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 \(101.32 \mathrm{kPa}\) of air? Explain.

Short answer

(a) The triple point in a phase diagram is the unique point where all three phases (solid, liquid, and gas) coexist in thermodynamic equilibrium at specific temperature and pressure conditions. It is significant because small changes in temperature and/or pressure can cause phase changes at this point. (b) In the given scenario, measuring the triple point of water is not possible due to the presence of air, as the pressure is a combination of water vapor and air pressure. To accurately measure the triple point of water, all other gases must be removed.

Step-by-step solution

(a) Significance of the Triple Point in a Phase Diagram

The triple point in a phase diagram is a unique point where all three phases (solid, liquid, and gas) of a substance coexist in thermodynamic equilibrium. It signifies the specific temperature and pressure conditions necessary for all three phases to be present simultaneously. It is important because at this triple point, very small changes in temperature and/or pressure can cause a substance to spontaneously change phase.

(b) Is it possible to measure the triple point of water in this scenario?

In this scenario, liquid water, water vapor, and ice are in equilibrium under an air pressure of 101.32 kPa. However, the presence of air complicates the system, as the pressure we are measuring is not the partial pressure of the water vapor but the total air pressure in the vessel. The triple point of water occurs at a very specific temperature and pressure (0.01 °C and 611.657 Pa). When the pressure within the vessel is 101.32 kPa (which includes the partial pressure of the water vapor and the partial pressure of air), the equilibrium with ice, liquid, and vapor would be different than what is needed for the triple point. Therefore, it is not possible to directly measure the triple point of water under these conditions. To accurately measure the triple point of water, all other gases must be removed so that only water is present in the system.

Key concepts

Phase Diagram

Imagine a map that tells you how a substance behaves under different temperatures and pressures. That's essentially what a phase diagram does. It is a graphical representation of the physical states of a substance under various conditions of temperature and pressure.
A typical phase diagram has three main regions: solid, liquid, and gas. The lines separating these regions show the conditions where two states can coexist in equilibrium.
One of the most interesting features on a phase diagram is the "triple point." This is a unique spot where all three phases exist together in perfect harmony. At the triple point, a substance can be solid, liquid, and gas, all at once.
What makes the triple point so fascinating is that it's not just any random temperature and pressure. It's a very specific combination unique to each substance. For water, the triple point is at 0.01°C and a pressure of 611.657 pascals. Understanding the triple point is important because it provides deep insight into the properties and behavior of the substance across different phases.

Thermodynamic Equilibrium

Equilibrium might make you think of balance, and that's exactly what it is. Thermodynamic equilibrium is when a system's macroscopic properties like temperature, pressure, and phase remain constant over time. Essentially, nothing is changing in the system.
Imagine a glass of water with some ice cubes on a hot day. At first, the ice melts and cools the water until all three parts—ice, water, and air—are in a state where no net change occurs. This is thermodynamic equilibrium at its simplest form.
Reaching equilibrium means that the exchange of energy and particles in the system is perfectly balanced. No new energy is added or lost, and the phases stop changing.
However, in real-world settings, reaching perfect equilibrium can be tough. Factors like impurities or changing external conditions can tweak the balance. But once equilibrium is achieved in a controlled environment, it becomes a perfect space for studying the properties of substances.

Water Phases

Water has the remarkable ability to exist in multiple phases—ice (solid), liquid water, and steam (gas). How water transitions between these phases depends heavily on temperature and pressure.
At temperatures below 0°C, water is typically in its solid form as ice. As the temperature rises above 0°C but remains below 100°C, ice melts into liquid water. This happens frequently in the natural world and in our daily lives.
Raise that temperature above 100°C at standard atmospheric pressure, and water becomes steam, a gaseous state. This phase transition is the principle behind boiling water.
But here's something cool; these phases are not strictly tied to one temperature. For example, under high pressure, water can remain liquid below 0°C or become steam at temperatures less than 100°C.
This demonstrates water's versatile phase transitions, which play critical roles in natural systems and various industrial processes.