Questions: Triple Point and Phase Coexistence

Question 1

For a pure substance (one component) with all three phases coexisting, the Gibbs phase rule gives F = 0. What does this imply about the triple point?

• A. The triple point can occur over a range of temperatures at fixed pressure
• B. The triple point is a single unique (T, P) coordinate — there are no free variables to adjust while maintaining three-phase coexistence
• C. The triple point can only exist at atmospheric pressure
• D. F = 0 means the system has zero entropy and is at absolute zero

Answer: (B)

F = C − P + 2 = 1 − 3 + 2 = 0. Zero degrees of freedom means there is no freedom to adjust temperature or pressure while maintaining three-phase coexistence. The triple point is thus a single point on the phase diagram — a specific (T, P) pair — not a line or region. This is why every substance has exactly one triple point, and why water's triple point (273.16 K, 611.7 Pa) is so reproducibly precise that it served as the definition of the Kelvin scale.

Question 2

You heat a solid sample of a substance at a pressure below its triple point pressure. What phase transition sequence occurs?

• A. Solid → liquid → gas, as usual
• B. Solid → gas directly (sublimation), because the liquid phase is thermodynamically unstable below the triple point pressure
• C. No transition occurs — the substance cannot change phase below the triple point pressure
• D. Gas → solid (deposition), because low pressure favors the solid phase

Answer: (B)

Below the triple point pressure, the liquid phase does not appear on the phase diagram as a stable state. As you add heat to a solid at this pressure, you cross directly from the solid region into the vapor region — sublimation. This is exactly why dry ice (solid CO₂) sublimates at atmospheric pressure: CO₂'s triple point is at about 5.1 atm, well above atmospheric pressure, so at 1 atm the liquid phase of CO₂ is inaccessible regardless of temperature.

Question 3

The triple point of water occurs at approximately atmospheric pressure (around 101,325 Pa).

• T. True
• F. False

Answer: False

False — water's triple point is at 611.7 Pa, which is less than 1% of atmospheric pressure (101,325 Pa). This is why we never observe all three phases of water coexisting in everyday conditions: atmospheric pressure is far above the triple point pressure, so as we heat ice at 1 atm, it melts to liquid before it can coexist with vapor. Only in a partial vacuum near 611.7 Pa and 273.16 K would you see ice, liquid water, and water vapor simultaneously.

Question 4

The triple point of a pure substance is a fixed, apparatus-independent (T, P) coordinate that is a fundamental property of that substance.

• T. True
• F. False

Answer: True

True — this is what makes the triple point scientifically powerful. Unlike the normal melting point or boiling point (which change with applied pressure and dissolved impurities), the triple point is defined by thermodynamic equilibrium of three phases, and the Gibbs phase rule guarantees it is fully determined (F = 0). Every sample of pure water, anywhere, will have its triple point at exactly 273.16 K and 611.7 Pa. This reproducibility made it the defining fixed point of the Kelvin temperature scale.

Question 5

Explain using the Gibbs phase rule why the triple point is a single point rather than a line or region on the phase diagram.

Model answer: The Gibbs phase rule is F = C − P + 2, where F is degrees of freedom, C is the number of chemical components, and P is the number of coexisting phases. For a pure substance (C = 1) with three phases coexisting (P = 3): F = 1 − 3 + 2 = 0. Zero degrees of freedom means there are no intensive variables (temperature or pressure) that can be freely adjusted while maintaining three-phase coexistence. The state is completely determined — there is exactly one (T, P) pair where this can occur. A two-phase boundary has F = 1 (a line: you can vary T and P must adjust accordingly). With three phases, all freedom is exhausted and the result is a point.

Contrast with the melting curve: solid and liquid coexist (P = 2), giving F = 1, so coexistence is possible along an entire line of (T, P) pairs. Add a third phase and you lose the last degree of freedom — only one point satisfies all the simultaneous equilibrium conditions.