Phase diagrams show which phase or phases of a substance are stable at different conditions. This cheat sheet covers pure substance diagrams using pressure and temperature, plus binary diagrams that show composition and temperature at fixed pressure. Students need it to predict melting, boiling, sublimation, and mixtures during heating or cooling.
It also helps connect graph features to lab observations like boiling points, eutectic mixtures, and phase changes.
Key Facts
- For a pure substance phase diagram, each region represents one stable phase, such as solid, liquid, gas, or supercritical fluid.
- A phase boundary shows two phases in equilibrium, so points on the liquid vapor line represent liquid and gas coexisting.
- The triple point is the unique condition where solid, liquid, and gas coexist in equilibrium at one and one .
- The critical point is the end of the liquid vapor boundary, above which the substance is a supercritical fluid and liquid gas distinction disappears.
- The Gibbs phase rule is , where is degrees of freedom, is components, and is phases.
- For a binary phase diagram at constant pressure, the condensed phase rule is , so for , .
- In a two phase region of a binary diagram, a horizontal tie line gives the compositions of the two phases at that temperature.
- The lever rule for two phases is , where is the overall composition.
Vocabulary
- Phase diagram
- A graph that shows the stable phases of a substance or mixture under different conditions such as temperature, pressure, and composition.
- Triple point
- The temperature and pressure where solid, liquid, and gas phases of a pure substance coexist in equilibrium.
- Critical point
- The end of the liquid vapor equilibrium curve where the liquid and gas phases become indistinguishable.
- Eutectic point
- The lowest melting temperature in a binary system where a liquid transforms into two solid phases at a fixed composition.
- Tie line
- A horizontal line across a two phase region of a binary phase diagram used to read the compositions of coexisting phases.
- Lever rule
- A method for calculating the relative amounts of two coexisting phases from distances along a tie line.
Common Mistakes to Avoid
- Confusing a phase boundary with a single phase region is wrong because a boundary means two phases coexist in equilibrium, not one phase only.
- Reading binary diagram composition from the wrong axis is wrong because composition is usually on the horizontal axis, while temperature is usually on the vertical axis.
- Using the overall composition as the composition of each phase is wrong because the phase compositions must be read from the ends of the tie line.
- Applying the full phase rule to a constant pressure binary diagram is wrong because constant pressure removes one variable, giving .
- Assuming all substances have the same solid liquid boundary slope is wrong because substances like can have a negative melting curve slope while many substances have a positive one.
Practice Questions
- 1 A pure substance has and is in a single phase region. Use to find .
- 2 At the triple point of a pure substance, and . Use to find and explain what it means.
- 3 A binary alloy has overall composition B. At a certain temperature, the tie line endpoints are B and B. Use to find the phase mass ratio.
- 4 Why does crossing a phase boundary on a pure substance phase diagram cause a phase change, while moving within one region does not?
Understanding Phase Diagrams (Pure Substance & Binary)
A phase diagram becomes useful when you treat a change in conditions as a journey across the graph. On the usual pressure and temperature diagram, heating at constant pressure moves horizontally to the right. Compressing a sample at constant temperature moves upward.
Each time the path crosses a boundary, energy goes into rearranging particles rather than simply raising their temperature. This is why a heating curve can flatten during melting or boiling.
The added energy breaks or weakens attractions between particles. The temperature remains nearly steady until the change is complete.
The shape of a boundary carries physical meaning. Along the liquid to gas boundary, higher temperature requires higher pressure to keep particles close enough to remain liquid. This connects directly to vapor pressure and boiling.
A liquid boils when its vapor pressure matches the surrounding pressure. At high altitude, lower air pressure means this match occurs at a lower temperature, so water boils below its usual temperature. The solid to liquid boundary can reveal density differences.
Water is unusual because its solid form is less dense than its liquid form. Increasing pressure can therefore favor liquid water over ice, although this effect is small in most everyday situations.
The phase rule is best understood as a counting tool. It tells you how many conditions can be changed independently without changing the number of phases present. For one pure substance in a single phase area, pressure and temperature can both vary.
On a boundary, choosing one fixes the other if both phases must remain present. At the triple point, neither can be freely changed while keeping all three phases together.
This helps students avoid treating every point on a graph as equally flexible. Some conditions are broad ranges, while others are tightly constrained.
Binary diagrams need extra care because composition has two meanings. The overall composition describes the complete sample. The compositions at the ends of a tie line describe the individual phases within that sample.
During cooling, a solid may form with a composition different from the original liquid. The remaining liquid then becomes richer in the other component. The lever rule finds how much of each phase is present, not the composition of each phase.
The phase amount is proportional to the opposite section of the tie line. Use the same composition scale throughout, whether it is mass percent or mole percent.
Real materials rarely reach equilibrium instantly. Cooling an alloy quickly can trap atoms in arrangements that differ from the diagram prediction. Some reactions are slow, and small crystals may form before the whole sample can adjust.
Phase diagrams still give the equilibrium destination, while cooling rate explains whether the material reaches it. When studying, identify the axes first, note whether pressure is fixed, then trace a path from the starting condition to the final condition.
Label the phases encountered, their compositions, and their relative amounts separately. This prevents the most common errors in diagram questions.