Problem 42 - Chemistry: The Central Science

Question

Predict the sign of \(\Delta S_{\text {sys }}\) for each of the following processes: (a) Gaseous Ar is liquefied at \(80 \mathrm{~K}\). (b) Gaseous \(\mathrm{N}_{2} \mathrm{O}_{4}\) dissociates to form gaseous \(\mathrm{NO}_{2}\). (c) Solid potassium reacts with gaseous \(\mathrm{O}_{2}\) to form solid potassium superoxide, \(\mathrm{KO}_{2}\). (d) Lead bromide precipitates upon mixing \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\mathrm{KBr}(a q)\)

Step-by-Step Solution

Answer

(a) ΔS_system < 0 (negative) (b) ΔS_system > 0 (positive) (c) ΔS_system < 0 (negative) (d) ΔS_system < 0 (negative)

Step 1: (a) Gaseous Ar is liquefied at 80 K

: Liquefaction of a gas involves a decrease in disorder as the gas molecules are condensed into a liquid state. This results in a decrease in entropy. Therefore, the sign of ΔS_system for this process is negative.

Step 2: (b) Gaseous N2O4 dissociates to form gaseous NO2

: The dissociation of gaseous N2O4 to form gaseous NO2 increases the number of gas molecules from 1 to 2, and hence an increase in disorder. This leads to an increase in entropy. Therefore, the sign of ΔS_system for this process is positive.

Step 3: (c) Solid potassium reacts with gaseous O2 to form solid potassium superoxide, KO2

: During this reaction, solid potassium reacts with gaseous oxygen to form solid potassium superoxide. The number of moles of gas decreases from 1 (O2) to 0, which corresponds to a decrease in disorder. Thus, the sign of ΔS_system for this process is negative.

Step 4: (d) Lead bromide precipitates upon mixing Pb(NO3)2(aq) and KBr(aq)

: In this process, two aqueous solutions are mixed, leading to the formation of a solid precipitate (lead bromide). The reaction involves a transition from an aqueous state to a solid state, resulting in a decrease in disorder. Hence, the sign of ΔS_system for this process is negative.

Key Concepts

Gaseous States

Gases are one of the fundamental states of matter, alongside liquids, solids, and plasma. They are characterized by their high kinetic energy and the large distances between particles. This gives them the ability to expand to fill their container fully and to be highly compressible. Unlike solids, gases have neither fixed shape nor fixed volume.

Because gas particles move freely and rapidly, the state of disorder, or entropy, in a gaseous state is quite high compared to liquids and solids. In thermodynamics, entropy is a measure of the randomness or disorder within a system. The more random the particles are, the higher the entropy.

When considering changes in gaseous states, like in the liquefaction or dissociation processes, it's crucial to understand how these changes impact entropy. For instance, when a gas liquefies, as in the case of argon gas being turned into liquid at low temperatures (80 K), there is a marked decrease in entropy because the particles’ movement becomes restricted.

• High entropy in gases due to particle freedom
• Changes from gas to liquid decrease entropy due to increased particle order

Liquefaction

Liquefaction is the process where a substance in its gaseous state is converted into a liquid. This can occur when the gas is subjected to cooling or pressurization. In terms of molecular dynamics, liquefaction involves a significant decrease in kinetic energy, which leads to gas molecules coming closer together and eventually forming a liquid.

For example, when gaseous Argon is cooled down to 80 K, it is transformed into a liquid. In this process, the disorder of the system reduces considerably as the random movement of gas particles is restricted as they come closer.

Consequently, the entropy of the system decreases when a gas is liquefied, as seen in thermodynamic processes:

• Reduction in particle movement when gas liquefies
• Decrease in system disorder and entropy

Dissociation Reactions

Dissociation reactions involve the breakdown of a compound into its constituent parts. In the gaseous phase, this often involves the splitting of a molecule into simpler molecules or atoms, resulting in an increase in particle number and, thereby, an increase in entropy.

A classic example is the dissociation of gaseous \(N_2O_4\) to form \(NO_2\). Initially, there is one \(N_2O_4\) molecule, but upon dissociation, it forms two \(NO_2\) molecules. This increase in the number of gas molecules leads to a significant increase in the disorder of the system, elevating its entropy.

Dissociation processes are important in chemical reactions and are influenced by temperature and pressure. In these reactions:

• Number of particles usually increases
• Entropy of the system generally increases

Precipitation Reactions

Precipitation reactions are reactions where two solutions are mixed, resulting in the formation of a solid precipitate. This can be seen when mixing solutions of lead nitrate and potassium bromide to form solid lead bromide.

The formation of a solid from a solution involves a reduction in disorder because the particles become more organized in the solid state compared to their more random arrangements in aqueous solutions. As a result, the entropy of the system decreases when a solid precipitate forms.

Key points to consider with precipitation reactions include:

• Transition from aqueous to solid state reduces entropy
• Leads to a more ordered system configuration