Treatise on Thermodynamics (1903) — part 11 of 14

the equilibrium remains indeterminate, since there are more unknown quantities than determining equations. For this reason there is no direct connection between the depression of freezing point, the elevation of the boiling point, etc., on the one hand, and electrical conductivity on the other. For the one set of quantities depends on the total number of the dissolved molecules, charged or uncharged, while the other depends on the number and nature of molecules charged with electricity (ions), which cannot, in general, be calculated from the former. Conversely, a disagreement between the depression of the freezing point as calculated from the conductivity, and as observed, is not in itself an objection to the theory, but rather to the assumptions made in the calculation concerning the kinds of molecules present. Eaoult was the first to establish rigorously by experi- ment the relation between the depression of the freezing point and the number of the molecules of the dissolved substance ; and van't Hoff gave a thermodynamical explana- tion and generalization of it by means of his theory of osmotic pressure, xipplication to electrolytes was rendered possible by Arrhenius' theory of electrolytic dissociation. Thermodynamics has led quite independently, by the method here described, to the necessity of postulating chemical changes of the dissolved substances in dilute solutions.

§ 274. Each Phase contains both Constituents in Appreciable Quantity. — The most important case is the evaporation of a liquid solution, in which not only the solvent, but also the dissolved substance is volatile. The general equation of equilibrium (218), being applicable to

DILUTE SOLUTIONS, 253

mixtures of perfect gases whether the mixture may be supposed dilute or not, holds with corresponding approxi- mation for a vapour of any composition. The liquid, on the other hand, must be assumed to be a dilute solution.

In general, all kinds of molecules will be present in both phases, and therefore the system is represented by

Wg m(j, Wi wii, W2 ^'^2 • • • I ^0' ^'^0' ^1' "^1' ^^' ^2 • • •

The molecules have the same molecular weight in both phases. The total number of molecules in the liquid is

w = Wo + % + ?i2 + • • • (nearly = «o), in the vapour

w' = Wq' ■- nx -V n.{ -V . . .

The concentrations of the different kinds of molecules are, in the liquid,

in the vapour,

Wn Wi W2

c„ = — ; ci = — ; cg = — ; ° n n n

The reaction

vq '. vi '. Vi :...'. vq : VI : V2 : . . . = Stoq '.Ini'.^n^^: ...: Shq : 8%' : ^n2 : . . .

consists in the evaporation of a molecule of the first kind, and therefore

Vo = 0, Vi = - 1, V2 = 0, . . . Vq = 0, Vi = 1, V2' = 0, . . .

The equation of equilibrium becomes

• log ci + log ci = log K,

or

^ = K.

254 THERMODYNAMICS.

For every hind of molecule, which possesses tlie same molecular weight in both phases, there is a constant ratio of distribution, which is independent of the presence of other molecules (Nernst's law of distribution).

If, on the other hand, a molecule of the solvent evaporate, we have,

vq = — 1, vi = 0, V2 = 0, . . . I'o' = 1, vi = 0, V2 = . . . ;

and the equation of equilibrium becomes

• log Co + log Cq' = log K,

where

-log..-.<^ = log(l + -±^)=-±^-

= ci 4- C2 + (239)

:. C1 + C2+ ... + log < = log K, . . (240)

where Ci, c.2, . . ., the concentrations of the molecules dis- solved in the liquid, have small values. Two cases must be considered.

Either, the molecules «Iq in the vapour form only a small or at most a moderate portion of the number of the vapour molecules. Then the small numbers Ci, C2, . . . , may be neglected in comparison with the logarithm, and therefore

log Co = log K.

This asserts that the concentration of the molecules of the solvent in the vapour does not depend on the composi- tion of the solution. An example of this is the evaporation of a dilute solution, when the solvent is not very volatile, e.g. alcohol in water. The partial pressure of the solvent (water) in the vapour is not at all dependent on the con- centration of the solution, but is equal to that of the pure solvent.

Or, the molecules mQ in the vapour far outnumber all the other molecules, as, e.g., when alcohol is the solvent in

DILUTE SOLUTIONS. 255

the liquid phase, water the dissolved substance. The con- centrations Ci, C2 . . . must not be neglected, and, as in (239),

log Co' = - (ci' + C2' 4- . . . .) ; equation (240) therefore becomes

(ci + C2 + . . .) - (c/ + 02'+...) = log K.

This relation contains an extension of van't Hoflfs laws concerning the elevation of the boiling point, the diminution of the vapour pressure, etc., and asserts that wlien the substance dissolved in the liquid also passes in part into the vapour, the elevation of boiling point or the diminution of the vapour pressure depends 710 longer on the concentrations of the moleeules dissolved in the liquid, hut on the difference of their concentrations in the liquid and in the vapour. If this difference be zero, the distillate being of the same composition as the liquid, the elevation of the boiling point and the diminution of the vapour pressure vanish. This conclusion has already been reached from a more general point of view (§ 219). If the concentration of the dissolved substance in the vapour bo larger than that in the liquid, as may happen in the evaporation of an aqueous solution of alcohol, the boiling point falls, while the vapour pressure rises.

Exactly analogous theorems may, of course, be deduced for other states of aggregation. Thus, the more general statement of the law concerning the freezing point would be : If both the solvent and the dissolved substance of a dilute solution solidify in such a way as to form another dilute solution, the depression of the freezing point is not proportional to the concentrations of the dissolved substances in the liquid, but to the difference of the concentrations of the dissolved substances in the liquid and solid phases, and changes sign with this difference. The solidification of some alloys is an example.

While these laws govern the distribution of the mole- cules in both phases, the equilibrium within each phase

256 THE R MOD YNA MICS.

obeys the laws, which were deduced in § 262, etc. We again meet with the laws of dissociation, association, etc. (Nernst).

§ 275. Three Independent Constituents in one Phase. — Two dissolved substances in a dilute solution will not affect one another unless they have certain kinds of molecules in common, for there is no transformation possible, and there- fore no special condition of equilibrium to fulfil. If two dilute solutions of totally different electrolytes in the same solvent be mixed, each solution will behave as if it had been diluted with a corresponding quantity of the pure solvent. The degree of the dissociation will rise to correspond to the greater dilution.

It is different when both electrolytes have an ion in common, as, for example, acetic acid and sodium acetate. In this case, before mixing there are two systems :

noHaO, Wi CH3.COOH, n. H, H3CH3.COO,

and ?io' H2O, n; CHg.COONa, ni Na, n^ CH3.COO.

As in (222), for the first solution,

^' = K, or ^ = K, . . . . (241)

for the second, ^! = K', or ^ = K'. . . . (242)

After mixing the two, we have the system

TioHaO, niCHg-COOH, n^CHa-COONa, n^K, njia, /IsCHa'COO, where, necessarily,

oIq = Uq + Uq (number of H2O molecules) ii^ 4- Hi = ih' + W2' (number of Na atoms) ni + n^ = Wi + ih (number of H atoms) lis + fH = 115 (number of + ions = number of — ions).

(243)

DILUTE SOLUTIONS. 257

The total number of molecules in the system is

ii = Hq + ill + «2 + >h + >'h + ft5 (nearly = Hq). The concentrations are

fin fil - I'h - ih _ fli . W5

" n n n n n n

In the system there are two different reactions,

v^^'. vi '. vi ' i'3 : vi ' V5 = cll^j : 8/7i : S/I2 • 0AI3 : S/i4 : S»5, possible ; first, the dissociation of one molecule of acetic acid,

I'O = 0, VI = - 1, l'-2 = 0, Va = 1, )'4 =^0, V5 = 1,

and therefore the condition of equilibrium is, by (218),

• log ci + log C3 + log C5 = log K,

^=K,or?^ = ^^^'^, = K;. (244)

second, the dissociation of a molecule of sodium acetate,

Vq = 0, Vl = 0, V.2 = - 1, l^J = 0, 1/4 = 1, I'.-. = I5 whence, for equilibrium,

• log C2 + log C4 + log C5 = log K', or i - = K',

or ^ii^= /^-^^ ^ = K\ . . . (245)

The quantities K and K' are the same as those in (241) and (242). They depend, besides on 6 and jh only on the nature of the reaction, and not on the concentrations, nor on other possible reactions. By the conditions of equilibrium (244) and (245), together with the four equations (243), the values of the six quantities Wq, ni, . • . wg ^^^ uniquely

s

258 THERMODYNAMICS.

determined, if the original solutions and also the number of molecules Wp, wi, . . . and »„', n/ . . . be given.

§ 276. The condition that the two solutions should be isohydric, i.e. that their degree of dissociation should remain unchanged on mixing them, is evidently expressed by the two equations

ill = ui, and n^ = iii,

i.e. the number of undissociated molecules of both acetic acid and sodium acetate must be the same in the original solutions as in the mixture. It immediately follows, by (243), that

//g = n-2, Hi = n^, 7I5 = n-2 + n-J.

These values, substituted in (244) and (245), and combined with (241) and (242), give

n^{ri2jj-jh) _ \r - ^^ ni{nQ + Hq) ~ ~ ni n^

n-ljih + t^) _ -rr, _ n^'^ whence the single condition of isohydric solutions is

or, the two solutions are isohydric if the concentration of

the common ion CH3COO is the same in both. This pro- position was enunciated by Arrhenius, who verified it by numerous experiments. In all cases where this condition is not realized, chemical changes must take place on mixing the solutions, either dissociation or association. The direc- tion and amount of these changes may be estimated by ima- gining the dissolved substances separate, and the entire solvent distributed over the two so as to form isohydric solutions.

DILUTE SOLUTIONS. 259

If, for instauce, both solutions are originally normal (I gram molecule in 1 litre of solution), they will not be isohydric, since sodium acetate in normal solution is more strongly dissociated, and has, therefore, a greater concentration of

CHs.COO-ions, than acetic acid. In order to distribute the solvent so that the concentration of the common ion

CH3.COO may be the same in both solutions, some water must be withdrawn from the less dissociated electrolyte (acetic acid), and added to the more strongly dissociated (Na-acetate). For, though it is true that with decreasing dilution the dissociation of the acid becomes less, the con- centration of free ions increases, as (262) shows, because the ions are now compressed into a smaller quantity of water. Conversely, the dissociation of the sodium acetate increases on the addition of water, but the concentration of the free ions decreases, because they are distributed over a larger quantity of water. In this way the concentration of the

common ion CH3.COO may be made the same in both solutions, and then their degree of dissociation will not be changed by mixing. This is also the state ultimately reached by the two normal solutions, when mixed. It follows, then, that when two equally diluted solutions of binary electrolytes are mixed, the dissociation of the more weakly dissociated recedes, while that of the more strongly dissociated increases still further.

§ 277. Three Independent Constituents in Two Phases. — We shall first discuss the simple case, where the second phase contains only one constituent in appreciable quantity. A solution of an almost insoluble salt in a liquid, to which a small quantity of a third substance has been added, forms an example of this case. Let us consider an aqueous solution of silver bromate and silver nitrate. This two-phase system is represented by

yioHaO, «i AgBrOs, Ug AgNOg, Wg Ag, ;i4Br03,^t5N03 | < AgBrOg.

26o THERMODYNAMICS.

The conceutrations are

_ S _ '^'1 _ i_^ ' _ !!o' _ 1

""""»,' ^'~ „' '"' ~ « ' •••' ''•' < '

where // = n^ + ;/i 4- "2 + "-3 + Wi + "5 (nearly = Xf).

Of the possible reactions,

Vq '. vi : v-2 '. V3 '. I'i : V.J : vj = tu^ : 6ni : 6'^2 • ^% • o'*4 • 0^5 : cUq ,

we shall first consider the passage of one molecule of AgBrOa from the solution, viz.

v^^ = 0, I'l = — , V) = 0, . . . v^ = 1.

The condition of equilibrium is, therefore,

• log ci + log c; = log K

or ci = g (246)

The concentration of the undissociated molecules of silver bromate in the saturated solution depends entirely on the temperature and the pressure.

We may now consider the dissociation of a molecule of AgBrOg into its two ions.

!'„ = 0, I'l = - 1, V-i = 0, 1'3 = 1, Vi = 1, V5 = 0, Vq = 0,

and, therefore,

• log Ci + log ^3 + log Ci = log K',

C3C4 _ ,,,

or, by (246), c,Ci=j^, (247)

• • ^

i.e. the product of the concentrations of the Ag and BrOg

ions depends only on temperature and pressure. The con-

centration of the Ag-ions is inversely proportional to the

DILUTE SOLUTIONS. 261

concentration of the BrOg-ions. Since the addition of silver

nitrate increases the number of the Ag-ions, it diminishes

the number of the BrOa-ions, and thereby the solubility of the bromate, which is evidently measured by the sum Ci + c^. We shall, finally, consider the dissociation of a molecule of AgNOs into its ions.

'0 = 0, I'l = 0, 1/2 = - 1, 1-3 = 1, 1-4 = 0, ir-, = 1, „^' = 0,

whence, by ('^^18),

^' = K" (248)

To equations (246), (247), and (248), must be added, as a fourth, the condition

and, as a fifth, the value of Ci + C5, given by the quantity of the nitrate added, so that the five unknown quantities, Ci, c.^, <h, <^h ^5, are uniquely determined.

The theory of such influences on solubility was first established by Nernst, and has been experimentally verified by him, and more recently by Noyes.

§ 278. The more general case, where each of the two phases contains all three constituents, is realized in the distribution of a salt between two solvents, which are them- selves soluble to a small extent in one another (e.g. water and ether). The equilibrium is completely determined by a combination of the conditions holding for the transition of molecules from one phase to another with those holding for the chemical reactions of the molecules within one and the same phase. The former set of conditions may be summed up in Nernst's law of distribution (§ 274). It assigns to each kind of molecule in the two phases a constant ratio of distribution, which is independent of the presence of other dissolved molecules. The second set is the conditions of

262 THE R MOD YNA MICS.

the coexistence of three independent constituents in one phase (§ 275), to which must be added Arrhenius' theory of isohydric solutions.

§ 279. The same method applies to four or more inde- pendent constituents combined into one or several phases. The notation of the system is given in each case by (216), and any possible reaction of the system may be reduced to the form (217), which corresponds to the condition of equili- brium (218). All the conditions of equilibrium, together with the given conditions of the system, give the number of equations which the phase rule prescribes for the determi- nation of the state of equilibrium.

When chemical interchanges between the different sub- stances in solution are possible, as, e.g., in a solution of dis- sociating salts and acids with common ions, the term degree of dissociation has no meaning, for the ions may be combined arbitrarily into dissociated molecules. For instance, in the solution

«.„ HgO, wi NaCl, »^2 KCl, n^ NaNOa, n^ KNO3, % Na, n^ K,

m CI, ns NO:,

we cannot tell which of the Na-ions should be regarded as belonging to NaCl, and which to NaNOa. In such cases the only course is to characterize the state by the concen- trations of the dissolved molecules.

The above system consists of water and four salts, but, besides the solvent, only three are independent constituents, for the quantities of the Na, the K, and the CI determine that of the NO3. Accordingly, by § 204 (a = 4, /3 = 1) all the concentrations are completely determined at given temperature and pressure by three of them. This is inde- pendent of other kinds of molecules, and other reactions, which, as is likely, may have to be considered in establishing the conditions of equilibrium.

§ 280. If in a system of any number of independent

DILUTE SOLUTIONS. 263

constituents in any number of phases, the condition of equilibrium (218) is not satisfied, i.e. if for any virtual isothermal-isopiestic change

^vo log C(, + vx log ci + V2 log C2 + . . . J log K,

then the direction of the change which will actually take place in nature is given by the condition d>V > (§ 147). If we now denote by Vq, vi, vg . . ., simple whole numbers, which are not only proportional to, but also of the same sign as the actual changes which take place, then we have, by (215),

^1^0 log Co + VI log ci 4- V2 log C2 + . . . < log K,

for the direction of any actual isothermal isopiestic change, whether it be a chemical change inside any single phase, or the passage of molecules between the different phases. The constant K is defined by (218).

To find the connection between the difference of the expressions on the right and left and the time of the reaction is immediately suggested, and, in fact, a general law for the velocity of an irreversible isothermal isopiestic process may be thus deduced. We shall not, however, enter further into these considerations in this book.

CATALOGUE

Of the Author's Publications on Thermodynamics, excluding the applications to Electricity, with a reference to the para- graphs of this book, which deal with the same point.

" Ueber den zweiten Hauptsatz der mechanischen Warmetheorie.

Inaugural-dissertation." Miinchen. Th. Ackermann. S.

1-Gl. 1879. (§§ 106-136.) " Gleichgewichtszustiinde isotroper Korper in Yei*schieden Tempe-

raturen, Habilitationsschrift." IMiinchen. Th. Ackermann.

S. 1-63. 1880. (§§ 153-187.) " Die Theorie des Sattigungsgesetzes." Wied. Ann, 13. S. 535-

543. 1881. (§ 172.) "Verdampfen, Schmelzen, und Sublimiren." AVied. Ann, 15.

S. 446-475. 1882. (§§ 188-106.) '* Ueber das thermodynamische Gleichgewicht von Gasgemengen."

Wied. Ann. 19. S. 3.58-378. 1883. (§§ 232-248.) "Das Princip der Erhaltung der Energie." Leipzig. B. G.

Teubner. S. 1-247. 1887. (§§ 55-105.) "Ueber das Princip der Vermehrnng der Entropie." Erste

Abhandlung. Gesetze des Yerlaufs von Reaktiouen, die

nach constanten Gewichts-verhaltnissen vor sich gehen.

Wied. Ann. 30. S. 562-582. 1887. (§ 206-212.) " Ueber das Princip der Vermehrung der Entropie." Zweite

Abhandlung. Gesetze der Dissociation gasformiger Yerbin-

dungen. Wied. Ann. 31. S. 189-203. 1887. (§ 232-

248.) " Ueber das Princip der Yermehrung der Entropie." Dritte

Abhandlung. Gesetze des Eintritts beliebiger thermodyna-

mischer und chemischer Reaktionen. Wied. Ann. 32.

S. 462-503. 1887. (§§ 232-279.) "Ueber die Molekulare Constitution verdiinnter Lcisungen."

CA TALOGUE. 265

Zeitsclir. f. pbys. Chem. 1. S. :)77-582. 1887. (§§ 271,

273.) " Das chemische Gleichgewicht in verdUnnten Losnngen." Wied.

Ann. 34. S. 139-154. 1888. (§ 2G2 f., §§ 208-273.) "Ueber die Hypothese der Dissociation der Salze in sehr ver-

diinnten Losnngen." Zeitsehr. f. phys. Chem. 2. S. 343.

1888. (§ 271.) " Ueber die Dampfspannung von verdiinnten Losnngen fliichtiger

Stoffe." Zeitchr. f. phys. Chem. 2. S. 405-414. 1888.

(§ 274). *' Ueber den osmotischen Druck." Zeitsehr. f. phys. Chem. 6.

S. 187-189. 1890. (§§ 229, 272.) "Allgemeines zur neuren Entwicklung der Warmetheorie."

Zeitsehr. f. phys. Chem. 8. S. 647-650. 1891. (§ 136.) " Bemerkung iiber das Carnot-Clausius'sche Princip." Wied.

Ann. 46. S. 162-166. 1892. (§ 134.) " Erwiderung auf einen von Herrn Arrhenius erhobenen Ein-

wand." Zeitsehr. f. phys. Chem. 9. S. 036 f. 1892. (§ 253.) " Der Kern des zweiten Hauptsatzes der Warmetheorie." Zeitsehr.

f. d. phys. nnd chem. Unterricht 6. S. 217-221. 1893.

(§§ 100-115.) " Grundriss der allgemeinen Thermochemie." Breslau. E.

Trewendt. S. 1-140. 1893. (§§ 1-66, 92-152, 197-279.) "Gegen die neuere Energetik." Wied. Ann. 57. S. 72-78.

1896. (§§108-113.)

INDEX

The nvmbers refer to pages.

Abnormal vapour densities, 30

Absolute temperature, 6 ; deduced from Thomson and Joule's experiments, 127-131

Acetate, silver, 244 ; sodium, 256

Acetic acid, 237

Adiabatic process, 59, 109

Affinity of hydrogen for oxygen, 112

Aggregation, states of, 69, 132; co- existence of states of, 153

Air, composition of, 11

Ammonium carbamate, evaporation of, 188

Ammonium chloride, evaporation of, 188

Andrews, 14, 140

Apt, Dr. Eichard, 14

Arrhenius, 235, 238, 258

Arrhenius' theory of electrolytic dis- sociation, 252 ; theory of isohydric solutions, 262

Atmospheric pressure, 4

Atom, definition of, 25

Atomic heat, 34

Avogadro's law, 25, 27

B

198

Babo's law,

Bams, 20

Berthelot. 71-73, 243

Berthelot's principle, 113

Binary electrolyte, 237 Bodenstein, 219 Boiling point, elevation of, 200 Boyle and Gay-Lussac, 197 Boyle's law, 5, 57

Calorie, laboratory, 33 ; large, 33 ; mean, 33 ; small, 33 ; zero, 33

Calorimetric bomb, 71

Cantor, Hr., 227n.

Carbon, combustion of, 74

Carbon dioxide, Van der Waals' con- stants for, 14 ; isotherms of, 15

Carnot's theory, 36; cycle, 62, 106

Catalogue, 264

Characteristic constant, 11

Characteristic equation, 5, 6, 11 ; deduced from Thomson and Joule's experiments, 126

Clapeyron, 142

Clausius, 87

Clausius' equation, 14, 140; form of second law, 96 ; notation, 55 ; state- ment of first and second laws, 101

Coefficient of compressibility, 8 ; of elasticity, 7 ; of expansion, 7 ; of pressure, 7

Coexistence of states of aggregation^ 153

Combustion, of carbon, 74 ; influence of temperature on, 76

Condensed system, 181

Condition of complete reversibility of

268

INDEX.

a process, 94: of equilibrium, 115, 136, 176 ; of a gas mixture, 215- 217

Conductivity of water, electrical, 236

Conservation of energy, 38, 40

Constituents, independent, 173

Corresponding point, 161

Crafts, 220

('ritical point, 17, of COj, 19 ; pres- sure, 17 ; solution temperature, 182 ; specific volume, 17 ; temperature, 17, 152

Curves of evaporation, 158, 161 : of fusion, 158, 161 ; of sublimation, 158, IGl

Cycle of operations, 44

D

Dalton's law, 10, 20

Davy, 36

Decrease of free energy bv dilution, 112

Deductions from second law of thermo- dynamics, 105

Density, specific. 7 ; abnormal vapour, 30 '

Depression of freezing point, 250

Developable surface, 164

Deviation from perfect gases, 13, 123

Difference of specific heats, 121

Diffusion, 9 ; increase of entropy by. 214; irreversible, 214

Dilute solutions, 223-263 ; energy of, 224 ; entropy of, 226 ; thermo- dynamical theory of, 222 ; volume of. 225

Dilution, decrease of free energy by, 112; heat of, 198 ; infinite, 7o'; law of, of binary electrolytes, 238

Direction of natural process, 108

Dissipation of energy, 101

Dissociation, graded, 221 ; of H^SO^. 238; of hydriodic acid, 219; of iodine vapour, 220 ; of water, 234 ; Arrhenius' theory of electrolytic, 252

Distribution law (Nernst's), 254

Divariant system, 181

Duhem, llim. I Dulong and Petifs law, 34 i Dyne. 4

E

Elasticity, coefficient of, 7

Electrical conductivity of water. 236

Electrolyte, binary, 237

Electrolytic dissociation, Arrhenius' theory of, 252

Elevation of boiling point, 200

Endothermal process. 37

Energetics, 79, 84

Energy, change of, 43 ; conservation of, 38, 40; definition of, 39; dis- sipation of, 101 ; free, 110 ; internal. 47 ; internal, of perfect gas, 57 : latent, 110; of a solution, 70; of dilute solution, 224 ; of gas mixture. 209; potential, 45; total, 110; zero, 44

Energy, free, of perfect gas, 113

Entropy, definition, 97 ; diminution of, 93; increase of, by diffusion, 214; maximum value, 117; of a gas, 89 ; of a system of gases, 92 ; of dilute solution, 225 ; of gas mix- ture, 209-214; principle of increase of, 100 ; specific, 119

Equation, characteristic, 5, 6, 11 ; deduced from Thomson and Joule's experiments, 126; Clausius', 14, 140 ; Van der Waals', 13

Equilibrimn, thermal, 2 ; conditions of, 115, 136, 176; of gas mixture, 215, 217

Equivalent weight, 23

Equivalents, number of, 23

Euler, 176

Evaporation of ammonimn carbamate, 188 ; of ammonium chloride, 188 ; theory of, 135

Exothermal process, 37

Expansion, coefficient of, 7

External conditions of equilibrium. 136 ; effect, 39 ; variable, 178 ; work in complete cycle, ,14 ; work in re- versible process, 51. ri2

INDEX.

269

Favrc, 74

First law of theruiodynauiics, 38, 42.

46 Free energy, 110; change of, with

temperature, 113; decrease of, by

dilution, 112; minimum value of,

117; of a perfect gas, 113 Freezing point, depression of, 250 Function % 114 Fundamental point (triple), 15,*);

pressure, 154; temperature, 154;

temperature of ice, 154 ; triangle,

159 Fusion, curve, 158, 161 ; theory of, 135

G

Gas constant, i~i ; thermometer, 3 ; volume, 27

Gas mixture, 9 ; energy of, 209 ; en- tropy of, 209-214 ; volume, 28

Gases, perfect, 5, 57

Gaseous system, 207-222

Gay-Lussac, 24, 57

Gay-Lussac's law, deviations from, 123

Gibbs, 73, 173. 212, 232

Gibbs's phase rule, 179, 232

Graded dissociation, 221

Gram-calorie, mechanical equivalent of, 41

H

Heat, absorbed, 53 ; atomic, 34 ; capa- city, 33 ; conception of, 1 ; molecu- lar, 34 ; molecular, of perfect gases, 58 ; of combustion, 75, 76 ; of dilu- tion, 198 ; of formation of CO^, of CSj, of CH„ 75; of fusion, 37; of neutralization, 73 ; of precipita- tion, 201 ; of solidification, 201 ; of solution, 190 ; of sublimation, 37 of vaporization, 37 ; quantity, 32 specific (definition). 33 ; total, 36 unit, 32

Heat and work, analogy between,'53

Heat effect, 37 ; at coa^tant pressure, 71 ; in thermochemistry, 68 ; of dilution of HjSO^, 70

Heat function at constant pressure, 73

Heat, latent, theory, 140; approxima- tion fonnula, 143

Heating at constant pressure, 56 ; at constant volume, 56

Henry's law, 242

Hertz, H., 146

Heterogeneous system, 180

Heydweiller, 234

Him. 148

Homogeneous substance, 138 ; svstem, 119-131

Horstmann, 188

Hydriodic acid, dissociation of, 219

Hydrobromamylene, 30

Hydrogen, afl5nity of, for oxygen, 112

Hydrogen peroxide, 74

Independent constituents, 173

Inertia resistance, 116

Infinite dilution, 70

Infinitely slow compression, 50 ; pro- cess, 49-51

Inflection, point of, 17

Influence of pressure on specific heat, 123; of temperature on combustion, 76

Int«rnal conditions of equilibrium, 136 ; variable, 178

Internal energy, 47; of perfect gas, 48

Iodine vapour, dissociation of, 220

Irreversible diffusion, 214

Isobaric change, 7

Isochoric change, 7

Isohydric solutions, 258; Arrhenius' theory of, 262

Isomorphous substance, 182

Isopiestic change, 7

Isopycnic change, 7

Isothermal processes, 110

27©

INDEX.

Isothermal -isopiestic process, 114 Isotherms of COj, 15 Isotropic bodies, 3

Jahn, 24.'')

JoiUe, 36

Joule's experiments, 40-42, 47

Joule and Thomson's absolute tempera- ture, 127-131 ; experiments, 48, .■J7, (theory) 124

Kirchhoff, 191 Kirchhoffs formula, l'J8 Kohlrausch, 234 Konowalow, 196 Krigar-Manzel, 99«. Kundt. 122

L

Latent energy, 110

Latent heat. 37, 140, 143 ; from phase

rule, 187-189 Laws: Avogadro's, 25, 57; Babo's,

198 ; Boyle's, 5, 57 ; Dalton's,

10, 20; Dulong and Petit's, 34;

Gay-Lussac's, 6, 24, 57; Henry's,

242; Mariotte's, o; Nernsfs, 254;

Neumann's (Regnault), 35; Ost-

wald's, 238; Van't HofPs, 255;

Wullner's, 199 Laws of thermodynamics. See First

andL Second Lead sulphide, 68 Liquefaction pressure, 20 Lowering of freezing point, 202; of

vapour pressure, 199, 250

M

Mariotte's law, 5

Maximum value of entropy, 117; of

free energy, 117; of >F, 118 Maximum work, 111 Maxwell, 87

Mechanical equivalent of a gram- calorie, 41 : of heat, 40 ; of heat in absolute units, 42

Meier, Fr., 220

Melting point of ice, 146 ; lowering of, by pressure, 146

Membranes, semipermeable, 29, 203

Meyer, Robert, 62

Mixture of gases, 9

Mixtures, 20

Molecular heat, 34; of perfect gases, 58

Molecular weight, 22 : apparent, 28

Molecules, number of, 25

N

Naccari, 242

Natural process, direction of, lOS

Nerast, 242, 254, 261

Nernst's law of distribution, 254

Neumann, F., 35

Neutralization, heat of, 73

Nitrogen oxides, 23 ; peroxide. 30

Non-variant system, 179

Noves. 261

Osmotic pressure, 204, 251 Ostwald's law, 238 Oxides of nitrogen, 23

Pagliani, 242

Partial pressures, 10

Perfect gases, 5, 57 ; system, 44

Phase, defined, 173 ; rule, 179

Phosphorus pentachloride, 30

Planck, 228

Point {n + 2)-ple, 179 : of inflection,

17; triple, 155, 180; quadruple,

180 ; quintiple, 180 Porous plug experiments, 48 Potassium chlorate, 182 Potential, energy, 45 ; thermodynamic.

1 1 5»t.

INDEX.

271

I'recipitation, heat of, 201

Pressure coefficient, 7 ; of mercury, 9

Pressure, fundamental, 154 : osmotic,

204, 251 ; of liquefaction, 20 Principle of Berthelot, 113 Process, adiabatic, 109 ; endothermal,

37; isothermal, 110; isothermal-

isopiestic, 114; exothermal, 37 Processes, periodic, 83 ; reversible and

irreversible, 82

Q

Quadruple point, 180 Quantity of heat, 32 Quintiple point, IHO

R

Ratio of specific heats, 59, 122 Kegnault, 58, 143, 148 Resistance inertia, IIG Reversibility of a process, complete,

condition of, 94 Roozeboom, Bakhuis, 179 Rumford, 36

Saturation point, IG

Second law of thermodynamics, in- troduction, 77 ; proof, 86 ; possible limitations, 103; deductions, 105; test of, 147, 148

Semipermeable membranes, 29, 203

Silbermann, 74

Silver acetate, 244 ; bromate, 259 ; nitrate, 244, 259

Singular values, 37

Sodium carbonate, 73 ; hydrate, 73

Solidification, heat of, 201 ; pressure, 20

Solution, heat of, 190 ; isohydric, 258

Solutions, dilute, 223-2G3

Solvent, 196

Sound, velocity of, 61

Specific density, 7

Specific entropy, 119

Specific heat, 33 ; at constant pressure, 56, 59, 120 ; at constant volume, 56, 59, 120 ; influence of tem- perature on, at constant pressure, 123; of saturated vapour, 150; of steam, 148

Specific heats, difiPerence of. 121 ; ratio of, 59, 122

Spring, 20

States of aggregation, 69, 132 : co- existence of, 153

Stohmann, 71

Sublimation, curve, 158, 161 ; theory of, 135

Substance, isomorphous, 182

Succinic acid, 243

Sulphur, 31 ; dioxide and water equilibrium, 180

Sulphuric acid, dissociation of, 238

Surface, developable, 164

System, condensed, 181 ; divariant, 181; gaseous, 207-222; hetero- geneous, 180; homogeneous, 119- 131 ; non-variant, 179 ; perfect, 44 : univariant, 180

Temperature, absolute, 6 ; critical, 17, 152; critical solution, 182; definition of, 2, 3 ; fundamental, 154; fundamental, of ice, 154

Thallium chlorate, 182

Theoretical regions, 19

Thermal equilibrium, 2

Thermochemical symbols, 68

Thermodynamic potential, 115

Thermodynamical theory of dilute solutions, 222 ; of fusion, vaporiza- tion, and sublimation, 135

Thermometer, gas, 3

Thiesen, 140

Thomsen, J., 68, 73, 235

Thomson, 36, 87, 146. See Joule and Thomson

Transformability of heat into work, 80

Triangle, fundamental, 159

Triple point, 155, 180

272

INDEX.

Uuit of heat, 32 Univariaat system, 180

V

Van der Waals' constants for CO^, 14 ;

equation, 13 Van't Hoff's laws, 255 Vaporization curve. 158, 161 ; theory

of, 135 Vapour densities, abnormal, 30 Vapour pressure, lowering of, 199 Variable, internal and external, 178

W

Warburg, 122

Water, dissociation of, 231

Weights molecular and equivalent!

22, 23 Work, and heat, analogy between, 53 ;

external, in reversible process, 51 ;

maximum, 111 Wullner's law. 199

Zero calorie, 33 ; energy, 44 ; state, 92

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