Problem 58 - Chemistry The Central Science In Si Units

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.

Step-by-Step Solution

Answer

The triple point is where solid, liquid, and gas phases coexist. You cannot measure the triple point of water at 101.32 kPa, as it differs from the triple point pressure and temperature.

Step 1: Understanding the Triple Point

The triple point of a substance is a specific condition on a phase diagram where the three phases (solid, liquid, and gas) coexist in equilibrium. At this point, the temperature and pressure are fixed and unique for each substance. For water, the triple point occurs at 273.16 K and 0.6117 kPa.

Step 2: Examining the Given Condition

The problem specifies a condition of 101.32 kPa air pressure. This is much higher than the pressure at water's triple point, which is 0.6117 kPa. At 101.32 kPa, water's phases cannot coexist as they do at the triple point.

Step 3: Critical Analysis: Can Triple Point Be Measured?

To accurately measure the triple point, water, ice, and vapor must be at their equilibrium under the conditions of 273.16 K and 0.6117 kPa. The provided conditions of 101.32 kPa do not match these requirements, hence measuring the triple point under such conditions is not possible.

Key Concepts

Phase Diagram

A phase diagram is a graphical representation that showcases the different phases of a substance under varying temperature and pressure. It serves as a map that illustrates how substances like water transition between solid, liquid, and gas phases.

In these diagrams, the lines represent the borders or boundaries where two phases can exist in equilibrium. For water, these lines merge at a specific point known as the triple point. Each segment of the diagram provides valuable information about what phase a substance will be in given specific temperature and pressure conditions.

Water Equilibrium

At the triple point, water achieves a unique state of equilibrium where its solid, liquid, and gas phases can coexist. Equilibrium here means that each phase exists without any phase outnumbering another; they maintain balance seamlessly.

This equilibrium occurs at precise conditions, characterized by a temperature of 273.16 K and a very low pressure of 0.6117 kPa. It’s a significant scientific benchmark as it allows the precise calculations and calibration necessary in many scientific procedures.

Temperature and Pressure Conditions

Temperature and pressure are fundamental factors affecting the phase of water. In general, decreasing temperature or increasing pressure transitions water from gas to liquid and then to solid. The specific values of temperature and pressure determine which phase will predominantly appear.

For the triple point of water, the necessary conditions are precise: a temperature of 273.16 K and a pressure of 0.6117 kPa. Under these conditions, the phase change occurs uniformly without favoring one state.

Triple Point Measurement

The process of measuring the triple point involves ensuring that water reaches equilibrium under exact conditions. These conditions are critical: a temperature of 273.16 K and a pressure of 0.6117 kPa. If either parameter deviates, the triple point cannot be accurately measured.

In practical scenarios, measuring the triple point requires specialized vacuum apparatus to maintain the low pressure and calibrated thermometers or sensors to ensure the correct temperature. For example, at standard atmospheric pressure (101.32 kPa), these conditions cannot be met, making the measurement of the triple point impossible in such an environment.