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 watervapor, liquid water, and ice are in equilibrium under one atmosphere of air? Explain.

Short answer

The triple point in a phase diagram is significant because it represents the unique temperature and pressure at which all three phases (solid, liquid, and gas) of a substance can coexist in thermodynamic equilibrium, defining a standard state for a substance. However, it is not possible to measure the triple point of water in a vessel with water vapor, liquid water, and ice in equilibrium under one atmosphere of air, because the pressure is not at the precise triple point value (0.00604 atmospheres). Additionally, the presence of air introduces complications in measurements, as it affects the equilibrium between the water phases.

Step-by-step solution

Understanding the triple point

The triple point is a unique point in a phase diagram, where all three phases of a substance (solid, liquid, and gas) can coexist in thermodynamic equilibrium. This occurs at a specific temperature and pressure combination, and is important for understanding the phase behavior of a substance.

Significance of the triple point

The significance of the triple point lies in its ability to define a standard state for a substance. It has practical implications in science and industry as well, such as calibrating temperature scales and determining the appropriate conditions for handling and storing certain materials. Triple points can also help researchers and engineers design efficient processes involving phase changes, since they mark the boundaries between the different phase regions in a diagram.

Measuring the triple point of water

As mentioned in the exercise, we are given the following conditions: a vessel containing water vapor, liquid water, and ice, all of which are in equilibrium under one atmosphere of air. Unfortunately, we cannot directly measure the triple point of water under these conditions for the following reasons: 1. The triple point of water occurs at a specific pressure, which is about 0.00604 atmospheres (or 611.657 pascals, to be more precise). This value is different from the given atmospheric pressure of one atmosphere, meaning the equilibrium of the three phases won't be at their triple point. 2. The presence of air introduces additional complications. Air is a mixture of gases, including nitrogen, oxygen, and trace amounts of other gases, which can affect the equilibrium between the three phases of water. In order to accurately measure the triple point, you would need a closed system containing only water in its various phases, without any air present. In conclusion, the triple point is an important concept in the study of phase diagrams, as it allows us to understand the behavior of substances at the boundaries of their different phases. However, measuring the triple point requires precise control of both temperature and pressure, and cannot be achieved using the given conditions in this exercise.

Key concepts

Phase Diagram

A phase diagram is a graphical representation that showcases the conditions under which different phases of a substance exist. It maps out the state of a substance (solid, liquid, gas) based on varying temperatures and pressures.
A typical phase diagram features curves that separate different phase regions. These curves represent the equilibrium points where two phases coexist. The meeting point of these curves is known as the triple point.
Phase diagrams are essential in understanding the stability and transitions of materials.

• They allow scientists to predict what phase a substance will be in at any given temperature and pressure.
• They help in determining the conditions necessary for phase changes, such as boiling or melting.

Through phase diagrams, engineers can also design processes where the control of physical states is critical.

Thermodynamic Equilibrium

Thermodynamic equilibrium is a condition where a system's macroscopic properties remain constant over time. In more simple terms, it means that the system is balanced and stable, with no net change occurring.
When all phases of a substance coexist in thermodynamic equilibrium, it implies that the system is at a specific set of temperature and pressure where phase changes happen without any net movement of energy or mass between phases.
This state is crucial when measuring points like the triple point, as all phases must be in equilibrium to accurately define this unique point.

• Equilibrium ensures that the measurements of temperature and pressure are reflective of a true phase state, without external influences.
• It is also a foundational concept used to determine the thermodynamic properties of a system.

Without equilibrium, any readings or predictions about a substance's behavior in different phases would be inaccurate.

Standard State

The concept of a standard state is a reference point used in thermodynamics to describe the properties of elements and compounds under specific conditions.
For gases, the standard state is typically at a pressure of 1 atmosphere and a temperature of 298 K (25°C). This standardization helps in comparing the thermodynamic properties of different substances across various studies and applications.
The triple point of a substance offers a natural standard state, as it is a uniquely defined condition for a specific composition.

• For any substance, the triple point serves as a fundamental reference for temperature calibration, such as with the Kelvin scale, which is based on the triple point of water.
• In practical applications, scientists use standard states to identify and calculate changes in enthalpy, entropy, and Gibbs energy.

Understanding standard state conditions helps in ensuring consistent and reliable data across scientific investigations.

Phase Behavior

Phase behavior refers to the way different phases of a substance transition and interact under varying conditions. Recognizing how substances behave as they change phases is crucial in both everyday life and scientific endeavors.
At the triple point, all three phases of a substance meet, allowing us to observe phase behavior closely. This knowledge is used to help in processes such as refrigeration, purification, and material synthesis.

• The study of phase behavior allows for the optimization of storage and transportation of materials.
• It also aids in the design of chemical processes that rely on phase transitions, like distillation and crystallization.

Understanding phase behavior is vital because it influences how conditions are adjusted to induce desired phase transitions, ensuring efficiency in industrial and laboratory settings.