12.3 Phase Changes & Phase Diagrams
Key Takeaways
- Water's heat of fusion is approximately 80 cal/g (334 J/g) and its heat of vaporization is approximately 540 cal/g (2,260 J/g) — vaporization requires roughly six to seven times more energy than melting.
- Heat required for a phase change follows q = mL, which applies only at the constant-temperature phase-change plateau, never across a temperature change within a single phase (that instead requires q = mcΔT).
- The triple point is the unique pressure and temperature at which the solid, liquid, and gas phases of a substance coexist in equilibrium simultaneously; for water this occurs at 0.01°C and about 0.006 atm.
- Beyond the critical point on a phase diagram, the liquid and gas phases become indistinguishable, forming a single supercritical fluid.
- Water's solid-liquid phase boundary has an unusual negative slope because ice is less dense than liquid water, so increased pressure can melt ice at a fixed temperature near 0°C.
Phase changes — melting, freezing, vaporizing, condensing, subliming — are where thermodynamics becomes visible: a substance's physical state itself transforms, even while temperature holds perfectly constant during the transition. This section covers the quantities describing those transitions (thermal expansion and latent heat), the structure of heating curves, vapor pressure, and the phase diagram — the single graph summarizing which phase a substance occupies at any given pressure and temperature. Biological systems live almost entirely in the liquid-water region of water's phase diagram, but understanding boundaries and latent heats explains sweating, freeze injury, and why steam burns are severe.
Coefficient of Thermal Expansion
Most materials expand when heated and contract when cooled, because higher average kinetic energy increases the average spacing between particles. The coefficient of linear expansion (α) describes how much a solid's length changes per degree of temperature change:
ΔL = αL0ΔT
where L0 is the original length. For volumes — liquids, gases, or three-dimensional solids — the analogous relationship uses the coefficient of volume expansion (β), where β ≈ 3α for isotropic solids:
ΔV = βV0ΔT
Water is the MCAT's favorite exception to normal thermal expansion. Between 0°C and 4°C, liquid water actually contracts as it warms, reaching its maximum density at 4°C before expanding normally above that temperature. This unusual behavior is also why ice is less dense than liquid water and floats on it — a fact that returns in the phase-diagram discussion below. In lakes, the 4°C density maximum allows denser water to sink in winter while ice forms at the surface, insulating aquatic life rather than freezing the lake solid from the bottom up.
Heat of Fusion and Heat of Vaporization
A phase change — melting, freezing, vaporizing, condensing, subliming, or depositing — happens at constant temperature: all the heat added or removed goes into breaking or forming intermolecular attractions, not into raising kinetic energy or temperature. The heat required is:
q = mL
where L is the latent heat for that specific transition, a substance-specific constant, and m is mass. The heat of fusion (Lf) applies to melting and freezing; the heat of vaporization (Lv) applies to vaporizing and condensing. For water:
- Lf ≈ 80 cal/g (334 J/g) at 0°C
- Lv ≈ 540 cal/g (2,260 J/g) at 100°C
Notice Lv is roughly six to seven times larger than Lf. Vaporization demands far more energy than melting because it must fully separate molecules from all of their neighbors, overcoming essentially all intermolecular attraction, while melting only needs to disrupt rigid lattice order, leaving most attractive interactions intact within the resulting liquid.
Sign convention: q is positive for melting and vaporizing (heat absorbed, endothermic) and negative for freezing and condensing (heat released, exothermic), even though L itself is always tabulated as a positive number — the direction of the process, not the constant, sets the sign.
Sublimation (solid → gas) and deposition (gas → solid) skip the liquid phase. Dry ice (solid CO2) sublimes at atmospheric pressure; freeze-drying of biological samples exploits sublimation of ice under reduced pressure to remove water while preserving structure.
Worked Example: Heating Ice to Steam
How much heat is required to convert 10 g of ice at 0°C into steam at 100°C? This is a three-step problem, and each step must be calculated separately, because q = mcΔT applies only within a single phase, while q = mL applies only at the constant-temperature phase-change plateau.
Step 1 — melt the ice at 0°C: q1 = mLf = (10 g)(80 cal/g) = 800 cal
Step 2 — heat the liquid water from 0°C to 100°C: q2 = mcΔT = (10 g)(1 cal/g·°C)(100°C) = 1,000 cal
Step 3 — vaporize the water at 100°C: q3 = mLv = (10 g)(540 cal/g) = 5,400 cal
Total: q = q1 + q2 + q3 = 800 + 1,000 + 5,400 = 7,200 cal (7.2 kcal)
Notice that vaporization alone, step 3, accounts for 75% of the total heat — far more than melting or heating the liquid combined. This is exactly why steam burns are more severe than boiling-water burns at the same temperature: condensing steam releases its full 540 cal/g of latent heat directly into skin, on top of whatever further cooling happens afterward. Sweating works in reverse: evaporation of water from the skin absorbs large amounts of heat from the body (high Lv), cooling core temperature efficiently with relatively little mass of water lost.
How much heat is released when 5 g of steam at 100°C condenses completely into liquid water at 100°C? (Use water's heat of vaporization, 540 cal/g.)
Heating Curves
A heating curve plots temperature (y-axis) versus heat added (x-axis) for a fixed mass of substance. The curve has sloping segments where a single phase warms according to q = mcΔT, and flat plateaus where a phase change occurs at constant temperature according to q = mL. For water starting as ice below 0°C, the sequence is typically: heat solid ice → melt at 0°C (plateau) → heat liquid water → boil at 100°C (longer plateau, because Lv ≫ Lf) → heat steam.
On the MCAT, reading a heating curve means identifying which segment corresponds to which process, estimating relative latent heats from plateau lengths, and recognizing that temperature does not rise during a pure phase change even while energy is continuously added. Cooling curves reverse the sequence: condensation and freezing plateaus release heat (exothermic) while temperature holds steady.
Vapor Pressure and Boiling
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or solid) phase at a given temperature. Stronger intermolecular forces lower vapor pressure; higher temperature raises vapor pressure because more molecules have enough kinetic energy to escape into the gas phase. Boiling occurs when vapor pressure equals external atmospheric pressure — which is why water boils below 100°C at high altitude (lower atmospheric pressure) and above 100°C in a pressure cooker (higher external pressure).
This equilibrium between liquid and vapor is a dynamic balance: molecules continuously evaporate and condense at equal rates when the vapor pressure is established. The same idea appears later in chemical equilibrium (Section 12.5): forward and reverse rates match while macroscopic composition is constant.
Phase Diagrams: Triple Point and Critical Point
A phase diagram plots pressure on the y-axis against temperature on the x-axis and divides the graph into regions showing which phase — solid, liquid, or gas — is stable at each pressure-temperature combination. Three curves separate these regions: the melting (fusion) curve (the solid-liquid boundary), the vaporization (vapor pressure) curve (the liquid-gas boundary, ending at the critical point), and the sublimation curve (the solid-gas boundary).
Two special points matter most for the MCAT. The triple point is the unique pressure and temperature at which all three phases — solid, liquid, and gas — coexist simultaneously in equilibrium. It is a single fixed point for any given substance; water's triple point sits at 0.01°C and about 0.006 atm.
The critical point marks the end of the liquid-gas boundary curve. Beyond the critical temperature and critical pressure, the distinction between liquid and gas disappears entirely: the substance becomes a supercritical fluid with properties of both, and no amount of additional pressure will condense it back into a distinct liquid phase. Supercritical CO2 is used industrially for extractions (e.g., decaffeination) because its density and solvating power can be tuned by pressure without a liquid-gas interface.
Water's phase diagram has one famous quirk: its solid-liquid melting boundary has a negative slope, meaning increasing pressure on ice at a fixed temperature near 0°C can actually melt it, because liquid water is denser than ice. This is the opposite pattern from almost every other substance, where the solid form is denser than the liquid and the melting curve slopes positively instead. This negative slope is directly connected to why ice floats: the solid phase occupies more volume than the liquid phase for water specifically. Pressure melting of ice is also the classic (if simplified) explanation for how ice skates can lower the melting point of a thin film of ice under the blade.
Reading Phase Diagrams on Test Day
- Identify the three regions (solid, liquid, gas) — solid is usually the high-P, low-T corner; gas is low-P, high-T; liquid is in between.
- Locate the triple point (intersection of all three curves) and the critical point (end of the liquid-gas curve).
- Follow a horizontal (isobaric) or vertical (isothermal) path to predict which phase transitions occur as T or P changes.
- For water specifically, check the solid-liquid boundary slope — negative, not positive.
On a substance's phase diagram, at what point do the solid, liquid, and gas phases all coexist simultaneously in equilibrium?
Ice floats on liquid water, and applying additional pressure to ice near 0°C can cause it to melt. What do these two observations indicate about water's solid-liquid phase boundary compared to that of most other substances?
Common MCAT Traps
- Assuming temperature rises continuously while heating a substance. Temperature stays constant during any pure phase change, producing the flat plateaus on a heating curve — all added energy goes into the phase transition itself, not into raising temperature, until the transition is complete.
- Applying q = mcΔT across a phase change. Specific heat applies only within a single phase; crossing a melting or boiling point always requires switching to q = mL for that step, as in the ice-to-steam example above.
- Confusing the triple point with an everyday boiling or melting point. The triple point occurs at a specific, often sub-atmospheric pressure — about 0.006 atm for water — which is not the same as the familiar 0°C and 100°C values defined at 1 atm.
- Forgetting that a supercritical fluid is neither liquid nor gas. Past the critical point, there is no phase boundary left to cross and no latent heat to add; further heating or compression just changes density continuously instead of triggering a phase change.
- Assuming all solids are denser than their liquids. Water is the high-yield exception; its negative solid-liquid slope and floating ice both follow from ice's lower density.
- Mixing vaporization with boiling. Evaporation can occur at any temperature below the boiling point from the liquid surface; boiling is the bulk process that begins when vapor pressure equals external pressure throughout the liquid.