Phase Rule ll Lec # 4 ll Phase Diagram of Sulphur ll Dr Rizwana

TL;DR

Sulfur is modeled as a one-component system with four phases: rhombic solid, monoclinic solid, liquid sulfur, and sulfur vapor.

Briefing Cornell Notes

Briefing

Sulfur’s one-component phase diagram behaves differently from water’s because sulfur has multiple solid phases (including two solid allotropes) that can coexist at distinct “triple-point” conditions. In this system, temperature and pressure determine which phases—solid allotropes, liquid, or vapor—are stable, and equilibrium occurs along specific curves that separate phase regions.

The lecture frames sulfur as a one-component system with four phases in total: two solid forms (one described as rhombic and the other as monoclinic), plus liquid sulfur and sulfur vapor. As temperature increases at a given pressure, the diagram shows regions where only one phase is stable: solid (in different allotropic forms), liquid, or vapor. The key difference from water is how triple points appear. Water’s three phases meet at a single point (a single triple point), but sulfur’s diagram contains three triple points—meaning there are three separate conditions where any three phases coexist in equilibrium.

On the diagram, the axes are temperature (x-axis) and pressure (y-axis). The rhombic solid is stable in one region, monoclinic solid in another, liquid occupies its own region, and vapor occupies a fourth. Curves mark equilibrium boundaries between pairs of phases. A prominent sublimation curve represents the equilibrium between solid sulfur and sulfur vapor, described as the direct conversion of a solid into vapor. Additional boundary lines separate rhombic solid from monoclinic solid, rhombic solid from liquid, monoclinic solid from liquid, and liquid from vapor. Moving through these regions by changing temperature and pressure forces sulfur to transform from one phase to another.

The lecture then applies Gibbs phase rule to interpret degrees of freedom (F). For a one-component system, the general form is F = C − P + 2, where C is components (here C = 1). In most phase regions where only one phase is present (P = 1), the degrees of freedom come out as F = 2, meaning both temperature and pressure can vary independently while staying in the same single-phase region. Along equilibrium curves where two phases coexist (P = 2), the degrees of freedom drop to F = 1. At triple points where three phases coexist (P = 3), the degrees of freedom become F = 0, so temperature and pressure are fixed at those points.

Finally, the lecture connects the phase diagram to boiling and critical behavior. As temperature rises, liquid eventually reaches a boiling point where vapor begins to form; at the critical temperature and critical pressure, only vapor is observed. Overall, sulfur’s multiple triple points—unlike water’s single triple point—make it a useful exam-style comparison for predicting how many triple points exist and for calculating degrees of freedom in each region of a one-component phase diagram.

Cornell Notes

Sulfur is treated as a one-component system with four phases: rhombic solid, monoclinic solid, liquid sulfur, and sulfur vapor. Temperature and pressure define regions where only one phase is stable, while boundary curves mark conditions where two phases coexist (e.g., solid–vapor for sublimation, solid–liquid, and liquid–vapor). The diagram includes three distinct triple points where three phases coexist, unlike water’s single triple point. Using Gibbs phase rule for C = 1, degrees of freedom are F = 2 in single-phase regions, F = 1 along two-phase equilibrium lines, and F = 0 at triple points where temperature and pressure are uniquely fixed. Critical temperature and critical pressure mark the end of the liquid–vapor distinction.

Why does sulfur’s phase diagram have multiple triple points, and what does that mean physically?

Sulfur has multiple solid allotropes (rhombic and monoclinic) in addition to liquid and vapor. Because different combinations of three phases can coexist under different temperature–pressure conditions, the diagram contains three separate triple points. Each triple point is a fixed condition (degrees of freedom F = 0) where exactly three phases—such as rhombic solid + liquid + vapor, or rhombic + monoclinic + liquid (depending on the specific triple point)—are in equilibrium simultaneously.

What do the equilibrium curves represent on the sulfur phase diagram?

Each curve separates two phase regions and corresponds to equilibrium between those two phases. For example, the sublimation curve represents solid sulfur ↔ sulfur vapor (direct solid-to-vapor equilibrium). Other lines represent equilibrium between rhombic solid and monoclinic solid, rhombic solid and liquid, monoclinic solid and liquid, and liquid and vapor. Crossing these curves by changing temperature or pressure forces a phase transformation.

How does Gibbs phase rule determine degrees of freedom in different parts of the diagram?

For a one-component system, Gibbs phase rule is F = C − P + 2 with C = 1. In single-phase regions (P = 1), F = 1 − 1 + 2 = 2, so both temperature and pressure can vary while remaining in that phase. Along two-phase equilibrium lines (P = 2), F = 1 − 2 + 2 = 1, so only one independent variable can change. At triple points (P = 3), F = 1 − 3 + 2 = 0, so temperature and pressure are fixed.

What is the significance of the sublimation curve in sulfur’s diagram?

The sublimation curve marks conditions where solid sulfur and sulfur vapor coexist in equilibrium. It reflects the direct conversion of a solid into vapor without passing through the liquid phase. On the diagram, this curve separates the solid region from the vapor region.

How do boiling and critical behavior relate to the liquid–vapor boundary?

As temperature increases, the system reaches a boiling point where liquid and vapor begin to coexist along the liquid–vapor equilibrium line. With further heating, the liquid–vapor distinction disappears at the critical temperature and critical pressure, where only vapor is present. Those critical values are the endpoint of the liquid–vapor coexistence behavior.

Review Questions

In sulfur’s one-component phase diagram, what phases coexist at a triple point, and what does F = 0 imply about temperature and pressure there?
Using F = C − P + 2 with C = 1, compute degrees of freedom for (a) a single-phase region, (b) a two-phase equilibrium line, and (c) a triple point.
Why does sulfur have three triple points while water has only one, based on the number and types of phases involved?

Key Points

1
Sulfur is modeled as a one-component system with four phases: rhombic solid, monoclinic solid, liquid sulfur, and sulfur vapor.
2
Temperature and pressure define phase-stability regions; boundary curves mark where two phases coexist in equilibrium.
3
Sulfur’s diagram contains three triple points (three distinct fixed T–P conditions where three phases coexist), unlike water’s single triple point.
4
Gibbs phase rule for C = 1 gives F = 2 in single-phase regions, F = 1 along two-phase equilibrium curves, and F = 0 at triple points.
5
The sublimation curve represents solid–vapor equilibrium (solid converting directly to vapor).
6
Boiling corresponds to the liquid–vapor coexistence line; critical temperature and critical pressure mark the point where only vapor remains.

Highlights

Sulfur’s multiple solid allotropes create three separate triple points, each with fixed temperature and pressure (degrees of freedom F = 0).

Equilibrium curves separate phase regions and include a sublimation curve for solid–vapor coexistence.

Degrees of freedom follow a clear pattern: F = 2 (single phase), F = 1 (two phases), and F = 0 (three phases at triple points).

Critical temperature and critical pressure end the liquid–vapor distinction, leaving only vapor. 

Topics

Phase Diagrams
Sulfur Allotropes
Gibbs Phase Rule
Triple Points
Sublimation Curve

Mentioned

Dr Rizwana Mustafa