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 \(\mathrm{O}_{2}(t) ?\) Explain. (c) As it is heated, will solid \(\mathrm{O}_{2}\) sublime or melt under a pressure of 1 atm?

Short answer

The phase diagram of O$_2$ can be sketched using the given information. O$_2$(s) will float on O$_2$(l) as its density is lower due to the crystal structure. When O$_2$(s) is heated under a pressure of 1 atm, it will melt, as the pressure is greater than the triple point pressure (1.14 torr) and the solid-to-liquid phase boundary will be crossed.

Step-by-step solution

Sketch the phase diagram for O2

Using the given information about the melting and boiling points, triple point, and critical point, we can sketch a phase diagram for O2. Normal Melting Point: -218°C (Solid to Liquid phase boundary) Normal Boiling Point: -183°C (Liquid to Gas phase boundary) Triple Point: -219°C and 1.14 torr (Point where Solid, Liquid, and Gas phases coexist) Critical Point: -119°C and 49.8 atm (Point where the distinction between Liquid and Gas phases disappears)

Determine if O2(s) floats on O2(l)

To determine if O2(s) will float on O2(l), we must compare the densities of solid and liquid O2. Due to the crystal structure of solid O2, its density is lower than that of liquid O2. This means that O2(s) will float on O2(l).

Determine if O2(s) will sublime or melt under 1 atm when heated

To determine if O2(s) will sublime or melt under a pressure of 1 atm when heated, we need to look at the phase diagram and identify where O2(s) would be if it was at 1 atm. 1 atm is approximately 760 torr which is greater than the pressure at the triple point (1.14 torr). Therefore, the phase boundary between O2(s) and O2(l) will be crossed when O2(s) is heated under a pressure of 1 atm, and O2(s) will melt instead of undergoing sublimation.

Key concepts

Normal Melting Point

The normal melting point is the temperature at which a solid turns into a liquid under standard atmospheric pressure (1 atm). For oxygen (\(\mathrm{O}_2\)), this occurs at \(-218^{\circ} \mathrm{C}\). This is a crucial point on the phase diagram as it marks the boundary between the solid and liquid phases under normal conditions. At this temperature, molecules in the solid phase gain enough energy to overcome their rigid structure.
They begin to move freely, forming a liquid. When conditions are at 1 atm, this is the precise temperature where this transformation happens.Understanding the melting point is important for predicting behavior in various conditions. It helps us know whether a substance will be solid or liquid at a given temperature.

Triple Point

The triple point of a substance is the unique set of conditions where all three phases—solid, liquid, and gas—can coexist in equilibrium. For oxygen, this occurs at \(-219^{\circ} \mathrm{C}\) and \(1.14\) torr. At the triple point, the energy and arrangement of molecules balance so differently, that
the substance cannot favor one phase over the others.
This makes the triple point an important reference in thermodynamics and a key element in phase diagrams.Knowing the triple point allows scientists to calibrate thermometers and understand fundamental properties of the substance. It also helps visualize how phase transitions occur under varying conditions.

Critical Point

The critical point marks the end of the liquid-gas boundary in a phase diagram. For oxygen, this point is at \(-119^{\circ} \mathrm{C}\) and \(49.8\) atm. Beyond this point, the substance becomes a supercritical fluid, merging characteristics of both gas and liquid phases. A supercritical fluid has no surface tension, enables rapid diffusion like a gas, but also dissolves materials as well as a liquid. At and beyond the critical point, the density of the substance becomes uniform, and it is no longer possible to distinguish whether the substance is in a liquid or gaseous state. Understanding this concept helps in fields like materials science and engineering, where extracting or purifying substances using supercritical fluids is common.

Phase Transition

Phase transitions occur when a substance changes from one state of matter to another, such as from solid to liquid (melting), liquid to gas (boiling), or solid to gas (sublimation). These transitions are marked on a phase diagram by the boundaries between different phases. In oxygen's phase diagram, phase transitions help us understand behavior under various pressures and temperatures. For example, heating solid oxygen at 1 atm will cause it to melt rather than sublime.
This means, at pressures above the triple point pressure, the solid will convert first to a liquid and then to gas as the temperature increases.

Density Comparison

To determine if one phase of a substance will float on another, we compare their densities. In the case of oxygen, the solid phase (\(\mathrm{O}_2(s)\)) will float on the liquid phase (\(\mathrm{O}_2(l)\)). This is because solid oxygen has a lower density than liquid oxygen. Density is tied to the arrangement and spacing of molecules, and often solids are denser because their molecules are tightly packed. However, for substances like oxygen, the solid form expands slightly more than the liquid form, making it less dense. Understanding density comparison helps in predicting floating behavior, which is essential in applications like cryogenics and storage.