Question

The phase diagram of a hypothetical substance is (a) Estimate the normal boiling point and freezing point of the substance. (b) What is the physical state of the substance under the following conditions: (i) \(T=150 \mathrm{~K}, P=0.2 \mathrm{~atm}\) (ii) \(T=100 \mathrm{~K}, P=0.8 \mathrm{~atm},(\mathrm{iii}) T=300 \mathrm{~K}, P=1.0 \mathrm{~atm} ?\) (c) What is the triple point of the substance? [Section 11.6\(]\)

Short answer

The normal boiling point and freezing point can be estimated by locating the intersection points of the melting and vaporization curves with the 1 atm pressure line on the phase diagram. The physical state of the substance under the given conditions can be determined by locating the corresponding points on the phase diagram and identifying the phase: (i) T=150 K, P=0.2 atm; (ii) T=100 K, P=0.8 atm; (iii) T=300 K, P=1.0 atm. The triple point is found by locating the point on the phase diagram where all three phase lines meet.

Step-by-step solution

Estimate the normal boiling point and freezing point

On a phase diagram, the line separating the solid and liquid phases is the melting curve. The point where this curve intersects the line indicating atmospheric pressure (1 atm) represents the normal freezing point. Similarly, the line separating the liquid and gas phases is the vaporization curve, and its intersection with the atmospheric pressure line represents the normal boiling point. To estimate these points, examine the given phase diagram and locate the intersection points of the melting and vaporization curves with the 1 atm pressure line.

Determine the physical state under the given conditions

For each of the given conditions, locate the point corresponding to the temperature (T) and pressure (P) on the phase diagram. Then, identify the phase (solid, liquid, or gas) the substance is in at that point. (i) T=150 K, P=0.2 atm (ii) T=100 K, P=0.8 atm (iii) T=300 K, P=1.0 atm

Find the triple point of the substance

The triple point is a unique point on a phase diagram where all three phases (solid, liquid, and gas) coexist in equilibrium. To find it, locate the point where the solid-liquid, liquid-gas, and solid-gas lines all meet on the phase diagram.

Key concepts

Normal Boiling Point

The normal boiling point of a substance is an essential concept on the phase diagram. It is the temperature at which the substance transitions from a liquid to a gas under atmospheric pressure of 1 atm. The phase diagram visually represents this with a curve known as the vaporization curve.
Understanding the intersection of this curve with the 1 atm line is crucial because:

• It helps determine the temperature at which a liquid will start to boil under standard conditions, meaning no additional pressure applied.
• Knowing the normal boiling point allows for the prediction of phase changes under different scenarios.
• It is relevant for processes such as distillation where boiling points play a critical role.

By examining the phase diagram, you can find the vaporization curve and where it crosses the line for 1 atm to accurately estimate the normal boiling point. This straightforward observation provides a valuable understanding of how substances behave at different temperatures and pressures.

Freezing Point

The freezing point, another key feature of a phase diagram, marks the temperature where a liquid becomes a solid at 1 atm. On the phase diagram, this is indicated where the melting curve intersects the atmospheric pressure line.
Here’s why it's important:

• The freezing point tells us about the temperature at which a liquid solidifies, which is essential in studying the thermal properties of materials.
• It is particularly significant in climatic and environmental studies, affecting how substances behave in natural settings.
• Understanding freezing points aids in determining suitable conditions for storage and use of various substances.

In practice, when you look at the phase diagram, you aim to find where the line dividing solid and liquid phases meets the 1 atm pressure line. This provides a visual cue that helps estimate the freezing point quickly and efficiently.

Triple Point

The triple point is a fascinating concept in phase diagrams as it represents a unique set of conditions where all three phases, namely solid, liquid, and gas, coexist in equilibrium. It is a point where the solid-liquid, liquid-gas, and solid-gas lines meet.
This point is critical because:

• It signifies the only conditions under which all three phases can stably exist together.
• Understanding the triple point allows scientists to explore the fundamental properties of substances.
• It provides insight into the precise conditions needed for phase transitions, useful in scientific experiments and applications.

To find the triple point, one must locate the intersection of all three phase boundary lines on the phase diagram. This helps in the accurate prediction of phase stability and transitions under different temperatures and pressures.