A substance's solid-liquid phase boundary has a negative slope (dP/dT < 0) on its phase diagram. What physical property of the substance does this imply?
AThe solid phase is denser than the liquid phase, so pressure stabilizes the solid
BThe liquid phase is denser than the solid phase — applying pressure destabilizes the solid, favoring the denser liquid
CThe latent heat of melting is negative, meaning the substance releases energy upon melting
DThe substance sublimes rather than melts at atmospheric pressure
The Clausius-Clapeyron slope is dP/dT = L/(TΔv), where Δv = v_liquid − v_solid. A negative slope means Δv < 0, i.e., the liquid is denser than the solid (v_liquid < v_solid). Water is the classic example: ice is less dense than liquid water, so applying pressure favors the denser liquid phase and melts the ice. This anomalous negative slope is why ice skating works and why increased pressure can melt ice below 0°C.
Question 2 Multiple Choice
Why does solid CO₂ (dry ice) sublime directly to gas at atmospheric pressure, without passing through a liquid phase?
ACO₂ is a gas at room temperature, so its solid form is metastable and immediately decomposes
BCO₂'s triple point is at 5.1 atm — atmospheric pressure is below the triple point, so the liquid phase is never stable at 1 atm
CCO₂ lacks a liquid-gas coexistence curve because it is a linear molecule
DThe critical point of CO₂ is below room temperature, which eliminates the liquid phase entirely
A horizontal line at 1 atm on CO₂'s phase diagram crosses from the solid region directly into the gas region — it never passes through the liquid region, because the liquid region only exists above 5.1 atm. The triple point is the minimum pressure at which liquid CO₂ can exist. Below that pressure, you move directly from solid to gas (sublimation) as temperature increases. The location of the triple point is thus directly diagnostic of whether a substance can be liquid at a given pressure.
Question 3 True / False
The triple point of a substance is a small range of temperatures and pressures where most three phases can coexist, and its location shifts depending on how quickly the sample is heated.
TTrue
FFalse
Answer: False
The triple point is a unique, invariant point — a single specific temperature and pressure where all three phases simultaneously coexist in equilibrium. It is fixed by the molecular properties of the substance. It is so reproducible that the triple point of water (273.16 K, 611.7 Pa) serves as a primary calibration standard for thermometry. Heating rate, sample history, and external conditions do not affect where the triple point is — they can affect whether you reach it, but not its location.
Question 4 True / False
Above the critical point, increasing pressure on a gas will eventually trigger a sharp, discontinuous condensation transition to liquid.
TTrue
FFalse
Answer: False
The critical point is precisely where the sharp liquid-gas distinction disappears. Above T_c and P_c, there is only one supercritical fluid phase — no phase boundary exists, and you can move continuously from gas-like to liquid-like conditions without any discontinuous transition. Supercritical CO₂, used in industrial extraction, exploits this: its density and solvent power vary continuously with pressure, with no sudden phase jump.
Question 5 Short Answer
At any point on a phase boundary in a phase diagram, what determines which phase is stable on each side, and what is true right at the boundary itself?
Think about your answer, then reveal below.
Model answer: On each side of a boundary, the stable phase is the one with the lower Gibbs free energy G = U + PV − TS at those conditions. Different phases have different T and P dependences of G (primarily through their entropy and volume differences). At the boundary itself, both phases have exactly equal Gibbs free energy — this coexistence condition G₁(T,P) = G₂(T,P) defines the curve, and the Clausius-Clapeyron equation gives its slope dP/dT = L/(TΔv).
This equal-G framework unifies all phase behavior: the ice-water boundary has a particular slope because of water's anomalous density; CO₂ has its triple point at high pressure because of its molecular interactions; the critical point is where the G difference between liquid and gas vanishes continuously. Reading a phase diagram as a map of Gibbs free energy minimization turns a collection of empirical facts into a single coherent principle.