Which of the following processes are accompanied by an...

Which of the following processes are accompanied by an increase in entropy of the system? (No calculation is necessary.) (a) Dry ice, $\mathrm{CO}_{2}(\mathrm{~s})$, sublimes at $-78^{\circ} \mathrm{C}$ and then the resulting $\mathrm{CO}_{2}(\mathrm{~g})$ is warmed to $0^{\circ} \mathrm{C}$. (b) Water vapor forms snowflakes, $\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) .$ (c) Iodine sublimes, $\mathrm{I}_{2}(\mathrm{~s}) \longrightarrow \mathrm{I}_{2}(\mathrm{~g})$ (d) White silver sulfate, $\mathrm{Ag}_{2} \mathrm{SO}_{4}$ precipitates from a solution containing silver ions and sulfate ions. (e) A partition is removed to allow two gases to mix.

Which of the following processes are accompanied by an increase in entropy of the system? (No calculation is necessary.) (a) Dry ice, $\mathrm{CO}_{2}(\mathrm{~s})$, sublimes at $-78^{\circ} \mathrm{C}$ and then the resulting $\mathrm{CO}_{2}(\mathrm{~g})$ is warmed to $0^{\circ} \mathrm{C}$. (b) Water vapor forms snowflakes, $\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) .$ (c) Iodine sublimes, $\mathrm{I}_{2}(\mathrm{~s}) \longrightarrow \mathrm{I}_{2}(\mathrm{~g})$
(d) White silver sulfate, $\mathrm{Ag}_{2} \mathrm{SO}_{4}$ precipitates from a solution containing silver ions and sulfate ions. (e) A partition is removed to allow two gases to mix.

Key Concepts

Entropy

Entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a system. It is central to the second law of thermodynamics, which states that for an isolated system, the total entropy tends to increase over time. In processes where energy is spread out more widely at the molecular or atomic level, entropy increases.

Phase Transitions

Phase transitions refer to changes between different states of matter—such as from a solid to a gas or a liquid—which involve significant changes in entropy. For instance, when a substance sublimates (transitions from a solid directly into a gas), there is a marked increase in molecular freedom and disorder compared to the structured state of a solid, leading to an increase in entropy.

Mixing Processes

Mixing processes involve combining two or more substances, which results in the molecules of each component becoming more randomly distributed throughout the system. This increase in randomness typically leads to an increase in entropy, as the system moves toward a more disordered, higher-probability configuration.

Precipitation

Precipitation is the process in which dissolved ions come together to form a solid from a solution, leading to the formation of a crystalline lattice. This ordering of ions into a structured arrangement results in a decrease in entropy, because the random distribution of ions in the solution becomes more organized in the solid state.

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