Question

Consider the following data for xenon: Triple point: \(-121^{\circ} \mathrm{C}, 280\) torr Normal melting point: \(-112^{\circ} \mathrm{C}\) Normal boiling point: \(\quad-107^{\circ} \mathrm{C}\) Which is more dense, \(\mathrm{Xe}(s)\) or \(\mathrm{Xe}(I) ?\) How do the melting point and boiling point of xenon depend on pressure?

Short answer

Xe(l) is denser than Xe(s). The melting point of xenon decreases with increasing pressure, while the boiling point increases with increasing pressure.

Step-by-step solution

Understand the given information

We know xenon's triple point is at -121°C and 280 torr, and the normal melting and boiling points are given as -112°C and -107°C, respectively.

Comparing the phases of Xe

A triple point is a unique temperature and pressure where a substance can coexist in equilibrium between all three phases (solid, liquid, and gas). From the given information, we know Xe(s) can transition to Xe(l) when heated at the triple point pressure of 280 torr. Similarly, Xe(l) can transition to Xe(g) with further heating to reach the boiling point. Since we are asked to compare densities, we can consider that a substance's density in liquid phase is generally higher than that in solid phase when its melting point decreases with increasing pressure. From the table, we see that Xe(s) transitions to Xe(l) with an increase in temperature while the pressure remains constant at 280 torr. Therefore, we can conclude that Xe(l) is more dense than Xe(s).

Melting point dependence on pressure

The melting point of a substance such as xenon is the temperature at which the substance transitions from solid to liquid phase. Since Xe(s) transitions to Xe(l) with heating at the constant pressure (280 torr), as discussed earlier, we can infer that xenon's melting point decreases as pressure increases.

Boiling point dependence on pressure

The boiling point of a substance is the temperature at which that substance transitions from liquid to gas phase. Since Xe(l) transitions to Xe(g) with heating when at the constant pressure given in the triple point, we can infer that the boiling point of xenon increases with increasing pressure. In conclusion, Xe(l) is denser than Xe(s), and the melting point of xenon decreases with increasing pressure while the boiling point increases with increasing pressure.

Key concepts

Triple Point

At its core, the triple point of a substance is a unique state where it can coexist as a solid, liquid, and gas, all in equilibrium. For xenon, this occurs at a temperature of \( -121^{\circ} \text{C} \) and a pressure of 280 torr. This special point is significant because it is the only set of conditions where all three phases can be present simultaneously, making it a crucial reference point in phase transition studies.
Understanding the triple point helps explain the behavior of xenon under varying temperature and pressure conditions. At the triple point, xenon solid can become liquid if the temperature is slightly increased, or it can change to gas if the temperature is elevated enough. This phenomenon highlights how sensitive xenon's phase can be to changes as it nears these critical points.

Density Comparison

Density is a measure of how much mass is contained in a given volume, and this property can differ between the solid and liquid phases of a substance. Generally, substances are denser in their solid form; however, xenon is an exception. For xenon, a decrease in its melting point with increased pressure can indicate that the liquid phase has a higher density than the solid phase.

• When xenon's solid form (\( \text{Xe}(s) \)) turns to liquid (\( \text{Xe}(l) \)) under the conditions of its triple point, the liquid is observed to be denser.
• This condition arises because the structure of the solid phase is less efficient in packing xenon atoms compared to the liquid phase at higher pressures.

Therefore, in comparing the densities of xenon's solid and liquid phases, we see that \( \text{Xe}(l) \) is indeed more dense than \( \text{Xe}(s) \) under the influence of the triple point conditions.

Melting Point Dependency

A substance's melting point is the temperature at which it changes from solid to liquid. For xenon, this temperature can be influenced by pressure. When pressure increases, the melting point can shift.

• This means that, as pressure is applied, xenon's molecular interactions result in a requirement for less temperature (energy) to transition from solid to liquid, indicating a decrease in its melting point.
• This behavior suggests that the solid structure of xenon does not hold together as robustly under increased pressure, which is why we observe a lower melting point.

Consequently, when analyzing xenon's phase transition behavior with added pressure, it's clear this influences and decreases its melting point.

Boiling Point Dependency

The boiling point is the temperature at which a liquid becomes a gas. Pressure plays a pivotal role in determining this phase change temperature for substances, including xenon.

• As pressure on xenon increases, its boiling point also increases; thus, it requires more heat (energy) to convert from a liquid to a gaseous state.
• This rise in boiling point with pressure reflects the need for additional energy to overcome the stiffer molecular interactions, which are more pronounced under higher pressure conditions in the liquid phase.

Understanding this relationship is crucial for practical applications involving xenon, as it allows predictions on how xenon will respond to various conditions when transitioning from a liquid to a gas.