WORLEY: THE SURFACE TENSION OF MIXTURES. PART 11. 273XXX.-The Surface Tension of Mixtures. Part 11.Mixtures of Perfectly Miscible Liquids and theRelation. between Their Surface Tensions andVapour Pressures.By RALPH PALLISER WORLEP.THERE is an obvious although not very simple relationship betweenthe vapour pressure and the surface tension of a pure liquid, andlikewise of a mixture of liquids. In the case of the latter theseproperties can be made to vary by altering the proportions ofthe constituent liquids, and it seemed to be of interest t o learnwhether in mixtures of liquids deviations from a general lawgoverning the vapour pressures were accompanied by correspondingdeviatiom in the case of surface tensions.I n spite of the fact that the surface tensions of a considerablenumber of mixtures have already been determined, the surfacetensions and the vapour pressures have not been investigated forthe same mixtures, and it was therefore impossible to draw anyconclusions from the work of others.Such being the case, it was decided to find the surface tensionsof mixtures of the following three pairs of liquids, since theirvapour-pressure curves, determined by Zawidski (Zeitsch.physikal.Chem., 1900, 35, 129), belong to three characteristic and verydifferent types.1. Benzene arbd Ethylene Dich1oride.-The vapour pressure-composition curve corresponds with the theoretical straight line.2. Acetoge and Carbon Disu1phide.-In this case the vapourpressure-composition curve lies above the theoretical straight line,and passes through a maximum value.3.Pyridine and Acetic Acid.-In this case the vapour pressure-composition curve lies below the theoretical straight line, andpasses through a minimum.Various formuh have been proposed to express the surfacetension of a mixture in terms of the surface tension of the com-ponents, but experiment has shown that none is of universalapplication. According to Volkmann (Ann. Phys. Chem., 1882,[iii], 16, 320), the surface tension of a binary mixture is repre-sented by the formula S= V,S, + V,S,, where V , and Vz are thevolumes of the liquids in the mixture expressed fractionally, andS , and 8, their surface tensions when unmixed.Whatmough (Zeitsch. phtysikal. Chem., 1902, 39, 158) modifiedthis formula to take into account the change in volume which takesVOL.cv. 274 WORLEY: THE SURFACE TENSION OF MIXTURES. PART 11.place on mixing, and proposed the following : S = R ( YIS, + V2S,),R being the ratio of the calculated to the observed density. It wasfound that the observed values of only a few mixtures agreed withthose calculated, the majority being too small, whilst in some casesthe curve passed through a minimum value. I n two or three caseslle attempted t o show that a relation existed between surfacetension and relative compressibility. I n the other cases no attemptwas made to account for the divergence between observed andcalculated results, nor were the surface tensions compared withother physical properties of the mixtures.It is to be noted that the admixture rule for finding the vapourpressure of a mixture deals with molecular proportions, whilst thatfor surface tension deals with volumes. The mixtures experimentedon were therefore made up by volume, and not either by weightor molecular proportions, either of which ways would seem a t firstglance to be superior.The surface tensions were determined in exactly the same manneras that employed in the previous paper, and the symbols in thetables have the same significance.The densities are referred t owater at 4O.1.-Benzene and Ethyleize Dichloride.The benzene was treated with concentrated sulphuric acid inthe cold and then distilled, the whole passing over between 7 9 Oand 80°, and the portion used between 7 9 O and 79.5O.The ethylene dichloride was treated with potassium hydroxide,and then with sulphuric acid, and the portion used distilled between84O and 84.5OThe surface tensions of the pure liquids were first determinedover a range of temperatures, and three mixtures were made upof different proportions, and the surf ace tensions likewise f ~ u n d .The results are contained in tsbular form below.t.14"4570TABLE I .S u r f a c e T e n s i o n of B e n z e n e .T (em.).tl. h (em.).0 -0 1528 0.8854 4.3110.01528 0.8545 3.8610 -01528 0.8300 3'474TABLE 11.Sqr face Tensiou of Ethyle?te DdcA lo r i d e .12.5" 0.01528 1'2579 3.38543 0-01528 1-2184 3.0555.28.60624 '72521 '60731.91427.88WORLEY: THE SURFACE TENSION OF MIXTURES.PART 11. 275TABLE 111.Benzene (30 c.c.) and Ethylene Dichloride (20 c.c.).14.5" 0.01528 1.0297 3.807 29.32245 0'01528 0.9975 3-428 25'62770 0'01528 0.9695 3.119 22 $25t. r (cm.). d. h (em.). s.TABLE IV.Benzene (20 c.c.) and Ethylene Dichloride (30 c.c.).15" 0 -01 528 1.1055 3.614 29'94441 0.01528 1.0730 3.324 26.73058 0-01528 1-0515 3'124 24.620TABLE V.Benzene (40 c.c.) and Ethylene Dichloride (10 c.c.).14" 0.01528 0'9605 4.030 28 '94250 0 *O 1528 0.9268 3'547 24.634The results contained in the above tables were first plottedgraphically, and from the curves formed the following table con-taining the data f o r surface tension and composition a t 20° and50° was compiled. The calculated results were obtained by meansof the admixture rule mentioned above.TABLE VI.Surface Tension of Mi.n:tures of Benzene and Ethylene Dichloride.Vol. per cent., c A 5 / \C,H,Cl,.Observed. Calculated. Observed. CaI cula ted.0 30.90 - 26'92 -40 29-30 29'68 25-73 25-7360 28'60 30.25 25-10 25-1480 28'1 8 28.42 24-60 24-60S a t 20". S a t 50".h100 27.80 I 24.00 -The curves obtained by plotting these numbers are shown inFig. 1. It will be seen that a t 50° the observed and the calculatedvalues agree very well, whilst a t 20° the observed values are slightlyless than those calculated. Now reference to Zawidski's paper(loc. cit.) shows that a t 50° the observed values of the vapourpressures of mixtures of these two liquids agree absolutely withthose calculated from the admixture rule.As far as can be judgedfrom these two liquids, therefore, there is close agreement in theproperties of surface tension and vapour pressure of mixtures, inthat the laws as regards each are obeyed.T 2'76 WORLEY: THE SURFACE TENSION OF MIXTURES. PART 11.2 . 4 a r b o n Ddsulphide and Acetone.The carbon disulphide was treated with concentrated sulphuricacid and then distilled, the whole passing over at 46'5O.The acetone was dried over calcium chloride and distilled, theportion used passing over between 5 6 O and 56.5O.The surface tensions of both the pure liquids and mixtures ofthe two in varying proportions a t different temperatures are con-tained in the tables followingto.14"28.544FIU. 1. 11 I I I0 20 40 60 so .- 10:Ethylene diddoride. 170l. p w cent. Benmze.TABLE VII.Surface Tension of Carbon Disulphide.r (cm.). d. h (cm.). S.0.01528 1.2716 3'358 332.0210'01528 1.2521 3.196 29.9710.01528 1 -2292 3-012 27.746TABLE VIII.Surface Tension of Acetone.14-4" 0 - 01 528 0.7988 3.92555 0.01528 0.7770 3 '63053 0.01528 0-7563 3'32523.46921-13918 -84WORLEY: THE SURFACE TLNSION O F MIXTURES. PART IJ. 2'7'7to.16"38TABLE I X .Carbon Disulphide (40 c.c.) and Acetone (10 c.c.).r (cm.). d. h (cm.). S.0'01528 1-1649 3.063 26.7380.01528 1.1320 2.826 24 *542TABLE X.Carbon Disulphide (35 c.c.) andl Acetone (29 c.c.).15" 0.01528 1.0419 3.195 24'94829.5 0.01528 1 *0230 3-033 23 -25439 0.01528 1'0124 2.905 22-039TABLE XI.Carbon, Disulphide (10 c.c.) and Acetone (40 c.c.).18" 0.01528 0-8760 3.558 23.35638 0.01528 0'84996 3-290 20.910As in the last case these results were plotted graphically, andthe following table, showing the surface tension and composition a tloo and 35O, was compiled from the curves plotted.TABLE XII.Mixtures of carbon Disulphide and Acetone.S at 35". S at 10".Vol.per cent., r h\Acetone. Observed. Calculated. Observed. Calculated.20 27'40 30-85 24-79 2'7.3540 25.50 28.64 22-65 25-3024.31 25'70 21 '28 22.52 80- 28-98 - 0 32.55- 100 24 '00 - 21 -00These results are shown graphically in Fig. 2. At both tem-peratures the observed values are considerably below those calculated(shown by dotted line in diagram). Now, according to Zawidski,the vapour pressures of mixtures of these two liquids are muchgreater than those calculated, the curve, instead of being a straightline, passing through a maximum.It appears therefore that whenthe vapour-pressure curve of a mixture diverges from the theoreticalstraight line in one direction, the surfacetension curve diverges inthe opposite direction.3.-Pyridine and Acetic Acid.The pyridine was obtained from commercial pyridine by frac-tional distillation, the portion kept for use passing over betwee278 WORLEY: THE SURFACE TENSION OF MIXTURES. PART 11.1 1 2 O and 1 1 8 O .that Zawidski stated the same of the sample used by him.It was therefore not pure, but it may be notedThe acetic acid distilled between 1 1 7 . 5 O and 1 1 8 O .TABLE XIII.Surface Tension of Pyrid,iue.13" 0.01528 0-9882 5.13249 0,01528 C-9545 4.60480 0.01528 0.9062 4.1720 T (em.).d. h (cm.).TABLE XIV.Surface Tension of Acetic Acid.14.5" 0 -0 1 528 1.0553 3'43952 0.01528 1.0162 3'10175 0-01528 0.9913 2.869S.38.00032.93528'33427.19523-61821-30WORLEY: THE SURFACE TENSION OF MIXTURES. PART 11. 2791".17"5276TABLE XV.1'ydin.e (37.5 c.c.) a d A c e t i c Acid (12.5 c.c.).r (em.). d. h (em.). S.0.01528 1.0175 4.765 36.3340-01528 0.9860 4 '332 32.0060 *O 1 528 0.9595 4.012 28.848TABLE XVI.P y r i d i n e (27 c.c.) alzd A c e t i c A c i d (23 c.c.).12" 0-01528 1 -0585 4-485 36'57747 0*01528 1 *0265 4.145 31.88675 0.01528 0.9975 3'850 28-780TABLE XVII.P y r i d i n e (15 c.c.) and A c e t i c A c i d (35 c.c.).14" 0.01528 1.0871 4.084 33.28149 0.01528 1.0537 3.779 29.82675 0-01525 1'0230 3.554 27 '247As in the previous cases these results were plotted graphically,and from the curves drawn the following table was compiled.TABLE XVIII.Mixtures of P y r i d i n e and A c e t i c *4cid.S at 40".S at 80".Vol. per cent., V- r A bC,H,02. Observed. Calculated. Observed. Calculated.0 34.30 - 28.32 -25 33'59 31.85 25-32 26'4546 32-65 29 *85 28-00 24-8230'63 27-40 26-79 23'00 70100 24'73 - 20 -80 -These results are plotted graphically in Fig. 3. I n this case theobserved values are much greater than those calculated, and thecurves tend to pass through a maximum value. Reference t o thepaper of Zawidski mentioned above shows that mixtures of pyridineand acetic acid form a minimum vapour-pressure curve a t 80'05O.This case is exactly the opposite of the previous one, and appearsto verify the contention that the properties of surface tension andvapour pressure of mixtures vary in opposite directions.As had been anticipated, the above results show that a markedrelationship does exist between the surface tensions and vapourpressures of mixed liquids.The relationship may be summarisedin the three following rules280 WORLEY: THE SURFACE TENSION OF MIXTUREF. PART 11.(i) I f a t any given temperature the vapour pressures of mixturesof two liquids agree with the values calculated by the rule ofadmixture in molecular proportions, then a t that temperature thesurface tensions of the mixtures agree with those calculated bythe formula S = V,S, + V2S2.(ii) If the vapour pressures are greater than those calculated,then the surface lensions are less than those calculated.1 I I I I I0 20 40 60 80 100Pyridbc.Yo,?. per ceibt. Acetic acid.(iii) I f the vapour pressures are less than those calculated, thenthe surface tensions are greater than those calculated.It had been intended to investigate mixtures of benzene andcarbon tetrachloride, since the vapour-pressure curve lies only alitt.le above the theoretical straight line (Zawidski), The surfacWORLEY: THE SURFACE TENSION OF MIXTURES. PART 11. 281tensions of mixtures of these two liquids were, i t was found, deter-mined by Ramsay and Aston (Zeitsch.physikal. Chem., 1894, 15,92), who showed that the observed values were a little below thecalculated values. It follows therefore that mixtures of these twoliquids behave in accordance with the above rules. So also domixtures of ether and carbon disulphide, which form a maximumvapour-pressure curve (Guthrie, Phil. Mag., 1883, [v], 18, 513),and tend to form a minimum surface-tension curve (Whatmough,The case of mixtures of the alcohols with water is very instruc-tive, and offers further proof of the validity of the foregoing rules.The vapour pressures of mixtures of these in all proportions werefound by Konovalov (Ann. Phys. Chem., 1881, [iii], 14, 34). Withincreasing molecular weight of the alcohol, the vapour-pressurecurves rise higher and higher above the straight line, and in thecase of both propyl and isobutyl alcohols the curves pass through amaximum value.The greatest differences between observed andcalculated values, a t the temperature when the vapour pressure ofeach pure alcohol is 400 mm., are roughly as follows :blethyl alcoliol and water.. ..................112 9 , Ethyl ,, ,) ....................Propyl ,, ,, .................... 203 ,,GoButyl ,, ,, 315 2 9loc. c i t . ) .43 m u ......................The surface tensions of mixtures of the same liquids and waterwere determined by Duclaux.With increasing molecular weight of the alcohol the surfacetension-composition curves fall more and more below the theoreticalstraight lines.The maximum differences are roughly :Me hyl alcohol and water ................... 14 degrees..................... Ethyl ,, 9 , 21 ,,iyoPropy1 ,, 3 , 26 , IisoButyl ,, , , ..................... 41 , I.....................These mixtures therefore show a striking agreement with therules laid down, and show, moreover, that the greater the divergenceof the vapour-pressure curve from the theoretical straight line, thegreater is the divergence of the surfacetension curve, but in theopposite direction.It may be noted in passing that no difference is to be drawnbetween mixtures the surface tensions of which diverge from thetheoretical straight line and those the surface tensions of whichform either a maximum or minimum as the case may be, these beingformed only when the surface tensions of the pure liquids happento be near together.This greatly simplifies the classification ofmixtures proposed by Whatmough. It Beema also, that mixturesVOL. cv. L282 CURTIS AND KENNER:may obey the admixture rule at one temperature, and not at others,as in the case of benzene and ethylene dichloride.Finally, it appears that the relationship between surf ace tensionsand vapour pressures of mixtures holds good also f o r solutions ofsolids in liquids. All salts increase the surface tension and decreasethe vapour pressure of liquids. An experiment made by the authorwith solutions of sulphur in carbon disulphide gave the followingresults. G is the number of grams of sulphur dissolved in 100 C.C.of the liquid, and S is the surface tension a t 31O:Q. S.0 29.60010 30 505G. S.20 31-18230 31.593The surface tension is noticeably increased. This fact points tothe relationship holding good for all mixtures.It may be remarked, also, that thc vapour pressures of solutionsof aniline, phenol, and isobutyl alcohol in water are considerablygreater than that of water, and therefore much above the theoreti-cal values, whilst their surface tensions were shown in a previouspaper to be greatly below the theoretical values. Moreover,Eonovalov (Zoc. cib.) found that the ratio between the observed andcalculated vapour pressures of a saturated solution of isobutylalcohol in water diminished but slightly between Oo and 80°, aresult in accordance with the rate of change of surface tension withtemperature of that solution. The vapour pressures of aqueoussolutions of aniline and phenol over a range of temperatures havenot yet been found, but from results from measurement of the fateof change of surface tension, i t is probable that the ratio of theobserved to the calculated vapour pressure would diminish rapidlywith rise of temperature.UNIVERSITY COLLEGE,AUCKLAND, N. Z