2 X 96600 X 0*102 = 19,700 joules strong acid to the weak. (2) Distil two mols of water from the weak acid to the strong this will effect the same change in distribution of water as in the electrical case. But further, we have to transfer two mols of H2SO, from the As H2SO, has no measurable vapour pressure, we must proceed as follows: separate the quantity 2(H,SO,.10H2O) from the stronger acid; distil 20H,O from the weak acid into this, so that its composition comes to be 2(H2SO,.20H,O). It can then be mixed without change of energy with the weaker acid, which possesses the same composition. The required amount of H2SO, has now been transferred, but the vessel of weak acid contains 20H,O more than it did. This excess must therefore be distilled back into the strong acid. The required changes are then accomplished. The amount of work done in these various processes has been calculated by Dolezalek.1 It consists essentially of the work done by the aqueous vapour in expanding from higher to lower pressure, and for the particular case considered is 19,900 joules. The discrepancy of one per cent. between this and the electrical estimate is, of course, attributable to experimental errors-the agreement, in fact, is very good. This method of calculating the change of free energy by the vapour pressure is only possible if no new chemical materials are involved in the reaction, consequently in only a few cases. The ordinary voltaic cell in which one metal displaces another from solution is beyond its reach. We cannot, then, compare the results of two methods of calculating free energy, and are thrown back on the electrical determination; but as the conclusion that any method will give the same result is deduced strictly from the fundamental principles of thermodynamics, it is worthy of entire confidence. Measurement of electromotive force may then be looked upon as a means of determining the change of free energy in a chemical reaction, and the most widely applicable means. 1 See Theorie des Blei-Akkumulator (Knapp: Halle). (ii) THE GIBBS-HELMHOLTZ EQUATION. There are great experimental difficulties in measuring the latent heat of action of a voltaic cell. Fortunately, however, there is an indirect means that is quite easy. It is well known that a close connection holds between the latent heat of evaporation of a liquid and the temperature coefficient of its vapour pressure; a similar thermo-dynamic relation holds between the latent heat of a cell and the temperature coefficient of its electromotive force. This relation forms one of the most essential parts of the theory, as given by Gibbs, Helmholtz (loc. cit.), and others. = The relation is: Latent heat quantity of electricity conveyed × absolute temperature × temperature coefficient of electromotive force; or, in symbols, if F = electricity conveyed by the reaction in cell, dE increase of E (the electromotive force) per degree, The last equation gives the means of calculating heats of reaction by merely measuring the electromotive force of a cell at two (or more) temperatures. Numerous examples of this equation have been worked out. We will first take Streintz's measurements on the lead accumulator referred to above. For acid of density 1153 the E.M.F. of an accumulator is found to increase 0'00032 volts per 1° rise of temperature (Streintz), or o'00037 (Dolezalek). We may then take the mean The temperature of Streintz's measurement of latent heat was the freezing-point, i.e. 273° absolute. Hence L = 2 X 96,600 X 273 X 0'000345 = 18,200 joules whereas direct measurement gave 17,400. The accumulator (with ordinary strength of acid) has a positive temperature coefficient, and therefore positive latent heat; the same is true of the Daniell. The Clark, on the other hand, has negative latent heat, and electromotive force decreasing with rise of temperature. The latter is the more frequent case. Amongst the best verifications of the Gibbs-Helmholtz relation are those of Jahn given in the following table. The last latent heat as calculated from the heat two columns show the :ZnSO4 +100H2O:Zn 10962 +0000034 50526 Cu:CuAc2aq :PbAc2+100H2O:Pb o'47643 +0000385 21684 Ag:AgBr :ZnBr2+25H2O:Zn 084095 -0'000106 O'9740 -0'000202 44332 46986 +2654 +2510 The first of these cells was taken as an instance of Kelvin's rule, in § 2. It will now be seen that even the slight discrepancy -one per cent.-that exists between the electrical work and the heat of reaction is accounted for by the thermodynamic treatment. The Clark and cadmium cells have been carefully examined from the thermodynamic point of view by Cohen; they present certain points of interest in the treatment of the thermo chemical data. 1 Wied. Ann., 28. 21-43, 491-508 (86); 50. 189–192 (93). 2 The quantities of work and heat are given in calories. The heat was measured in a Bunsen calorimeter. Jahn gives at first o'2394, afterwards 0.2362 cal. = I joule. The Clark cell1 at 18° (291° abs.) has an electromotive force of 14291 volts (mean of determinations by Kahle, Jaegar, and Callendar and Barnes); it falls off, in the neighbourhood of that temperature, by o'0012345 volts per 1° rise of temperature. Hence, taking (with Cohen) the faraday as 96,540 coulombs, we have and W = 1'4291 X 2 X 96,540 =275,920 joules L = 291 X (-0'0012345) X 2 X 96,540 69,360 joules Q=WL = 345280 joules. = This, then, is the electrical determination of the heat of reaction in the Clark cell. That reaction is usually described as Zn + Hg2SO1 = 2 Hg + ZnSO ̧ The data for calculating its thermal value are— Heat of formation of ZnSO, (Thomsen) 230,090 calories Now, Cohen or about 233,000 joules. This is far too low; but the salt formed in the cell is really the hydrate ZnSO,.7HO, which has a considerably greater heat of formation, as anhydrous zinc sulphate has a strong affinity for water. According to Thomsen, the "heat of hydration" is 22,690 cal.; adding this, Q becomes 77,780 cal., or about 327,000 joules. This is still six per cent. below the electrical determination. points out that the heptahydrate is formed in a solution already saturated, and can only get its water of crystallisation by withdrawing some from the solution; this, however, is necessarily accompanied by precipitation of some salt already in solution; hence the reaction in the cell will not be completely expressed unless this is taken into account. If the saturated solution has composition ZnSO.aH2O, then the water given up on crystallisation is a 7, and the amount required for union with 1 1 Cohen, Zeitschr. phys. Chem., 34. 62–68 (1900). ZnSO, can be obtained from solution. 7 The complete reaction is therefore a Zn+ ̧ ́-ZnSO ̧.aH ̧O+Hg.SO ̧=2Hg+ ZnSO1+7H2O 7 a-7 At 18° a = 16.81, and the measurements of J. Thomsen show that zinc sulphate in passing from the state of heptahydrate crystals to that of saturated solution absorbs 4694 cal. Introducing these numbers into the equation, we get for the total heat of reaction, 77,780 + 7 16.81 7 X 4694 81,127 = cal. This, with Jahn's value for the mechanical equivalent of heat (0*2362 cal. = 1 joule)1 gives 343,500 joules, about one-half per cent. below the electrical determination. The cadmium cell 2 requires similar treatment, but as it is made with amalgam instead of pure cadmium there are three parts to the heat of reaction. (a) 1 gram atom Cd is withdrawn from amalgam. (b) The cadmium so set free reacts with Hg2SO to form 2 Hg + CdSO.. (c) The CdSO, withdraws water from saturated solution, to form the hydrate CdSO..HO. The latter process follows the equation where a, as before, is the number of mols of water to one of salt, in the saturated solution. To determine (a) a cell was constructed with one electrode of pure electrolytically deposited crystalline cadmium, the other of amalgam, in solution of CdSO. The amalgam used was 14.3 per cent. It has since been found that this amalgam is subject to slow changes due to a "transition" to another state 1 It may be remarked, however, that this value (4'234 joules = I cal.) is certainly incorrect; it is probably 4'184 (Day, Phys. Rev., 6. 193-222 (1898)). 2 Cohen, Zeitschr. phys. Chem., 34. 612–620 (1900). |