Question

Phase Diagrams Argon has a normal boiling point of 87.2 \(\mathrm{K}\) and a melting point (at 1 atm) of 84.1 \(\mathrm{K}\) . Its critical temperature is \(150.8 \mathrm{K},\) and its critical pressure is 48.3 atm. It has a triple point at 83.7 \(\mathrm{K}\) and 0.68 atm. Sketch the phase diagram for argon. Which has the greater density, solid argon or liquid argon?

Short answer

Sketch a phase diagram with temperature on the x-axis and pressure on the y-axis; indicate the normal boiling point, melting point, critical point, and triple point. Typically, the solid phase of a substance is denser than its liquid phase, hence solid argon is likely to be denser than liquid argon.

Step-by-step solution

Sketch the Phase Diagram

Begin by drawing a graph with temperature on the x-axis and pressure on the y-axis. Mark the normal boiling point at 87.2 K with a horizontal line at 1 atm indicating the liquid-gas phase transition. Mark the melting point at 84.1 K with a horizontal line at 1 atm indicating the solid-liquid phase transition. Indicate the critical point at (150.8 K, 48.3 atm) with a dot. Draw the triple point at (83.7 K, 0.68 atm) with a dot and ensure that the solid-liquid, solid-gas and liquid-gas lines intersect at this point. The lines should reflect that to the left of the triple point solid and gas are in equilibrium, above it liquid and gas, and to the right, solid and liquid.

Label the Phases

Label the areas enclosed by the phase lines with the appropriate phase: solid, liquid, or gas. The area to the left of the solid-gas line is where solid argon is stable, the area under the liquid-gas line and to the right of the solid-liquid line is where liquid argon is stable, and the area above the liquid-gas line is where gaseous argon is stable.

Determine the Densities

In general, the density of solids is greater than that of liquids for most substances at a given pressure due to closely packed particles in the solid phase. Therefore, based on this common property of materials, solid argon would typically be denser than liquid argon. However, without specific data on the densities of argon in these phases, this cannot be definitively stated.

Key concepts

Critical Temperature

The critical temperature of a substance is a key concept to grasp when studying phase diagrams. It represents the highest temperature at which a gas can be converted to a liquid by applying pressure. Above this temperature, the gas cannot be liquefied, no matter how much pressure is applied. This is because the kinetic energy of the particles is too high for intermolecular forces to bring them together into a liquid state.

The critical temperature of argon is given as 150.8 K. This means argon cannot exist as a liquid above this temperature. The significance of the critical temperature is immense as it defines the boundary beyond which distinct liquid and gas phases do not exist. In the phase diagram, the critical point is marked where the liquid-gas boundary line ends. Understanding this concept is crucial because it determines the conditions under which a substance can be stored or transformed.

Triple Point

Understanding the triple point of a substance is pivotal when interpreting phase diagrams. The triple point is the unique set of temperature and pressure conditions at which all three phases of a substance (solid, liquid, and gas) coexist in equilibrium. For argon, the triple point occurs at 83.7 K and 0.68 atm. At this precise point, the phase boundaries for solid-liquid, liquid-gas, and solid-gas converge. It's the only set of conditions where argon can be observed in all three phases simultaneously.

The triple point is not only theoretical but also a practical thermodynamic reference. It serves as a standard fixed point in the International Temperature Scale. By fully absorbing the concept of the triple point, students can appreciate the delicate balance between the phases of matter and how a slight change in either temperature or pressure can shift a substance from one phase to another.

Solid-Liquid-Gas Equilibrium

To conquer the concept of phase diagrams, one must grasp the principle of solids, liquids, and gases in equilibrium. The term 'equilibrium' denotes a state of balance where two phases coexist without the net transformation of one phase into another over time. For instance, at any point along the solid-liquid boundary on the phase diagram, solid and liquid argon can exist together without any change in the amount of either phase.

In the phase diagram of argon, the lines separating the phases represent the conditions under which two phases are in equilibrium. The slope of the solid-liquid line indicates how the melting point changes with pressure; for most substances, increased pressure raises the melting point. Understanding the equilibrium between different states of matter is crucial when studying the phase behaviour, such as the sublimation of solids or the condensation of gases, and for processes involving the purification or separation of substances by changing their phases.