Question

Predict the sign of \(\Delta S^{\circ}\) for each of the following changes. a. \(\mathrm{K}(s)+\frac{1}{2} \mathrm{Br}_{2}(g) \longrightarrow \mathrm{KBr}(s)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(\mathrm{KBr}(s) \longrightarrow \mathrm{K}^{+}(a q)+\mathrm{Br}^{-}(a q)\) d. \(\mathrm{KBr}(s) \longrightarrow \mathrm{KBr}(l)\)

Short answer

In summary, the signs of ΔS° for each reaction are as follows: a. ΔS° is negative b. ΔS° is negative c. ΔS° is positive d. ΔS° is positive

Step-by-step solution

Analyze Reaction (a)

Reaction (a): K(s) + 1/2 Br2(g) → KBr(s) The reaction involves a solid reactant and a gaseous reactant forming a solid product. There is no increase in the number of moles of gas, as the product is a solid. Therefore, the entropy of the system is expected to decrease.

Predict the Sign of ΔS° for Reaction (a)

ΔS° for Reaction (a) is expected to be negative, as the entropy has decreased.

Analyze Reaction (b)

Reaction (b): N2(g) + 3 H2(g) → 2 NH3(g) In this reaction, there are 4 moles of gaseous reactants forming 2 moles of gaseous products. The number of moles of gas decreases, so the entropy of the system will decrease.

Predict the Sign of ΔS° for Reaction (b)

ΔS° for Reaction (b) is expected to be negative, as the entropy has decreased.

Analyze Reaction (c)

Reaction (c): KBr(s) → K+(aq) + Br-(aq) A solid reactant is dissolving into two aqueous ions. Dissolution usually results in an increase in entropy, as the dissolved particles have more freedom to move around in the solution compared to being in a rigid solid state.

Predict the Sign of ΔS° for Reaction (c)

ΔS° for Reaction (c) is expected to be positive, as the entropy has increased.

Analyze Reaction (d)

Reaction (d): KBr(s) → KBr(l) Here, a solid is changing its state to a liquid. The liquid state has more freedom of motion compared to the solid state, hence, the entropy will increase.

Predict the Sign of ΔS° for Reaction (d)

ΔS° for Reaction (d) is expected to be positive, as the entropy has increased. In summary: a. ΔS° is negative b. ΔS° is negative c. ΔS° is positive d. ΔS° is positive

Key concepts

Thermodynamics

Thermodynamics is a branch of physics and chemistry that explores the relationships between heat, work, temperature, and energy. It provides a framework to understand how energy transfers in physical systems. One of the central concepts in thermodynamics is entropy (denoted as \( S \)), which measures the degree of disorder or randomness in a system.

When analyzing chemical reactions, changes in entropy (\( \Delta S \)) help us predict whether processes are likely to occur spontaneously. A process with a positive \( \Delta S \) means that the disorder of the system has increased, often indicating a spontaneous reaction. Conversely, a negative \( \Delta S \) suggests decreased disorder, often requiring energy input to occur.

• Entropy changes are crucial in determining the feasibility and direction of reactions.
• Understanding \( \Delta S \) assists in evaluating how energy is distributed in a chemical process.
• Entropy influences equilibrium, reaction rates, and phases of matter transition.

Being aware of entropy changes can help you comprehend how chemical systems behave under various conditions.

Chemical Reactions

In chemical reactions, the rearrangement of atoms leads to the transformation of substances, often involving changes in physical and chemical properties. Reactions may result in the formation or breaking of bonds, affecting the system's entropy.

Consider Reaction (a) from the original exercise, where a solid potassium \((\mathrm{K}(s))\) and a gaseous bromine \((\mathrm{Br}_2(g))\) form potassium bromide \((\mathrm{KBr}(s))\). This reaction leads to a decrease in the overall number of gaseous particles, hence decreasing the system's entropy.

• In reactions forming more stable or complex structures, entropy tends to decrease.
• Bond formation often leads to reduced randomness, as observed when gases condense to form solids or liquids.
• Reactivity and reaction rates can be influenced by the initial state of reactants and the energetic requirements to reach the final state.

Understanding the entropy changes during reactions helps predict their spontaneity and direction.

Gaseous State

The gaseous state is characterized by particles moving freely and occupying more space compared to liquids and solids. This state has the highest entropy because gases have the most disordered arrangement.

In Reaction (b) from the original exercise, gaseous nitrogen \((\mathrm{N}_2(g))\) and hydrogen \((\mathrm{H}_2(g))\) molecules react to form fewer molecules of ammonia \((\mathrm{NH}_3(g))\). Although both reactants and products are gases, the decrease in the number of molecules means a decrease in entropy.

• Gas reactions involving a reduction in molecule number generally decrease entropy.
• Increased pressure or temperature can influence the entropy of gaseous substances, affecting reaction dynamics.
• The freedom of movement plays a critical role in determining how gases mix and the nature of the resulting reactions.

The study of gases and their behavior offers insights into the fundamental concepts of thermodynamics and chemical processes.