Question

For each of the following processes, specify whether entropy increases or decreases. Explain each of your answers. (a) Assembling a jigsaw puzzle $$ \text { (b) } \mathrm{I}_{2}(s)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{IF}_{3}(g) $$ (c) A precipitate forming when two solutions are mixed (d) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) 6 \longrightarrow \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) (e) \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) $$ \text { (f) } \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{NaCl}(a q) \longrightarrow $$ \(\mathrm{PbCl}_{2}(s)+2 \mathrm{NaNO}_{3}(a q)\)

Short answer

(a) Decreases, (b) Increases, (c) Decreases, (d) Increases, (e) Increases, (f) Decreases.

Step-by-step solution

Understanding Entropy

Entropy is a thermodynamic quantity representing the amount of disorder or randomness in a system. Generally, processes that increase the degree of randomness (or chaos) lead to an increase in entropy, while those that lead to more order result in a decrease in entropy.

Assembling a Jigsaw Puzzle

In this process, a jigsaw puzzle starts as a collection of separated pieces. As the puzzle is assembled, the pieces come together to form a complete picture. This process results in increased order, thus entropy decreases because the system moves from many possible arrangements (high disorder) to one specific arrangement (low disorder).

Chemical Reaction I2(s) + 3F2(g) -> 2IF3(g)

In this reaction, iodine ( I2 ) in solid form and fluorine ( F2 ) in gaseous form react to form iodine trifluoride ( IF3 ) in gaseous form. Since gases generally have higher entropy than solids, the formation of gas from a solid increases the system's disorder. Hence, entropy increases.

Precipitation Reaction

When a precipitate forms from the mixing of two solutions, a solid is produced. This usually results in a decrease in entropy because the ions that were free in solution become bound in a solid lattice structure, reducing randomness in the system.

Combustion of Glucose

The reaction involves glucose ( C6H12O6 ) reacting with oxygen ( O2 ) to produce carbon dioxide ( CO2 ) and water ( H2O ), both as gases. During this combustion, gases are produced and thus the randomness and the number of gaseous molecules increase, leading to an increase in entropy.

Decomposition of Calcium Carbonate

Calcium carbonate ( CaCO3 ) decomposes into calcium oxide ( CaO ), a solid, and carbon dioxide ( CO2 ), a gas. The production of a gas increases the disorder of the system, leading to an increase in entropy.

Precipitation Reaction of Pb(NO3)2 and NaCl

In this reaction, the mixing of aqueous lead(II) nitrate and sodium chloride produces a solid precipitate of lead(II) chloride. The formation of a solid from aqueous ions decreases the degree of disorder in the system, thus decreasing entropy.

Key concepts

Thermodynamics

Thermodynamics is the study of energy and its transformations. It plays a key role in understanding how systems behave. It helps explain why certain processes occur naturally and why others require additional energy.

In thermodynamics, we study various laws and principles governing energy exchanges. The second law of thermodynamics introduces the concept of entropy. This law states that the total entropy of an isolated system can never decrease over time. Rather, it either increases or remains constant, explaining why energy tends to disperse and spread out if it's not hindered.

• Entropy measures the disorder or randomness in a system.
• An increase in entropy signifies greater disorder.
• Processes that lead to increased entropy tend to be more spontaneous.

Understanding entropy helps in predicting the feasibility and direction of chemical reactions and physical processes.

Disorder

Disorder is often associated with entropy in thermodynamics. When we talk about disorder, we refer to how unpredictable a system's state is. Higher disorder usually means a higher number of possible arrangements or configurations.

A process that increases disorder usually involves the transformation of a system into a state with more freedom or randomness. For instance, gas molecules spreading out in a room represent high disorder because the molecules are in constant, random motion.

• Disorder is crucial in understanding why certain processes are favorable.
• Systems naturally evolve towards states with higher randomness.
• An increase in gaseous molecules in a system generally contributes to greater disorder.

In summary, increased disorder aligns with increased entropy, meaning a spontaneous direction for processes.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, with changes in energy and often entropy. When reactants convert into products, the atomic and molecular structures rearrange.

The entropy of a system can either increase or decrease depending on the nature of the reaction:

• Reactions that produce gas from solids or liquids usually increase entropy due to the added molecular randomness.
• Conversely, reactions forming solids from solutions, like precipitation, usually lower entropy.
• Understanding the change in entropy helps predict reaction spontaneity.

By studying reactions like decomposition or combustion, one observes how energy is released or absorbed, influencing the degree of disorder. The changes in entropy reflect the shifts in systemic disorder from reactants to products, impacting whether a reaction proceeds spontaneously.

Precipitation

Precipitation is a chemical reaction resulting in the formation of a solid from a solution. This process involves the transition of ions or molecules from a more disordered soluble state to a less disordered solid state.

When a precipitate forms, the ions once freely moving in solution become fixed into a crystalline solid structure, decreasing the system's entropy.

• Formation of a solid lowers the randomness compared to when the ions were freely moving in the solution.
• Precipitation is typically accompanied by a physical change visible as the solid forms and settles out of solution.
• The decrease in entropy reflects the organized structure of the precipitate.

Understanding the phenomenon aids in grasping how solutions can transition to solids and how this affects systemic entropy.

Combustion Reactions

Combustion reactions are exothermic reactions where a substance combines with oxygen, releasing energy in the form of heat and light. A classic example is the burning of glucose, which produces carbon dioxide and water.

During combustion, complex molecules break down into simpler particles, often resulting in increased disorder due to the increased gas production.

• Combustion increases entropy because gases are generated from the reaction.
• The energy release is highly spontaneous, driven by the substantial disorder increase.
• The products of combustion are often stable gases, which possess higher entropy than the reactants.

By examining combustion, one can see how energy transformation impacts entropy and how it highlights the tendencies in natural processes towards increased disorder.