Reading a Phase Diagram: Water – Phase Diagrams (Senior 5 Chemistry) | Ganzaa

Phase Diagrams

Lessons

Senior 5 · Chemistry

Phase Diagrams

4 lessons

Lesson 2 of 4

Reading a Phase Diagram: Water

25 min

One map for three states

An iceberg floats with about nine-tenths of its volume below the sea surface. Ice floats because it is less dense than liquid water: when water freezes, its molecules lock into an open, hydrogen-bonded lattice that takes up about 9 % more space. That single fact gives water's phase diagram a shape found in very few other substances. A phase diagram is a map: choose a temperature and a pressure, and it tells you which phase is stable there.

Definition

Phase diagram: a graph of pressure against temperature showing the conditions under which each phase of a substance is stable.

Phase boundary (equilibrium curve): a line on the diagram along which two phases are in equilibrium: the melting (fusion), vaporisation and sublimation curves.

Triple point: the single temperature and pressure at which solid, liquid and gas are all in equilibrium. Water: 0.01 °C (273.16 K) and 611.657 Pa.

Critical point: the end of the liquid–gas curve, above which liquid and gas can no longer be told apart. Water: 373.946 °C and 22.064 MPa. Above the critical temperature a gas cannot be liquefied by pressure alone; the substance is a supercritical fluid.

Sublimation: the direct change from solid to gas (and deposition, gas to solid).

Figure 10.2: The phase diagram of water. The axes are stretched so that every feature can be seen; the pressure scale covers more than five powers of ten.

Reading the diagram

Areas: one phase is stable. You can change both temperature and pressure (a little) and stay in the area.
Lines: two phases coexist in equilibrium. The vaporisation curve, from the triple point to the critical point, is the vapour pressure curve of Lesson 1; where it meets 101.3 kPa you read the normal boiling point, 100 °C. Pick a temperature on a line and the pressure is fixed.
Triple point: all three phases coexist, and neither the temperature nor the pressure can change. It is so reproducible that it was used to define the kelvin.
Critical point: the liquid–gas line stops. Beyond it the density of the "liquid" and the "gas" have become equal and the boundary between them disappears.

The number of variables you can change freely is given by the phase rule, $F = C - P + 2$ , where $C$ is the number of components (1 for pure water) and $P$ the number of phases present: $F = 2$ in an area, 1 on a line and 0 at the triple point.

Why the melting line leans to the left

For almost every substance the solid is denser than the liquid, so squeezing a liquid favours the solid and raises the melting point: the melting line leans to the right. Ice is the exception. One mole of ice occupies 19.65 cm³, one mole of liquid water at 0 °C 18.02 cm³. By Le Chatelier's principle, raising the pressure on ice at its melting point favours the change that reduces volume, ice → water, so ice melts at a lower temperature under pressure. The melting line therefore slopes up to the left: experimentally the melting point falls by about 0.0075 °C for each extra atmosphere.

Following a path across the diagram

Heat ice at 101.3 kPa from −20 °C (move right along the dashed line): it melts at 0 °C, the liquid warms, and it boils at 100 °C. Repeat at 0.3 kPa, below the triple-point pressure: the horizontal line now passes from the solid area straight into the gas area, so the ice sublimes. Liquid water cannot exist at any pressure below 0.61 kPa.

Worked example

Problem. Use Figure 10.2 to describe what happens when (a) water vapour at 150 °C and 101.3 kPa is compressed at constant temperature to 1 MPa; (b) steam at 400 °C is compressed to 30 MPa; (c) ice at −5 °C and 101.3 kPa is put under steadily increasing pressure.

Solution.

Moving straight up at 150 °C, the line crosses the vaporisation curve (at about 0.48 MPa, the vapour pressure of water at 150 °C): the vapour condenses, and at 1 MPa the water is liquid.
400 °C is above the critical temperature, 374 °C, so no liquid forms at any pressure; at 30 MPa (above 22.1 MPa) it is a supercritical fluid.
Moving straight up at −5 °C, the line eventually crosses the leftward-leaning melting curve, and the ice melts under pressure, roughly when $\frac{5}{0.0075} \approx 670\,\mathrm{atm}$ has been added. (At very high pressures other, denser forms of ice appear, but they are beyond this diagram.)

Worked example

Problem. A 60 kg skater stands on one blade whose edge touches the ice over 3.0 mm × 20 cm. A common explanation says the pressure melts the ice under the blade. Test this claim with the figure of 0.0075 °C per atm ( $g = 9.81\,\mathrm{m\,s^{-2}}$ , 1 atm = 101 325 Pa).

Solution.

$p = \frac{F}{A} = \frac{60 \times 9.81}{(3.0 \times 10^{-3}) \times 0.20} = 9.81 \times 10^{5}\,\mathrm{Pa} = 9.7\,\mathrm{atm}$

$\Delta T_{\text{melt}} = 9.7 \times 0.0075 = 0.073\,^\circ\mathrm{C}$

Answer: the melting point falls by less than a tenth of a degree. Even if only a tenth of that area touched the ice, it would fall by under 1 °C, yet people skate on ice at −10 °C. Pressure melting cannot be the main reason: friction heating and a thin, liquid-like layer on the surface of ice matter more.

Warning

The triple point is not the normal melting point. The normal melting point (0.00 °C) is read at 101.3 kPa; the triple point (0.01 °C) is at 0.61 kPa. Also, do not label the area beyond the critical point "gas": above the critical temperature and pressure it is a supercritical fluid.

Tip

To find the stable phase, put your finger on the (T, p) point. Moving right (heating) takes you towards gas; moving up (compressing) takes you towards the denser phase, which for water near 0 °C is the liquid, not the solid.

Science Explained: Triple Point Phase Diagrams. Watch how each area, line and point of a phase diagram is read, then try the practice questions in the video before checking the answers.

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Practice

State the phase(s) present for water at: (a) 50 °C, 101.3 kPa; (b) −10 °C, 0.1 kPa; (c) 0.01 °C, 0.61 kPa; (d) 500 °C, 25 MPa.
How many degrees of freedom does pure water have (a) in the liquid area; (b) on the boiling curve; (c) at the triple point?
Describe what happens when ice at −20 °C and 0.2 kPa is warmed slowly to 50 °C at constant pressure.
Explain why the melting curve of water has a negative slope.
The vapour pressure of water at 120 °C is 199 kPa. At what pressure does water boil at 120 °C? Name one device that uses this.
Steam is to be liquefied by compression alone. Explain why this is possible at 300 °C but not at 400 °C.
A student claims that because water boils at 100 °C, the critical temperature is "the boiling point at high pressure". Evaluate this claim.

Show answersHide answers

(a) liquid; (b) solid; (c) solid, liquid and gas; (d) supercritical fluid.
(a) $F = 1 - 1 + 2 = 2$ ; (b) $F = 1 - 2 + 2 = 1$ ; (c) $F = 1 - 3 + 2 = 0$ .
0.2 kPa is below the triple-point pressure (0.61 kPa), so the ice sublimes directly to vapour; no liquid forms, and the vapour then warms to 50 °C.
Ice is less dense than water. Higher pressure favours the smaller-volume phase, the liquid, so the melting point falls as pressure rises.
At 199 kPa, the pressure at which the vapour pressure equals the outside pressure; a pressure cooker or an autoclave.
300 °C is below the critical temperature (374 °C), so the vaporisation curve exists there and compression crosses it; at 400 °C there is no liquid–gas boundary to cross.
Partly true: the boiling point does rise with pressure along the vaporisation curve, and the critical point is its highest point. But the critical temperature is a limit, not a boiling point: above it, there is no boiling at any pressure, because liquid and gas are no longer distinct.

Sources and credits

Triple and critical points of water: International Association for the Properties of Water and Steam (IAPWS), as given in the NIST Chemistry WebBook: Water, US National Institute of Standards and Technology. Densities of ice and water: CRC Handbook of Chemistry and Physics.
Image: Iceberg in the Arctic with its underside exposed.jpg by AWeith, via Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Triple Point Phase Diagrams, Science Explained, embedded from YouTube.
The text, Figure 10.2, worked examples and Practice items were written and drawn by Ganzaa.
This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1One map for three states

2Reading the diagram

3Why the melting line leans to the left

4Following a path across the diagram

One map for three states

Reading the diagram

Why the melting line leans to the left

Following a path across the diagram