THERMODYNAMICS OF DILUTEMOLTEN SILVERNITRATE
August, 1959
theory thus predicts a decrease in the size of the loop with increasing temperature and molecular size. Also it is to be expected that the point of hysteresis inception would move to lower relative pressures as the thickness of the adsorbed layer increases. A later form of the “open-pore” theory, as developed by Cohan, l 3 suggests that capillary condensation on adsorption would be assisted by a free-energy decrease due to the cylindrical film of liquid on the capillary walls. On adsorption, the pressure over a cylindrical film of radius r, is given by pa =
Poe-rV/rRT = p,e-rV/(ro-D)RT
where rc is the true radius of the pore and D is the thickness of the adsorbed film. On desorption, the pressure will be determined by the Kelvin equation pd
= poe-2rv/rcRT
This leads to a relation between the radius corresponding to the pressure a t the point of hysteresis inception and the thickness of the adsorbed film D. Thus when P , = P d = Pee- r V / ( r o - D ) R T and rc = 2 0 the thickness of the film is given by
yJf D = d RT -loge PI/Po where PI is the pressure at the beginning of hystere-
sis and is equal to PI =
Pae-rV/DRT
The present work indicates that one adsorbed (13) L. H. Cohan, J . Am. Chem. Soc., 60, 433 (1938); 66, 98
1259
layer is sufficient to initiate capillary condensation in the smallest capillaries. No progressive change in size of the loop was observed on ascending the series, but the range in size of the adsorbate molecules may have been too small to produce an observable effect. Table IV summarizes capillary condensation data for the various adsorbates. By comparing the pressure at the beginning of hysteresis (column 3) with the thickness of the adsorbed layer (column 7) it is seen that, for homologous series such as the normal paraffins and cycloparaffins, hysteresis begins progressively earlier on increasing the size of the adsorbate molecule. This is in accordance with the predictions of the “open-pore” theory but not with the “ink-bottle” theory. Column 5 gives the upper limit of hysteresis and the difference between columns 3 and 5 gives an indication of the size of the loop. Column 6 gives the value of the thickness of the adsorbed layer calculated from Cohan’s relation. This shows only a rough qualitative agreement with the value based on the assumption of hexagonal close packing, column 7. Column 8 gives the ratio of r L to Dhex,which is seen to lie between 2 and 3-a result which agrees with the observations of Emmett and Cines14for gases on porous glass and with those of Brown and Foster4 for amines on silica gel. Acknowledgments.-The author is indebted to Dr. D. C. Jones for his direction of this work and to the Governors of Queen Mary College for financial assistance. Thanks are due also to the Ministry of Education for the award of a maintenance grant. (14) P. H. E m m e t t and RI. Cines, THIS JOURNAL, 81, 1248 (1947).
(194.4).
THE THERMODYNAMICS OF DILUTE SOLUTIONS OF AgN03 AND KC1 IN MOLTEN ICNO3, FROM ELECTROMOTIVE FORCE MEASUREMENTS. I. EXPERIMENTAL BY MILTON BLANDER, F. F. BLANKENSHIP AND R. F. KEWTON Oak Ridge National Laboratory,l P . 0 . Box Y , Oak Ridgg, Tennessee Received December $8, 1868
Measurements of the activities of AgN03 were made in a fused salt concentration cell a t 370 and 436’ in dilute solutions of A + and C1- ions. The activities of AgNOa obeyed the Nernst law at the low concentrations of AgNOs measured when no ions were present The dissolution of KC1 in a AgNOa-KNOs mixture lowered the activity of AgN03. The lowering was larger the larger the amount of KCl added and for a given concentration of KCI was also larger the smaller the initial concentration of AgNO3. This shows that the Nernst law is not obeyed for AgN03in the presence of C1- ion.
81-
Introduction No general theory of molten salt solutions has as yet been presented. As a consequence, much of the recent work on thermodynamics of molten salt solutions has been reported in terms of complex ion formation; such interpretations have obvious deficiencies and may yield a misleading picture of ionic interactions in the melt. If the molten system is of sufficient simplicity it is possible to derive a theory which takes account of non-random mixing in the melt. These studies afford a basis for testing the quasi-lattice model (1) Operated for the United States Atomio Energy Commission by the Union Carbide Corporatias.
of molten reciprocal salt systems presented in the subsequent paper.2 Laity3 from e.m.f. measurements on AgN03NaNOa mixtures showed that the deviations from ideality of AgN03 in NaN03 are small. Freezing point lowering measurements indicate that the KNO3-KCI system behaves i d e a l l ~ . Flengas ~ and Ridea15 demonstrated the applicability of the Nernst equation t o silver-silver nitrate electrodes (2) M. Blander, THIS JOURNAL,63, 1262 (1959). (3) R. W. Laity, J . Am. Chem. Soc., 79, 1849 (1957). (4) E. Kordes, W. Rergman and W. Vogel, 2. Elsktrochem., 85, 600
(1951). (5) S. N.Flengas and E. I
