Question

Without using Appendix B, predict the sign of \(\Delta S^{\circ}\) for (a) \(2 \mathrm{~K}(s)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{KF}(s)\) (b) \(\mathrm{NH}_{3}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Br}(s)\) (c) \(\mathrm{NaClO}_{3}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{ClO}_{3}^{-}(a q)\)

Short answer

(a) Negative, (b) Negative, (c) Positive

Step-by-step solution

Analyze Reactants and Products for (a)

Identify the phases and general state of disorder: Reactants: 2 K(s) is a solid, and F2(g) is a gas. Product: 2 KF(s) is a solid. A gas becoming a solid generally suggests a decrease in entropy.

Predict the Sign of \(\Delta S^{\circ}\)\ for (a)

\(\Delta S^{\circ}\)\ will be negative for the reaction since the transition from a more disordered state (gas) to a less disordered state (solid) decreases entropy.

Analyze Reactants and Products for (b)

Identify the phases and general state of disorder: Reactants: NH3(g) and HBr(g) are gases. Product: NH4Br(s) is a solid. Two gases forming a solid typically indicates a decrease in entropy.

Predict the Sign of \(\Delta S^{\circ}\)\ for (b)

\(\Delta S^{\circ}\)\ will be negative for the reaction since the transition from gas to solid decreases entropy.

Analyze Reactants and Products for (c)

Identify the phases and general state of disorder: Reactants: NaClO3(s) is a solid. Products: Na+(aq) and ClO3-(aq) are aqueous ions. Solid dissociating into ions in solution usually signifies an increase in entropy.

Predict the Sign of \(\Delta S^{\circ}\)\ for (c)

\(\Delta S^{\circ}\)\ will be positive for the reaction since the transition from a solid to dissolved ions increases entropy.

Key concepts

Entropy

Entropy is a measure of disorder or randomness in a system. Think of it as the spread of energy molecules: more spread equals more disorder. Here's a simple way to understand it: imagine a clean room versus a messy room. The messy room represents high entropy, while the clean room represents low entropy.
Entropy increases when:

• Solids melt into liquids.
• Liquids evaporate into gases.
• Solids dissolve into ions in solution.

On the other hand, entropy decreases when:

• Gases condense into liquids.
• Liquids freeze into solids.
• Gases or liquids turn into solids.

The second law of thermodynamics states that the total entropy of an isolated system always increases over time. This helps us understand why certain processes, like ice melting, are spontaneous.

Phase Changes

Phase changes involve transitioning from one state of matter (solid, liquid, gas) to another. Each change in phase impacts entropy differently.
For instance, when a solid turns into a liquid (melting) or a liquid turns into a gas (evaporation), the system's entropy increases because the particles have more freedom to move and are more disordered.
Conversely, when gas condenses into a liquid or liquid freezes into a solid, entropy decreases. The particles are more ordered and have less freedom to move.
In the exercise example (a), a gas (F2) reacts with a solid (K) to form another solid (KF). Here, entropy decreases because the gaseous molecules become part of a more ordered solid structure. Thus, \(abla S^{\circ}\) is negative.

Chemical Reactions

Chemical reactions can also change entropy. Different reactions can either increase or decrease the system's disorder.
Take example (b) from our exercise: Two gases, NH3 and HBr, react to form a solid, NH4Br. As gases are more disordered than solids, this reaction leads to a decrease in entropy, making \(abla S^{\circ}\) negative.
Understanding the reactants and products' states of matter in a reaction helps us predict entropy changes.
For a reaction that produces more gas molecules than it consumes, entropy generally increases. When the reaction results in fewer gas molecules, entropy usually decreases.

Disorder

Disorder, in chemical terms, refers to how spread out and random the molecules are in a system. More disorder means higher entropy.
Think of molecules moving around randomly in a gas versus closely packed in a solid. A gas represents high disorder and high entropy, while a solid represents low disorder and low entropy.
In example (c) of our exercise, NaClO3(s) dissociates into Na+(aq) and ClO3-(aq), changing from an ordered solid to disordered ions in solution. This increase in disorder means entropy rises, making \(abla S^{\circ}\) positive.
Understanding disorder helps predict whether a chemical reaction will increase or decrease entropy. Always consider the states of reactants and products: solids to liquids or gases increase disorder, while gases to liquids or solids decrease it.