2000 APPLEOEY: THE VISCOSITY OF SALT SOLUTIONS.CCX1.-The Viscosity of Salt Solutions.By MALCOLM PERCIVAL APPLEBEY.THE changes in viscosity produced when salts are dissolved inwater have been the subject of many important researches sincePoiseuille's classical work on the flow of liquids in capillary tubes.The results obtained by the earlier workers in this field may besummarised a,s follows :(1) The effect of salts on the viscosity of water is small, but;generally positive. Some salts, however (for example, potassiumchloride), diminish the viscosity of water.(2) The effect of salts in increasing the viscosity increases morAPPLEUEY : THE VISCOSITY OF SALT SOLUTIONS. 2001rapidly than the concentration ; the salts wliich diminish theviscosity have, however, less effect as concentration increases.Aminimum value is reached a t a certain concentration. The additionof more salt then raises the viscosity.(3) The effect of a salt in increasing the viscosity of water isadditively composed of a factor expressing the effect of the cationand a factor expressing the effect of the anion, when the solution issufficiently dilute.(4) The temperature-coefficient of the viscosity of a dilute saltsolution is approximately equal to that of water.These researches were necessarily confined to concentrated s o htions, since the methods used were not of sufficient accuracy t omeasure the small changes in viscosity produced by small quantitiesof dissolved salt. It should also be noted that the earlier work isvitiated by the fact that the authors did not investigate thebehaviour of their apparatus with respect to Poiseuille’s law, butalways assumed its rigid validity.The velocity of flow in theviscometers used was always greater than the limiting velocity atwhich eddying begins, and aboke which Poiseuille’s law is notrigidly obeyed. The error thus caused in the determinations cannotbe calculated from the data given.Within recent years attention has been directed to the phenomenaof viscosity in dilute solutions. The work of Kohlrausch (Proc.Roy. Soc., 1903, 71, 338) and that of Bousfield and Lowry (Phil.Trans., 1905, 204, A , 253) has shown the importance of studyingchanges of viscosity for the interpretation of the results obtainedin conductivity determinations. The applica.tion of Stokes’ theoremto strong eIectrolytes has made the knowledge of the viscosityeffect of salts in dilute solution of great importance in the measure-ment of ionisation and the application of the dilution law to thesesolutions.The advance in the accuracy of relative viscosity deter-minations necessary for the investigation of these problems wassecured by the important work of Gruneisen (Wiss. A bh. Phys.-Tech.Reichs., 1905, 4, 151). The theory of the viscometer was verythoroughly investigated by him, and methods of standardisationwere developed which enabled him t o determine the deviation ofany viscometer used from the simple Poiseuille law. His experi-ments were a11 corrected for this deviation, and furnish the firstaccurate determinations of viscosity in dilute solutions.Investigations have also been carried out by Hosking (Phil.Mag.,1904, [ ~ i ] , 7, 469), who has studied the effect of temperature andconcentration over wide limits for lithium chloride, whilst Bousfieldand Lowry (Phil. Trans., 1906, 206, A , 101) have also made someobservations on dilute solutions2002 APPLEBEY: THE VISCOSITY OF SALT SOLUTIONS.The work of Griineisen is remarkable for the discovery of ageneral phenomenon which the less exact methods of earlier workershad not revealed. He has shown that the viscosity-concentrationcurve for all salts has a change of curvature at the dilute end inthe sense that the first particles of salt added to water have agreater effect in increasing, or a less effect in diminishing, theviscosity of water than subsequent additions. The change ofcurvature is scarcely noticeable unless the curve is plotted on avery large scale.A much more convenient method is to plot thedifferential quantity :Relative viscosity - 1Molecular concentration’against the cube-root of t.he concentration as recommended byGruneisen.This change of curvature was observed by Griineisen with everymember of a large series of salts investigated by him. No sucheffect has ever been found in solutions of non-electrolytes. It isnot surprising therefore that Griineisen has endeavoured to connectthe phenomenon with ionisation. The following formula given byhim corresponds with the observations with fair accuracy over aconsiderable range :~- VI’lO- - Aa + B(l - a) + Cm,rnwhere ?/’lo = relative viscosity,m = molecular concentration,Q =degree of ionisation,The present work was undertaken with the following objects :(1) To carry the investigations to greater dilutions thanGriineisen reached, and thus t o thest his formula;(2) To determine the effect of temperature, especially in dilutesolutions ; and(3) To investigate the connexion between the viscosity of itsolution and its molecular and ionic conditions.Materials.-It was thought advisable t o investigate thoroughlysome one salt over wide ranges of temperature and concentration.Lithium nitrate was chosen, as its high solubility permits theinvestigations to be carried to very high concentrations.It wasobtained either from Kahlbaum or from Merck in the form ofcrystalline lumps with an indefinite amount of water of crys-tallisation. It appeared to be a mixture of the two hydrates,LiN03,4H20 and LiN0,,3H20, described by Donnan and Burt(Trans., 1903, 83, 335). It was recrystallised before use in the formof the trihydrate. A spectroscopic examination showed noand A , B, and C are constantsAPPLEHEY: THE VISCOSITY OF SALT SOLUTIONS. 2003impurities except a trace of sodium. The water used was con-ductivity water free from dust. The dissolved air was removed byexhaustion in the cold just before use. This precaution is necessaryto prevent the appearance of air-bubbles in the apparatus duringdeterminations.I'repumtion G f Solutions.-The anhydrous salt is extremelyhygroscopic, and very prolonged heating is necessary to bring it toa constant weight.The making up of solutions by weight is thus avery tedious process. It was therefore decided to determine theconcentration of the solutions used by means of a previously deter-mined density curve at 2 5 O . The dehydrationthis purpose did not present such difficulties, asless of the salt was necessary for a determination.The labour was also much lessened by the useof a specimen crystallised at about 70°, whichwas practically anhydrous. An appropriateweight of the salt was dehydrated by heating it,for at least twenty-four hours in a smallplatinum crucible in an air-bath heated by boil-ing aniline. The crucible was allowed to coolin a desiccator, and then weighed in a stopperedglass bottle.The correct weight of water wasthen weighed into a widemouthed stopperedbottle, and the crucible dropped in.Density Determinations.--The determinationsa t 2 5 O and 1 8 O were made in U-shaped pykno-meters of test-tube glass, holding about 10 C.C.Each pyknometer was weighed against a counter-poise, and the results were corrected fordisplaced air. The density of each solution wasdetermined with two separate pyknometers.On account of the expansion of the solutionbefore weighing, these pyknometers couldnot be used at Oo. The form shown inof the salt forFIG. 1.Fig. 1 was used for this temperature. The pyknometers used heldabout 20 C.C. The results usually agreed to 0.00002, although theagreement was not always so good at Oo.This is due, in part, tothe difficulty of temperature regulation, and in part to the con-tamination of the ground surface, in which the stopper fits, withsolution in some experiments. Simple wiping with a filter-paper(the usual method of cleaning the open end of a pyknometer) failsto remove this. The error might have been avoided if the stopperhad been ground on outside instead of inside the open end of thepyknonieter. F o r the purpose of viscosity determinations, however2004 APPLEBEY : THE VlSCOSlTY OF SALT SOLU'l'lUNS.an accuracy of 0*0001 is amply sufficient at Oo, and the errors werenever so large as this.Thefollowing equatibn was found to express the results with sufficientexactness to justify its use for calculating concentrations :where 8 = density of solution,The densities determined a t 25*01° are given in table I.~ ~ = 2 5 .1 0 3 (S - so) - 16.33'7 (S - sJ2,so = density of water,rn = concentration expressed in gram-molecules per 1000 gramsThe degree of accuracy obtained in determining concentrations inof solution,this manner may be seen by the second column of table I.TABLE I.--Densi{y of solutions of lithium nitmte at 25.01O.Concen tra1 ioncalculatedConcentration. from equation.0.0 0.00-1296 0.12960.1378 0.13880-1458 0.14630'1571 0.15770'1'124 0'17280-1971 0.198 10,2137 0.21 440'3145 0.31370.3255 0.32380.3605 0.36060,3905 0.3899"0.4248 0'40160'4851 0.48550'6066 0.60610 8283 0.82810.9059 0'9050*O '9960 0.98611 '0968 1.09601'2763 1.27521.8639 1.86332.2027 2'20202'4602 2.45913,4086 3'4093*5?376 5'849D25.01"4",-- \APyknometer PyknometcrI.11.1.00225 -1 *00262 1 '002631.00293 1 *002911.00338 1 -003381.00396 -1-00500 1005001.00565 1.005671 *00967 1.009io1'01008 1'010081-01158 1 -011551.01275 1.012771.01325 1.013251'01664 1-016681.02160 1.021631.03077 1 030821.03400 1'034021-03741 1.037411.04206 1 '042051.04967 1 -049671.07529 1'075271'09047 1.090471.10223 -1'14759 1'147581 -28344 1 '28340- -Meandensity.0.997071.002251.002621.002921.003381 '003961 *005001 .OD5661009691~010081.011571.012761 '01 3251 -0 16661-021611'030801'034011'0374 11 -042051'04967l.Oi5281'090471'102231'1 45591'28342The three solutioiis marked with asterisks show divergences con-siderably greater than the errors in determining the increase indensity.I n all three cases the concentrations calculated from thedensities are smaller than those calculated from the weighings.It is most probable that the salt used in these experiments was notfully dehydrated. These values have been omitted in calculatingthe constants of the equation.The The densities at 1 8 O and Oo are given in tables V and VIAPPLEBEY: THE VISCOSITY OF SALT SOLUTIONS. 2005values at 1 8 O agree very well with those determined by Kohlrauschand used by Gruneisen. The density determined by Perkin (Trans.,1893, 63, 68) for a 2-63 weight-normal solution (=18*17 per cent.)at 25O is, however, considerably higher than that read off mycurve.Viscosity Determinations.--The use of viscometers of the Ostwaldtype in the measurement of relative viscosity depends on thevalidity of the law of Poiseuille, which is expressed by the equation :7 r p 4 t?I= -*lv 9where q is the coefficient of absolute viscosity,p is the mean pressure producing flow,Yis the volume of liquid which flows through the capillary inthe time t,c is the radius, andE the length of the capillary.Since r, I, and V are constants depending only on the dimensionsof the viscometer, the relation :7 = pt x constantshould hold good for different liquids in the same viscometer, andif experiments are carried out with the same liquid flowing underdifferent pressures, the product pt will have a constant value whenthe viscometer obeys Poiseuille’s law.Griineisen (Zoc.cit.) has shown that this condit.ion is by no meansrigidly fulfilled by viscometers of the Ostwald type acting undertheir own hydrostatic pressure. He has found that the variationof pt is due to the fact that above a certain limiting velocity theflow of liquid in the viscometer is not steady, but that some of thepotential energy is expended in forming eddies within the liquid.Hence the liquid is not forced down the capillary so quickly as itshould be if Poiseuille’s law held good, that is, t is greater thandemanded by the simple law, and in consequence pt has a greatervalue than the ccnstant found with slow flow.Thus the phenomena of flow under varying pressures may besummarised as follows.When the pressure is small and the timelarge, pt is constant; on increasing the pressure and diminishingthe time, a point is reached where eddy-formation begins. Beyondthis point pt continually increases, and Poiseuille’s law no longerholds. The readings of a viscometer are only trustworthy whenthe time of flow is so large as to ensure that the product pt remainsconstant (for the same liquid) over the whole range of variation intime of flow to be observed in the actual determinations. Griineisenhas tested several viscometers in a manner similar to that to bedescribed later, and has published ( h e .cit.) the pt-t curve2006 APPLEBEY : THE VISCOSlTY OF SALT SOLUTIONS,obtained. He has then calculated a correction for the variation inp t over the region of his experiments, and applied this throughouthis work.It was thought possible to construct viscometers in which thiscorrection should be negligible by reducing the velocity of flowconsiderably below the limits attained by Gruneisen.This diminution in velocity of flow may be secured in threedistinct ways :(a) By reducing the diameter of the capillary.( b ) By lengthening the capillary.( c ) By reducing the hydrostatic pressure in the viscometer bybringing the two bulbs as near together as possible.(a) Some experiments were tried with viscometers constructedwith very fine capillaries.It was found, however, that the resultswere almost invariably vitiated by dust. The final form ofviscometer adopted had a capillary radius of about 0.2 mm.; thusmy tubes were considerably smaller than Gruneisen's, the radius ofwhich varied between 0.34 and 0.48 mm.( b ) and ( c ) To lengthen the capillary in the ordinary Ostwaldtype of viscometer is to increase the pressure proportionally. Theform shown in Fig. 2 was therefore adopted.* The bulbs cannotbe brought nearer together than a certain limiting distance depend-ing on the capillary rise in the viscometer; otherwise the liquidnever falls below the lower mark. I n the viscometers used, thelower mark was etched very near to the bulb where the capillarywits slightly enlarged.At the completion of the experiment, themeniscus came to rest a few millimetres below the mark. Thedimensions of the viscometers finally adopted were :Radius of capillary ..................... 0.2 mni.Length of capillary .....................Volume of bulb ...........................Mean difference of level .............. 10.8 cm. (approx.).How far the results given by any particular viscometer are vitiatedby eddy-formation also depends on the amount of irregularity in thecapillary (and especially at the ends of the capillary, where the flowsuddenly changes). I n the construction of a viscometer anythingapproaching a sudden change of diameter should be avoided. Thejunction of capillary and bulb should have the form of a smoothcone, as shown in Fig.2.11 t o 22 em.7 C.C. (approx.).* The same object has been attained by Griineisen by winding the capillary in aspiral. This method is, however, open to the objection that much of the energywhich should be expended in driving the liquid on is used iu changing the directinnof flow as the capillary bends. This results in a very high valne for the Griineiseneddy-correction. Since it was hoped to avoid the Griinciseii correction altogether 110experiments have been performed with spiral capillariesAPPLEBEV : THE VISCOSITY OF SALT SOLtJ’rIONS. 2007St an dard isat i o n of I’iscom e t e rs .-Alt hough from the dimensionsof the viscometers it was probable that Poiseuille’s law would beobeyed within the limits of experimental error, it was necessaryto carry out special tests so as to be certain that irregularities inthe glass were not present of such magnitude as to produce eddiesand thereby cause the viscometers to disobey the simple law. Themethod here described is similar to that used by Griineisen.I norder to test a viscometer, it is necessary to observe its time offlow under varying pressures when filled with water, and toinvestigate the variation of the product pt. The pressure in anyFIG. 2.K rirr, a c 0particular experiment is the sum of the external preksure appliedand the hydrostatic pressure due to the head of liquid in theviscometer. The latter varies during the experiment, and anaverage value has to be found in the following way.First, the small arm of the viscometer is attached to a, watermanometer, and the pressure directly read off by means of a,reading-telescope and scale, together with the level at which thewater stands in the viscometer.This determination is repeated forseveral different positions of the liquid in the viscometer, and acurve is drawn representing the variation in pressure head as th2008 APPLEREP : THE VISCOSITY OF SALT SOLIJTIONS.liquid falls in the viscometer. Secondly, by means of the reading-telescope, the time necessary for flow from the upper mark toknown distances below the mark is measured. By combining thesecurves, namely, variation of pressure with depth and variation oftime with depth, a curve is drawn which shows the variation ofpressure with time throughout the whole tube.From this a, valueis obtained for the average hydrostatic pressure during flow. Thisis usually approximately equal to the pressure at mean time, butdiffers from that calculated from the difference of level at meantime owing to surface effects; for exa.mple, in one viscometer :Meail hydrostatic prcssurc ......... 10.60 cm. of water at 25"Pressure at mean time , , . ...... ... ... 10'55 ,, ,, ,,Difference of level a t mean time ... 10.99 ,, ,, ,,measures the surface-tension effect, and will be considered later.The difference between the first and third of these numbersFIG. 3.The times of flow have now to be measured when a known escessof pressure is applied at the small arm of the viscometer. For thispurpose it is necessary to have an arrangement capable of exertinga small pressure, which shall keep quite constant during theexperiment.'I have found the apparatus shown in Fig. 3 to workvery satisfactorily. The vessels A and B, which contained water,were so large that the movement of the air into the bulb of theviscometer during flow made no measurable alteration in thedifference of level in A and B measured by the water manometer C.The pressure of the air in B remained constant t o 0.1 mm. ofwater during the experiment when the cork of B and the rubberconnexions were painted with celluloid varnish so as to preventleakage. The pressure in B can be varied by allowing air to escapefrom D or by forcing in air with a bicycle-pump at E. The rangAPPLEIZEP : THE VISCOSITT OF SALT SOLUTIONS.200910.94 758 '4 829711 *205 739.5 828611.93 695 8 830113-15 630'8 829513.69 605.0 828214.38 5i7.5 530414-85 558.8 829815.23 543.6 827915.83 524 ' 6 830416 '47 503.6 829417'14 483.6 828917.85 466*0 831818 '54 447'6 829919.26 431.4 830920.09 415.7 831120.96 396-5 831121.61 384.6 831121,868 380.8 832622.89 363.9 833023-94 348.5 834324.20 344.0 832524-75 337 2 834625*20 331.1 834425.68 3252 838125-94 321.7 834527.27 307.4 8383FIG. 4.Pressurex titne.840083008200300 400 500 600 700 800 secs.values of p t , although varying considerably, do not, a t low pressures,differ by more than the experimental error. A t higher pressures,p t rises above its normal value, the increase becoming rapid as thepressure increases.The experimental error in standardising isunfortunately much greater than that of the viscosity deter-minations. It is thus not quite certain that the tube obeysPoiseuille's law with the necessary accuracy. The following facts,however, indicate that the assumption is justifiable :(1) Within the attainable limits of accuracy of standardisationno deviation from Poiseuille's law can be detected until the timeof flow falls well below the minimum time of flow in the actualdeterminations.VOL. XCVII. G 2010 APPLEBEP: THE VISCOSITY OF SALT SOLUTIONS.(2) The times of flow of any pair of tubes filled with water werein the same ratio as the times of flow for any solution determined.This shows that either the tubes obey the law rigidly, or that theyall deviate to the same extent.(3) The velocity of flow in the capillaries of my viscometer isonly about one-fifth of that prevailing in Gruneisen’s experiments.The correction applied by him for deviakion from Poiseuille’s lawis only 0.045 per cent, for a normal solution of lithium nitrate.It is therefore probable that the deviation of my tubes fromPoiseuille’s law is not more than 0.01 per cent., and is consequentlynegligible for solutions less concentrated than normal.Time.-This was measured by means of a carefully tested stop-watch, which was always in a constant state as regards winding atthe beginning of each determination (the watch was always woundto its fullest extent half an hour before filling the viscometer). I nthe later experiments an electromagnetic device wits used to startand stop the watch.The error in time determinations with astop-watch is not greater than 0.2 sec., and with a large numberof determinations the error of the mean result is not more than0.1 sec. In view ofthe magnitude of the other errors of the determinations, particularlythe temperature effect, since with water a difference of 0.005O a t1 8 O produces a change of 0.2 sec. in the time of flow of the quickesttube used, it seemed useless to attempt any more accurate deter-mination of time.Cleaning.-As the deposition of the least particle of solid inthe capillary introduces errors far larger than the variations inviscosity which tho viscometers were designed to measure, it is ofthe greatest importance to clean the tubes thoroughly after eachdetermination with water containing no solid matter in solutionor suspended.I n this research, conductivity water made by distillation in aclosed apparatus (Hartley, Campbell, and Poole, Trans., 1908, 93,428) was used for washing the tubes.Before use it was carefullyexamined to see whether it contained any solid matter.The conductivity of water gives no certain indication of itssuitability f o r this purpose, for the conducting impurities remainingin a sample of good, distilled water are volatile (carbon dioxide andammonia) and have no effect in the viscometer, whilst, on the otherhand, organic impurities or suspended solids render the wateruseless, although their presence is not indicated by conductivitydeterminations.Consequently those samples of water which showedno suspended solid were chosen rather than those with a lowconductivity. The average conductivity of the water used wmThis is an error of 1 in 8000 at its maximumAPPLEBEY : THE V[SCOSITY OF SALT SOLUTIONS. 2011about 1 x 10-6 mho at 18O. The water was quite free from organicimpurities.In spite of all precautions, the tubes frequently became con-taminated with dust. When this happened, the tube was chargedwith a few C.C. of nitric acid and one drop of alcohol, and leftovernight.The presence of dust is betrayed by (1) the irregularity of theresults; (2) the failure of the tube to give the same time of flowfor water after washing and drying.After cleaning, the tube is dried by gentle heating, while itcurrent of air, freed from dust by passage through cotton-wool, isdrawn through it.Filling.-The viscometers are filled by pipettes of such contentas to fill them from the middle of the upper to the middle of thelower bulb.With this arrangement the alteration of hydrostaticpressure due to small variations in the volume filled in by thepipette is a minimum. The liquid (and, if necessary, the pipette)to be used is first brought to the temperature at which the experi-ment is to take place. The error of the pipettes was measured byweighing successive fillings of water. The greatest variation in sixfillings of an 8.7 C.C. pipette was 0.0022 C.C. Since the averagediameter of the lower bulbs of the viscometers at their widestparts was 3.8 cm., the greatest error occasioned by variations inthe volume of liquid delivered by the pipette will bein the head of liquid, and since the average head is 10.6 cm.ofwater, the error so occasioned is only 0.002 per cent., which isconsiderably less than the errors in determining the times of flow.The use of a pipette for filling the viscometer is therefore justified.When filled, the viscometer is fitted with the apparatus shownin Fig. 2 ( A ) , the object of which is to allow the liquid in theviscometer to be forced up the capillary, and to run down withoutcontact with dusty air. The liquid is forced up by pinching therubber tubing A , and applying pressure by means of it small hand-bellows a t B.The air which enters is freed from dust by a tightcotton-wool plug in C.* When the liquid has risen above theupper mark, the tube A is released, and the air pressure equalisesitself on the two sides of the viscometer. During the actual experi-ment no air from the outside enters. The friction of the air in Awas found to be negligible.As it is of great importance that the viscometer should be fixed* When the liquid in the viscometer is hygroscopic, and in all low temperatureexperiments the air is dried before passing into B.6 Q 2012 APPLEREP : THE VISCOSITY OF SALT SOLUTIONS.rigidly and always in exactly the same position, a special holder wasdesigned [Fig. 2 (B)]. The viscometer is fixed by means of thescrew A with its wider arm resting in two V grooves 13, B and across ( x in Fig.2) etched on the capillary, resting upon a linescratched on the sidepiece C. The whole apparatus, which isconstructed of stout brass, is now fitted on the brass plate D, threesteel pointe E, E, E fitting exactly into three conical holes F, F, P.The points being fitted, the two parts are fixed together rigidly bya nut which is screwed down on the screw G, which passes througha hole in the front plate. (The nut must not. be screwed down tootightly, or the steel points may be distorted.)The back plate is firmly attached to a wooden cross-piece supportedby two wooden uprights fixed firmly to the bench and supportedby stays so as t o be very rigid. The wooden parts were made ofwell-seasoned wood to avoid warping.With this apparahs theviscometer can be brought to exactly the same position for eachdetermination.Temperature.-Experiments were carried out at 25O, No, and Oo.For the experiments a t 25O and 18O the viscometers were immersedin thermostats holding 30 to 40 litres of water, which was kept inrapid motion by a good stirrer. Constancy of temperature wassecured by Lowry spiral regulators, gas heating being used for the25O bath, electric for the 18O bath. No variation of temperaturewaa ever observed on a thermometer divided into wide twentieths,which could be read t o 0-005°. The Oo bath was a well-stirredmixture of crushed ice and water. It usually remained constantt o 0'02O during an experiment. The results were calculated to Ooby the use of a temperature correction.Method of Ezperiment.-The time of flow is found for pureconductivity water, viscometer and pipette are then dried, and thesolution t o be determined is filled in.The time of flow is thenmeasured several times. Finally, the viscometer and pipette areagain cleaned and dried, and the water value is again determined.This precaution is necessary, as the water values sometimes slowlyincrease during successive fillings, owing to contamination withorganic matter or incomplete washings, and the change is so smallas to escape notice in any other way. In most of the determinationsperformed in this research, the original and final water valuesagreed to 0.2 sec. I n a few cases, where it was obvious by theappearance of a large and irregular water value after a constantsolution value that contamination had occurred in the final waterfilling only, the original water value was used in calculation.Calculation of Results.-The simple Poiseuille law gives APPLEBEY: THE VlSCOSlTY OF SALT SOLUTIONS.2013where 7 = viscosity,t = time of flow,p = hydrostatic pressure in the tube, andq0, to, and p , are the corresponding values for water.The average pressure producing flow is that of a column of waterequal to the mean difference in level diminished by a, quantityexpressing the buoyancy OP the air in which the experiment takesplace, and by a quantity depending on the surface effects, pro-portional to the surface tension.This pressure has been determinedin the course of standardising the tubes. It is equal to:where H = mean difference of level,H(S0 - A) - Kyo,so = density of water,A = 97 9 , air,yo = surface tension of water,K = a constant depending on the form of the apparatus.All the other terms in this expression being known, the constantThe pressure for the liquid to be determined will be:The relative viscosity q/q, is therefore given by the expression :andcan be evaluated.H(s - A) - Ky.or t H(8 - A) - Ky --t,’ P(s,-A) ’where P is the hydrostatic pressure in cm. of water as measured ins t an ditr disa ti on :or t s - x H - K y / st;s0-x P ’ *- _____where the small correction A is omitted from the surface-tensionfactor.It is to be noted that! no kinetic energy correction is to beapplied in calculating the results of experiments with viscometersin which the capillary opens into a reservoir of the same liquid.The correction calculated by earlier observers (Hagenbach, Pogg.Ann., 1860, 109, 385 ; Finkener, see Gartenmeister, Zeitsch.physikaJ.Chem., 1891, 6, 524) is only applicable when the liquidflows from the capillary directly into the air. I n viscometers ofOstwald type, however, the gain of kinetic energy at the beginningof the capillary is balanced by a lms of kinetic energy on emergingfrom the capillary into the lower bulb. The net increase of kineticenergy is therefore negligible, especially in viscometers of the slow-flow type described in the foregoing. Griineisen has shown tha2014 APPLEBEY: THE VISCOSlTY OF SALT SOLUTIONS.the introduction of such st correction into the pt values instandardising a good tube entirely destroys the regularity of theresults.I have therefore followed his practice, and omitted anycorrection for kinetic energy.The times of flow for water in the viscometers used are given inthe following table :TABLE 111.-Timss o f j o w for water (in aeconds).Time of flow T h e of flow Time of flowViscometer. at 25-01". at 18". at 00.4 1023-a 1207'7 2053'8R 800'2 943'5 1604-4703'6 830.3 1411'6 S- 6013'9 A3 - 7381'1--The slow tubes A and B were only used for very dilute solutions.Since the Griineisen correction for these determinations would haveFIG. 5.been negligible, these tubes were not standardised. The viscositydeterminations are given in tables IV, V, and VI.The viscositiesof the solutions at 18O are calculated from the equation developedabove.The surface tensions are interpolated from the values oAPPLEBEY : THE VISCOSITY OF SALT SOLUTIONS. 2015Gradenwitz (Diss. Breslau, 1902) and Piepenstock (Diss. Munich,1908). These determinations were unfortunately only carried outat 18O. The introduction of the surface-tension correction into theresults at 25*01° and Oo has therefore been impossible. At thesetemperatures the relative viscosities are calculated by the simpleformulaFor the purpose of comparison, the uncorrected viscosities at 1 8 Oare included in table V.PIG. 6.11/90 - 1 ~ _ _rn0-160'140'120 -100-160'140'120.100 '081 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 410 x Jconcentmtion.The viscosities of the more dilute solutions at 18O are plotted inFig.5, while the molecular viscosity increments at the three tem-peratures are given by Fig. 6. Fig. 6 also contains Gruneisen'svalues at 1 8 O and the curve given by his equation:______ q'%-l - - A a + B ( l -a)+Cm.r2016 APPLEBEY: THE VISCOSITY OF SALT SOLUTIONS.TABLE IV.Viscosities at 25*01°.ViscosityRelative viscosity Meail incrementD?,f"J" Uonceiitratioii visco- (s - ~ ) t relative q/vo - 1S. v2. 10rnl. meter. q/qo=(gx viscosity. Pn0'149 ~:~~~~~ 0.0174 2 '59 4 1 -00265 *Oo2'S 1.00255s 1-004C54 1 -00395R 1.006750'99824 3'10 R 1 '00395 1'0040 0.133 0 '99827 0'02990 -99933 3 3 4 X 1 *0068 1'0067 0.1190-99934 0'0567 4 1.00661 '00038 0*0825 S 1 *0097S 1 '009851 *00035 4.355 4 1 *01005 1 -0099 0.120R 1 *02641.00642 6.155 S 1.0266 1 -0267 0'11451 *00642 0'2333 4 1.02711.0356 1.01008 1.01008 0-3238 6.867 $ .03525 1.0354 0-10951.0405 0'1111 1 'C402 ::::::: 0'3643 7.142 1'040810597 1,01884 8'136 1.0598 1.05975 0'1110 1'01882 0'53851.0979 1,09805 1*0080 0'1131 1-03240 0.8666 9'5334 1.1117 1.036561.03660 0'9663 B 1'11049 '886 S 1.11145 1'1112 0.11511 '1 567 0'1191S 1.31515 1.3151 0-13873.8541 15.678 1-74075 0'19221*20848 4,578 16.60 4 2-0577 2.0577 0'23101'208331'283441'28340 5?3491'15671'15671.05134~:~~~~~ 2'2719 13'14G 1.315110.96 1'05146 S3.0255 0'346 B 3.0274 3-024 18-0APPLEBEY: THE VISCOSITY OF SALT SOLUTIOKS. 2017303% RTABLE V.42u,I19% n8 w ..A h*ib[Soh tionmadeup 0'00724by1veight.J1.93 0.99392 1.0004 $ iii;;;; 1*00124 1.0C125 0.172A 1*00200 0.997600.99759 0.0131 2.36 ~:~~~~~ 1.0007 1.00199 1002GO 1.00201 0'1530.99758S 1'00470.99858 o.99858 0.0379 3-36 1.00016 1.0014 f i::::; 1.0047 1'0047 0.124A 1.004694 1.00905H 1'00921'00019 1.00022 0-0784 4-28 ::::::: 1-0023 S 1.0089 1,00905 1.0090 0'1155.25 1.004521.00453 1.0036 2, ~:~~~~ 1,01545 1.01535 0.1061*002851.00285 0*1446 ::;:;;: 0.2653 6-43 1.00951 1*0061 ::g:i 1.0278 1.0276 0.1041.02563 1.03562 0 7034 8'59 i : ~ ~ ~ ~ ~ 1.0151 4 1.0737 1.0737 1'0731 0.10391,05001 1.05003 1'283 10.87 1.05245 1.0273 S 1.1441 1.1438 1.14395 1.1429 0.11134 1.1697R 1.16991.05811 1.05806 1.471 11.37 ::::::; 1'0313 S' 1.17015 1-1699 1.16565 0.114713.62 1.10818 S 1.349713 .66 1 *lo9591.10812 1.0508 R.1.34985 1 3172 0.1373 1.104981.10498 2'5281.10956 1.0512 R 1.3579 1.3579 1'3552 0.1393 1'106441'10643 2'5501.133411'13342 3.120 14.61 1.13685 1.0618 11 1'4906 1.4906 1'48695 0,15611.133431.14a75 1.0648 Iz 1.53685 1.5367 1.5327 0'1624 1.141221.14120 3*279i:;;;: 4.363 16'34 ''*Oo8 1.2010 1'0812 i::::: 1-9346 1.9274 0-2125S 1.35794 1,3579514.86 1.14475 4 1.5362018 APPLEBEP : THE VISCOSITY OF SALT SOTJUTIONS.TABLE VI.Viscosities at 00.Viscosityincre-Xean mentrelative q/qo - 1viscosity.RelativeviscosityVisco- 9 -(s - h)tD'$ meter.~ o - ( ~ o h ) f , 'Concen-trationDF"Jln m.[Solutionmade up 0.0401by weight]loin,,3 '42 1'0032 0'0801 -000391.00038 0'0833 4 '37 1'0058 0.070[Soh tionmade tip 0.1026by weight]1.00447 R 1.00771-00449 4 1.00755 4 '68 1.0076 0.0741-00990 I; 1.01561.00990 4 1 *0153 6-12 1.01545 0.06751.018181.0181 51.018174S4R4R4SRIz5'444A'4-8SRS41'02781.02791.027751.02781 -03241 *032551'03261.06161.06161'08731.087751.13441'13461,13441.20671 *206751.20661.27681.27711.27701.08751.013911 *01389 0'4279 7 '48 1'0278 0.06657.849-5010.401.02099 1-0325 0.06751 '03775 1.0616 0.07181.043641.043681.050211 '05019 1'0875 0.07721-070401.07036 11'63 1'1345 0'08551.085781.08583 2.0991-0857812.80 1.09505 1 2067 0.09841.114661 '1 14531.1 14661.104511.10451 2'508 13.59 1.2770 0'1104Discussion of' Results.-The viscosities determined at 18O agreevery satisfactorily with those obtained by Gruneisen.The valuesobtained for the most dilute solutions, however, differ considerablyfrom those calculated from the formula proposed by him. Thecourse of the curve given by Gruneisen's equation :d?!d = Ba+R(l -a)+Cm171is shown by the dotted line in Fig. 6. When m=0, that is, atinfinite dilution, a= 1 and k1 = A . The increment curve oughtAPPLEBEY : THE VISCOSITY OF SALT SOLUTIONS. 2019therefore to cut the axis of ordinates at a distance A from theorigin. The actualcourse of the increment curve is, however, quite different.Thevalues obtained in the most dilute solut,ions are already muchgreater than this value, and the curve is still rising.It may be noted that the most dilute point obtained by Gruneisenhimself also lies considerably higher than the value calculated fromhis equation. Nor is this an isolated case. Out of ten saltsinvestigated by him at sufficiently great dilut,ion, in eight the mostdilute solutions give values too high for his equation. The deter-The value of A given by Griineisen is 0015868.mination of k1 for these dilute solutions involves a very largemexperimental error, as has been indicated by the size of the circlesround the determined points in Fig. 6. The general nature of thephenomenon nevertheless precludes the view that these high valuesare due to errors of determination, for, if that were the case, thedeterminations should be equally distributed above and below thecalculated curve.These considerations, together with the determinations at greaterdilutions than Gruneisen's, show that, although his equation repre-sents the facts over it certain range, it is not valid for allconcentrations.Gruneisen's equation contains the assumption that the effects ofion and undissociated salt respectively are distinct and separable,and that each is in all cases proportional to the concentration ofthe component considered.The second assumption can only be trueif the process of solution is simply a mechanical mixing.There is general agreement among physical chemists that theprocess of ionisation in electrolytes is accompanied by combinationbetween the ions and the water molecules.Since water is a highlyassociated substance and consists of a mixture of simple andpolyrnerised molecules, the extraction of water molecules from thesystem by the ions of the salt must be accompanied by a readjust-ment of the water equilibrium, polymerised molecules breakingdown in order to restore the equilibrium. The effect of the ionson the viscosity of the system is therefore twofold: (1) the simplemixture effect, increasing the viscosity by remon of the great sizeof the hydrated ions; (2) the effect on the water equilibrium."* It should be noted that the effect of the salt on the water equilibrium does notinvolve a change in the equilibrium constant, but is simply a dilution effect similarto that observed by Dixon and Peterkin on diluting nitrogen peroxide ~ i t h an inertgas (Trans., 1899, 75, 613).Thus, if the concentrations of simple and polymerisedmolecules in pure water be c1 and c,, and the addition of an ionised substance lead tothe extraction of x simple molecules of water, the concentrations of simple and poly2020 APPLEBEY : TIiE VISCOSITY OF SALT SOLUTIONS.The disappearance of the maximum density phenomenon whensalts are dissolved in water shows that the effect on the waterequilibrium is a depolymerisation. This effect will therefore leadto a diminution of viscosity. The diminution will not, however,depend alone on the concentration of the ions, but also onthe amount of polymeride present.The effect will thus slowlydecrease with successive additions of salt.Another factor of which we must not lose sight is the changein size of the solvent envelope round the ion, the amount of watercombined with each ion becoming greater on dilution.I n the following pages an attempt has been made to deduce atheoretical connexion between the viscosity of a solution and themolecular and ionic phenomena involved in its formation.It has been tacitly assumed in the above that viscosity is a directfunction of molecular size. The general validity of this relation isestablished by the following facts :(1) Liquids which are known to be highly associated have usuallyalso a high viscosity.Propyl alcohol .................. 2.25 0.0223The following examples may be cited:Association Factor.* Viscosity a t 2 O O .iisoPropyl alcohol ............... 2.86 0.0243up-Dihydroxypropane ......... (large) 0.4479Glycerol ........................... (very large) 10.69 (at 18'28"),+Ethyl alcohol ..................... 2-74Ethyl acetate ..................... 0.99Ethyl ether .................... 0.99Acetic acid ........................ 3'620.01 2020.012320.004510.00237* Ramsay and Shields, Trans., 1893, 63, 1089.-f Gartenmeister, Zeitsch. physikal. Cham., 1891, 6, 524.2 0. G. Jones, Phil. Mag., 1894, [v], 37, 451.(2) The work of Heydweiller (TVied. Ann., 1895, 59, 193) onthe viscosity of liquids a t high temperatures.The viscosity ofwater diminishes much more rapidly than that of unassociatedliquids when the temperature is raised from Oo to 50°. Above 50°,when the association is small, the rate of diminution is approximatelythe same as that of unassociated liquids.merised molecules in the solution will be c ' ~ and c'~, where (neglecting the change ofvolume on solution)c1 f nc, = C ' ~ + m',, + x,c,n -c' and -- -1 =k,cn c'nfrom which it follows that, siiice x is a positive quantity,or that the extraction of siniple molecules by the salt leads to a diminution in theassociation of the water remainingAPPLEBEY : THE VISCOSITY OF SALT SOLUTIONS. 2021(3) The effect of pressure on the viscosity of water (Cohn, Ivied.Ann., 1892, 45, 666). An increase of pressure always brings aboutan increase in viscosity in the case of non-associated liquids.At lowtemperatures the viscosity of water, however, first diminishes withincrease of pressure, reaches a minimum value, and then rises inthe normal manner. Since the association of water is accompaniedby an increase of volume, as is shown by the maximum densityphenomenon, the effect of pressure must be to break down theassociated molecules. The marked diminution in viscosity, whichis superimposed on, and in the initial stages entirely masks, thenormal effect of pressure, can only be occasioned by this diminutionin molecular size.(4) The effect of different ions on the viscosity of water is in thereverse order of their mobilities, for example :Viscosity of Mohilityflalt.N/lO-solution a t 18". of cation.* Lithium nitrate ............... 1.0113 42'6t SOdlUln ,, ............... 1.0044 22.62 Cesium ,, ............... 0.9933 T8.S* Applebey. .i- Gruiieisen, Zoc. cit.2 Unpublished result kiiidly comniunicated by Mr. T. R. Merton.t Potassium ,, ............... 0.9941 7 5 . 5There is much evidence to show that ions of small mobility areheavily loaded with water molecules, and are thus larger than themore mobile ions.Since the ions in a salt solution are enclosed in a water envelope,it is probably justifiable to neglect the specific chemical differencebetween hydrated ion and water-molecule, and to assume a rigidconnexion between mean molecular volume and viscosity. As thesimplest assumption, it has been supposed that these quantities aredirectly proportional.*The different molecular species present in a salt solution are:(a) Simple water molecules, H,O;( b ) associated water molecules, assumed to be triple, (H20)3;( c ) ions, hydrated to an unknown extent, Li+ +xH,O, NO,- + yH,O;(d) undissociated molecules, possibly combined with water,(e) in strong solutions salt complexes, (LiNO&.The two kinds of water molecule are in kinetic equilibrium withone another.Their proportions in pure water can be obtainedfrom the association constant in the following manner :LiNO, ;* Dunstan and Thole have shown that these quantities are approsimatrlyproportional for different organic liquids which are not associated (Procr, 1907, 23,19)2022 APPLEBEY : THE VISCOSITY OF SALT SOLUTIONS.Let a be the association factor for water at 1 8 O .c1 ,, ,, concentration of single molecules H20 in gram-c3 ,, ,, concentration of triple molecules (H,O), in gram-molecules per litre.molecules per litre.Then 3 C , + C l = [I,c3 + c1and 54c, + 18c, = lOOOs, where s is the density of water.Then a -1 (3 -a)c3::(a- l)q, or c3= cz- , 3 - aand 5 4 ( r c ) c l + 18c, = 1 0008,3 - a1000s(3-a) and cQ= loo08 (a-1)36a 'whence c1 =36aNow for the equilibrium (H20)3 3H@we havewhenceTaking a t 18O Ramsay's value of 1.65 for the association constant(Zeitsch.p h y s i k d Chem., 1895, 15, 106) and 0.99863 as the density,The value of k thus found can be used to calculate the effect ofTaking a solution of weight normality m, density s, and degreeE = 0*0009347.the salt on the water equilibrium.of ionisation a,1000 C.C.of the solution weigh 1000s grams.Of this the salt accounts for Mms grams (where M=molecularweight of the salt), leaving (1000 - Mms) grams of water.Now, i f w be the average hydration number for the two ions,that is, if 1 gram-molecule of the salt, completely ionised, combineswith 2w molecules of water, the amount of water thus removedfrom the system is :2masw x 18 grams.The free water is therefore reduced to:(1000 - Mm - 36maw)s grams.Letting c1 and c3 as before represent the concentration of singleand triple molecules, we have:or, since c3=k x c13,54c3+ 18c, = (1000 - M m - 36maw)s,5411.~~3 + 18c, = (1000 - M m - 36maw)sAPPLEBEY : THE VISCOSITY OF SALT SOLUTIONS. 2023froin which c1 and c3 can be obtained (most conveniently by trial).The total number of gram-molecules in a litre of solution is:c l + c 3 + m ( l + a ) .The mean molecular volume is therefore :1000C,C3 + ms( 1 + a)’The mean molecular volume in pure water is:1000where cI1 and cl3 are the concentrations of single and triplemolecules in pure water.On the assumption that viscosity is proportional to meanmolecular volume, we have therefore :+ CIS’7 - ctl + ctg - - __yo c1 + CQ + m2s(l +a)’Owing to the absence of accurate determinations of several ofthe quantities involved in this treatment, and especially of thehydration numbers at different concentrations, it is at presentimpossible to submit the equation to it quantitative test.It may,however, be noted that the course of the calculated viscosityincrement curve corresponding with the equation agrees with theactual form observed in on0 important respect. The calculatedcurve shows the phenomenon of a minimum increment at about0.5 normal, as does the observed curve. As an illustration of thisthere has been included in Fig. 6 a curve representing the viscosityincrement calculated on the assumption that the hydration of theions is constant and equal to 6.3 molecules of water per ion. Thecurve has been calculated with Ramsay’s value for the associationof water a t 1 8 O , and with values of a obtained from Kohlrauschand Maltby’s conductivity determinations (Sitzungs b er.K . A kad.Wiss. Berlin, 1899, 655) by means of the relation:where X = molecular conductivity, and A, = molecular conductivity a tinfinite dilution.The calculated curve differs considerably from the observed,although they are of the same general shape. A very inconsiderablechange in hydration is, however, sufficient to bring the curves intoharmony. The ~ a l u e s of the hydration necessary have been foundby trial, and are collected in the following table2024 APPLEBEY : THE VISC081TT OF SALT SOLUTIONS.No: xiality.0’007240.01310.03790’07840’14460’26530.70341.0Hydration calculated fromviscosity in gram-moleculesof water per gram-moleculeof ion.8 -07.56.56.36 *16.16.056-05These values are in good agreement with those obtained by othermethods for various salts.For lithium nitrate itself Wymper(Proc. Roy. SOC., 1907, 79, 576) obtained a value of 13 for thehydration of a molecule of the salt in a normal solution (from the“ neutral salt effect ” in the inversion of sucrose). For potassiumchloride in normal solution, Philip (Trans. Furaduy SOC., 1907, 3,145) gives 9.4, and Caldwell (Proc. Roy. SOC., 1906, 78, 290) 11molecules of water per molecule of salt, whilst for more dilutesolutions Bousfield (Proc. Roy. SOC., 1904, 76, 563) gives 12. I naccordance with its smaller mobility, the lithium ion seems to berather more hydrated than the potassium ion.From the results obtained a t 25*01°, the same method ofcalculation giSes values for the hydration numbers about 0.3 higherthan those obtained at 18O.A similar small increase of hydrationwith temperature is indicated by the conductivity values of manysalts (Noyes, see Washburn, Tech. Quart., 1908, 21, 425).Hydration inSalt. Normality. niols. per ion.For other salts, Griineisen’s values at 1 8 O give:Sodium nitrate ... .. . , , . 0.1 3.40.05 3.5Lithium chloride . , , , , , 0.1 8 *8Salts which are less hydrated than these, however, give impossiblevalues. Thus, potassium nitrate gives small, and czsium nitratelarger, negative values. In view of these negative values, it maybe recalled that Rennie, Higgin and Cooke (Trans., 1908, 93, 1162)found that czsium nitrate diminished the rate of solution of copperin nitric acid, whilst sodium nitrate and lithium nitrate greatlyaccelerated the action.To sum up, this method of calculating the hydration, like themethods depending on the concentrating effect of neutral salts inchemical reactions, gives values approximating to the truth forsubstances which are much hydrated, but gives values too lowfor less hydrated substances. It is not improbable that the failureof all these methods of calculation in this respect depends on somehitherto unconsidered factor in the equilibrium of salt solutionRUHEMANN : TRIKETOHYDRINDENE HYDRATE. 2025which becomes of increasing importance as the hydrationdiminishes.Summary.-1. It has been found possible to construct visco-meters in which the flow of liquid is so slow that, for solutions whoseviscosity differs 'little from that of water, Poiseuille's law is obeyedwith an error of not more than one part in 10,000. The methodsused in testing the viscometers are described.2. A correction has been introduced for the variation in surfaceeffects when different liquids are used in the viscometer.3. Determinations of density and viscosity have been carried outwith lithium nitrate solutions at Oo, 1 8 O , and 2 5 O over a large rangeof concentration.4. The formuIa of Griineisen is found not to represent thephenomena of dilute solution.5. A method of calculating the viscosity of salt solutions fromtheir hydration numbers, or vice versa, has been described. Theapplication of this method to the viscosities of lithium nitratesolutions at 18O gives results consistent with the estimates of ionichydration made by other observers.6. The application of tho methcct to other salts is discussed.I am greatly indebted to Mr. D. H. Nagel and Mr. H. B. Hartlegfor much valuable advice and enccuragement during the progressof this work.pH TSICAL CHEMIS'I'RY LABORATOI~Y,~ ~ A L L I u L AND TILINITY COLLEGES,OXFORD