a) Decrease; (b) Decrease; (c) Increase; (d) Increase.

Step-by-step solution

Understanding Entropy

Entropy is a measure of the disorder or randomness of a system. Generally, processes where solid or liquid reactants form gases typically have increased entropy, as gases have more possibilities of particle configuration. Conversely, when gas becomes liquid or solid, entropy usually decreases.

Analyzing Process (a)

In process (a), water vapor, which is a gas, condenses into liquid water as dew at 0°C. Since the process is going from gas to liquid, it is going from a more disordered state to a less disordered one. Therefore, the entropy of the system decreases.

Analyzing Process (b)

In process (b), aluminum solid (\(\mathrm{Al}(\mathrm{s})\)) reacts with liquid bromine (\(\mathrm{Br}_{2}(\ell)\)) to form solid \(\mathrm{Al}_{2} \mathrm{Br}_{6}(\mathrm{s})\). Since both the reactants and the product are in condensed (solid or liquid) states and the product is a single solid, the system experiences a decrease in entropy.

Analyzing Process (c)

In process (c), solid calcium carbonate (\(\mathrm{CaCO}_{3}\)) decomposes to form solid calcium oxide (\(\mathrm{CaO}\)) and gaseous carbon dioxide (\(\mathrm{CO}_{2}\)). Here, a solid forms both another solid and a gas, which increases the disorder as gas particles have more freedom of movement compared to solids. Therefore, entropy increases.

Analyzing Process (d)

In process (d), one mole of solid silver chloride (\(\mathrm{AgCl}(\mathrm{s})\)) decomposes to form one mole of solid silver (\(\mathrm{Ag}(\mathrm{s})\)) and 0.5 moles of gaseous chlorine (\(\mathrm{Cl}_{2}(\mathrm{g})\)). This transformation contributes to an increase in entropy due to the formation of a gas from a solid.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationship between heat, work, and energy.
It studies how energy is transferred and transformed in a system.
In thermodynamics, one of the key concepts is entropy, which is a measure of disorder or randomness in a system.
The laws of thermodynamics govern how energy changes occur in physical processes and chemical reactions.
For example, the Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time.
This dictates that natural processes progress in the direction of increasing entropy.
Understanding these laws can help predict whether certain processes will occur spontaneously.
For instance, a system will move toward a state of higher entropy if possible.
This principle is crucial in determining the feasibility and spontaneity of reactions and phase changes.

Phase Changes

Phase changes refer to the transitions between the different states of matter: solid, liquid, and gas.
These changes are physical transformations that can involve either an increase or decrease in entropy.

• Condensation: Involves gas turning into a liquid. As with water vapor forming dew, this results in a decrease in entropy because the molecules in a liquid are more ordered than those in a gas.
• Evaporation: When a liquid becomes gas, such as boiling water turning into steam, the entropy increases because gas molecules have more freedom of movement.
• Melting and Freezing: Transition between solid and liquid phases, where melting increases entropy and freezing decreases it.

Phase changes play a significant role in determining the direction of processes in thermodynamics, often driven by energy changes and shifts in entropy.

Chemical Reactions

Chemical reactions involve rearranging atoms to break and form chemical bonds.
They can alter the entropy of the system. In reactions, if products are in a more disordered state than the reactants (e.g., forming gases), the entropy increases.
An illustration can be seen in the decomposition of compounds where solids form gases, enhancing the disorder.
Such processes are frequently observed in endothermic reactions where energy is absorbed, often resulting in increased entropy.
Conversely, exothermic reactions, which release energy, might result in more ordered products if they move toward a lower entropy state.
This ties into how energy considerations and entropy changes dictate whether or not a reaction is favorable under given conditions.

Disorder in Systems

Disorder in systems, often referred to as entropy, describes the degree to which energy is dispersed or spread out in a system.
This concept helps explain why certain processes occur naturally and why some require external energy inputs. In terms of molecular behavior:

• Systems with more disorder (higher entropy) generally have components that are more freely moving, such as gas molecules compared to those in liquids or solids.
• Processes that lead to increased molecular disorder, like decomposition into gases, are usually accompanied by an increase in entropy.
• Understanding how disorder affects reactions can provide insight into reaction spontaneity and the flow of energy in chemical processes.

Recognizing changes in disorder is essential for predicting the outcomes of physical and chemical processes and aligns with the overarching principles of thermodynamics.