THE VIYC'QSITY AND DENSITY OB BUSIDIUM NITRATE SOLUTIONS. 403 L1V.-The Viscosity and Density of Rubidium Nitrate Xolutions. By HAROLDGREVILLESMITH,JOHNHULTON WOLFENDEN and SIR HAROLD HARTLEY. THEfollowing measurements carried out in 1922 were undertaken to complete our knowledge of the viscosity and density of aqueous solutions of the alkaline nitrates. Gruneisen (Wiss. Abh. Phys. Tech. Reichmnstalt 1904 4,239) has made measurements on the nitrates of sodium and potassium and lithium and cEsium nitrates have been studied in this laboratory by Applebey (J.y1910,97,2000) and Merton (ibid. p. 2454) respectively. EXPERIMENTAL. Materials.-The rubidium nitrate used was Merck's pure salt ; spectroscopic examination showed it to be free from all but negligible amounts of the other alkali metals.The salt was dried to constant weight at 210"immediately before use in every case. The conduc- tivity of the water used in making up solutions and in washing out pyknometers and viscometers ranged from 0.5 to 2 gemmhos. Temperature Control.-All the measurements were carried out ill two electrically controlled thermostats. The temperatures of the baths were determined by a thermometer which had been standard- ised by the Reichsanstalt and whose ice-point was confirmed in the course of the present work. The corrected temperatures of the two baths were 1840"& 0.005"and 26.01" 0.005" and tlie fltict,untions from tlie mean did not exceed 0.003". Results. TABLEI.-Viscosities at 18.00" and 25.01'.-&. C kh t,/ttoat 18". t,/L at 25.01'. N at Viscomete'1' Viscometer R.V. at N at Viscometer Viscomete'r R.V. at s01tll* KtC. 18". €3 2. G 3. 18". 25-01'. B 2. G 3. 25-01". A 0,09244 0.0932 1 0.98281 0.98300 0.99261 0.09306 0.98473 0.98464 0.99422 B 0.14440 0.14641 0.97303 0.97272 0-9877 0.1461 6 0.97604 0,97637 0.99100 C 0.18531 0.18870 0.96475 0.96487 0.98386 0.18838 0.96955 0-96957 0.98850 D 0.25123 0.25762 0.95283 0.952 7 8 0.97846 0.25716 0-95934 0.95825 0.98490 F 0.47418 0.49800 0.9 1556 0.91525 0.96278 0.49702 0.92635 0-92 62 6 0.97383 G 0.47581 0.49988 0.91460 0.91460 0.96225 0.49888 0.92564 0.92531 0.97326 H 0-71402 0.76984 0.87831 0.87821 0.94826 0.76815 0.89256 0.89266 0.96308 1 0.89168 0.98051 0-854G3 0-85431 0-94100 0.97821 0.87 130 0.87130 0.95877 J 0.98708 1-09699 0.84238 0.84206 0.93740 1.09434 0.86000 0.85982 0.95629 K 1.26927 1.4566 0~81010 0.81041 0.93128 1.4528 0-83109 0.83107 0.95421 L 1.5505 1.8391 0.78330 0.78334 0-9306 1.8341 0.80639 0.80682 0-95715 M 1.78637 2.1799 0.76418 0.76398 0.93388 2.1735 0.78976 0,78977 0.96394 TABLE11.-Densities at 18*00' and Values at 18-00'.Values at 25.01". F Pyknometer Pyknometer Pyknometer Pykno-Pykno-Pykno-\ Soh. ATtA*. 33. P. X. Mean.* meter M. meter P. meter X. Mean.* A 0.09244 1.009766 1.009767 1.00977 1.009665 1.009664 1.00966 B 0.14440 1.0 15309 1.01531 1.0 15144 1.015165 1.01515 Y C 0.1853 1 1.01973 1.01978 1-01973 1.0 1955 1-01960 1.01955 1 D 0.25122 1.02690 1.02690 1.02663 1.02663 E 0.36693 1.039536 1.039535 1.03954 1.039159 1.039 152 1.03916 F 0-47418 1.051702 1.051 752 1.051 70 1.051239 1.05 1265 1.05124 G 0.47581 1.052033 1.05204 1.051564 1.05156 H 0.7 1403 1.07970 1.07967 1.07967 1.07899 1.07897 1.07897 I 0.89168 1* 101144 1-1011S9 1.101 14 1.100267 1.100329 1.10027 J 0.98708 1.112880 1.112382 1.11288 1.111923 1.111941 1.11193 K 1.26925 1.149196 1.149225 1.14980 1.147982 1-1480 16 1.14798 L 1.5505 1.18783 1.18783 1.18637 1.18637 31 1.7863i 1-221956 1.22196 1a3202 75 1-2202s * See p.400. AND DENSITY OF RTJBIDIUM NITRATE SOLUTIONS. 405 I 'iscosity Menszcrewaent .-The method of measurementl aucl the viscometers md holders used were similar to those described by Applebey and by Merton. Every solution was measured in two viscometers both of which the late W.G.A. Hutchinson had shown by the constancy of tlw pressure-time product to obey Poiseuille's law. The time intervals ranging from 600 to 950 seconds were measured on a stop-watch graduated in fifths of a second and fitted with an electromagnetic release. The results are given in Table I in which Nwand N are respectively the weight normality (mols. per 1000 g. of solution) and the volume normality (mols. per litre) t and tware respectively the times of flow of solution and of water and R.V.is the mean relative viscosity (see below). Density Measurement .-The density of every solution was measured in two pyknometers of about 25 C.C. capacity the technique of Hartley and Barrett (J.,1911,99 1072)being followed. The results are shown in Table 11.Discussion of Results. Viscosity.-The relative viscosity of the solutions was calculated from the formula Following the practice of Applebey and of Merton no kinetic-energy correction was introduced. No correction was made for surface tension but the error involved is probably within the error of time measurement for solutions less concentrated than N/4. The agreement between independent determinations of the same solution in both viscometers suggests an average error of about one part in 10,000parts in the measurements of relative viscosity. This compares favourably with the concordance recorded by other ob-servers who have used more than one viscometer. The form of the viscosity-concentration curves at both temper- atures is similar to that of Gruneisen's curves for potassium nitrate and of Merton's curves for czesium nitrate.When the viscosity increment defined as (R. V. -l)/Nw,is plotted against the cube root of the weight normality the curve shows the minimum which Griineisen obtained with a number of salts In Fig. 1 the viscosity increments for the completed series of alkaline nitrates and for nitric acid at 18" are plotted against the cube root of the weight normality; it will be seen that the value of the increment decreases regularly with increase of atomic number. The inadequacy of most of the attempts to represent the relative viscosity-concentration curve of an electrolyte solution by an equation is well known. Thus the equations of Einstein (Ann. 406 SMITH WOLFENDEN AND HARTLEY THE VISCOSITY Ph.ysiE 1906,19,289) and of Herz (2.moly.Chem. 1917 99 132) do not admit of tho possibility of " negative viscosity "; that of Arrhenius (2. physikal. Ghem. 1888,1,285) -predicts no minimum in either relative viscosity or viscosity increment. ; that of Applebey (loc. cit.) predicts a viscosity increment minimum but when applied to our results for rubidium nitrate postulates an average hydration number for the two ions of about -3 ;the semi-empirical equation of Gruneisen (Zoc. cit.) is equally unsatisfactory when applied to our results since in spite of its three arbitrarily fixed constants it fails FIG. 1. 0.6 1.0 V Weight normal5 to reproduce with anything approaching the experimental accuracy the form of the viscosity increment-concentration curve.A much more promising form of equation correlating the viscosity and concentration of an electrolyte solution has recently been put forward by Jones and Dole (J.Amer. Chern. Xoc. 1929 51 2950) whose experimental data for the fluidity of barium chloride solutions were adequately represented over a concentration range 0.005-1.00M by the equation + = 1 + Adz + Bc where c is expressed in mds. per litre. They further showed tthat their equation is equally applicable to all the other published data on salts which increase flie AND DENSITY OF RUBIDIUM NITRATE SOLUTIONS. 407 viscosihy of water. In the ca-.seof caesiuoi nitrate which dimiiiishes tlic viscosity of water they found that the equation was obeyed over a more limited concentration range up to 0-2N.Moreover qualita- tive arguments based on the Debye-Huckel theory were advanced for believing that the coefficient A must always be negative i.e. that the relative viscosity of all electrolytes must be greater than unity at sufficiently high dilution. Dole and Falkenhagen (Physikal. Z. 1929,30 611) have developed this point of view mathematically and evaluated the constant A for the special case of a binary electro- lyte whose ions have equal mobilities. Experimental confirmation has recently been obtained by Joy and Wolfenden (Nature 1930 126 994) in the case of dilute aqueous solutions of potassium chloride. FIG.2. 0.060 ''0.040 -l-i I 2 0.020 0 5 1.0 1.5 dc.In view of these considerations it is of interest to compare the present experimental results with the Jones-Dole equation. As these authors point out the most convenient way of testing the validity of the equation is to plot (+ -l)/& against dzand to see if it straight line is obtained with a negative intercept on the axis of zero concentration. The data recalcula,ted in this way are shown in Table I11 and plotted in Fig. 2. It is clear from the figure that the intercept (which is numerically equal to A) is negative at 18" diminishes with rising temperature and is probably still negative at 25". The curves show convergence to linearity as the dilution increases but a,sin the case of cmium nitrate the Jones-Dole equation is valid only at concentrations less than about 0.2N.Density.-The concordance between the densities determined in the different pyknometers is in all cases well within the probable 40s SMITH WOLFENDEN AND HAltTLEP THE VISCOSITY TABLE111. l8*00". '5.01". Soltn. A B C D 14' G H I J K L M dc 0-3053 0.3826 0.4344 0.5075 0.7067 0.7070 0.8774 0.9902 1.0473 1.2069 1.3560 1.4765 1.00755 1.0 1244 1.0 1640 1.02201 1.03866 1.03923 1.05456 1.06270 1.06678 1.07379 1.0745 7 1.07080 4. (+ -1)/& 0-0247 0.0325 0.0378 0.0434 0.0548 0.0555 0.0622 0.0633 0.0637 0.0611 0.0550 0.0425 4;; 0.3050 0.3823 0.4340 06071 0.7050 0.7063 0.8764 0.9890 1.0469 1.2052 1.3542 14741 1.00581 1.00908 1.01 163 1.01533 1.02687 1.02747 1.03833 1.04300 1.04671 1-04799 1.04477 1.03741 $0 (4-l)/\'Z 0*01906 0.02375 0.0268 0.0302 0.0381 0.0389 0.0437 0.0435 0.0437 0-0398 0.033 1 0.0254 error of the viscosity measurement to which they are auxiliary.With the exception of solutions A E and J the concordance is liowever less satisfactory than might be expected in accurate pyknometry. This is attributable to the fact that the limited amount of rubidium nitrate available compelled us with all except the above-mentioned solutions to transfer the same quantity of solution from the first to the second pyknometer instead of making simultaneous determinations in two pyknometers. The evapor- ation incidental to this transfer and the second filling invariably AND DENSITY OIi' RUBIDIUM EI'J!RA'I% SOLUTIONS. 409 caused an increase in the density as measured in the second pykno- meter.We have therefore adopted the lower (and earlier) density value whenever the density of the solution was not measured on independent portions of the solution in the two pyknometers. We have calculated from t4he density results the contraction on solution of 1 mol. of rubidium nitrate at various concentrations. More significant results are obtained by calculating the " molecular solution volume " of the salt at various concentrations since the latter method has the substantial advantage that the density of the solid salt and the anomalies introduced by polymorphism etc. are not involved in the calculation. Table IV shows the molecular solution volume of rubidium nitrate at 18" and 25.01" over the concentration range measured and in Fig.3 this function for the completed series of alkaline nitrates at 18" is plotted against weight TABLEIV. Molecular solut,ioii Molecular solutioii vol. (C.C.). vol. (C.C.). -7 At At At At Soltn. Nto. 18.00". 25-01". Soltn. N,. 18-00". 25-01". A 0.09244 42.81 44.09 H 0.71402 44.18 45.08 B 0.14440 43.08 44.22 I 0-89168 44.54 45.40 C 0.18531 42.98 43.98 J 0.98708 44-98 46.82 D 0.25122 43-26 44.34 K 1.26927 45.65 46.06 E 0.36693 43.57 44.61 L 1.5505 45.54 46.27 F 0.47418 43.87 44-81 M 1.78637 46.27 46-76 G 0-47581 43.83 44.82 (Themolecular volume of solid rubidium nitrate is 47.64 c.c.) normality. The values for lithium nitrate are calculated from the data of Applebey those for sodium and potassium nitrates from the data of Gruneisen and those of czesium nitrate from the data of Merton.Summary. (1) The relative viscosity and the relative density of aqueous solutions of rubidium nitrate have been measured at 18" and 26" over the concentration range 0.092-1.786N. (2) The relative viscosity of rubidium nitrate solutions can be represented by the Jones-Dole equation at concentrations below O-ZN and the coefficient A of those authors is shown to have the negative value and negative temperature coefficient which they postulate. (3) The molecular solution volume of rubidium nitrate is shown to fall in the normal periodic sequence of the alkaline nitrates. BALLIOL AND TRINITYCOLLEGELABORATORY OXFORD. [Received,December 23rd 1930.1