Problem 22 - General Chemistry

Question

The triple point of a solid is at \(5.2 \mathrm{~atm}\) and \(-57^{\circ} \mathrm{C}\). Under typical laboratory conditions of \(P=0.98\) atm and \(T=23^{\circ} \mathrm{C}\), this solid will a. remain solid indefinitely b. boil c. melt d. sublime e. condense

Step-by-Step Solution

Answer

The solid will sublime.

Step 1: Understanding the Triple Point

The triple point of a substance is the condition (temperature and pressure) under which all three phases (solid, liquid, and gas) can coexist in equilibrium. For this solid, the triple point occurs at a pressure of \(5.2 \text{ atm}\) and a temperature of \(-57^{\circ} \text{C}\). Any phase change at the conditions given in the problem will occur relative to these benchmarks.

Step 2: Compare Given Conditions to Triple Point

Under the conditions of \(P=0.98\) atm and \(T=23^{\circ} \mathrm{C}\), compare these with the triple point conditions. At \(0.98\) atm, the pressure is much lower than the triple point pressure (\(5.2\) atm). Moreover, \(23^{\circ} \text{C}\) is significantly higher than \(-57^{\circ} \text{C}\). These specific deviations suggest that under these conditions, the solid is more likely to transition directly to a gas, rather than melt into a liquid.

Step 3: Identify the Phase Transition (Sublimation)

At pressures lower than the triple point pressure, the solid phase can directly transition into the gas phase, a process known as sublimation. Given both the significant temperature increase and pressure decrease from the triple point, the solid will sublimate rather than melt or do other transitions.

Key Concepts

Triple Point

The triple point of a substance is a unique state where all three phases—solid, liquid, and gas—exist together in equilibrium. This occurs at a specific combination of temperature and pressure. For instance, in the provided exercise, the triple point is found at a pressure of 5.2 atm and a temperature of \(-57^{\circ} \text{C}\).
What makes the triple point special is that it serves as a reference for determining how a substance might behave under different conditions. The transition to any single phase depends on how far the conditions deviate from this point.
The triple point acts as a sort of 'map compass' in thermodynamics, helping us determine the likely phase transitions when subjected to different environmental pressures and temperatures.

Sublimation

Sublimation is the process where a substance transitions directly from a solid to a gas, bypassing the liquid state. This occurs under conditions where the substance's temperature and pressure fall below its triple point.
For instance, in the exercise example, given the laboratory conditions of 0.98 atm and 23°C, the pressure is much lower, and the temperature is much higher than those at the triple point (5.2 atm and -57°C). Such conditions favor sublimation for the given solid, as the surrounding atmosphere provides inadequate pressure to keep the substance in a liquid state between the solid and gas phases.
Sublimation is a fascinating process, often observed in materials like dry ice, which sublimates at room temperature under normal atmospheric pressure, allowing it to transform directly into a gas without melting.

Pressure and Temperature Effects

Pressure and temperature are crucial factors influencing phase transitions in substances. They determine whether a substance will remain in its current state or change into another phase.
When the environmental pressure is lower than the pressure at the triple point, and the temperature is higher, as seen in the given laboratory conditions, the solid is more likely to sublimate.
Important observations include:

• Lower pressure generally facilitates the transition to the gas phase.
• Higher temperatures provide the energy necessary for molecules to break free from their solid state and enter the gas phase.

The effects of pressure and temperature aren't just limited to sublimation. They also guide processes such as melting, boiling, and condensing, by pushing the substance into the right combination of energy states where these transitions can occur.