Which substance has the higher entropy? (a) dry ice (solid...

Which substance has the higher entropy? (a) dry ice (solid $\mathrm{CO}_{2}$ ) at $-78^{\circ} \mathrm{C}$ or $\mathrm{CO}_{2}(\mathrm{g})$ at $0^{\circ} \mathrm{C}$ (b) liquid water at $25^{\circ} \mathrm{C}$ or liquid water at $50^{\circ} \mathrm{C}$ (c) pure alumina, $\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}),$ or ruby (Ruby is $\mathrm{Al}_{2} \mathrm{O}_{3}$ in which some $\mathrm{Al}^{3+}$ ions in the crystalline lattice are replaced with $\mathrm{Cr}^{3+}$ ions.) (d) one mole of $\mathrm{N}_{2}(\mathrm{g})$ at 1 bar pressure or one mole of $\left.\mathrm{N}_{2}(\mathrm{g}) \text { at } 10 \text { bar pressure (both at } 298 \mathrm{K}\right)$

Which substance has the higher entropy?
(a) dry ice (solid $\mathrm{CO}_{2}$ ) at $-78^{\circ} \mathrm{C}$ or $\mathrm{CO}_{2}(\mathrm{g})$ at $0^{\circ} \mathrm{C}$
(b) liquid water at $25^{\circ} \mathrm{C}$ or liquid water at $50^{\circ} \mathrm{C}$
(c) pure alumina, $\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s}),$ or ruby (Ruby is $\mathrm{Al}_{2} \mathrm{O}_{3}$ in which some $\mathrm{Al}^{3+}$ ions in the crystalline lattice are replaced with $\mathrm{Cr}^{3+}$ ions.)
(d) one mole of $\mathrm{N}_{2}(\mathrm{g})$ at 1 bar pressure or one mole of $\left.\mathrm{N}_{2}(\mathrm{g}) \text { at } 10 \text { bar pressure (both at } 298 \mathrm{K}\right)$

Key Concepts

Pressure Effects on Gases

For gases, pressure influences entropy by affecting the volume and, consequently, the number of accessible microstates. At higher pressures, the gas molecules are confined to a smaller volume, reducing entropy, while lower pressures allow for greater expansiveness and higher entropy.

Entropy

Entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a system. It reflects how energy is spread out among the particles and is an important factor in determining the spontaneity of processes.

States of Matter and Entropy

Different states of matter—solids, liquids, and gases—exhibit varying levels of entropy due to differences in molecular mobility and arrangement. Gases, with their high degree of freedom, generally have much higher entropy compared to liquids and solids, where the particles are more closely packed and ordered.

Temperature Effects on Entropy

Temperature plays a crucial role in determining entropy as it affects the kinetic energy of particles. Higher temperatures increase molecular motion, leading to an increase in the number of accessible microstates, and thus higher entropy.

Structural Order and Impurities

The degree of structural order within a substance impacts its entropy. A highly ordered, pure crystalline solid has lower entropy compared to a solid in which structural defects or impurities are present, as the latter increases randomness and the number of possible configurations.

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