Question

Provide an explanation for each of the following phenomena: (a) Solid argon (m.p. \(-189.2^{\circ} \mathrm{C}\); b.p. \(-185.7^{\circ} \mathrm{C}\) ) can be prepared by immersing a flask containing argon gas in liquid nitrogen (b.p. \(-195.8^{\circ} \mathrm{C}\) ) until it liquefies and then connecting the flask to a vacuum pump. (b) The melting point of cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) increases with increasing pressure exerted on the solid cyclohexane. (c) Certain high-altitude clouds contain water droplets at \(-10^{\circ} \mathrm{C}\). (d) When a piece of dry ice is added to a beaker of water, fog forms above the water.

Short answer

(a) Argon solidifies due to reduced temperature and pressure. (b) High pressure favors solid state, increasing melting point. (c) Lack of nucleation sites keeps droplets liquid. (d) Sublimation of dry ice cools air, forming fog.

Step-by-step solution

Understanding Argon Solidification

Solid argon can be prepared by cooling argon gas below its melting point using liquid nitrogen as a coolant. Liquid nitrogen has a boiling point of \(-195.8^{\circ} \mathrm{C}\), which is much lower than argon's melting point \(-189.2^{\circ} \mathrm{C}\). The vacuum pump removes evaporated argon, aiding the solidification by reducing pressure and thus allowing argon to solidify more readily.

Pressure Effect on Cyclohexane Melting Point

The melting point of a substance can change with applied pressure, according to the Clausius-Clapeyron relation. For cyclohexane, the structure of the solid is likely more compact than the liquid, meaning increased pressure favors the solid state, thus raising its melting point to balance the system's thermodynamics.

Water Droplets in High-Altitude Clouds

Water can exist in a supercooled liquid state below its freezing point in clouds at high altitudes. This is because there can be a lack of nucleation sites or substances around which ice crystals can form, allowing water droplets to remain liquid despite low temperatures.

Fog Formation from Dry Ice

When dry ice (solid carbon dioxide) is added to water, it rapidly sublimates and cools the surrounding air. The cold, sublimated carbon dioxide causes water vapor in the air to condense into tiny droplets, forming fog.

Key concepts

Phase transitions

Phase transitions are fundamental processes that occur when a substance changes its physical state based on variations in temperature and pressure. The main types of phase transitions include melting, freezing, vaporization, condensation, sublimation, and deposition. Each transition involves a change in energy and structure at the molecular level, which can be influenced by the surrounding environmental conditions.

When solid argon is prepared using liquid nitrogen, it undergoes a phase transition from gas to solid. This process is known as deposition, where gas transforms directly into a solid without passing through a liquid phase, due to a combination of low temperatures and reduced pressure facilitated by a vacuum pump.

Understanding these transitions helps in mastering thermodynamic principles, which are pivotal in many scientific and industrial processes, enhancing our ability to manipulate materials for desired applications.

Clausius-Clapeyron relation

The Clausius-Clapeyron relation is a crucial thermodynamic equation that describes the change in vapor pressure with temperature during a phase transition. It is especially helpful in understanding how pressure affects the melting and boiling points of substances.

In the example of cyclohexane, this relation explains why its melting point increases under higher pressure. When pressure is applied, the solid state, often denser than the liquid, becomes more stable. The Clausius-Clapeyron equation mathematically quantifies this effect, predicting the shift in phase equilibrium. Thus, understanding this relation allows us to predict and control the conditions needed for desired phase changes.

Supercooling

Supercooling is a fascinating phenomenon where a liquid remains in its liquid state below its normal freezing point. This occurs because the liquid lacks nucleation sites, which are necessary for solid structure formation. Consequently, water droplets in high-altitude clouds can remain liquid at temperatures as low as -10^{ ext{°C}}.

In nature, supercooling allows clouds to maintain water droplets at lower temperatures, affecting weather patterns and precipitation. Understanding supercooling not only informs meteorological studies but also aids in the development of technologies like frost-resistant coatings and enhanced refrigeration systems.

Sublimation

Sublimation is the direct transition of a substance from a solid to a gas, bypassing the liquid phase, driven by conditions of pressure and temperature where this becomes thermodynamically favorable. Dry ice, which is solid carbon dioxide, sublimates at room temperature, making it an ideal substance for demonstrations of this process.

Adding dry ice to water facilitates the sublimation process, cooling the surrounding temperature and causing atmospheric water vapor to condense into fog. This dramatic transition exemplifies how substances can change phase under certain environmental conditions, proving crucial not only in educational demonstrations but also in practical applications like freeze-drying and cooling systems.