Solid Carbon Dioxide

When a quantity of liquid carbon dioxide evaporates quickly the heat of vaporisation is withdrawn from the remaining liquid, which consequently freezes to a snowlike mass. This fact was observed by Thilorier; and an apparatus was devised by Natterer to be fixed to the valve of a cylinder of liquid carbon dioxide, so that when the valve is opened and the liquid is forced out by the pressure of the gas within the cylinder a quantity of carbon dioxide " snow" may be obtained. The apparatus consists of a cylindrical metal box, made in two parts which fit tightly together, and provided with a tube for the entrance of the liquid carbon dioxide, and pierced with holes beneath two hollow handles through which the gaseous carbon dioxide may escape. A piece of coarse canvas held over the valve of the cylinder whilst the liquid is escaping suffices, however, to collect some of the solid without the use of the box.

Solid carbon dioxide is crystalline, and has been obtained in cubes and octahedra; when formed by the cooling of the liquid in bulk it is colourless and transparent like ice. It evaporates in the air without melting; this process is slow, however, because of the high heat of vaporisation.

The sublimation temperature at atmospheric pressure is -78.2° C.; and the vapour pressures at different temperatures are shown in the following table (Zeleny and Smith):

Temperature ° C.	Pressure.	Temperature ° C.	Pressure.
-56.4 (triple point)	5.11 atm	-100	119 mm
-60	3.92 atm	-110	43 mm
-70	1.88 atm	-120	14 mm
-80	657 mm	-130	2.5 mm
-90	288 mm	-150	0.05 mm

The density of the compressed "snow" is 1.2, whilst that of the " ice " is 1.56 at -79° C. The " snow " may be handled without harm, but when pressed upon the skin for twenty seconds or more it produces blisters.

Solid carbon dioxide is now a commercial article, and is used therapeutically with more or less success in the treatment of the following diseases: warts, moles, erysipelas, eczema, lupus, and certain ulcers. When employed in conjunction with certain liquids solid carbon dioxide is a valuable cooling agent. By passing a current of air at 18° C. through the following mixtures the following temperatures are obtained: solid carbon dioxide with ethyl or methyl alcohol -85° C., with methyl chloride or acetaldehyde -90° C., with ethyl acetate -95° C., with acetone -98° C.; whilst if the air is previously cooled to -80° C. the temperature obtained with acetone is -110° C. The theory of these phenomena from the standpoint of the phase rule has been worked out by Roozeboom.

Equilibrium diagram of the physical states of carbon dioxide.

When a substance can exist in three physical states there is one condition under which the three states co-exist in equilibrium. If these states are represented on a pressure-temperature diagram (Fig.) this condition is expressed by a point called the triple point. The triple point for carbon dioxide is at -56.4° C. and 5.1 atm. pressure; and it is represented in Fig. 4 at O₁.

O₁A, O₁B, and O₁C are the boundaries between liquid and vapour, solid and vapour, and solid and liquid respectively, and show the dependence of boiling-point, sublimation-point, and melting-point respectively upon pressure. The point O₄ corresponds with -7.5° C. and 2800 kg. per sq. cm. The upper part of the curve O₁C, i.e. the part O₄C, is broken to show a metastable condition, and the curves O₄D and O₄E are the boundaries of two forms of solid carbon dioxide discovered by Tammann. Solid I can exist under the conditions represented by the curve O₄C as far as 10.5° C. and 4000 atm., but when the pressure is lowered it melts and passes into the more stable Solid II. The curve O₄E, along which Solid II and liquid can co-exist in equilibrium, has been traced as far as 10.9° C. and 3487 atm. When the pressure on Solid I above -7.5° C. is increased the solid does not melt, but approaches the condition represented along the curve O₄D. in which the two solid forms are equally stable. This curve has been traced to 15° C. and 4900 atm. O₄ is thus a triple point at which liquid carbon dioxide and its two solid forms co-exist in equilibrium, and by extending the curves AO₁, BO₁, DO₄, and EO₄, the imaginary triple points O₂ and O₃ come into view.

The specific heats of carbon dioxide and of other gases have been determined by the method of Regnault, which consists in leading the heated gas through a spiral tube immersed in water and determining the amount of heat given up to the water ; and by the method of Mallard and Le Chatelier, in which, from the pressure developed in an enclosed space by explosion, the temperature attained is calculated, and thence from the known thermal data of the reaction the specific heat of the gas is derived.

Holborn and Austin, employing the method of Regnault, estimated the specific heat of carbon dioxide at constant pressure and different temperatures to be:

Temperature ° C.	Specific Heat.	Temperature ° C.	Specific Heat.
0	0.2028	400	0.2502
100	0.2161	600	0.2678
200	0.2285	800	0.2815

the general expression being:

Ct = 0.2028 + 0.0001384. - 0.00000005t².

Holborn and Henning have more recently obtained a slightly different expression:

Ct = 0.2010 + 0.0000742t – 0.000000018t²;

and Swann, employing an electrical method, found the specific heat to be 0.20202 at 20° C. and 0.22121 at 100° C.

Various thermal properties of carbon dioxide at low temperatures have been studied by Jenkin and Pye.

The ratio of the specific heats at constant pressure and constant volume (Cp/Cv) has been estimated by numerous observers. Owing to the variation of the specific heat with pressure this ratio must correspondingly vary. The following values have been estimated by Amagat at 50° C. and various pressures:

Atm.	Cp/Cv.
50	1.708
60	1.903
70	2.327

H. W. Moody has found Cp/Cv at 20° C. and 760 mm. pressure to be 1.3003, whence Cp has been calculated to be 0.2008 under the same conditions.

The molecular heat of carbon dioxide at constant volume (Cv) and the ratio Cp/Cv = γ, have been estimated by Crofts by finding the temperature at which mixtures of this gas with electrolytic gas are fired by adiabatic compression; and the values of Cv have also been calculated from the formula

Cv = 6.6 + 0.0023t,

with the following results:

Temperature Interval ° C.	γ	Cv observed.	Cv calculated.
15.532	1.254	7.815	7.823
15.545	1.253	7.847	7.853
15.557	1.252	7.878	7.881
15.570	1.251	7.909	7.911

The heat of sublimation of solid carbon dioxide was found by Behn to be 142.4 calories per gram at -79° C.; and the heats of vaporisation per gram of liquid carbon dioxide at different temperatures are, according to Cailletet and Mathias, as follow:

t ° C.	Heat of Vaporisation.
-25	72.23 calories.
0	57.48 calories.
30.0	11.60 calories.
30.82	3.72 calories.

The heat of formation of carbon dioxide is the same as the heat of combustion of carbon (q.v.), and therefore varies according to the kind of carbon which is burnt. Thomsen gave the value 96,960 calories for (C,O₂) by the combustion of wood-charcoal; whilst the values obtained by Berthelot were:

Diamond.	Graphite.	Amorphous Carbon.
94,310 calories.	94,810 calories.	97,650 calories.

Through explosion in a calorific bomb, Berthelot obtained the value 68,300 calories for the reaction (CO,O).