Problem 58 - Chemistry The Central Science

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 1 atm of air? Explain.

Step-by-Step Solution

Answer

The triple point in a phase diagram is the point where all three phases of a substance (solid, liquid, and gas) can coexist in equilibrium, which defines the unique pressure and temperature conditions required for the simultaneous existence of these three phases. It is significant because it indicates when a substance can transition directly from one state to another without passing through intermediate states. The triple point of water occurs at approximately 0.01°C (273.16 K) and a pressure of 611.7 Pa (0.00604 atm). However, it is not possible to measure the triple point of water in the given scenario, as the air pressure inside the vessel is 1 atm, which is much higher than the required pressure. Therefore, the equilibrium of water vapor, liquid water, and ice under 1 atm of air will not take place at the triple point, and a precise measurement would not be possible.

Step 1: Understanding the Triple Point

The triple point in a phase diagram is the point where all three phases of a substance (solid, liquid, and gas) can coexist in equilibrium. This point is significant because it defines the unique pressure and temperature conditions required for the simultaneous existence of these three phases.

Step 2: Significance of the Triple Point

The triple point holds importance because it indicates the specific conditions when the substance can transition directly from one state to another. For instance, from solid to gas (sublimation) or from gas to solid (deposition) without passing through intermediate states. Additionally, at the triple point, melting point and freezing point are equal, and boiling point and condensation point are equal.

Step 3: Analyzing the Given Scenario

The exercise asks us to explore the possibility of measuring the triple point of water by measuring the temperature in a vessel where water vapor, liquid water, and ice are in equilibrium under 1 atm of air. First, let's consider the triple point of water, which occurs at approximately 0.01°C (273.16 K) and a pressure of 611.7 Pa (0.00604 atm).

Step 4: Explaining the Measurement Possibility

It is not possible to measure the triple point of water in the given scenario, as the air pressure inside the vessel is 1 atm. For the triple point of water to occur, the pressure should be 0.00604 atm, which is much lower than the pressure mentioned in the exercise. As a result, the equilibrium of water vapor, liquid water, and ice under 1 atm of air will not take place at the triple point, and a precise measurement would not be possible.

Key Concepts

Phase Diagram

A phase diagram visually represents the different phases a substance can exist in under varying temperature and pressure conditions. It’s like a map for understanding how matter changes between solid, liquid, and gas. These diagrams have lines that separate different phases and areas that show the conditions where a phase is stable. Crossing a line means changing from one phase to another, like ice melting into water.

The most important part of a phase diagram is where all lines intersect at one point, called the triple point. Here, all three phases coexist in perfect harmony. For many substances, the phase diagram can explain everyday phenomena, such as why ice floats or how you can boil water at room temperature in a vacuum.

Using these diagrams, scientists and students can predict how substances behave at different conditions and understand concepts related to material science, chemistry, and even meteorology.

Phase Equilibrium

Phase equilibrium occurs when different phases of a substance exist together without any change over time. Each phase is stable and does not change into another phase, despite being in contact. At equilibrium, the rates of change between phases are balanced. For example, water might evaporate into vapor at the same rate that vapor condenses into liquid.

This concept is essential when talking about the triple point on a phase diagram. At the triple point, solid, liquid, and gas forms of a substance can all exist together in perfect balance. Understanding phase equilibrium helps scientists control processes such as distillation or crystallization, where maintaining balance between phases is crucial.

This equilibrium is also the reason why ice and liquid water can coexist in a glass at 0°C, as long as conditions remain constant.

Pressure and Temperature Conditions

Pressure and temperature conditions define the specific point on a phase diagram where a substance changes phases. Imagine them like dials on a machine that lets you move from solid to liquid to gas. By adjusting these dials, you can reach any phase of the substance.

For instance, you need to know about specific pressure and temperature conditions to understand the triple point of water. The triple point is where all three phases meet, and for water, it happens at precisely 0.01°C and a pressure of 611.7 Pa (or 0.00604 atm). This is much lower than the standard atmospheric pressure of 1 atm.

In daily life, understanding these conditions can explain why water boils at lower temperatures in high altitudes or how pressure cookers can speed up cooking by using higher pressures to increase the boiling point of water. These conditions are vital for industrial processes and scientific experiments where controlling phase changes is key.