Question

(a) What is the significance of the triple point in a phase diagram? (b) Could you measure the triple point of water by measuring the temperature in a vessel in which water vapor, liquid water, and ice are in equilibrium under one atmosphere of air? Explain.

Short answer

The triple point in a phase diagram represents the unique temperature and pressure at which solid, liquid, and gas phases of a substance coexist in equilibrium. It is significant because it allows transitions between any of the three phases without changing the temperature and pressure. However, measuring the triple point of water under one atmosphere of air is not possible because its pressure (approximately 611.657 Pa) is considerably lower than one atmosphere (approximately 101.3 kPa). To measure the triple point of water, the pressure should be controlled to be around 611.657 Pa, while maintaining the temperature at 0.01°C.

Step-by-step solution

Part (a) - Significance of the Triple Point

In a phase diagram, the triple point represents the unique temperature and pressure at which the three phases of a substance (solid, liquid, and gas) coexist in equilibrium. It is significant because it is the only point where all three phases can be in equilibrium with each other. This equilibrium implies that the substance can transition between any of the three phases without changing the temperature and pressure.

Part (b) - Measuring the Triple Point of Water

To measure the triple point of water, one would need to ensure that water vapor, liquid water, and ice can coexist in equilibrium in a closed vessel. The equilibrium should be maintained under controlled conditions of pressure and temperature. However, the exercise specifies that the triple point measurement must be made under one atmosphere of air (approximately 101.3 kPa). The triple point of water occurs at a pressure of approximately 611.657 Pa, and a temperature of about 273.16 K (or 0.01°C). This pressure is considerably lower than one atmosphere of air. Therefore, it would not be possible to measure the triple point of water under one atmosphere of air, as the required pressure for the equilibrium between water vapor, liquid water, and ice would differ from the given condition. To measure the triple point of water, one would need to utilize a closed vessel in which the pressure would be controlled to be around 611.657 Pa, while maintaining the temperature at 0.01°C. In such a setup, water vapor, liquid water, and ice would be in equilibrium, and the triple point could be measured accurately.

Key concepts

Phase Diagram

A phase diagram is a graphical way to represent the states of matter of a substance as temperature and pressure vary.
Imagine it like a map that shows you where different states of a substance—solid, liquid, and gas—exist and coexist.
In these diagrams:

• The x-axis usually shows temperature.
• The y-axis shows pressure.
• Lines, or curves, on the diagram represent transitions between different phases.

One of the crucial points on a phase diagram is the triple point. This is where all three phases can exist in equilibrium. It highlights specific conditions under which a substance can transition between solid, liquid, and gas seamlessly without changing either temperature or pressure.

Equilibrium

Equilibrium in a phase diagram refers to the condition where the phases of a substance are stable and don’t change over time.
In the context of the triple point, equilibrium signifies a perfect balance where solid, liquid, and gas phases coexist.
For equilibrium:

• The rates of phase changes between solid, liquid, and gas are equal.
• The energy exchange is balanced.
• No net change in the amount of each phase occurs.

This state is delicate, and it demonstrates the intricate relationship between the phases at specific temperature and pressure values. The science of phases explains why small changes in these conditions can tip the balance and shift the substance into another phase.

Water Phases

Water is a fascinating substance because it behaves uniquely under various conditions of temperature and pressure. It exists mainly in three phases: solid (ice), liquid (water), and gas (vapor).

• Ice: The solid state, where water molecules are tightly packed in a lattice structure.
• Liquid: A fluid state that adapts to the shape of its container but retains a definite mass.
• Vapor: A gaseous state with molecules freely moving, occupying space without definite volume.

Understanding these phases is crucial when considering the triple point, where all these states exist together.
This coexistence in water only happens precisely at the triple point conditions, making it an essential benchmark in thermodynamic study.

Temperature and Pressure

The conditions of temperature and pressure are like the steering controls for determining the phase of a substance. They are pivotal in identifying the state in which a substance like water exists.

• Temperature: Usually measured in degrees Celsius or Kelvin, temperature affects the kinetic energy of molecules.
• Pressure: Measured in units like atmospheres or pascals, pressure relates to how much force is applied per unit area.

At the triple point of water, the temperature is very precisely 0.01°C (or 273.16 K), whereas the pressure is about 611.657 Pa.
These values indicate the precise environment necessary for all three water phases to coexist. Any tiny deviation outside these conditions, whether increasing or decreasing, can cause a shift where one phase dominates over the others, underscoring the delicate balance at play.