565 EXCHANGE Conductivity and Viscosity in Glyc erol and in Binary Mixtures of Glycerol with Ethyl Alco- hol, with Methyl Alco- hol, and with Water DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JAMES SAMUEIv GUY BALTIMORE June, 1911 EASTON, PA.: ESCHENBACH PRINTING Co. 1911 Conductivity and Viscosity in Glyc- erol and in Binary Mixtures of Glyceroi with Ethyl Alco- hol, with Methyl Alco- hol, and with Water DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JAMES SAMUEL GUY \\ BALTIMORE June, 1911 EASTON, PA.: ESCHKNBACH PRINTING CO. I9II TABLE OF CONTENTS. Acknowledgment 4 Introduction 5 EXPERIMENTAL. Apparatus 10 Solutions ii Solvents 1 1 Salts 12 Viscosity 12 Temperature Coefficients 12 Conductivity Data in Glycerol 13 Conductivity Data in Mixed Solvents 27 Comparison of Temperature Coefficients 47 Viscosities and Fluidities in Glycerol 50 Viscosities and Fluidities in Mixed Solvents 51 Salts with Negative Viscosities 52 DISCUSSION OF RESULTS. Conductivity 52 Viscosities and Fluidities 66 Negative Viscosity Coefficients 68 Summary of Conclusions 7 1 Biography 72 251860 ACKNOWLEDGMENT. The author desires to express his deep sense of gratitude to President Remsen, to Professor H. N. Morse, to Professor H. C. Jones, to Professor E. Renouf, to Professor C. K. Swartz, and to Associate Professor Acree for valuable advice and instruction which have been received both in the labora- tory and in the class-room. Special thanks are due to Professor Jones, at whose sugges- tion this investigation was undertaken and under whose direction it was carried out. Conductivity and Viscosity in Glycerol and in Binary Mixtures of Glycerol with Ethyl Alco- hol, with Methyl Alcohol, and with Water INTRODUCTION Jones and Schmidt, 1 in a previous paper published from this laboratory, gave a detailed historical sketch of the work of Jones with Lindsay, 2 Carroll, 3 Bassett, 4 Bingham, 5 Rouiller, 6 McMaster, 7 Veazey, 8 and Mahin, 9 dealing with the relations existing between conductivity and viscosity of a large number of electrolytes in binary mixtures of methyl alcohol, ethyl alcohol, acetone, and water. Schmidt worked with binary mixtures, and introduced glycerol as one of the solvents. The results of these investigations have been to show that curves representing fluidity and conductivity have, in general, the same form, whether they show maxima or minima as the composition of the mixture is changed. A fuller discussion of the results and conclusions drawn from the first seven of these investigations has been published as Monograph No. 80 of the Carnegie Institution of Washing- ton (1907). In all of these publications, due credit has been given to previous workers in this field, hence mention of their results need be made only in so far as they bear upon points of interest in this investigation. The work of Jones and Veazey 10 included a study of the conductivities and fluidities of cupric chloride and potassium sulphocyanate in mixtures of the same general composition as those used by Jones and Bingham. 11 Copper chloride 1 Am. Chem. J., 42, 37 (1909). 2 Ibid., 28, 329 (1902). 3 Ibid., 32, 521 (1904). * Ibid., 32, 409 (1904). 6 Ibid., 34, 481 (1905). Ibid., 38, 427 (1906). 7 Ibid., 38, 325 (1906). Z. physik. Chem., 61, 641 (1908). 9 Ibid., 69, 389 (1909). 10 Am. Chem. J., 37, 405 (1907). Ibid., 34, 481 (1905). gave results that were about normal, i. e., the curves repre- senting conductivity and fluidity were very similar. One of the most interesting points brought out in the in- vestigation of Jones and Veazey was the fact that in certain of the mixtures the solution of potassium sulphocyanate gave a viscosity that was less than that of the pure solvent. Euler 1 had noted that certain salts had the power to lower the viscosity of water, and explained this fact by the aid of the "electrostriction theory" of Drude and Nernst, 2 ac- cording to which there exists about every ion, by virtue of its charge, a strong electrostatic field, which causes a strong compression of the liquid in this field. Wagner and Miihlenbein 3 showed that Euler's reasoning could not hold, since the viscosity of a liquid could be lowered by the addition of certain nonelectrolytes whose viscosity was even greater than that of the solvent. In a word, the effect could not be due to any phenomenon specific to ions, since the molecules could produce the same change. Jones and Veazey 4 offer a possible explanation of this phe- nomenon. A careful study of all the viscosity data avail- able showed that only certain salts of potassium, rubidium, and caesium had the power of lowering the viscosity of water. The work of Thorpe and Rodger 5 had indicated that, in all probability, viscosity was a direct function of the skin friction of the ultimate particles present. This being the case, it is not surprising that some salts of the above named metals do not produce this effect, since it is clear that viscosity is an additive property of both the ions present. The one might tend to decrease, the other to increase the viscosity, and the final results would depend upon whether or not the sum of these two opposing influences was positive or nega- tive. These same three metals occupy the maxima on the well-known atomic volume curve of Lothar Meyer. 6 This, of course, means that these metals have very large atomic volumes. 1 Z. physik. Chem., 25, 536 (1898). 2 Ibid., 15, 79 (1894). 3 Ibid., 46, 867 (.1903). 4 Am. Chem. J., 37, 405 (1907). 5 Phil. Trans., 185, A, 307 (1894). e Ann. Chem. (Liebig), Suppl., 7, 354 (1870). With these facts at hand, Jones and Veazey offer the fol- lowing simple explanation as to how any substance may lower the viscosity of the solvent in which it is dissolved. If the atomic volume of the added electrolyte is larger than the molecular aggregates of the solvent, then the relative amount of skin friction in a given volume of solution would be decreased, and hence, according to the hypothesis of Thorpe and Rodger, 1 the viscosity, which is a direct function of the skin friction, would be decreased. Jones and Veazey use the same reasoning to account for an increase in viscosity when water and alcohol are mixed. Parts of these liquids, as shown by the method of Ramsay and Shields, 2 exist, when pure, in a highly associated condition. Jones and Lindsay, 3 in measuring the conductivities in such a mixture, had noted a minimum conductivity in a mixture containing fifty per cent, of each solvent. In a word, at this point the conductivity was less than that in either solvent independently. They offer the following explanation. Jones and Murray 4 showed that when two highly associated liquids, which in terms of the hypothesis of Dutoit and Aston 5 would have strong dissociating powers, are mixed, the one breaks down the molecular association of the other. This decrease in association would lessen the power of the solvent to dissociate a given electrolyte into its ions, and thus decrease the conduc- tivity. Jones and Murray actually found that the molecular weights of water, formic acid and acetic acid, when mixed in pairs, showed smaller values than in the pure homogeneous condition. This change in the molecular aggregation would increase the skin friction and thus increase the viscosity. This lowering of viscosity is of importance as bearing upon some facts established in this investigation, and these will be discussed later. It is well known that in a strongly dissociating solvent 1 Loc. cit. 2 Z. physik. Chem., 12, 433 (1893). 3 Am. Chem. J., 28, 329 (1902). 4 Ibid., 30, 193 (1903). 5 Compt. rend., 125, 240 (1897). 8 the conductivity of a ternary electrolyte is, in general, larger than that of a binary one in the same solvent since there is a larger number of ions present. Jones and Veazey 1 were able to show that potassium sulphocyanate in ethyl alcohol gave a larger molecular conductivity than copper chloride, while in aqueous solution the reverse was true. This, in the opinion of Jones and Veazey, was due to the fact that ethyl alcohol, being a relatively weak dissociating agent, had, at moderate dilutions, the power of breaking copper chloride down into only two ions. This fact will be referred to again under the discussion of the results obtained in this investiga- tion. Cattaneo 2 measured the conductivities of a few salts in glycerol and found values much smaller than in water. Schott- ner 3 and Arrhenius 4 measured the viscosities of glycerol and mixtures of this solvent with water and with other nonaqueous solvents. By far the larger part of the work, with glycerol as a solvent, has been done by Jones and Schmidt. The present investigation is a continuation of their work. Jones and Schmidt have shown that glycerol is an excellent solvent and, in all probability, a fairly good dissociating solvent, since it has a dielectric constant of 16.5 at 1 8, and an association factor of 1.8 at the same temperature. With such a dielectric constant and association factor glycerol, according to the Thompson 5 -Nernst 6 and Dutoit and Aston 7 hypotheses, should have a dissociating power approximately equal to that of ethyl alcohol. Jones and Schmidt believed that the extremely small conductivities shown by solutions of electrolytes in glycerol were due to the high viscosity of this solvent. With these facts before us, an attempt was made to study the relative ionic velocities of electrolytes in glycerol. The apparatus used for this purpose was that devised by Jones and 1 Loc. cit. 2 Rend R. Accad. Lincei, [5] 2, II, 112 (1893). 3 Wtenu Her., 77, II 682 (1878). 4 Z. physik. Chem., 1, 285 (1887). s Phi!. Mag., 36, 320 (1893). 6 Z. ph3'sik. Chem., 13, 531 (18941. 7 Lcc. cit. Basse tt, 1 and used subsequently in this laboratory. 2 A normal solution of copper chloride in such an apparatus was subjected to a current of 120 volts for forty-eight hours, and only a few milligrams of silver were deposited in the voltameter. Al- though no final data concerning the migration velocities were obtained, yet the above experiment was sufficient to show that the movement of the ions in solutions of glycerol must be extremely slow as compared with the movement of ions in water and the alcohols, etc. Jones and Getman 3 had measured the amount of solvation of glycerol in aqueous solution. This work has been repeated and was found to contain an error, probably in the strength of the solution. The following table shows that the amount of solvation is extremely slight even in the most dilute solutions. Table A Cor. N A A/m Wsol- Wglyc- W water Percent. L L' 0.2 0.383 1.91 25.1600 0.4603 24.6997 1.20 1.86 1.89 0.4 0.773 !-93 2 5- 2I 5o 0.9206 24.2944 2.82 1.86 1.88 0.8 1.627 2.03 25.4925 1.8413 23.6512 5.39 1.86 1.92 1.2 2.528 2.10 25.6300 2.7619 22.8681 8.52 1.86 1.92 1.6 3.482 2.18 25.9025 3.6826 22.2199 ii. 12 1.86 1.94 2.0 4.451 2.22 26.0650 4.6032 21.4618 14.15 1.86 1.90 2.4 5.764 2.34 26.2450 5.5238 20.7212 17.11 1.86 1.64 2.8 6.986 2.46 26.4375 6.4445 19.9930 20.03 J - 86 !-95 In this table N is the normality of the solutions, A the observed lowering of the freezing point corrected for the separation of ice, A/m the molecular lowering of the freezing point, W &ol the weight of 25 cc. of solution, W^ glyc the weight of glycerol in 25 cc. of solution, H/ water the weight of water contained in 25 cc. of solution, L the theoretical molecular lowering of the freezing point referred to 1000 grams of solvent, and L' the observed corrected lowering on the same basis. It is seen that the observed and theoretical molecular lowerings 1 Am. Chem. J.. 32, 429 (1904). 2 Ibid., 36, 427 (1906). 3 Ibid., 31, 303 (1904). 10 are nearly the same, indicating that the substance does not show any marked hydra tion in the solutions worked with. EXPERIMENTAL Apparatus In this investigation the Kohlrausch method of measuring conductivity has been employed, the improved Kohlrausch slide-wire bridge, resistance box, induction coil, and telephone receiver being used. The entire apparatus was made and carefully calibrated by Leeds, Northrup and Co., Philadelphia, and, in addition, the standard resistance was checked by the United States Bureau of Standards, Washington, D. C. The new form of bridge is a great improvement over the ordinary Wheatstone bridge, both in convenience and accuracy. By means of such a bridge readings may be checked, under favorable conditions, to one-tenth of a millimeter. The conductivity cells were of the same type as those de- scribed by Jones and Schmidt 1 and Jones and Kreider. 2 Such cells, as has been stated, have very small constants, and hence are well adapted to measuring the conductivity of solutions with high resistances. In every case the cell con- stants were determined by means of a fiftieth-normal potas- sium chloride solution, and checks made at frequent intervals showing only slight variations in the cell constants through- out the entire investigation. The molecular conductivity of the fiftieth-normal potassium chloride solution was taken as 129.7 reciprocal Siemens units at 25. The constant temperature baths were regulated by elec- trically-controlled regulators, devised by Reid, 3 and were kept within o.o2 of the desired temperature. The ther- mometers were carefully standardized by means of a certifi- cated Reichsanstalt instrument. All flasks, burettes, and other apparatus were carefully calibrated, by weighing, to hold aliquot parts of the true liter at 20. 1 Loc. cit. 2 Am. Chem. J., 45, 295 (1911). /&*., 41, 148 (1909). II Solutions For the work at 25, 35, and 45, solutions were made up at 20, while for the higher temperature work, the solutions were made up at 50. In all cases the mother solution was made by direct weighing of the carefully dried, anhydrous salt, and from this the N/SO and N/ioo solutions were made by dilution. These solutions then served as the mother solutions for the N/2oo and N/4OO, from which, in turn, the N/8oo and N/i6oo solutions were made. The highest dilution was made by diluting the N/4OO solution four times. Measurements were not made at dilutions higher than sixteen hundred, on account of the extremely high resistance and consequent difficulty in making the readings. In pure glycerol measurements were made at intervals of 10 from 25 to 75, while in the mixed solvents they were made only at 25, 35, and 45. Solvents Glycerol. The glycerol used was Kahlbaum's best double- distilled product, and had a mean specific conductivity of about 0.9 X icr 7 at 25. Schmidt had showed that redis- tillation did not essentially improve the glycerol. Its specific gravity showed that it contained about 0.02 of a per cent, of water. The two lots obtained from Kahlbaurn showed some- what different viscosities, as is indicated in the experimental results. Water. The water was purified by the method of Jones and Mackay, 1 with the modification as mentioned by Schmidt, and had a mean specific conductivity of 1.5 X io- 6 at 25. Ethyl and Methyl Alcohols. The ethyl alcohol was puri- fied by several distillations from the very best quality of lime, and block-tin condensers were always used. It had a mean conductivity of 1.8 X io~ 7 at 25. The methyl alcohol was first distilled from a small amount of dilute sulphuric acid and then several times from lime. It had a mean specific conductivity of 2.0 X io~ 6 at 25. 1 Am. Chem. J., 17, 83 (1895). 12 Salts In all cases, Kahlbaum's purest articles were used, and these were recrystallized at least three times from conduc- tivity water, carefully dried at 125, and the solutions made by direct weighing. Viscosity The viscosity measurements were made by means of the Ostwald viscosimeter as modified by Jones and Veazey, 1 and the size of the capillary so regulated as to be best adapted to glycerol measurements. The method of calibration has been discussed in detail by Schmidt. 2 Viscosity was cal- culated from the formula JL = Sl in which y is the viscosity coefficient for the liquid in question, rj Q that of water, S the specific gravity of the liquid, t the time of flow of the same, S the specific gravity of water at the given temperature, and t Q the time of flow of the water. Fluidity was calculated from the formula where 6 represents the fluidity. The values of T? O are taken from the work of Thorpe and Rodger, 2 being 0.00891 at 25, 0.00720 at 35, 0.00598 at 45, 0.005057 at 55, 0.004355 at 65, and 0.003786 at 75. Temperature Coefficients The temperature coefficients, both in per cent, and in conduc- tivity units, have been calculated, the latter being simply the actual increase in molecular conductivity per degree rise in temperature, while the former were calculated from the formula 10 1 Z. physik. Chem., 61, 641 (1908). 2 Loc. cil. 13 The temperature coefficients of fluidity were calculated in the same way. Viscosity measurements were made only with the tenth- normal solutions, since at higher dilutions the difference between the viscosity of the solution and that of the solvent was very slight. Table I Molecular Conductivity of Potassium Nitrate in Glycerol at 25, 35, 45 V n v 25 \ / I O 0-337 0.681 1 [.248 50 0.368 0.754 ^ [-384 100 0-373 0.769 ] [.419 200 0.397 0.818 i t-509 400 0.397 0.818 ] [.510 800 0.412 0.845 : t-569 1600 o . 43 1 o . 900 i t-739 Table II Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 O.IO2O 0.0833 O.O344 0.0567 50 0.1050 0.0835 0.0386 o . 0630 100 0.1061 0.0847 0.0396 o . 0650 200 0.1060 0.0845 0.0421 0.0691 4OO 0.1060 0.0846 0.0421 0.0692 800 0.1051 0.0857 0.0433 0.0724 I600 0.1084 0.0932 0.0469 0.0839 Table III Molecular Conductivity of Potassium Chloride in Glycerol at 25, 55, 45 V //i> 25 fty 35 l*v 45 10 0.385 0.772 [.413 50 0.405 0.841 .516 IOO 0.412 0.844 .538 200 0.415 0.850 545 400 0-439 0.852 571 800 o . 443 o . 870 .623 1600 0.536 0.915 .630 14 Table IV Temperature Coefficients Per cent. Cond. units V 25-35 35^5 25-35 35-45 10 o . 1005 o . 0830 0.0387 0.0641 50 o. 1074 o . 0804 0.0436 0.0675 100 o. 1048 O.O822 0.0432 0.0694 200 o. 1047 0.0818 0-0435 0.0695 400 0.0941 o . 0844 0.0413 0.0719 800 0.0964 0.0865 0.0427 0-0753 1600 0.0708 0.0781 0.0379 0.0715 Table V Molecular Conductivity of Potassium Bromide in Glycerol at 25, 55, 45 V ti v 25 fig 35* l*v 45 10 0.366 0.752 1-376 50 0.369 0.752 .396 100 0.384 0.778 434 20O 0.385 0.782 435 400 0.386 O.SOI 527 800 0-390 0.821 ] 578 1600 0.413 0.877 3 [.667 Table VI Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35 -45 10 0.1054 0.0829 0.0386 0.0624 50 o. 1041 0.0857 0-0383 o . 0644 100 o. 1028 0.0843 0.0394 0.0656 2OO O.I03I 0.0835 0.0397 0.0653 400 o. 1080 o . 0906 0.0415 O.O726 800 o . i 104 0.0922 0.0431 0.0757 1600 O.II23 0.0901 o . 0464 0.0790 Table VII Molecular Conductivity of Sodium Chloride in Glycerol at 25 45 V M,25 ifl 35 v 45 10 0.328 0.666 .223 50 0-351 o. 711 319 100 0-353 0.720 350 200 0.372 0-753 409 400 0-375 0.765 .1 .421 800 0.391 o . 806 .588 1600 0-395 0.825 ] .629 Table VIII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 o. 1030 0.0838 0.0338 0-0557 50 o. 1024 0.0855 0.0360 o . 0608 100 o. 1038 0.0872 0.0367 o . 0630 200 o. 1024 0.0871 0.0381 0.0656 400 o. 1040 0.0856 0.0390 0.0656 800 o. 1 06 1 0.0970 0.0415 0.0782 1600 o. 1090 0.0 9 74 o . 0430 o . 0804 Table IX Molecular Conductivity of Sodium Iodide in Glycerol at 25 ( \ 35, 45 V t t v 25 M,35 7,45 10 0.342 o . 690 ] .265 50 0.364 0-737 .361 IOO 0.366 0-745 3 372 200 0-379 0.761 397 400 0.397 0.786 ] 452 800 0.388 0.760 1 [.418 1600 0-447 O . 840 3 1-557 Table X Temperature Coefficients Per cent. Cond. units V 25 -35 35-*5 25-35 35-45 10 0.1027 0.0833 0.0348 0-0575 50 0. 1021 0.0846 0.0373 0.0624 IOO 0.1035 0.0841 0.0379 0.0627 200 o. 1019 0.0836 0.0382 0.0636 400 0.0978 0.0847 0.0389 . 0666 800 0.0959 0.0865 0.0372 0.0658 1600 0.0879 0.0853 0-0393 0.0717 Table XI Molecular Conductivity of Sodium Bromide in Glycerol at 25, 35, 45 V ,25 W 35 /IT, 45 10 0.318 0.646 . 192 50 0-331 0.678 .260 IOO 0.332 0.682 293 200 0-359 0-734 .367 400 0.363 0-754 1 .410 800 0-379 0.784 .] .465 I6OO 0.384 0.791 -I [.515 IS Table XII Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25 -35 35-45 IO 0. 1034 .0846 0.0328 O.O546 50 0. 1046 .0864 0.0347 0.0582 100 0. 1054 .0884 0.0350 . 06 I I 2OO 0. 1042 .0868 0.0375 0.0633 400 0. 1077 o .0870 0.0391 0.0656 800 0. 1067 .0869 0.0405 0.068 1 1600 0. 1068 .0913 o . 0407 0.0724 Table XIII Molecular Conductivity of Sodium Nitrate in Glycerol at 25, 35 , 45 V W p25 l'-v 2 C O ^45 10 O 303 0. 617 I.I29 50 331 0. 677 239 100 338 0. 707 .284 200 355 0. 735 362 400 358 0. 737 J .378 800 372 0. 766 .412 1600 386 0. 796 544 Table XIV Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25 -35 35 -45 IO 0. 1033 0.0828 0.0314 0.0512 50 O. 1046 0.0830 0.0346 0.0562 100 0. 1096 0.0818 0.0369 0.0577 2OO 0. 1070 0.0851 0.0380 0.0627 400 O. 1058 0.0870 0.0379 0.0641 800 0. 1058 0.0843 0.0394 o . 0646 1600 O. 1062 o . 0940 O.O4IO 0.0748 Table XV Molecular Conductivity of Ammonium Chloride in Glycerol at 25, 35, 45 V ft v 25 f i v 35 Q f ' V 45 10 393 0.801 I 452 50 .411 o 849 I 543 IOO .426 0.879 i .605 200 o .427 0.889 i .623 4OO 432 0.889 i 639 800 .440 0.931 i .696 1600 o .442 0.948 I .709 17 Table XVI Temperature Coefficients Percent. Cond. units V 25 -35 35 -45 25 -35 35-45 10 0. 1038 . 08 I 2 o . 0408 0.0651 50 0. 1065 0.0808 0.0438 o . 0694 IOO O. 1063 0.0827 0.0453 O.O726 200 O. I080 0.0825 0.0462 0.0734 400 0. 1057 o . 0844 0.0457 0.0750 800 O. III3 0.0822 O.O49I 0.0765 I6OO O. 1123 o . 0803 o . 0506 0.0761 Table XVII Molecular Conductivity of Ammonium Bromide 45 W>45 I-39I 1.490 I-53I 1.632 I .642 1.694 I . 864 Table XVIII Temperature Coefficients Per cent. Cond. units in Glycerol at 25, 35, V l*o 25 /* 35 10 0-373 0.758 50 0.391 0.802 IOO 0-397 0.824 2OO 0.422 0.878 400 0.430 0.889 800 0.444 O.926 I6OO 0.492 1.034 V 25 35 35-45 25-35 35-45 10 o. 1032 0.0835 O -0385 0.0633 50 O. IO5I 0.0850 o .O4II 0.0688 IOO 0. 1075 0.0856 o 0427 0.0707 2OO O. 1080 0.0862 o 0456 0.0754 4OO O. 1069 0.0847 o 0459 0.0753 800 0. 1092 0.0829 o .0482 0.0768 1600 0. 1 102 o . 0803 .0542 0.0830 Table XIX Molecular Conductivity of Ammonium Nitrate in Glycerol at 25, 55, 45 V t*v25 iiv3S ^,45 10 0.345 0.696 1.272 50 0.-379 0.778 1.440 loo 0.392 0.805 1.488 200 o . 407 o . 840 i . 547 400 0.417 0.869 1-594 800 0.396 0.825 1-579 1600 0.437 0.917 1.651 iS Table XX Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0. 1020 0.0832 0.0351 0.0576 50 0.1053 0.0851 0.0399 0.0662 100 o. 1058 0.0850 0.0413 0.0683 200 o. 1063 o . 0844 0-0433 0.0707 400 o. 1084 0.0835 0.0452 0.0725 800 o. 1084 O.O9I4 0.0429 0.0754 1600 0.1095 0.0802 o . 0480 0.0734 Table XXI Molecular Conductivity of Barium Chloride in Glycerol at 25, 35, 45 V fjL-v 25 Aty 35 j u*45 10 0.315 0.664 .221 50 0.432 0.915 695 100 0.464 0.978 .803 200 0.502 I . 056 951 400 0.520 I . 101 994 800 0.561 I.I97 2 [.230 I6OO 0.565 1.332 a .368 Table XXII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 o. 1108 0.0839 0-0349 0-0557 50 O.III5 0.0853 0.0483 0.0780 100 o. 1108 o . 0844 0.0514 0.0825 200 0.1103 0.0852 0-0554 0.0895 400 o. 1116 o . 081 i 0.0581 0.0893 800 0.1134 0.0863 0.0636 0.1033 I6OO 0.1358 0.0778 0.0767 o. 1036 Table XXIII Molecular Conductivity of Barium Bromide in Glycerol at 25, 35 , 45 V n v 25 ^35 10 0.330 0.696 50 0.396 0.832 ioo 0.426 0.900 2OO 400 800 I6OO ,u v 25 0-330 0.396 0.426 0-443 0.474 0.520 0-530 0.938 I .001 1.127 1-157 I-3M- 1-566 1.698 1-774 1.896 2. 115 2.200 19 Table XXIV Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35 -45 10 0. 1109 0.0888 0.0366 0.0618 50 0. iioi 0.0882 o . 0436 0.0734 I GO O. III2 0.0887 0.0474 0.0798 200 0. 1117 0.0894 0.0495 0.0836 400 0. III2 0.0894 0.0527 0.0895 800 0. 1148 0.0876 o . 0607 0.0988 I6OO O. 1180 o . 0900 0.0627 o. 1043 Table XXV Molecular Conductivity of Barium Nitrate in Glycerol at 25, 55, 45 V fi v 25 fi v 35 ti v 45 10 0.246 0.517 0.959 50 0.347 0.738 .367 ioo 0.368 0.792 .479 200 0.401 0.871 .634 400 0.414 0.904 .719 800 0.456 0.988 .871 1600 0.462 0.991 1-897 Table XXVI Temperature Coefficients Per cent. Cond. units V 25-35 35-t5 25-35 35 -45 10 0. IIOI 0.0854 0.0271 o . 0442 50 o. 1126 0.0852 O.O39I 0.0629 IOO O.II52 0.0867 0.0424 0.0687 2OO o. 1170 0.0876 o . 0470 0.0763 400 o. 1168 O.O9OI o . 0490 O.O8I5 800 o. 1166 0.0893 0.0532 0.0883 I6OO 0.1145 0.0914 0.0529 o . 0906 Table XXVII Molecular Conductivity o) Calcium Bromide in Glycerol at 25, 55, 45 V ?* V 25 f t v 35 ^ 45 10 0.245 0.519 0.972 50 0.324 0.687 1.298 ioo 0.340 0.729 1-374 200 0.373 0.803 I-5H 400 0.386 0.833 1.556 800 0.395 0.882 1.721 1600 0.408 0.909 1-743 20 Table XXVIII Temperature Coefficients Per cent. V 10 50 IOO 200 400 800 1600 25-35 O. IIl8 O. 1120 o. 1144 O.II52 O.II57 0.1233 O. 1226 35-45 0.0873 0.0888 0.0883 0.0886 0.0951 0.0918 Cond. units 25-35 35 -45 3 0.0274 0.0363 0.0389 0.0453 . 06 I I o . 0645 o . 0430 0.07II 0.0447 0.0487 0.0501 0.0723 0.0839 0.0834 <0 35, 45 Table XXIX Molecular Conductivity of Strontium Bromide in Glycerol at 2$ ( v 10 50 45 100 20O 400 800 1600 0.264 0.340 0.365 0.388 0.391 0.409 0.428 0.556 0.717 0.776 0.831 0.876 0.886 0.924 054 .362 .468 .581 659 .681 758 Table XXX Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0. 1106 0.0895 0.0292 o . 0498 50 O. 1108 0.0899 0.0377 0.0645 IOO 0. 1126 0.0892 O.O4II 0.0692 200 0. H33 0.0903 0.0443 0.0750 4OO O. 1189 0.0893 0.0485 0.0783 800 0. 1166 0.0895 0.0477 0-0795 I6OO O. 1162 o . 0902 o . 0496 0.0834 Table XXXI Molecular Conductivit in Glycerol at 25 V M;25 10 0.235 50 0.323 loo 0.349 2OO 0.392 400 0.401 800 0.4II I6OO 0.449 55 of , 45 Strontium Nitrate o 0-501 0.687 0.744 0.833 0.872 0.891 0-945 0-934 .292 394 563 .686 .671 759 21 Table XXXII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 o. 1127 o . 0864 0.0266 0-0433 50 0. II2I 0.0885 0.0364 o . 0605 100 O.II3I 0.0871 0-0395 0.0650 200 0. II2I 0.0876 0.0441 0.0730 400 O.H73 0.0933 0.0471 0.0814 800 o . i i 70 0.0874 o . 0480 0.0780 1600 0. I 102 0.086 I o . 0496 0.0814 Table XXXIII Molecular Conductivity of Cobalt Chloride in Glycerol at 25, 35, 45 01 V 10 50 100 2OO 400 8oo 1600 0.270 0.369 0.391 0-455 0-473 0-497 0.519 0.546 0.744 0.784 0.911 0-959 1.005 i .040 .003 373 450 .691 779 -856 .920 Table XXXIV Temperature Coefficients Per cent. Cond. units V 25 -35 35 -45 25-35 35-45 10 0.1023 0.0836 0.0276 0.0457 50 O.IOI5 o . 0846 0.0375 0.0629 100 o. 1004 0.0849 0.0393 o . 0666 200 o. 1004 0.0857 0.0456 0.0780 400 o. 1027 0.0855 o . 0486 0.0820 800 0. 1022 0.0847 O.O5O8 0.0851 1600 0. 1002 0.0846 0.0521 o . 0880 Table XXXV Molecular Conductivity of Cobalt Bromide in v 10 50 100 2OO 400 800 I6OO 1 Schmidt. Glycerol at 25, 55, 45 fi v 25 0.364 0.460 0.468 0.514 0-533 0-552 0.564 A*, 35 0-744 0.932 0-953 1.045 i .076 1.103 i .091 /^45 370 .702 743 .911 .967 2.031 2.005 22 Table XXXVI Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 0.1043 0.0841 0.0380 0.0626 50 o. 1026 O.O826 0.0472 O.O77O 100 o. 1036 0.0829 0.0485 0.0790 200 0.1032 0.0827 0.0531 0.0866 400 O. IO2I 0.0827 0-0543 0.0891 800 0.0998 0.0841 0.0551 0.0928 1600 0.0934 0.0837 0.0527 0.0914 Table XXXVII Molecular Conductivity of Potassium Chloride in Glycerol at 55, 65, 75 V V 55 10 2.391 3.755 5.601 50 2.601 4- I2 4 6.176 100 2.707 4-252 6.300 200 2.734 4-34 1 6.489 400 2.738 4-470 6.691 800 2.817 4.562 6.862 1600 2.940 4-693 6.891 Table XXXVIII Temperature Coefficients Per cent. Cond. units V 55-65 65-75 55 -65 65 -75 IO 0.0570 0.0491 0. 1364 o. 1846 50 0.0586 0.0497 O. 1523 0.2052 100 0.0571 0.0482 0. 1545 o . 2048 200 0.0588 o . 0496 O. 1607 0.2148 4OO 0.0632 0.0499 0. 1732 0.2221 800 0.0623 o . 0504 O. 1745 0.2300 1600 0.0596 o . 0470 0. 1753 0.2198 Table XXXIX Molecular Conductivity of Potassium Bromide in Glycerol at 55, 65, 75 V /it; 55 n v 65 fi v 75 10 2.293 3-6i9 5-33 2 50 2.453 3-906 4.786 100 2.557 4.062 6.080 200 2.6o6 4-122 6.154 400 2^680 4-275 6.317 800 2.705 4.286 6.408 1600 2.770 4.400 6.897 23 Table XL Temperature Per cent. V 55-65 65-75 ' 10 0.0576 0.0473 50 0.0592 0.0481 loo 0.0587 0.0496 2OO O.O572 0.0493 400 0.0594 0.0477 800 o . 0584 o . 0496 1600 0.0588 0.0568 2 Coefficients Cond. units 55-65 65-75 0.1326 0-1453 0.1505 O.I5I6 O.I7I3 0.1880 0.2018 0.2032 0-1595 O.I58I o. 1630 o . 2042 O.2I22 0.2497 Table XLI Molecular Conductivity of Glycerol at 55, 65, 7 v fi-v55 M,65 10 2.006 3-153 50 2.203 3-500 IOO 2.299 3.656 200 2.325 3.683 400 2-397 3-7I5 800 2.438 3.760 1600 2-493 3-965 Sodium Bromide in 4-763 5.262 5-504 5.566 5-753 5.864 5-938 Table XLII Temperature Coefficients Per cent. Cond. units V 55-65 65-75 55-65 65-75 10 0.0570 0.0510 O.II47 o. 1610 50 0.0588 0.0503 0.1297 o. 1762 IOO 0.0590 0.0505 0.1357 0.1848 2OO 0.0584 0.05II 0.1358 0.1883 400 0.0550 0.0548 O.I3I8 0.2038 800 0.0542 0-0559 0.1322 0.2104 1600 0.0590 0.0497 0.1472 0.1973 Table XL1II Molecular Conductivity of Sodium Iodide in v 10 50 IOO 200 400 800 1600 Glycerol at 55, <*5, 75 An; 55 ltv6S 2. 101 3-300 2.246 3-568 2-347 3-731 2-377 3-756 2.441 3-865 2.410 3-833 2-591 4.263 A4,75 4.878 5-407 590 .604 .822 745 6-415 24 Table XLIV Temperature Coefficients Per cent. Cond. units V 55-65 65-75 55-65 65-75 10 0.0570 0.0478 o. 1199 0.1578 50 0.0588 0.0515 0.1322 0.1839 100 0.0589 o . 0498 0.1384 0.1859 2OO 0.0581 0.0492 0.1379 0.1848 400 0.0584 0.0506 o. 1424 0.1957 800 0.0591 o . 0498 0.1423 o. 1912 I6OO o . 0644 o . 0644 o. 1672 0.2152 Table XLV Molecular Conductivity of Ammonium Chloride in Glycerol at 55, 65, 75 V ,55 to 65 ft v 75 10 2 243 3- 576 5 -378 50 2 727 4- 312 6 442 100 2 .9OO 4- 610 6 .880 200 3 . IOI 4- 946 7 423 400 3 -314 5- 257 7 -855 800 3 389 5- 400 8 .078 1600 3 -645 5- 750 8 .780 n 26 Table LII Temperature Coefficients Per cent. Cond. units V 55 -65 65-75 55-65 65-75 10 0.0594 0.0503 0.1333 o. 1802 50 0.0581 0.0493 0.1585 0.2130 100 0.0589 o . 0492 o. 1710 0.2270 200 0.0592 0.0501 0.1845 0.2477 400 0.0587 o . 0494 0.1943 0.2598 800 0.0593 0.0495 O.2OII 0.2678 1600 0.0577 0.0527 0.2105 o . 3030 Table LIH Molecular Conductivity of Cobalt Chloride in Glycerol at 55, 65, 75 V M,55 ^65 /* 75 10 1.789 2.778 4. 102 50 2-373 3.686 5-447 100 2 .610 4-074 6.024 200 2.890 4-5I3 6.687 400 3.104 4.864 7.236 800 3.286 5-I78 7-750 1600 3-471 5-503 8.247 Table LIV Temperature Coefficients Per cent. Cond. units V 55 -65 65-75 55-65 65-75 10 0.0553 0.0476 o 0989 0.1324 50 0.0553 0.0477 O.I3I3 o. 1761 100 0.0560 o . 0478 o. 1464 0.1950 2OO 0.0561 o . 048 i o. 1623 0.2174 400 O.0566 0.0487 o. 1760 0.2372 800 0.0575 o . 0496 0.1892 0.2572 1600 0.0585 0.0497 0.2032 0.2744 Table LV Molecular Conductivity of Cobalt Bromide in Glycerol at 55, 65, 75 ft, 75 10 2.340 3.676 5.462 50 2.905 4.561 6.841 100 2.952 4.628 6-954 200 3.229 5.068 7-584 400 3-338 5 -242 7-904 800 3 429 5.420 8-549 1600 3.400 5-399 8. 112 Table LVI Temperature Coefficients Per cent. Cond. units V 55-65 65-75 55-65 65-75 IO 0.0571 o . 0485 0.1336 0.1786 50 0.0571 o . 0499 o. 1656 O.228O 100 0.0568 o . 0503 o. 1676 0.2326 2OO 0.0569 o . 0496 0.1839 0.2516 400 0.0572 0.05II o . i 904 0.2662 800 0.0582 0.0596 o. 1991 0.3129 1600 0.0588 o . 0508 0.1999 0.2713 Table LVI I Molecular Conductivity of Potassium Chloride in Glycerol at 25, 35, 45 V fi v 25 fi v 35 /45 10 59-8i 74-52 90.16 50 65.00 81.89 98-63 ioo 66.68 82.94 101.08 200 68.13 85.34 103.36 400 74-87 93 -4 112.24 800 77 85 96.30 116.68 1600 78.99 98.98 121.32 Table LXII Temperature Coefficients Per cent. Cond , units 25 -35 35-45 25-35 35-45 0.0341 0.0275 0.804 0.869 0-0345 0.0294 0.872 0-995 0.0336 0.0316 0-873 1-095 0.0338 o . 0300 0.887 1.056 0.0344 0.0294 0.983 I.I28 0.0344 0.0282 I .007 I . IO9 0-0345 0.0273 1-055 I . 121 Table LXIV Temperature .Coefficients Per cent. Cond. units V 25 -35 35-4S 25-35 35-15 10 0:0246 0.0212 I.47I 1.564 50 0.0258 O.O2O4 1.689 I .674 100 O.O244 0.0216 1.626 I.8I4 200 0.0253 0.02 I I I.72I 1.802 400 0.0243 O.O2O6 I.8I7 I .920 800 0.0238 0.0213 1-845 2.038 I6OO 0.0253 0.0226 1.999 2.234 Table LXV 10 50 100 200 4OO 800 1600 -Molecular Conductivity of Potassium Chloride in Water at 25, 55, 45 m,25 0Z/35 120-4 129.7 132.0 135-3 137-7 I38.I H0.3 143.0 154-5 158.5 161.6 165.4 165-8 169.3 166.7 181.2 184.7 189.3 193-8 194.8 197.9 Table LXV I Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 IO 0.0188 0.0158 2.26 2-37 50 0.0192 O.OI7I 2.48 2.67 100 O.O2OO 0.0166 2.65 2.62 2OO 0.0195 O.OI7I 2.63 2-77 400 0.0201 O.OI7I 2.77 2.84 800 0.0201 O.OI74 2.77 2.90 I6OO O.O2O6 0.0169 2 .90 2.86 Table LXV II Molecular Conductivity of Potassium Chloride in a Mixture of 75 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 V M;25 ^35 10 .21 2.05 50 .31 2.25 ioo .35 2.34 200 .41 2.43 400 f -53 2.63 800 -54 2.67 1600 -59 2.72 3.26 3.59 3.69 3-90 4.22 4.27 4.32 30 Table LXVIII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25 -35 35 -45 10 0.0694 o . 0590 0.084 O 121 50 0.0717 0.0596 0.094 134 100 0.0733 0.0577 0.099 135 200 0.0723 o . 0605 0. 102 O .147 400 0.0719 o . 0605 0. 110 159 8oo 0.0733 0.0599 O.H3 0. 160 1600 0.0710 0.0588 O.II3 o 160 Table LXIX Molecular Conductivity of Potassium Chloride in a Mixture of 50 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 V ^25 M,35 ^45 10 3.07 4.48 6.29 50 3-54 5-2i 7-38 ioo 3.76 5.63 7.86 200 4.09 5.94 8.37 400 4.40 6.56 9.27 800 4.52 6.76 9.61 1600 4.62 6.84 9.79 Table LXX Temperature Coefficients Per cent. Cond. units V 25-35 35^5 25-35 35-45 10 0.0459 o . 0404 O.I4I O.lSl 50 o . 047 i 0.0420 o. 167 0.217 IOO o . 0500 0.0396 0.187 0.223 200 0.0451 o . 0409 0.185 0.243 400 o . 0490 0.0413 0.216 0.271 800 0.0491 o . 042 i 0.224 0.285 1600 0.0481 0.0431 0.222 0.295 Table LXXI Molecular Conductivity o) Potassium Chloride in a Mixture of 25 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 V M,25 ^35 ^,45 10 7.26 9.31 11.94 50 8.31 10.78 I3.6I ioo 9.29 12.15 J 5-39 200 9.97 13.02 16.61 400 11-32 I5-3 1 1 9- 1 5 800 11.88 15.68 20.28 1600 12.37 16.31 21.06 Table LXXII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 O.O28I O.O282 0.205 0.263 50 0.0297 0.0262 0.247 0.283 100 0.0308 0.0267 0.286 0.324 200 o . 0306 0.0276 0.305 0-359 400 0.0352 O.O25I 0-399 0.384 800 0.0320 0.0293 0.380 0.460 1600 0.0319 0.0281 0-394 0-475 Table LXXIII Molecular Conductivity of Potassium Chloride in a Mixture of 75 Per cent. Glycerol with Methyl Alcohol at 25, j 5 , 45 V fi v 25 fi v 35 /t45 10 50 ioo 200 400 800 1600 2.22 2.41 47 58 78 83 2.83 3.58 3.93 4.07 4-21 4.52 4 . 64 4.62 5-43 5.91 6. i i 6.38 6 . 88 7.07 6.99 Table LXXIV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35H15 10 . 06 1 2 0.0517 0.136 0.185 50 0.0630 0.0505 0.152 o. 198 IOO o . 0640 o . 0500 o. 160 0.204 200 0.0632 0.0515 0.163 0.217 4OO 0.0625 0.0522 0.174 0.236 800 0.0639 0.0524 0.181 0.243 1600 0.0632 0.0515 0.179 0.237 Table LXXV Molecular Conductivity of Potassium Chloride in a Mixture of 50 Per cent. Glycerol with Methyl Alcohol at 25, j 5 , 45 V 10 50 ioo 200 400 800 1600 8.10 9.24 9.59 10.05 11.04 11.20 11.38 11.09 12.75 13.17 13-77 15-20 15-34 15-63 I 4-54 l6 -7i 17-48 18.22 20.17 20.41 20.64 32 Table LX XV I Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 0.0369 0.03II 0.299 0-345 50 0.0378 o . 03 i i 0-351 0.396 IOO 0.0374 0.0326 0.358 0.431 2OO 0-0375 0.0323 0.372 0-445 400 0.0376 0.0324 0.416 0-497 800 0.0371 0.0330 0.414 0.507 1600 0.0365 0.0321 0.425 0.501 Table LXXVII Molecular Conductivity of Potassium Chloride in a Mixture of 25 Per cent. Glycerol with Methyl Alcohol at 25, 35, 45 V w, 25 ^35 0045 10 21.76 26.55 3 1 - 11 50 25.85 31.45 37-75 loo 27.57 33-65 40-36 200 28.72 35-34 42-30 400 3 J -oi 38-19 45 -5 1 800 33-15 40-70 48-85 1600 33-99 42-05 49-55 Table LXXV III Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35^5 10 0.0220 0.0172 0-479 0.456 50 0.0218 O . O2OO 0.560 0.630 IOO 0.0221 0.0199 0.608 0.671 2OO 0.0230 0.0197 0.662 0.696 400 0.0231 0.0193 0.718 0.732 800 0.0227 0.0200 0-755 0.815 1600 0.0237 0.0179 0.806 0-750 Table LXXIX Molecular Conductivity of Sodium Nitrat in Glycerol at 25, 55, 45 V ft v 25 fi v 35 w45 10 0.303 0.617 1.129 56 0.331 0.677 1.239 loo 0.338 0.707 200 0-355 0.735 400 0.358 0.737 800 0.372 0.766 1600 0.386 0.796 .284 .362 .378 .412 544 33 Table LXXX Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.1033 0.0828 0.0314 0.0512 50 o . 1046 0.0830 o . 0346 0.0562 100 o. 1096 0.0816 0.0369 0.0577 2OO o. 1070 0.0853 0.0380 0.0627 400 0.1058 0.0869 0.0379 0.0641 800 o. 1058 o . 0843 0.0394 o . 0646 I6OO o. 1062 0.0939 0.0410 0.0748 Table LXXXI Molecular Conductivity of Sodium Nitrate in a Mixture of 75 Per cent. Glycerol with Water at 25, 35, 45 10 4.88 7.46 10.80 50 5-37 8.39 12.03 100 5.45 8.44 12.33 200 5.63 8.68 12.58 400 6.09 9.35 13-65 800 6.34 9.75 14.20 1600 6.37 9-75 14-34 Table LXXXI I Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0529 o . 0448 0.258 0-334 50 0.0561 0.0434 0-302 0.364 IOO 0.0549 o . 0460 0.299 0.389 200 0.0541 0.0449 0.305 0.390 400 0.0534 0.0459 0.326 0.430 800 0.0538 0.0455 0.341 0-445 1600 0.0531 o . 047 i 0.338 0-459 Table LXXXI 1 1 Molecular Conductivity of Sodium Nitrate in a Mixture of 50 Per cent. Glycerol with Water at 25, 35, 45 V W25 M,35 /Z7>45 10 18.87 25.41 33-03 50 20.60 27.84 36.08 ioo 21.26 28.79 37-35 200 21.46 29.34 37-98 400 21.69 29.63 38-4 2 800 23.73 31-74 42-17 1600 24.53 32-57 43-69 34 Table LX XX IV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 o . 0348 0.0298 0.654 0.762 50 0.0350 0.0298 0.724 0.824 IOO 0.0352 0.0297 0.753 0.856 200 0.0367 0.0295 0.788 0.864 4OO 0.0365 0.0294 0.794 0.879 800 0.0338 0.0329 O.SOI 1.043 1600 0.0329 0.0341 0.804 I . 112 Table LXXXV Molecular Conductivity of Sodium Nitrate in a Mixture of 25 Per cent. Glycerol with Water at 25, 35, 45' v 10 50 IOO 200 400 800 1600 48.19 52.17 53-65 54-47 55-25 60.09 62.03 60.40 64.90 68.25 69.18 69.74 75-35 77-90 AT 45 73-81 80.77 82-75 84.41 86.03 93-20 96.30 Table LXXXV I Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35 e -45 10 0.0253 0.0222 I. 221 I-34I 50 0.0244 0.0244 1-273 .587 IOO O.O272 0.0213 1.460 450 2OO 0.0267 0.0221 L47I 523 400 0.0264 0.0233 L449 .629 800 0.0254 0.0236 1.526 .785 I6OO 0.0254 0.0235 1.587 .840 Table LXXXV 1 1 Molecular Conductivity of Sodium Nitrate in Water at 25, 35, 45 V t*o 25 ^35 /* 10 94-7 II3-4 133-2 50 103.8 125.0 147-5 IOO 104.7 127.0 149-5 200 107.8 130.5 153-2 400 II3-7 135-3 159-6 800 113.0 135.8 160. i I6OO 116.0 142.6 169.7 35 Table LX XXV Til Temperature Coefficients Per cent. V 10 50 IOO 2OO 400 800 I6OO 25-35 0.0198 0204 0212 O2 1 1 0190 0201 0230 35-45 0.0175 0.0180 O.OI76 0.0174 0.0179 0.0179 O.OI9O Cond. units 25-35 35-*5 I .87 I . 9 8 2 . 12 2. 25 2 23 2. 25 2 .27 2 . 27 2 .16 2 . 43 2 .28 2. 43 2 66 2. 7i Table LXX XIX Molecular Conductivity of Sodium Nitrate in a Mixture of 75 Per cent. Glycerol with Ethyl A Icohol at 25, 35, 45 V ^25 10 1.02 50 .17 IOO . 2O 2OO . 26 400 . 38 800 . 39 1600 .39 Table XC Temperature Per cent. V 10 50 IOO 2OO 400 800 1600 25-35 0.0736 0.0701 0.0742 0.0739 0.0721 o . 0746 0.0742 35-45 0.0576 o . 0605 0.0576 o . 0602 0.0582 0.0579 o . 0600 A^35 ^45 1.77 2.79 1.99 3-20 2.O9 3-30 2.19 3.51 2-37 3-75 2-43 3-84 2 .42 3-87 ire Coefficients Cond. units 25-35 35-45 0.075 O.IO2 0.082 O.I2I 0.089 O. 121 0.093 0.132 O.O99 0.138 o. 104 o. 141 0.103 0.145 Table XCI Molecular Conductivity of Sodium Nitrate in a Mixture of 50 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 V M,25 10 50 IOO 2OO 400 800 1600 3-08 3.68 3.89 4.04 4-52 4-70 4.80 Hv 35 4-49 5-4i 5-74 6.00 6.67 6-95 7-14 6.20 7.58 8.07 8.44 9-49 9.78 10. 18 36 Table XCII Temperature Coefficients Per cent. Cond. units V 25 -35 35-i5 25-35 35-45 10 0.0457 0.0381 o. 141 o. 171 50 o . 0470 o . 0400 0.173 0.217 100 0.0475 o . 0406 0.185 0-233 200 0.0478 o . 0406 o. 196 0.244 400 0.0475 O.O422 0.215 O.282 800 0.0478 0.0393 0.225 0.273 I6OO 0.0487 0.0426 0.234 0.304 Table XCIII Molecular Conductivity of Sodium Nitrate in a Mixture of 25 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 " V A* 25 /iz, 35 AH, 45 10 7.36 9.45 11.74 50 9-75 12.56 15.65 ioo 10.57 13.65 17.33 200 II-50 I4-85 18.87 400 12.89 16.85 2I -34 800 13-74 !7-7i 22.38 1600 14.00 18.36 22.72 Table XCIV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0284 0.0243 0.209 0.229 50 0.0288 0.0246 0.281 0.309 IOO 0.0292 O.O269 0.308 0.368 200 0.0290 0.0270 0-335 0.402 400 0.0305 0.0268 0.396 0-449 800 0.0288 O.O26l 0-397 0.467 1600 0.0305 o . 0244 0.436 0.436 Table XCV Molecular Conductivity of Sodium Nitrate in a Mixture of 75 Per cent. Glycerol with Methyl Alcohol at 25, 35, 45 V M,25 M,35 M,45 10 1.86 2.99 4.54 50 2.07 3.42 5.31 ioo 2.17 3.58 5-43 200 2.24 3-64 5.62 400 2.41 3-99 6-02 800 2.53 4.08 6.24 1600 2.49 4- J 3 6.26 37 Table XCVI Temperature Coefficients Per cent. Cond. units V 25 -35 35 -45 25 -35 35 -45 10 .0603 O. 0519 0. H3 155 50 .0652 O. 0552 0. 135 O .189 100 o .0650 0. 0521 0. HI O .185 200 .0714 0. 0544 0. 1 60 O . 198 400 .0654 0. 0510 O. 158 .203 800 o .0613 O. 0532 0. 155 .216 1600 o .0658 0. 0515 0. 164 o .213 Table XCVI I Molecular Conductivity of Sodium Nitrate in a Mixture of 50 Per cent. Glycerol with Methyl Alcohol at 25, 35, 45 V fi v 25 M>35 MIS 10 7-35 10.02 I3- 2 5 50 8.68 11.88 15.69 ioo 9.09 12.53 16.47 200 9.59 13-22 17-53 400 10.44 14.46 19.06 800 10.75 14.87 19-57 1600 10.80 15.08 19-57 Table XCVI II Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0363 0.0315 0.267 0.323 50 0.0368 O.O32O 0.320 0.381 IOO 0.0377 0.0314 0-344 0-394 200 0.0378 0.0304 0.363 0.431 4OO 0.0385 O.O3I8 0.402 0.460 800 0.0383 0.0316 0.412 0.470 1600 0.0390 0.0293 0.428 0.449 Table XCIX Molecular Conductivity of Sodium Nitrate in a Mixture of 25 Per cent. Glycerol with Methyl Alcohol at 25, 35, 45 V ti v 25 AT, 35 w 45 10 20.77 25.22 30.59 50 25.71 31.35 37.47 ioo 27.59 33-8i 40-3 1 200 28.8l 35.27 42.19 400 30.06 36.88 44-45 800 33-n 40.42 48.20 1600 34.00 41.82 49.76 Table C Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0214 0.0210 0-445 0-537 50 0.0223 0.0198 0.564 0.612 100 0.0224 0.0198 0.622 0.650 2OO O.O22O 0.0196 0.646 0.692 4OO 0.0225 0.0205 0.682 0-757 800 0.0218 0.0192 0.731 0.778 1600 0.0230 O.OI9I 0.782 0.796 Table CI Molecular Conductivity of Ammonium Bromide in Glycerol at 25, 35, 45 V ^25 i* v 3S H V 45 10 0-373 0.758 I-39I 50 0.391 0.802 1.490 IOO 0.397 0.824 I-53I 200 0.422 0.878 1.632 4OO o . 430 o . 889 I .642 800 o . 444 o . 926 1.694 I6OO 0.492 1-034 1.864 Table CII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-t5 10 0.1032 0.0838 0.0385 0.0633 50 O.I05I 0.0850 0.04II 0.0688 100 0.1075 0.0850 0.0427 O.O7O7 200 0.1080 0.0862 0.0456 0.0754 400 0.1069 0.0847 0.0459 0-0753 800 0.1085 0.0829 0.0482 0.0768 1600 0.1106 o . 0802 0.0542 0.0830 Table CHI Molecular Conductivity of Ammonium Bromide in a Mixture of 75 Per cent. Glycerol with Water at 25, 35, 45 V H V 2S fi v 35 M,45 10 5-53 8.48 12.28 50 5.91 9-14 I3-26 ioo 5.97 9.25 13.30 200 6.17 9-54 I3-83 400 6.62 10.28 I4-87 800 6.95 I0.8I 15-45 1600 7.29 11.20 15-88 39 Table CIV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0536 o . 0448 0.295 0.380 50 o . 0546 o . 0450 0.323 O.4I2 100 0.0548 0.0429 0.328 0.405 200 0.0546 o . 0446 0-337 0.429 4OO 0.0553 o . 0446 0.366 0-459 800 ^0555 0.0429 0.386 0.464 1600 0.0538 0.0420 0.391 0.468 Table CV Molecular Conductivity of Ammonium Bromide in a Mixture of 50 Per cent. Glycerol with Water at 25, 35, 45 V ^25 ^35 >i/45 10 24.31 32.58 42.06 50 25.74 34-54 44-59 100 26.62 35-6i 45-65 200 27.01 36.12 46.44 400 27.86 37.32 47.87 800 30.20 40-54 5 2 -33 1600 32-58 43-oo 54-79 Table CVI Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-3S 3S-45 10 o . 0340 0.0291 0.827 0.948 50 0.0341 O.O290 0.880 1.005 IOO o . 0340 0.0282 0.899 I .OO4 200 0-0334 0.0285 0.9II 1.032 400 0.0339 0.0278 0.946 1-055 800 0.0342 0.0288 1.034 I.I79 1600 0.0325 0.0275 I .042 I.I79 Table CVI I Molecular Conductivity of Ammonium Bromide in a Mixture of 25 Per cent. Glycerol with Water at 25, 35, 45 V ^,25 ^35 /H45 e 10 : ,.j 61.45 76.93 92.72 50 -;<;-, 66.55 83.43 101.38 loo '> -\ 67 .68 84 . 90 103 . 56 200 yjjjS 69.32 86.80 104.52 400 ,: : - 70.69 88.08 106.74 800 'y -:J 71.29 89.82 108.68 1600 o* 71-34 89.58 107.96 Table CVIII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 2 5-45 10 O.O249 0.0205 1.548 579 50 0.0254 0.0215 1.688 795 IOO 0.0255 0.0218 i . 722 .866 2OO 0.0251 0.0204 1.748 .772 400 0.0245 O.O2I2 1-739 .866 800 0.0258 0.0209 1.853 .886 I6OO 0.0255 0.0205 i .824 .838 Table CIX Molecular Conductivity of Ammonium Bromide in Water at 25, 35, 45 v 10 50 IOO 200 400 800 1600 122.7 I3L4 133-5 135-3 138.2 142.0 147.2 H-v 35 148.6 158.2 159-4 163.8 166.6 170.7 172.9 173.2 185.8 I87.I 191 . I 195-7 199-3 205.6 Table CX Temperature Coefficients Per cent. Cond. units V 25 -35 35 45 25 -35 35 ^5 10 0. 0212 O. 0165 2 59 2 .46 50 0. O2O2 0. 0174 2 .68 2 , 7 6 IOO 0. 0199 O. 0174 2 59 2 77 200 0. 02 1 1 0. 0168 2 -85 2, 73 400 0. 0205 O. 0170 2 .84 2 91 800 0. 0202 0. 0171 2 .87 2, 86 1600 O. Ol8o 0. 0183 2 57 3 27 Table CXI Molecular Conductivity of Ammonium Bromide in a Mixture of 75 Per cent. Glycerol -with Ethyl Alcohol at 25, 35, 45 10 50 IOO 200 400 800 1600 32 . 4 8 50 .61 55 65 67 25 55 59 77 2.62 2-85 2.82 3-55 3-97 .11 23 46 50 Table CXII Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25 -35 35 -45 10 o . 0704 0.0577 0. 093 .130 50 0.0689 0.0558 0. 102 .142 100 0.0703 0.0582 O. IO9 152 2OO 0.0721 o . 0560 O. 116 154 4OO 0.0699 0.0610 0. 107 .161 800 0.0721 0.0568 0. 120 O .161 1600 0.0699 0.0591 O. H5 .168 Table CXII I Molecular Conductivity of Ammonium Bromide in a Mixture of 50 Per cent. Glycerol with Ethyl Alcohol at 25, 35, 45 V /'- ; 25 Pv 35 pu 45 10 3 .69 5 43 7 59 50 4 30 6 .28 8 77 100 4 45 6 .76 9 .22 200 4 .68 6 ,90 9 .72 400 4 .72 7, .06 9 .88 8oo 5 .02 7< .48 10 45 1600 5 . 10 7< 59 10 5i Table CXIV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25 -35 35-45 10 .0472 0397 0. 174 O .216 50 O .0462 0.0396 0. 198 249 IOO O .0516 .0369 O. 231 .246 200 0475 .0401 O. 222 .282 400 0495 0399 0. 234 o .282 800 .0490 o 0393 0. 246 O .297 6OO .0489 .0389 o. 249 .292 Table CXV Molecular Conductivity of Ammonium Bromide in a Mixture of 25 Per cent. Glycerol with Ethyl Alcohol at 25, j 5 , 45 V /ty25 fi-v 35 Pv*5 10 8.51 10.85 13-39 50 10.54 13-94 *7-37 100 n-45 14.81 18.59 200 12.50 16.23 20.41 400 12.94 16.87 21.23 800 13.92 18.12 23.07 1600 14.38 18.91 24.05 42 Table CXVI Temperature Coefficients Per cent. Cond. units V 25-35 35-t5 25-35 35-45 10 0.0263 0.0237 0.234 0.254 50 0.0322 0.0247 0.340 0-343 100 0.0292 0.0255 0.336 0.378 2OO 0.0298 0.0259 0-373 0.418 400 o . 0303 0.0258 0-393 0.436 800 o . 0302 0.0273 0.420 0-495 I6OO 0.0314 0.0271 0-453 0.514 Table^CXVII Molecular Conductivity of Ammonium Bromide in Ethyl Alcohol at 25, J5, 45 V n v 25 n> 35 A* 45 10 16.7 19.3 21.6 50 23.8 27.3 30.9 ioo 26.9 31.1 35.5 200 29.8 34.7 39.8 400 34.5 40.0 47-2 800 37.6 44.2 51.0 1600 39.6 46.4 54.5 Table C XV III Temperature Coefficients Per cent. Cond. units V 250-35 35-45 25-35 35-45 10 0.0156 O.OII9 0.260 0.230 50 O.OI49 0.0130 0-350 0.360 IOO 0.0157 0.0137 0.420 0.440 2OO 0.0165 0.0144 0.490 0.510 400 0.0160 0.0180 0-550 0.720 800 0.0179 0.0154 O.66O 0.680 1600 0.0178 0.0173 0.680 0.810 Table CXIX Molecular Conductivity of Ammonium Bromide in a Mixture of 75 Per cent. Glycerol with Methyl Alcohol at 25, J5, 45 V H V 25 to 35" w/45 10 2.50 4.00 6.04 50 2.70 4.42 6-91 ioo 2.87 4.60 6.91 200 2.94 4.79 7-23 400 2.94 4.80 7.23 800 3.05 5-oi 7-53 1600 3.06 4-99 7-62 43 Table CXX Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25 -35 35 -45 IO 0. 0600 O.O5IO 0. 150 O. 2O4 50 0. 0636 0.0563 0. 172 O. 249 100 o. 0637 0.0502 O. 173 0. 231 2 GO o. 0629 0.05II O. 185 0. 244 400 0. 0633 0.0501 0. 186 0. 243 800 0. 0642 o . 0499 0. 196 O. 252 1000 o. 0631 0.0520 0. 193 0. 263 Table CXXI Molecular Conductivity of Ammonium Bromide in a Mixture of 50 Per cent. Glycerol with Methyl Alcohol <>t 25, 35, 45 V HT, 25 po 35 /4 , 45 10 9.66 13-03 16.86 50 10.99 14.78 19.33 100 11.33 15-44 21.13 200 n-74 16.06 21.03 400 11.99 16.43 21.59 8OO 12.22 I7.OO 22.3O 1600 12.63 !7-48 22.90 Table CXXII Temperature Coefficients Per cent. Cond. units V 25-35 35-^5 25-35 35~*5 10 o . 0348 0.0293 0-337 0.383 50 0-0345 o . 0308 0-379 0-455 100 0.0362 0.0368 0.411 0.569 200 0.0368 o . 0308 0.432 0-497 4OO 0.0372 0.0314 0-444 0.516 800 0.0398 0.0311 0.478 0.530 1600 0.0383 0.0310 0.485 0.542 Table CXXI II Molecular Conductivity of Ammonium Bromide in a Mixture of 25 Per cent. Glycerol with Methyl Alcohol at 25, 35, 45 V /45 10 59.1 65.4 73.0 50 74.2 82.9 91.7 ioo 79-5 90.3 99-5 200 83.3 94.1 105.7 400 89.3 98.5 111.5 800 90.9 102.2 1 17 .3 1600 93.4 105.0 118.3 Table CXXV I Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 0.0107 0.0116 0.630 0.760 50 0.0116 0.0106 0.870 0.880 IOO 0.0136 O.OIO2 I .080 0.920 200 0.0130 0.0123 I .080 i . 160 400 0.0103 0.0132 0.920 1.300 800 0.0125 0.0148 I.I30 1.510 I6OO 0.0124 0.0126 i . 160 1-330 Table CXXV II Molecular Conductivity of Strontium Chloride in Glycerol at 25, 35, 45 V n,2S 035 w,45 10 0.322 0.664 1.252 50 0.403 0.840 1-553 ioo 0.426 0.900 1-650 200 0-452 0.958 1-777 400 o . 475 i . 008 i . 866 800 0.483 1.037 1.934 1600 0.507 1-075 !-994 45 Table CXXVIII Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 o . 1062 0.0885 0.0342 0.0588 50 o. 1084 0.0855 0.0437 0.0718 100 O. III2 0.0833 0.0474 0.0750 200 0. IIl8 0.0854 o . 0506 O.oSlQ 4OO o. 1107 O.O85I 0-0533 0.0858 800 O.II50 o . 0863 0-0554 0.0897 1600 0. IIOI 0.0853 0.0568 O.O9I9 Table CXXIX Molecular Conductivity of Strontium Chloride in a Mixture of 75 Per cent. Glycerol with Water at 25, 35, 45 V n v 2S n v 35 AM; 45 10 5.85 9.13 13.38 50 6.90 10.82 16.08 100 7.29 n-45 16.78 200 7-76 I2 -34 18.07 400 8.61 i3- 6 3 19-99 800 9.21 14.56 21.23 1600 9.72 15.37 22.46 Table CXXX Temperature Coefficients Per cent. Cond. units V 25 -35 35-45 25-35 35-45 10 0.0560 0.0465 0.328 0.425 50 0.0565 0.0476 0.392 0.526 IOO 0.0571 o . 0466 0.416 0-533 2OO 0.0590 0.0467 0.458 0-573 400 0.0588 o . 0465 0.502 0.636 800 0.0581 0.0458 0-535 0.667 I6OO O.O58l 0.0458 0.565 0.709 Table CXXXI Molecular Conductivity of Strontium Chloride in a Mixture of 50 Per cent. Glycerol with Water at 25, 35, 45 10 28.08 38.38 51-30 50 33-35 45-12 59-31 loo 35 .19 48-17 63.40 200 36.84 50-59 66.13 400 38.74 52-59 69.16 800 42.03 56.88 74-78 1600 42.84 59 .08 79-39 4 6 Table CXX XII Temperature Coefficients Per cent. Cond. units V 25-35 3 -t5 25 -35 3 5-45 10 0.0315 0337 I 030 .292 50 0.0358 0315 I 177 .419 100 0.0369 o 0312 I 298 523 2OO 0.0373 0307 I 375 554 400 0.0356 0315 I 385 657 800 0-0354 0315 I 485 .790 1600 0.0378 0343 I 624 : 2.031 Table CXXXIII Molecular Conductivity of Strontium Chloride in a Mixture of 25 Per cent. Glycerol with Water 25, 35, 45 10 50 ioo 200 400 800 1600 79.7 92.2 97.7 102-3 103.8 107.1 109.2 100.5 II7.3 122.9 129.3 133.0 135 .6 137-3 122.3 H4 -2 152.2 159-8 163.0 168.7 170.2 Table CX XXIV Temperature Coefficients Per cent. Cond. units V 25-35 35-45 25-35 35-45 10 0.0261 0.0216 2.08 2.18 50 0.0271 0.0229 2-51 2 .69 IOO 0.0258 0.0239 2.52 2-93 2OO O.O26I 0.0235 2 . 7O 3-05 400 0.0281 0.0224 2.92 3-oo 800 O.O266 0.0243 2.85 3-3i 1600 0.0258 0.0238 2.8l 3-29 Table CXX XV Molecular Conductivity of Strontium Chloride 210.6 in Water at 25, 35, 45' v v 25 10 175-3 50 199.1 loo 207.5 200 215.4 400 224.5 80O 230.8 1600 235.9 249.1 252.5 262.7 274.8 279.0 285.6 //z>45 247.8 285.0 299.1 310.3 332-8 342-9 47 Table C XXXV I Temperature Coefficients Per cent. Cond. units V 25-35 35-*5 25-35 35-45 10 0.0201 O.OlSo 3-53 3-72 50 0.0250 0.0149 5-oo 3-59 IOO 0.0214 0.0146 4-50 4.66 200 0.0219 O.OI5O 4-73 4.76 4OO O.O224 O.OI7I 5-03 4.90 800 O.O2O9 0.0193 4.82 5.38 1600 0.0210 0.0200 4-97 5-73 Table C XXXV II Comparison of Temperature Coefficients of Ammonium Bromide from 25 to 55 in Mixtures of Glycerol and Water V 100 per cent. 75 per cent. 50 per cent. 25 per cent. per cent. IO O.IO32 0.0536 O.O34O O.O249 O.O2I2 50 O.I05I 0.0546 0.0341 0.0254 0.0204 ioo 0.1075 0.0548 0.0340 0.0255 0.0199 200 0.1080 0.0546 0.0334 0.0251 0.02 I I 400 0.1069 0.0553 0.0339 0.0245 0.0205 800 0.1085 0.0555 0.0342 0.0258 0.0202 1600 0.1106 0.0538 0.0325 0.0255 0.0180 Table CXXXVIII Comparison of Temperature Coefficients of Ammonium Bromide from 25 to 35 in Mixtures of Glycerol and Ethyl Alcohol V 100 per cent. 75 per cent. 50 per cent. 25 per cent. per cent. IO o .1032 .0704 0.0472 O .0263 O .0156 50 .1051 .0783 0.0462 .0322 .0149 IOO 1075 .0724 0.0516 .0292 0157 2OO o . I080 O .0721 0.0475 O .0298 .0165 400 . 1069 0755 0.0495 .0303 o .0160 800 .1085 .0721 o . 0490 .0302 o .0179 1600 . 1106 o .0699 0.0489 0314 .0178 Table CXXXIX Comparison of Temperature Coefficients of Ammonium Bromide from 25 to 35 in Mixtures of Glycerol and Methyl Alcohol 50 per cent. 25 per cent. per cent. 0.0348 O.O2O4 O.OIO7 0.0345 0.0214 0.0116 0.0362 0.0213 0.0136 0.0368 0.0218 0.0130 0.0372 0.0217 0.0103 0.0398 0.0218 0.0125 0.0383 0.0220 0.0124 V 100 per cent. 75 per cent. 10 o. 1032 O.O6OO 50 O.I05I 0.0636 IOO o. 1080 0.0637 2OO 0.1075 0.0629 400 o. 1069 0.0633 800 o. 1085 o . 0642 1600 o. 1106 0.0631 4 8 Table CXL Comparison of Sodium Nitrate from 25 and Water Temperature Coefficients of to 35 i n Mixtures of Glycerol V 100 per cent. 75 per cent. 50 per cent. 25 per cent. per cent. IO 0.1033 0.0529 0.0348 0.0253 0.0198 50 o. 1046 0.056l 0.0350 o . 0244 0.0204 IOO o. 1096 0.0549 0.0352 0.0272 0.0212 2OO o. 1070 O.O54I 0.0367 0.0267 0.02 1 1 400 o. 1058 0.0534 0.0365 0.0264 0.0190 800 o. 1058 0.0538 0.0338 0.0254 0.0201 1600 o. 1062 0.0531 0.0329 0.0254 0.0230 Table CXLI Comparison Sodium Nitrate from 25 and Ethyl Alcohol of Temperature Coefficients of to 35 in Mixtures of Glycerol V 100 per cent. 75 per cent. 50 per cent. 25 per cent. 10 0.1033 0.0736 0.0457 0.0284 50 o . 1046 0.0701 O.O47O 0.0288 IOO o. 1070 0.0742 0.0475 0.0292 200 o. 1096 0.0739 0.0478 0.0290 400 0.1058 0.0721 0.0475 0.0305 800 o. 1058 0.0746 0.0478 0.0288 1600 o. 1062 0.0742 0.0487 0.0305 Table CXLII Comparison of Temperature Coefficients of Sodium Nitrate from nd Methyl Alcohol 2 5 to 35 in Mixtures of Glycerol V 100 per cent. 75 per cent. 50 per cent. 25 per cent. 10 0.1033 o . 0603 0.0363 0.0214 50 o. 1046 0.0652 0.0368 0.0223 IOO o. 1070 0.0650 0.0377 0.0224 200 o. 1096 0.0714 0.0378 0.0220 400 o. 1058 0.0654 0.0385 0.0225 800 o. 1058 0.0613 0.0383 0.0218 1600 o. 1062 0.0658 0.0390 0.0230 Table CXLIII Comparison of Temperature Coefficients of Potassium Chloride from 25 to 35 in Mixtures of Glycerol and Water V 100 per cent. 75 per cent. 50 per cent. 25 per cent. per cent. 10 o. 1006 0-0554 0.0341 0.0246 0.0188 50 o. 1074 0.0556 0.0345 0.0258 0.0192 IOO o. 1049 0-0549 0.0336 0.0244 O . O2OO 20O o. 1047 0.0548 0.0338 0.0253 0.0195 4OO o . 0948 0.0550 0.0344 0.0243 O.O2OI 800 0.0962 0-0553 0.0344 0.0238 O.O2OI I6OO O.O7O7 0.0558 0-0345 0.0253 o . 0206 49 Table CXLIV Comparison of Temperature Coefficients of Potassium Chloride from 25 to 35 in Mixtures of Glycerol and Ethyl Alcohol V 100 per cent. 75 per cent. 50 per cent. 25 per cent. 10 o. 1006 0.0694 0.0459 0.0281 50 o . 1074 0.0717 0.0471 0.0297 100 o. 1049 0.0733 o . 0500 o . 0308 2OO o. 1047 0.0723 0.0451 0.0306 400 o . 0948 0.0719 o . 0490 O.G352 800 0.0962 0.0733 0.0491 0.0320 1600 o . 0707 0.0710 0.0481 0.0319 Table CXLV Comparison of Potassium Chloride from 25 c and Methyl Alcohol Temperature to 35 ( Coefficients of in Mixtures of Glycerol V 100 per cent. 75 per cent. 50 per cent. 25 per cent 10 o. 1006 O . OO I 2 0.0369 O.O22O 50 o. 1074 0.0630 0.0378 0.0218 100 o. 1049 o . 0640 0.0374 0.0221 200 o. 1047 0.0632 0.0375 O.O23O 400 o . 0948 0.0625 0.0376 0.0231 800 0.0962 0.0639 0.0371 0.0227 1600 0.0707 0.0632 0.0365 0.0237 Table CXLV I Comparison of Temperature Co efficients of Stron- tium Chloride from 25 to 55 in Mixtures of Glycerol and Water V 100 per cent. 75 per cent. 50 per cent. 25 per cent. per cent. 10 o . IO62 0.0560 0.0315 0.0261 0.0201 50 . 1084 0.0565 0.0358 O.O27I O.O25O IOO . III2 0.0571 0.0379 0.0258 O.O2I4 2OO .IIl8 0.0590 0.0373 0.0261 O.O2I9 400 o . IIO7 0.0588 0.0356 0.0281 0.0224 800 .1150 0.0581 0.0354 O.O266 0.0209 I6OO . IIOI 0.0581 0.0378 0.0258 0.0210 The last figure in all tables of "per cent." "temperature coef- ficients" should be disregarded. Table CXLV11 Viscosities and Fluidities of Solutions in Glycerol ai 25, 35, 45' Temp. coef. Salt 1) 25 1) 35 T) 45 6 25 035 045 25-35 35-45 KC1 6, .362 2.836 1.399 1571 0.3527 0.7147 0.124 0.103 KBr 6 197 2.760 1.376 1613 0.3623 0.7264 0.124 0.101 KNO 3 6 ,065 2.734 1.353 .1648 0.3659 0.7391 0.122 0.099 NaCl 6 .716 2.920 1.445 ,1613 0.3429 0.7143 0.124 0.106 NaBr 6 ,439 2.865 1.400 ,1553 0.3490 0.7143 0.124 0.106 Nal 6 .303 2.822 1.409 ,1586 0.3543 0.7105 0.124 0.101 NaN0 3 6 .288 2.803 1.405 ,1590 0.3546 0.7117 0.123 0.101 NH 4 C1 6 .142 2.741 1.360 ,1628 0.3649 0.7357 0.124 0.101 NH 4 Br 5 ,970 2.681 1.329 .1672 0.3729 0.7524 0.123 0.102 NH 4 NO 3 6 306 2.800 1.408 ,1587 0.3572 0.7097 0.124 0.099 BaCl 2 7 .447 3.288 1.626 .1343 0.3041 0.6150 0.126 0.102 BaBr 2 7 .100 3.199 1.571 .1409 0.3126 0.6366 0.122 0.103 BaCNOs^ 7 ,212 3.182 1.571 ,1387 0.3143 0.6516 0.126 0.107 SrCl 2 7.336 3.224 1.589 ,1363 0.3104 0.6291 0.127 0.103 SrBr 2 7 .337 3.219 1.574 ,1365 0.3107 0.6354 0.127 0.104 Sr(N0 3 ) 2 7 .640 3.335 1.640 ,1308 0.2998 0.6098 0.129 0.106 CaBr 2 7 .674 3.373 1.630 ,1303 . 2964 0.6135 0.127 0.106 Ca(N0 3 ) 2 7 .411 3.278 1.617 ,1350 0.3050 0.6184 0.125 0.103 Solvent 6.067 2.761 1.352 .1648 0.3683 0.7396 0.124 0.101 Table CXLVIII Viscosities and Fluidities of Solutions in Glycerol at 55, 65, 75 Temp. coef. Salt 1) 55 1) 65 T) 75 55 65 9 75 55 3 -65 < >5-75 KC1 0.7435 0.4353 . 2648 .345 2.297 3 776 071 064 KBr 0.7475 0.4353 0.2709 .338 2.297 3 692 065 o 061 NaBr 0.7664 0.4439 0.2689 .305 2.253 3 719 072 o 065 NH 4 C1 0.7366 0.4269 0.2613 .357 2.342 3 827 072 063 NH 4 N0 3 0.7284 0.4254 0.2618 .373 2.351 3 819 071 fc 062 CoCl 2 0.8225 0.4762 0.2884 .215 2.099 3 467 073 065 SrCl 2 0.8536 0.4932 0.2981 .172 2.028 3 355 073 065 Solvent 0.7415 0.4288 0.2620 1 .350 2.331 3 817 072 063 Table CXLIX Viscosities and Fluidities of Solutions in Glycerol at 55, 65, 75' Temp. coef. Salt ry 55 1} 65 T) 75 555 65 6 75 55 -65 65-75 KC1 .6387 3781 0.2334 .565 2.645 4.283 0.0689 0.0619 NH 4 C1 0.6457 3805 2318 .548 2.628 4.313 0.0697 0.0641 NH 4 N0 3 6251 3701 2291 .599 2.702 4.365 0.0689 0.0616 Nal 6524 3827 2340 .532 2.613 4.273 0.0705 0.0635 Ba(N0 3 ) 2 7080 o 4159 2544 .412 2.404 3.931 0.0702 . 0635 CoBr 2 o 7388 o 4292 2638 .353 2.329 3.789 0.0721 0.0629 Solvent 6370 3732 2309 .569 2.678 4.329 0.0706 0.0616 Table CL Viscosities and Fluidities of Solutions in Mixtures of Glycerol u-ith Water at 25, 35, 45 In Glycerol Temp. coef. Salt 7; 25 r l 35 ? 45 6 25 6 35 d 45 2 5-35 35-45 KC1 6 362 2 836 .399 1571 0.3527 0.7147 0.124 0.103 NH 4 Br 5 970 2 681 .329 1672 0.3729 0.7524 0.123 0.102 NaNOg 6 288 2 803 .405 1590 0.3546 0.7117 0.123 0.101 SrCl 2 7 336 3 224 .589 1363 0.3104 0.6291 0.127 0.103 Solvent 6 067 2 761 .352 1648 0.3683 0.7396 0.124 0.101 In 75 Per cent. Glycerol with Water KC1 NH 4 Br NaNO 3 SrCl 2 Solvent 0.3394 0.3278 0.3274 0.3642 0.3169 o .2003 .1932 .1947 .2179 .1884 0.1293 0.1249 0.1233 0.1326 0.1186 2.943 3.035 3.054 2.746 3.156 4.993 7 5.176 8 5.137 8 4 . 696 7 5.307 8 .733 .008 .111 .543 .431 0.069S 0.0699 0.0682 0.0713 0.0681 () .0549 .0547 .0558 .0606 .0586 In 50 Per cent. Glycerol -with Water KC1 0.06481 .04385 0.03187 15.27 22.82 31 37 . 0422 0347 NH 4 Br 0.06085 .04251 0.03102 16.43 23.52 32.05 0.0431 0321 NaNO 3 0.06333 0.04372 0.03216 15.79 22.87 31. 10 . 0447 0. 0363 SrCl 2 0.06607 .04563 0.03335 15.13 21 .90 29.99 0.0379 0.0369 Solvent 0.06109 0.04233 0.03114 16.37 23.63 32. 10 0.0438 0. 0358 In 25 Per cent. Glycerol with Water KC1 0.02054 o .01546 0.01246 48.68 64.67 SO .25 0.0328 o .0242 NH 4 Br 0.02046 o .01552 0.01226 48.88 64.50 81 .56 0.0320 0264 NaNO 3 0.02086 .01556 0.01235 47.95 64.28 80 .96 0.0340 o .0245 SrCl 2 0.02145 o .01614 0.01277 46.62 61.97 78 .31 0.0329 .0263 Solvent 0.01946 0.01466 0.01171 51.38 68.22 85.45 0.0327 0253 In Water KC1 0.00902 o .00729 0.00608 110.8 137.0 164 .6 0.0243 .0201 NH4Br 0.00894 o .00722 0.00609 112.0 138.6 164 .1 0.0246 o .0199 NaNO 3 0.00903 .00732 0.00608 110.8 136.6 164 .4 0.0236 .0202 SrCl 2 0.00927 .00749 0.00628 107.9 133.5 159.4 0.0237 0.0194 Solvent 0.00891 0.00720 0.00598 112.2 138.9 167.2 0.0237 0.0204 Table CLI Viscosities and Fluidities of Solutions in Mixtures of Glycerol with Ethyl Alcohol at 25, 35, 45 In 75 Per cent. Glycerol with Ethyl Alcohol Temp. coef. Salt KC1 NH 4 Br NaNO 3 Solvent KC1 NH 4 Br NaN0 3 Solvent 25 1.123 1.085 1.171 1.029 0.2175 0.2163 0.2213 0.2123 35 0.5942 0.5762 0.6185 . 5404 In 50 0.1377 0.1325 0.1360 0.1351 45 0.3387 0.3291 0.3509 0.3111 Per cent. 0.08840 0.08668 . 08906 0.08723 25 0.8904 0.9214 0.8547 0.9720 Glycerol with 4.598 4.731 4.523 4.712 35 1.683 1.736 1.635 1.830 Ethyl 7.381 7.550 7.353 7.402 45 2.952 3.039 2.850 3.215 Alcohol 11.31 11.54 11.23 11.46 25-35 0.0890 0.0885 0.0900 0.0912 0.0605 . 0595 0.0620 0.0600 35^5 ( 0.0754 0.0751 0.0762 0.0759 0.0533 0.0528 0.0527 0.0529 In 25 Per cent. Glycerol with Ethyl Alcohol KC1 0.04473 0.03263 0.02487 22.36 30.66 40.21 0.0371 0.0311 NH 4 Br 0.04396 0.03227 0.02442 22.75 31.01 40.94 0.0369 0.0326 NaNO 3 0.04464 0.03276 0.02481 22.40 30.52 40.31 0.0362 0.0320 Solvent 0.04184 0.03061 0.02303 23.90 32.77 43.42 0.0371 0.0324 In Ethyl Alcohol 0.01216 0.009526 0.007979 86.13 105.1 125.3 0.0219 0.0193 Solvent 0.0 1068 0.008683 0.007292 93.70 115.2 137.7 0.0227 0.0191 52 Table CHI Viscosities and Fluidities of Solutions in Mixtures of Glycerol -with Methyl Salt KC1 NaN0 3 Solvent KC1 NH 4 Br NaNO 3 Solvent KC1 NH 4 Br NaNO 3 Solvent NH 4 Br Solvent Alcohol at 25, 35 > 45 In 75 Per cent. Glycerol -with Methyl Alcohol 25 35 45 25 35 0.6308 .3512 0.2129 1.585 2.850 0.5999 .3347 0.2011 1.666 2.987 0.6362 .3590 0.2122 1.572 2.786 0.6242 .3519 0.2087 1.609 2.842 Temp. coef. 45 25-35 35-45 { 4.696 0.0797 0.0659 4.973 0.0793 0.0665 4.713 0.0771 0.0689 4.792 0.0763 0.0681 In 50 Per cent. Glycerol -with Methyl Alcohol 0.09521 0.06367 0.04474 10.51 15.70 22.35 0.0494 0.0423 0.09225 0.06300 0.04361 10.84 15.87 22.93 0.0464 0.0444 0.09717 0.06502 0.04574 10.29 15.74 21.87 0.0496 0.0436 0.09657 0.06512 0.04446 10.35 15.35 22.50 0.0484 0.0468 In 25 Per cent. Glycerol with Methyl Alcohol 0.020830.016310.0131 48.02 61.32 76.31 0.02760.0244 0.02064 0.01610 0.0130 48.46 62.11 76.01 0.0261 0.0223 0.02098 0.01627 0.0130 47.75 61.48 76.46 0.0287 0.0243 0.01886 0.01481 0.0119 53.01 67.53 83.71 0.0274 0.0240 In Methyl Alcohol 0.006254 0.005410 0.004745 159.9 184.8 211.2 0.0155 0.0143 0.005542 0.005066 0.004469 17 1.2 197.4 223.7 0.0157 0.0139 Table CLIII Table Showing Viscosities and Fluidities of Substances -which n'ere Found to Lower the Viscosity of Pure Glycerol at 25, 35, and 45 Temp. coef. Salt V 25 35 45 25 o 35 45 25-35 ?5-45 NaNO 3 0.10 5.367 2 425 1.222 0.1863 0.4125 0.8186 121 0.100 NH 4 Br 0.10 5.206 2 329 .187 0.1929 0.4264 . 8423 121 0.098 NH 4 Br 0.50 5.071 2 324 .189 0.1972 0.4302 0.8409 118 0.096 NH 4 I 0.10 5.108 o 320 .165 0.1957 0.4308 0.8583 118 0.098 NH 4 I 0.50 4.605 2 157 .080 0.2173 0.4745 0.9259 118 0.096 RbBr 0.10 5.183 2.332 .176 0.1975 0.4288 0.8502 117 0.098 RbBr 0.50 4.768 2 183 1.112 0.2098 0.4583 0.8998 6 118 0.096 Solvent. 5.298 2 .366 1.198 0.1888 0.4226 . 8347 118 0.097 DISCUSSION OF RESULTS A rise in temperature causes an increase in conductivity, which may be due to either or to both of the following causes : First, an increase in the number of the ions present, and second, an increase in the velocity of the ions. That the number of the ions does not generally increase with rise in temperature has been shown by direct measurement of the degree of dissociation by means of the conductivity method. This is in accord with the theory of Dutoit and Aston, 1 which 1 Loc. cit. 53 makes the dissociating power of a solvent a function of its own association. The degree of association of a solvent has been shown by the method of Ramsay and Shields 1 to decrease with rise in temperature; hence, its power to dis- sociate an electrolyte into its ions has been diminished. It is, however, true that the theory of Dutoit and Aston is only an approximation. The increase in velocity of the ions with rise in temperature must then be the one conditioning cause of the increase in conductivity. This change in velocity of the ions may be due to either or to both of the following causes : First, change in the viscosity of the medium through which the ions move; second, as Jones 2 and his coworkers have shown, to the change in complexity of the solvates which surround the ion. In no other solvent is the change in conductivity with change in temperature so pronounced as in the one which chiefly concerns this investigation, viz., glycerol. The chief cause of this change is largely the change in the viscosity of the solution, while we believe that there is some evidence brought out in this investigation that indicates the presence of glycerolates. Tables I to XXXVI, inclusive, give the molecular conductivi- ties at 25, 35 and 45 of all the electrolytes which we have studied in pure glycerol as a solvent. It is seen that in all cases the values for fi v are extremely small, but show, in general, a regular increase, both with increased dilution and with rise in temperature. Associated with each table of conductivity is a table giving; the temperature coefficients of conductivity, both in per cent, and in conductivity units. Since the latter show the actual increase in conductivity per degree rise in temperature, a dis- cussion of these data will bring out the most interesting points of this part of the work. Although the temperature coefficients of conductivity, when expressed in conductivity units, show, in general, a regular increase with increased dilution, yet this is much 1 Loc. cit. 2 Am. Chem. J., 35, 445 (1906). 54 more marked with ternary than with binary electrolytes. This fact has been observed by Jones 1 for aqueous solutions in a discussion of the work of West. 2 Results of the present investigation show that in glycerol the temperature coefficients of conductivity of any given substance, at high dilution, are larger than at lower dilution, and that the relative increase is greater with salts of barium, strontium, calcium, and cobalt than with salts of sodium, potassium and ammonium. These facts may be explained in terms of the theory of solvation. That solvation takes place in aqueous solution has been shown beyond reasonable doubt by Jones and his coworkers; and, indeed, Jones and Strong have obtained abundant spectroscopic evidence for solvates in glycerol as a solvent. If there is solvation, then, according to the mass law, in the more dilute solutions, where the amount of solvent per ion is greatest, we should expect to find the most complex solvates. Any change in temperature would produce the greatest effect where the solvation was greatest, that is, in the most dilute solutions. Again, this change in solvation should be more apparent in those salts which have the greater power of combining with the solvent, or, in the case of water, with those salts that have the largest number of molecules of water of crystallization. It cannot, of course, be said that salts of barium, strontium, calcium, and cobalt possess a power of combining with glycerol similar to that which they manifest towards water, but it is not surprising to find solvation more marked with these salts than with salts that have very slight hydrating power, such as the salts of sodium, potassium and ammonium. It is also true that salts of approximately the same hy- drating power show, in glycerol, temperature coefficients of the same order of magnitude. The molecular conductivities at low dilutions in nearly every case are smaller for ternary than for binary electrolytes, while at higher dilutions the reverse is true without excep- 1 Loc. cit. 2 Am. Chem. J.. 34, 357 (1905) 55 tion. This may be due to the fact that glycerol is only a fair dissociating agent, resembling methyl and ethyl alcohols, and has, at moderate concentrations, the power of producing only two ions from a ternary electrolyte, or at least dissociating a ternary electrolyte only to a moderate extent. One should expect to find the ternary electrolytes yielding more ions at higher dilutions, and, hence, showing a greater molecular conductivity than binary electrolytes under the same conditions. That this is true may be best shown by comparing the molecular conductivities of several of the binary and ternary electrolytes used. Salt fi v 10 fty 1600 KNO 3 0.337 0.431 KBr 0.366 0.413 NaCl 0.328 0.395 BaBr 2 0.330 0.530 Ba(NO 3 ) 2 0.246 0.462 Ca(N0 3 ) 2 0.283 0.472 SrCl 2 0.322 0.507 In the above table the molecular conductivities of several typical salts at 25 are compared at volumes 10 and 1600, respectively. These data confirm the above statement, that while at low dilutions a ternary electrolyte usually has the smaller molecular conductivity, at higher dilutions the re- verse is usually true. Tables XXXVII to LVI give the molecular conductivities and temperature coefficients of conductivity of all the salts studied at 55 , 65 and 75 . The same general relations hold at these temperatures as at the lower temperatures, viz., a regular increase in conductivity with increased dilution and rise in temperature; and a more marked increase, or a larger tem- perature coefficient, with those salts which in aqueous solutions possess the greatest power of hydration. The same reasoning employed above for the lower temperatures is applicable here. Tables LVII to CXXXVI, inclusive, contain the data for the molecular conductivity and temperature coefficients of con- ductivity, expressed both in per cent, and in conductivity units for potassium chloride, sodium nitrate, ammonium bromide, and strontium chloride in the various mixtures of glycerol with water, methyl alcohol, and ethyl alcohol. The results are plotted in Figures I to X, inclusive. H 150 25 50 Per cent. Glycerol Fig. I Conductivity of Potassium Chloride in Glycerol-Water at 25 57 - 5 ' 75 50 Per cent. Glycerol Fig. II Conductivity of Potassium Chloride in Glycerol-Ethyl Alcohol at 25 75 I 25 ro 50 Per cent. Glycerol Fig. Ill Conductivity of Potassium Chloride in Glycerol-Methyl Alcohol at 25 59 100 50 25 Per cent. Glycerol Fig. IV Conductivity of Sodium Nitrate in Glycerol-Water at 25* 6o - 5 I J 75 50 25 o Per cent. Glycerol Fig. V Conductivity of Sodium Nitrate in Glycerol-Ethyl Alcohol at 25 6i 75 50 25 o Per cent. Glycerol Fig. VI Conductivity of Sodium Nitrate in Glycerol-Methyl Alcohol at 25 62 T 5 125 I I I ioo 75 50 25 o Per cent. Glycerol Fig. VII Conductivity of Ammonium Bromide in Glycerol- Water at 25 50 25 o Per cent. Glycerol Fig. VIII Conductivity of jAmmonium Bromide in Glycerol-Ethyl Alcohol at 25 6 4 - 75 50 25 o Per cent, Glycerol Fig. IX Conductivity of Ammonium Bromide in Glycerol-Methyl Alcohol at 25 50 25 o Per cent. Glycerol Fig. X Conductivity of Strontium Chloride in Glycerol-Water at 25 66 These curves show that the conductivities in such mixtures do not follow the law of averages, but are always less. In every case there is a marked sagging of the curves, but in no instance was a minimum obtained. This deviation from the law of averages has been explained by the work of Jones with Lindsay and Murray, which has been discussed elsewhere in this paper. When glycerol is mixed with water, or with either of the alcohols, it is clear that the properties of the mixture are not additive, the one solvent tending to lessen the asso- ciation of the other; and, hence, their combined power of dis- sociating electrolytes is less than would be expected if there were no such lowering of each other's association. Potassium chloride and sodium nitrate are nearly insoluble in the alcohols, and yet curves expressing the conductivities of these salts in mixtures of the alcohols with glycerol are strikingly similar to those of ammonium bromide. This seems to indicate that the deviation from the law of aver- ages is due largely to the change in association of the glycerol. Tables CXXXVII to CXLVI, inclusive, give a comparison of the percentage temperature coefficients of conductivity from 25 to 35 of all the salts we have studied in mixed solvents. In pure glycerol these values are very large, being from ten to eleven per cent, per degree rise in temperature. They decrease very rapidly with the addition of either water or the alcohols. The temperature coefficients also decrease very rapidly with rise in temperature. VISCOSITIES AND FLUIDITIES Table CXLVII includes the viscosities and fluidities of the eighteen electrolytes whose conductivities I have studied. Measurements were made only with the tenth-normal solu- tions, since, at higher dilutions, the difference in viscosity between the solution and solvent is hardly large enough to be detected, much less measured. In nearly every case the viscosity of the solution is greater than that of the solvent. Ammonium bromide was found to be an exception to this rule, and will be discussed more fully. The temperature coefficients of fluidity are very large and almost equal to the 67 temperature coefficients of conductivity. That the former are larger than the latter is not surprising, since rise in tem- perature would decrease the dissociation and thus decrease the conductivity, which would, at least in part, offset the increase in conductivity caused by increase in fluidity. The ternary electrolytes show a much greater increase in viscosity than the binary electrolytes. It will be recalled that the salts which show the greatest increase in viscosity are those in which the solvation seemed to be the greatest. This increase in viscosity of the ternary over the binary electrolytes may be due to several causes. There may be a greater number of ions present, which, since the viscosity is a function of the skin friction, would increase the viscosity; or the molecules of the solvent, combined as solvates, may be so attached to the molecule of the solute as to hinder its move- ment. It is not supposed that in any case of solvation the molecules of the solvent are so held as to form a complex chemical molecule, since this would, of course, decrease the skin friction and thus lessen the viscosity of the solution. The fact that solutions of ternary electrolytes show greater viscosities than solutions of binary electrolytes may be a conditioning factor in the small molecular conductivity shown by them in the more concentrated solutions. It is, how- ever, hardly possible that this could account entirely for the phenomenon, since there is probably less actual dissociation of a ternary than of a binary electrolyte in the most concentrated solutions. It is probable, then, that the large viscosity of the ternary electrolytes in glycerol is due to a summation of at least two effects: The small atomic volumes of barium, strontium, calcium and cobalt, and possibly to some factor caused by solvation of the ions or molecules of the electrolytes, which, as stated above, would probably be greater with the salts of these metals than with salts of sodium, potassium and ammonium. Tables CXLVIII and CXLIX give the corresponding viscosity data at 55, 65 and 75. The same general relations seem to hold at the higher as at the lower temperatures. It was found necessary to give these results in two tables, since 68 the specific viscosity of the two samples of glycerol used in this part of the work differed to some extent. There was only a small difference in the specific conductivity of the two speci- mens used. This difference in viscosity may be due to some polymerization of the glycerol. The temperature coeffi- cients of fluidity at these higher temperatures are very similar to those of conductivity at the same temperatures. From the data obtained, we are justified in concluding that curves representing change in conductivity and change in fluidity with rise in temperature are very similar to one an- other. In a word, conductivity seems to follow fluidity quite closely over the range of temperature from 25 to 75. The fact that glycerol has such a very large temperature coefficient of viscosity presents the possibility of throwing some light upon the relation between viscosity and reaction velocity. It has long been felt that the viscosity of the medium in which the reaction is taking place must be taken into con- sideration, and if the velocity of some reaction could be fol- lowed, using glycerol as a solvent, it is highly probable that interesting results would be obtained. Glycerol, being such an excellent solvent, seems well adapted to such work. The viscosities and fluidities of solutions in the various mixtures of glycerol with the alcohols and with water are given in Tables CL to CLII, inclusive. Measurements were made only with the tenth-normal solutions, since the viscosities of the more dilute solutions differ very slightly from that of the solvent in each case. Curves representing the change in fluidity with concentration of glycerol are given in Figure XI. These curves are, in general, strikingly analogous to the curves representing the conductivities in the same mixtures, though it is seen that the increase in fluidity is more rapid than the increase in conductivity. The viscosities of the solutions are in nearly every case greater than that of the pure solvent. NEGATIVE VISCOSITY COEFFICIENTS One of the most interesting points brought out in this investigation is the fact that certain salts have been found to 6 9 . 150 H 2 . 700 CH 3 OH C 2 H 5 OH 50 25 Per cent. Glycerol Fig. XI Fluidity of Glycerol Mixtures at 25 yo lower the viscosity of glycerol. The fact that certain electro- lytes have the power to lower the viscosity of water has been known for some time, and the various theories put forward to explain such phenomena have been discussed elsewhere in this paper. Jones and Veazey 1 were the first to offer an apparently satisfactory explanation, the large atomic vol- umes of the metals whose salts produced such a change being the key to the phenomenon. The presence of elements with large atomic volumes, as has been stated, would decrease the amount of skin friction in a given volume of solution, and, thus, in terms of the theory of Thorpe and Rodger, would decrease the viscosity. Jones and Veazey pointed out that only salts of potassium, rubidium, and caesium produce a decrease in the viscosity of water, and that these salts do so in a direct ratio to their respective atomic vol- umes. Schmidt 1 had noted that the increase in viscosity of solutions in glycerol over that of the pure solvent was in an inverse ratio to the atomic volumes of the metals whose salts he studied ; but in no case did he find a negative viscosity coefficient in pure glycerol. The results showing negative viscosities in glycerol are given in Table CLIII. From this table it can be seen that one- tenth gram-molecule of rubidium bromide lowers the vis- cosity of glycerol about two per cent., while one-half gram- molecule lowers the viscosity of the solvent over eight per cent. This lowering of the viscosity of glycerol by a salt of rubidium is analogous to the lowering of the viscosity of water produced by the same salt. The explanation of this phenomenon may be sought for in the theory of Jones and Veazey, as elab- orated in the introduction to this paper, i. e., the large atomic volume of rubidium. Ammonium bromide and ammonium iodide produce the same effect on the viscosity of glycerol, as is seen in Table CLIII. It is clear that we can not speak of the atomic volume of ammonium, since we know of it neither in the "atomic" nor the "free" condition. It is, however, well known that 1 Loc. cil. ammonium is closely analogous chemically to potassium, caesium and rubidium, and it is not surprising to find it ex- hibiting the same physical behavior, such as the effect on the viscosity of a solvent. Summary of Conclusions Drawn from this Investigation (1) Glycerol forms mixtures with water, ethyl alcohol, and methyl alcohol whose properties are not additive. This is in agreement with the work of Jones and Schmidt. (2) Curves representing fluidity and conductivity are very similar to one another over the range of temperature from 25 to 75. (3) Salts which have the highest power of solvation show the greatest temperature coefficients of conductivity, and these are greater in the more dilute solutions. (4) In mixed solvents containing glycerol, with water, ethyl and methyl alcohols, the curves representing conductivity and fluidity are strikingly analogous. (5) The molecular conductivities of ternary electrolytes in glycerol at lew dilutions are usually smaller than those of binary electrolytes under the same conditions, while at high dilutions the reverse is generally true. (6) While the majority of the salts studied increase the viscos- ity of glycerol, yet certain salts of rubidium and ammonium lower the viscosity of glycerol. (7) Some evidence for the existence of glycerolates has been given. BIOGRAPHY. James Samuel Guy, the author of this dissertation, was born in Chester County, South Carolina, April i, 1884. His pre- liminary training was received in the public school of Lowry- ville, South Carolina. In the fall of 1902 he entered Davidson College, from which institution he received the degree of Bachelor of Science in 1905, and Master of Arts in 1906. During the years 1906-07 and 1907-08 he taught Mathematics in Fredericksburg College, Virginia. In the fall of 1908 he entered the Johns Hopkins University as a graduate student in Chemistry. His subordinate studies were Physical Chem- istry and Mineralogy. For the year 1910-11 he was appointed a Fellow in Chemistry. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. ocr 261- GAYLOP.G BfU MAKERS SYRACUSE, H.Y. AM