Carbon Dioxide, and Substances That Expand or Contract on Freezing

25 min

Why is dry ice "dry"?

Solid carbon dioxide is sold as "dry ice" to keep vaccines and laboratory samples cold. Leave a lump on a bench and it shrinks and disappears without ever forming a puddle. Drop it into water and it is wrapped in a white fog. The phase diagram of carbon dioxide explains both observations, and comparing it with water's shows why water is such an unusual substance.

The phase diagram of carbon dioxide

Figure 10.3: The phase diagram of carbon dioxide. The green point marks liquid and gas in equilibrium at 25 °C and 6.43 MPa. Compare the slope of the melting line and the height of the triple point with Figure 10.2.

The triple point (−56.6 °C, 518 kPa) lies above atmospheric pressure. At 101.3 kPa, a horizontal line passes from the solid area straight into the gas area. Solid carbon dioxide therefore sublimes at −78.5 °C and never melts in an open room: it is "dry". Liquid carbon dioxide exists only above 518 kPa, about 5.1 atm.
The melting line slopes to the right. Solid $\mathrm{CO_2}$ is denser than the liquid, so pressure favours the solid and raises the melting point. This is the normal behaviour of most substances.
The critical temperature is only 31.0 °C. At 25 °C, carbon dioxide liquefies once the pressure reaches 6.43 MPa, so a $\mathrm{CO_2}$ fire-extinguisher or gas cylinder at room temperature contains liquid with gas above it. On a day hotter than 31 °C, the contents become a single supercritical fluid.

Feature	Water	Carbon dioxide
Triple point	0.01 °C, 0.611 kPa	−56.6 °C, 518 kPa
Critical point	374.0 °C, 22.06 MPa	31.0 °C, 7.38 MPa
At 101.3 kPa, the solid…	melts at 0 °C	sublimes at −78.5 °C
Slope of melting line	negative (to the left)	positive (to the right)
Denser phase at the melting point	liquid	solid

Table 10.2: Water and carbon dioxide compared (NIST data).

Expanding or contracting on freezing

Whether a substance expands or contracts on freezing depends on how its particles pack in the solid compared with the liquid.

Most substances contract on freezing, because the particles pack more closely in an ordered solid: carbon dioxide, most metals (aluminium, copper, lead), paraffin wax. A candle that has just set has a hollow in the middle, where the shrinking wax drew in. For all of these, the melting line slopes to the right.
A few substances expand on freezing, because their solid has an open, directional structure: water (by about 9 %), silicon, germanium, gallium (by about 3.1 %), bismuth (about 3.3 %) and antimony. For these, the melting line slopes to the left.

In ice, each water molecule is hydrogen-bonded to four others at the corners of a tetrahedron. This holds the molecules farther apart than in the liquid, where hydrogen bonds constantly break and the molecules can crowd closer. Liquid water itself is densest at 3.98 °C.

Consequences. Water pipes and car radiators burst when they freeze, and water freezing in cracks splits rocks (frost wedging), so pipe insulation and antifreeze are needed in cold climates. Lakes freeze from the top down: the ice floats and insulates the water below, which stays near 4 °C, so fish survive the winter. Expansion of bismuth and antimony is used in alloys that fill every detail of a mould as they set.

Worked example

Problem. 1.000 dm³ of water at 0 °C (density 0.9998 g cm⁻³) freezes to ice of density 0.9167 g cm⁻³. Calculate the volume of the ice and the percentage expansion.

Solution. The mass does not change: $m = 1000 \times 0.9998 = 999.8\,\mathrm{g}$ .

$V_{\text{ice}} = \frac{999.8}{0.9167} = 1090.7\,\mathrm{cm^{3}} \qquad \text{expansion} = \frac{1090.7 - 1000}{1000} \times 100 = 9.07\,\%$

Answer: 1.091 dm³, an expansion of about 9.1 %. A sealed, full bottle has no room for this, so it cracks.

Worked example

Problem. Using Figure 10.3, describe what happens to carbon dioxide (a) when gas at 25 °C is compressed slowly from 101.3 kPa to 8 MPa; (b) when gas at 40 °C is compressed in the same way; (c) when $\mathrm{CO_2}$ gas at −70 °C is compressed from 101.3 kPa to 1 MPa.

Solution.

25 °C is below the critical temperature. Moving up, the line meets the vaporisation curve at 6.43 MPa: the gas condenses at constant pressure until it is all liquid; at 8 MPa it is liquid.
40 °C is above 31.0 °C. No phase boundary is crossed: the gas becomes steadily denser and, above 7.38 MPa, is a supercritical fluid. No liquid surface ever appears.
At −70 °C and 101.3 kPa the point lies just to the right of the sublimation curve (−70 °C is warmer than −78.5 °C), so the carbon dioxide starts as gas. Moving up, the line crosses the sublimation curve and the gas deposits as solid. Because −70 °C is below the triple-point temperature (−56.6 °C), the line never enters the liquid area: at 1 MPa the carbon dioxide is solid.

Warning

Safety with dry ice. At −78.5 °C it causes frostbite-like cold burns: handle it with insulated gloves or tongs, never bare hands, and never eat it or put it in a drink. Never seal it in a closed container: 1 kg of solid gives over 500 dm³ of gas at room temperature, enough to burst a bottle. In a small closed room the gas can build up and cause suffocation, so use it only where there is good ventilation.

First aid, following the CDC (NIOSH) Pocket Guide entry for carbon dioxide: for frostbite of the skin from dry ice, seek medical attention immediately, do NOT rub the area or flush it with water, and do not pull off clothing frozen to the skin. If the eye tissue is frozen, get medical help at once. A person who becomes dizzy or breathless near dry ice must be moved to fresh air and given respiratory support.

Tip

Look at two things on any one-component phase diagram: where the triple point is compared with 1 atm (above it, the solid sublimes in the open; below it, it melts), and which way the melting line leans (right: solid denser, contracts on freezing; left: solid less dense, expands on freezing).

Medielab HVL: Thermodynamics, Explaining the Critical Point. Watch carbon dioxide in a sealed cell as it is heated: the boundary between liquid and vapour fades away at the critical point and reappears on cooling.

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Practice

What is the minimum pressure at which liquid carbon dioxide can exist? Give it in kPa and atm.
State the phase of $\mathrm{CO_2}$ at: (a) −90 °C, 101.3 kPa; (b) 0 °C, 101.3 kPa; (c) 20 °C, 7 MPa; (d) 50 °C, 10 MPa.
Explain why dry ice does not melt in an open room but liquid $\mathrm{CO_2}$ can be seen in a thick glass tube under pressure.
Explain why the melting line of carbon dioxide slopes to the right.
A full, sealed 500 cm³ glass bottle of water is left in a freezer. Calculate the volume of ice formed if it all freezes (use 9.1 % expansion), and explain the result.
Gallium melts at 29.8 °C and expands by 3.1 % on freezing. Sketch the shape you would expect for its solid–liquid line on a phase diagram.
A technician says a $\mathrm{CO_2}$ cylinder at 35 °C "has run out" because she can no longer hear liquid sloshing inside. Evaluate this claim.

Show answersHide answers

518 kPa, about 5.11 atm (the triple-point pressure).
(a) solid; (b) gas; (c) liquid (20 °C is below 31.0 °C, and 7 MPa is above the 5.7 MPa vapour pressure at 20 °C); (d) supercritical fluid.
At 101.3 kPa, below the triple-point pressure, there is no liquid region, so the solid sublimes; in the sealed tube the pressure is above 518 kPa, where liquid is stable.
Solid $\mathrm{CO_2}$ is denser than liquid $\mathrm{CO_2}$ , so increasing pressure favours the solid and raises the melting point.
$500 \times 1.091 = 545.5\,\mathrm{cm^{3}}$ ; the extra 45 cm³ has nowhere to go, so the ice cracks the bottle.
A line that slopes up to the left from the triple point (like water's): pressure lowers the melting point because the liquid is denser.
Not necessarily. 35 °C is above the critical temperature (31.0 °C), so the contents are a single supercritical fluid with no liquid surface, even in a full cylinder. Weigh the cylinder, or let it cool below 31 °C, before concluding it is empty.

Sources and credits

Phase data for carbon dioxide and water: NIST Chemistry WebBook: Carbon dioxide and Water, US National Institute of Standards and Technology. Expansion of gallium and bismuth on freezing: CRC Handbook of Chemistry and Physics.
First aid: NIOSH Pocket Guide to Chemical Hazards: Carbon dioxide and its First Aid Procedures, US Centers for Disease Control and Prevention.
Image: Dry ice sublimation.jpg by Ибрагим Хаётов, via Wikimedia Commons, licensed under CC BY 4.0.
Video: Thermodynamics, Explaining the Critical Point, Medielab HVL, embedded from YouTube.
The text, Figure 10.3, the table, worked examples and Practice items were written and drawn by Ganzaa.

1Why is dry ice "dry"?

2The phase diagram of carbon dioxide

3Expanding or contracting on freezing

Why is dry ice "dry"?

The phase diagram of carbon dioxide

Expanding or contracting on freezing