Question

Consider the following data for xenon: $$ \begin{array}{ll}{\text { Triple point: }} & {-121^{\circ} \mathrm{C}, 280 \text { torr }} \\ {\text { Normal melting point: }} & {-112^{\circ} \mathrm{C}} \\ {\text { Normal boiling point: }} & {-107^{\circ} \mathrm{C}}\end{array} $$ Which is more dense, \(\operatorname{Xe}(s)\) or \(\operatorname{Xe}(l) ?\) How do the melting point and boiling point of xenon depend on pressure?

Short answer

Solid xenon (\(Xe(s)\)) is denser than liquid xenon (\(Xe(l)\)). The melting and boiling points of xenon depend on pressure, but the given data is not sufficient to determine the exact relationship. Further data or a phase diagram is needed to analyze the dependence of these properties on pressure.

Step-by-step solution

Understand the Phase Diagram and Xenon States

We know that the phase diagram is a representation of the phases (states) of a substance as a function of temperature and pressure. The three common states of a substance are solid, liquid, and gas, which can be distinguished by their densities. For xenon, we have the following data: - Triple point: \(-121 °C\) and \(280 \,\text{torr}\) - Normal melting point: \(-112 °C\) - Normal boiling point: \(-107 °C\) The triple point represents the unique set of conditions (temperature and pressure) where all three phases (solid, liquid, and gas) coexist in equilibrium. In this problem, we are interested in understanding the density differences between solid and liquid xenon.

Determine the Denser State Between Solid and Liquid Xenon

To determine which state is denser, we need to compare the melting point of solid xenon to that of liquid xenon. Here, we are given the normal melting point, which is the temperature at which the solid state becomes the liquid state under 1 atmospheric pressure (760 torr). At the normal melting point, we can compare the density of solid and liquid xenon: - If the temperature is higher than the melting point, the substance tends to be in liquid state - If the temperature is lower than the melting point, the substance tends to be in solid state Since the normal melting point of xenon is \(-112 °C\), and since the triple point is at \(-121 °C\), we can conclude that \(Xe(s)\) exists below the normal melting point, while \(Xe(l)\) exists above the normal melting point. However, the triple point is at a lower pressure than atmospheric pressure. Under such a low pressure, we can expect that \(Xe(l)\) will have a lower density than \(Xe(s)\), as it is still somewhat close to its gaseous phase. So, the denser state between solid and liquid xenon is \(Xe(s)\), i.e., solid xenon.

Analyze the Dependence of Melting and Boiling Points on Pressure

In general, the melting point of a substance increases with an increase in pressure, and the boiling point of a substance decreases with an increase in pressure. The provided data gives boiling points and melting points at "normal" atmospheric pressure. To understand how these properties change with pressure, we need to look at the phase diagram or have additional data points at different pressures. However, without further data or a detailed phase diagram for xenon, we cannot specifically determine the exact dependence of melting and boiling points on pressure. Generally, the melting point and boiling point of xenon will depend on pressure, but the given data is not enough to establish the exact relationship. In conclusion, solid xenon (\(Xe(s)\)) is denser than liquid xenon (\(Xe(l)\)). The melting and boiling points of xenon do depend on pressure, but further data would be necessary to establish the exact relationship between these properties and pressure.

Key concepts

Xenon and Its Properties

Xenon is a noble gas that is colorless, dense, and found in trace amounts in the atmosphere. It is often used in lighting and medical imaging. Xenon is interesting because, under certain conditions, it can exist in solid, liquid, and gas phases, similar to water. Understanding these phases requires knowledge of its phase diagram, which shows how xenon behaves at different temperatures and pressures.

In its solid form, xenon can look like a crystalline structure. As a liquid, it appears as a clear fluid, while as a gas, it has no color and no odor. The transitions between these states occur at specific temperatures and pressures, marked by key points such as the triple point, normal melting point, and boiling point.

Xenon's Triple Point

The triple point is a unique condition where all three phases of a substance—solid, liquid, and gas—can coexist in equilibrium. For xenon, the triple point occurs at -121°C and 280 torr.

At this point, you could have a block of solid xenon that is partially melting into a liquid and also evaporating into a gas, all occurring simultaneously. It showcases the delicate interplay between temperature and pressure in determining the state of matter.

This point is crucial for understanding phase changes and for studying the physical properties of xenon in different states. It also serves as a reference for calibrating thermometers and understanding the phase behavior of other substances.

Xenon's Melting Point

The melting point is the temperature at which a solid becomes a liquid. For xenon, this occurs normally at -112°C.

This temperature is defined under standard atmospheric pressure of 760 torr. Here, solid xenon transitions into a liquid, but it's important to note that pressure can affect this temperature. Increasing the pressure generally raises the melting point of substances.

In xenon's case, at different pressures, the melting point can shift. This is why understanding phase diagrams is crucial, as they depict how pressure influences the melting point, allowing better predictions and manipulations of state changes.

Xenon's Boiling Point

The boiling point is the temperature at which a liquid turns into a gas, occurring at -107°C for xenon under normal atmospheric pressure.

At this temperature, liquid xenon becomes gaseous, completing the transition from one phase of matter to another. Like the melting point, the boiling point depends on pressure. An increase in pressure typically results in a higher boiling point, while a decrease can lower it.

Understanding how boiling points vary with pressure is important in various applications, from industrial processes to scientific experiments, where control over state changes is necessary for efficiency and effectiveness.