Question

Use the following data to sketch a phase diagram for krypton: \(T_{\mathrm{t}}=-169{ }^{\circ} \mathrm{C}, P_{\mathrm{t}}=133 \mathrm{~mm} \mathrm{Hg}, T_{\mathrm{c}}=-63{ }^{\circ} \mathrm{C}, P_{\mathrm{c}}=54 \mathrm{~atm}\) \(\mathrm{mp}=-156.6^{\circ} \mathrm{C}, \mathrm{bp}=-152.3^{\circ} \mathrm{C} .\) The density of solid kryp- ton is \(2.8 \mathrm{~g} / \mathrm{cm}^{3}\), and the density of the liquid is \(2.4 \mathrm{~g} / \mathrm{cm}^{3}\). Can a sample of gaseous krypton at room temperature be liquefied by raising the pressure?

Short answer

Gaseous krypton cannot be liquefied at room temperature by increasing pressure.

Step-by-step solution

Understand the Data

Identify the key pieces of information given: \(T_{\mathrm{t}} = -169^{\circ}\mathrm{C}\), \(P_{\mathrm{t}}=133 \mathrm{~mmHg}\) for the triple point, \(T_{\mathrm{c}} = -63^{\circ}\mathrm{C}\), and \(P_{\mathrm{c}} = 54 \mathrm{~atm}\) for the critical point, as well as the melting point (\(-156.6^{\circ} \mathrm{C}\)) and boiling point (\(-152.3^{\circ} \mathrm{C}\)). Additionally, note the densities: solid krypton at \(2.8 \mathrm{~g/cm}^3\) and liquid krypton at \(2.4 \mathrm{~g/cm}^3\).

Plot the Triple Point

Mark the triple point on the phase diagram at \((-169^{\circ}\mathrm{C}, 133 \mathrm{~mmHg})\). This is where solid, liquid, and gas phases coexist.

Plot the Critical Point

Mark the critical point on the phase diagram at \((-63^{\circ}\mathrm{C}, 54 \mathrm{~atm})\). Above this point, krypton cannot exist as a liquid regardless of pressure.

Mark the Melting and Boiling Points

These points provide boundaries for phase changes. The melting point at \(-156.6^{\circ}\mathrm{C}\) will define the transition from solid to liquid, and the boiling point at \(-152.3^{\circ}\mathrm{C}\) defines liquid to gas at 1 atm pressure.

Sketch the Phase Boundaries

Draw the sublimation curve from the triple point to lower pressures, the melting curve from the triple point to higher pressures than the triple point, and the vaporization curve from the boiling point to the critical point.

Determine Effect of Increasing Pressure

Consider if a gaseous sample at room temperature can be liquefied by pressure. Room temperature is around \(25^{\circ}\mathrm{C}\), well above \(-63^{\circ}\mathrm{C}\), so you need to raise the pressure above the critical pressure, which is impractical.

Key concepts

Critical Point of Krypton

The critical point of krypton is an important part of its phase diagram. At a temperature of \(-63^{\circ}\mathrm{C}\) and a pressure of 54 atm, krypton reaches its critical point.

Here, the distinction between liquid and gas phases vanishes. That means above this temperature and pressure, krypton can no longer exist as a liquid.

This point defines the temperature and pressure above which it is not possible to liquefy krypton by increasing pressure alone.

Triple Point

The triple point of krypton is the condition at which all three phases - solid, liquid, and gas - coexist in equilibrium. For krypton, this occurs at \(-169^{\circ}\mathrm{C}\) and a pressure of 133 mmHg.

Understanding the triple point helps in mapping the phase boundaries. It's crucial for illustrating how krypton behaves under different conditions of temperature and pressure.

Melting Point

The melting point is the temperature at which krypton transitions from solid to liquid. For krypton, this happens at \(-156.6^{\circ}\mathrm{C}\).

This point is vital because it marks the phase change boundary between solid and liquid.

Why It Matters:

• Identifies the temperature at which solid krypton becomes a liquid.
• Useful for applications requiring krypton in a liquid state.

Boiling Point

Krypton boils, changing from liquid to gas, at \(-152.3^{\circ}\mathrm{C}\).

This point indicates the boundary of the liquid and gas phases. At this temperature, under 1 atm pressure, krypton transitions completely into a gaseous state.

Key Insights:

• Crucial for understanding krypton's behavior at standard atmospheric conditions.
• Essential for processes involving gaseous krypton.

Density of Krypton

Density is a measure of how much mass fits within a volume. Solid krypton has a density of \(2.8\ \mathrm{g/cm}^3\) while liquid krypton is \(2.4\ \mathrm{g/cm}^3\).

Knowing the density is important for identifying phases.

• Higher density in solids indicates tightly packed particles.
• Density differences help understand phase transitions.

Pressure Effects on Krypton Phases

The effect of pressure on krypton's phase is notable. Increasing pressure affects phase stability and transitions.

For a gaseous state at room temperature (around \(25^{\circ}\mathrm{C}\)), it's impractical to liquefy krypton by pressure alone because you would need to exceed the critical pressure of 54 atm.

Understanding Pressure:

• Pressure can change phase stability and transition lines.
• Critical pressure defines limits for liquid formation.