Question

The normal melting and boiling points of \(\mathrm{O}_{2}\) are \(-218{ }^{\circ} \mathrm{C}\) and \(-183{ }^{\circ} \mathrm{C}\) respectively. Its triple point is at \(-219^{\circ} \mathrm{C}\) and \(1.14\) torr, and its critical point is at \(-119^{\circ} \mathrm{C}\) and \(49.8\) atm. (a) Sketch the phase diagram for \(\mathrm{O}_{2}\), showing the four points given and indicating the area in which each phase is stable. (b) Will \(\mathrm{O}_{2}(s)\) float on \(\mathrm{O}_{2}(I)\) ? Explain. (c) As it is heated, will solid \(\mathrm{O}_{2}\) sublime or melt under a pressure of 1 atm?

Short answer

In the phase diagram of O₂, the solid phase is stable to the left of the melting point line, the liquid phase is between the melting and boiling point lines, and the gas phase is to the right of the boiling point line. Solid O₂ will float on liquid O₂ due to its lower density, and when heated under a pressure of 1 atm, solid O₂ will melt into liquid O₂.

Step-by-step solution

Sketch the phase diagram

In order to sketch the phase diagram of O₂, label the axes as Temperature (T) on the horizontal axis and Pressure (P) on the vertical axis. We will now plot the points and boundary lines given by the information in the exercise. - Normal melting point: Draw a vertical line at T = -218°C. - Normal boiling point: Draw a vertical line at T = -183°C. - Triple point: Plot a point at T = -219°C, P = 1.14 torr. - Critical point: Plot a point at T = -119°C, P = 49.8 atm. Join the triple point to the melting and boiling points, and join the critical point to the boiling point. The phase regions can now be indicated: - Solid (s): Area to the left of the melting point line. - Liquid (l): Area between the melting and boiling point lines. - Gas (g): Area to the right of the boiling point line. - Area above the critical point is the supercritical fluid region.

Determine if solid O₂ will float on liquid O₂

To determine if solid O₂ will float on liquid O₂, we need to compare their densities. In general, if the density of the solid is less than the density of the liquid, the solid will float. Due to the phase diagram structure and the fact that the slope of the solid-liquid phase boundary line is positive, the density of solid O₂ is indeed lower than the density of liquid O₂. Therefore, solid O₂ will float on liquid O₂.

Determine if solid O₂ will sublime or melt under a pressure of 1 atm

To find out whether solid O₂ will sublime or melt when heated under a pressure of 1 atm, we need to look at the phase diagram and see how it behaves at this pressure. At 1 atm pressure, the temperature will be between the melting point and the boiling point (i.e., between -218°C and -183°C). Based on the phase diagram, this corresponds to the liquid phase region. Therefore, upon heating, solid O₂ will melt and convert into liquid O₂ under a pressure of 1 atm.

Key concepts

Triple point

The triple point of a substance is a unique condition where all three phases of matter—solid, liquid, and gas—coexist in thermodynamic equilibrium. For oxygen (\r\( \mathrm{O}_{2} \)), the triple point occurs at \r\(-219^\circ \mathrm{C}\) and \r\(1.14\) torr. This means that at this precise temperature and pressure, you can find solid \r\( \mathrm{O}_{2} \), liquid \r\( \mathrm{O}_{2} \), and gaseous \r\( \mathrm{O}_{2} \) at the same time. The significance of the triple point is profound; it is used to define scales of temperature and as a reference point in phase diagrams, allowing us to predict the phase behavior of substances under different conditions.

The triple point also indicates the lowest pressure at which liquid water can exist. Below this pressure, water can only exist as a gas (vapor) or a solid (ice), but not as a liquid. Understanding the triple point can help in various scientific fields, including environmental physics and chemical engineering, and is crucial for studying the behavior of substances in extreme conditions.

Critical point

The critical point is another distinctive state in a phase diagram, representing the end of the line that demarcates the boundary between the liquid and gas phases. Beyond this point, the substance exists as a supercritical fluid which is not distinctly liquid or gas. For \r\( \mathrm{O}_{2} \), the critical point is \r\(-119^\circ \mathrm{C}\) and \r\(49.8\) atm. At temperatures and pressures above the critical point, the density of the liquid and the gas become the same, and the meniscus, which usually separates the liquid and gas phases, disappears.

A supercritical fluid exhibits properties of both gases and liquids. For example, it can diffuse through solids like a gas and dissolve materials like a liquid. Due to these unique properties, supercritical fluids are used in various applications, such as in the decaffeination of coffee beans and in supercritical fluid chromatography. The critical point allows for the exploration of matter's properties in an expanded state that isn't restricted by conventional phase boundaries.

Sublimation

Sublimation is a phase transition in which a substance moves directly from a solid to a gas phase without passing through the intermediate liquid phase. This process can be observed under certain conditions of temperature and pressure, usually at low pressures and temperatures below the substance’s triple point. When discussing oxygen, sublimation may occur when solid \r\( \mathrm{O}_{2} \) is heated at pressures below 1.14 torr, which is below its triple point pressure.

Sublimation is a fascinating phenomenon that plays a key role in fields such as atmospheric science, where it contributes to the formation of snow and ice features on Earth's surface. It's also used in technology, for example in freeze-drying food, where it allows for the preservation of taste, texture, and nutritional value by removing ice from frozen food through sublimation under low pressure. For dry ice, or solid carbon dioxide, sublimation occurs at atmospheric pressure, making it a common example used in classrooms to explain this phase transition.

Density of phases

The densities of different phases of substances play a pivotal role in determining how these phases interact with each other. Density, defined as mass per unit volume, typically varies between solid, liquid, and gaseous states. In most cases, solids are denser than liquids, which in turn are denser than gases. However, substances like water and oxygen are exceptions to this rule. For example, solid \r\( \mathrm{O}_{2} \) is less dense than liquid \r\( \mathrm{O}_{2} \), which is why solid \r\( \mathrm{O}_{2} \) floats on its liquid phase.

Density affects numerous physical behaviors and properties, such as buoyancy and phase stability. Understanding the density of the phases helps explain why certain anomalies occur, like the aforementioned behavior of \r\( \mathrm{O}_{2} \). These anomalies are due to the molecular structure and bonding within the substances. In educational contexts, such anomalies are perfect for challenging students to think critically about phase transitions and the properties of substances.