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 to liquid water at \(90^{\circ} \mathrm{C}\) and 1 atm pressure. (b) The exothermic reaction of \(\mathrm{Na}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) forms \(\mathrm{NaCl}(\mathrm{s})\) (c) The endothermic reaction of \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) produces an equilibrium mixture of \(\mathrm{H}_{2}(\mathrm{g})\) \(\mathrm{I}_{2}(\mathrm{g}),\) and \(\mathrm{HI}(\mathrm{g})\) (d) Solid NaCl dissolves in water forming a saturated solution.

Short answer

(a) Decrease, (b) Decrease, (c) Increase, (d) Increase in entropy.

Step-by-step solution

Determine the Process Type for Each Scenario

For each scenario, identify whether the physical or chemical process results in more organized or disordered states of matter. This is vital for assessing entropy changes.

Evaluate Case (a) Water Vapor Condensation

When water vapor condenses to liquid, the gaseous water molecules lose energy and become more ordered. This represents a transition from a more disordered to a more ordered state, thus leading to a decrease in entropy.

Evaluate Case (b) Formation of NaCl Solid

In this reaction, gaseous chlorine atoms and solid sodium combine to form solid NaCl. Solids have more order compared to gases, so this transition results in a decrease in entropy.

Evaluate Case (c) Equilibrium Reaction Producing Gases

This reaction involves mixing hydrogen and iodine gases to form a mixture of hydrogen iodide gas. Overall, the number of gas molecules remains similar but increases in complexity, typically resulting in a balance or slight increase in entropy.

Evaluate Case (d) Dissolution of NaCl in Water

As solid NaCl dissolves, it breaks into sodium and chloride ions dispersed in water. This results in increased disorder, evident from the transition from a solid to a solution, suggesting an increase in entropy.

Key concepts

Entropy Change

Entropy is a measure of disorder or randomness in a system. It helps us understand how energy is distributed within a chemical or physical process. When we talk about entropy change, we are referring to the shift in this level of disorder as a system undergoes a process.

Key points to remember about entropy change include:

• A process that increases the dispersal of energy or matter in a system typically results in an increase in entropy.
• Conversely, if the process results in a more ordered or structured system, it results in a decrease in entropy.
• The second law of thermodynamics tells us that in an isolated system, entropy tends to increase over time, meaning that spontaneous processes generally favor increased entropy.

By understanding these points, you can predict whether a given process will result in an increase or decrease in entropy.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. This transformation includes changes in bonds, states of matter, and energy levels.

Here's how chemical reactions relate to entropy:

• In reactions where the products are more disordered than the reactants, such as when gases are produced, entropy typically increases.
• When a gas forms a solid or when substances form more structured compounds, entropy tends to decrease. For example, when sodium and chlorine gas form solid NaCl, the system becomes more organized.
• Reactions can be either exothermic (releasing heat) or endothermic (absorbing heat). Both types of reactions can affect entropy differently depending on how they are coupled with changes in the physical nature of the reactants and products.

This understanding is vital for predicting the direction of entropy change in chemical reactions.

Systems and Surroundings

In thermodynamics, a system is the part of the universe we are focused on, and the surroundings are everything else. This distinction is crucial when analyzing chemical processes and entropy.

To understand this better, consider:

• The system is often where the chemical reaction or physical process we are interested in occurs, such as the reactants and products in a reaction vessel.
• The surroundings are everything outside of this system. For instance, the air or the container holding the chemicals can be considered part of the surroundings.
• Changes in the system’s entropy can affect the surroundings and vice versa. For example, an exothermic reaction may release heat into the surroundings, increasing their entropy.
• The concept of total entropy, which includes both the system and surroundings, provides a comprehensive picture of the spontaneity of a process.

Understanding systems and surroundings helps in evaluating the overall impact of a reaction on the entropy in the universe.

Physical Processes

Physical processes involve changes in the state of a substance, such as melting, freezing, or dissolving. These processes can also lead to entropy changes.

Important aspects of physical processes include:

• The transition from a solid to a liquid or gas generally increases entropy because the particles become more spread out and random.
• Conversely, when systems move from gas to liquid or liquid to solid, the entropy decreases as particles become more orderly.
• Dissolution, such as when a solid like NaCl dissolves in water, tends to increase entropy because the ions spread out in solution.
Li>Physical processes, much like chemical reactions, are guided by the tendencies towards increased disorder, or higher entropy.

Recognizing these patterns enables a deeper understanding of how different processes affect entropy.