THE VISCOSITY OF LIQUID MIXTURES. 83 VII.-- The Viscosity o,f Liquid Mixtures. By ALBERT ERNEST D UNSTAN and ROBERT WrLLrAnr WILSON. IN the two previous parts of this series, the viscosity conceutration curves of various liquid mixtures have been investigated, and it has been shown that these curves could be divided into three classes : (i) Those approximately obeying the law of mixtures, being concave to the axis of percentage composition, and having the greatest di- vergence from normal a t some point of simple molecular concentration. (ii) Those exhibiting definite maxima a t points corresponding with mixtures of simple molecular composition. Nearly all experimental work in this class has been done with aqueous solutions, and a great volume of evidence points to the conclusion that in such mixtures the formation of hydrates is always existent, producing groups of complexes in dynamic equilibrium even when definite compounds cannot actually be isolated.(iii) Those exhibiting minima which also are to be found at points of simple molecular composition. I n general, these liquid pairs which are made up of unimolecular non-associating components give viscosity concentration curves which, although frequently near the normal, yet sonietimes diverge consider- ably from it. I n the present communication, a brief account is given of certain empirical relationships which hold good for these viscosity concentra- tion curves (Zeit. physikal. Chem., 1906, 56, 370), and further u 254 DUNSTAN ANT, WILSON : experimental results in the shape of a curve for mixtures of water and sulphuric acid are adduced.It has been laid down in previous papers that increase in the viscosity coefficients implied increase in the masses of the colliding dipping particles whether they be simple molecules or loosely held complexes. Whereas, on the one hand, carbon disulphide, ether, the paraffins and other simple unimolecular liquids are mobile, the alcohols and acids are more viscous, glycol and glycerol notably so, whilst the comparatively enormous molecular massea of the jellies and colloids attain an almost infinite viscosity. A decrease in viscosity similarly may imply a decrease in complexity or the disintegration of the molecular groupings in solution, and this phenomenon is sometimes observed even when a more viscous com- pound is added to one of less viscosity.The experimental data in this work have been obtained in the same manner as in previous papers. The sulphuric acid was kindly supplied in considerable quantity by Dr. Messel, to whom we are glad of this opportunity of expressing our gratitude. The two specimens of this acid which we obtained were of special purity. The strength was determined by titration of the diluted acid, by conversion into barium sulphate, and from the density, using Pickering’s tables (Trans., 1890, 57, 64). Analysis of the first specimen : ‘1 By density .. . ,. . . . . By titration. .. . . . . . , ,, Gravimetrically . . . H2S0, = 09.57 ,, H,SO, = 99.5 per cent. H,SO, = 99.2 The second specimen gave as average of density determinations : H,SO, = 99.924 per cent.The water used was redistilled from alkaline permanganate and kept in well-stoppered Jena flasks. A large stock of 50 per cent. acid was made, and this served fo;. the middle determinations by addition either of water or acid. The strengths of the solutions were deter- mined mainly by Pickering’s tables of density ; frequent checks were made by titration and also by gravimetric analysis. The following table gives the percentage composition of the solutions, the density and the viscosity coefficients. These data are plotted on the accompanying curve (Fig. 1) :H2SO4 per cent. 99924 97 -513 95.723 93'410 92.300 91 -363 90-437 80.575 88.733 88.001 86.865 86.979 85.070 84.970 84-280 83.980 83'401 82.580 82.210 81 -544 110 100 90 80 70 j, u *$ 60 .'2.s 2 50 u u 40 4 30 20 10 THE VISCOSITY OF LIQUID MIXTURES. Density. 1'82714 1.83171 1'82986 1-823-18 1.81930 1'81476 1 '80982 1 -80525 1.799% 1 *79522 1.78650 1*78737 1.77160 1.77074 1 ,76447 1 T6069 1.75588 1.74750 1'74384 1'7371 9 Viscosity. 1 *06160 0 -8 57 61 0,83255 0.84211 0-85088 0.87158 Orn88508 0.951 32 0-91558 0 *9256S 0.93366 0.93527 0'94794 0.92966 0,92529 0 *9 1010 0 *go866 0'89842 0 *86 57 1 0.83108 FIG. 1. h2504 per cent. 81.086 80'243 79.838 79'528 78.242 76.271 74'746 70.519 69'205 67,209 64'643 58.356 51.640 49,858 43284 36'427 26.492 15.699 0 Density. 1.73197 1 '71844 1 *714 84 1 * i O O Y O 1.67756 1'65976 1'61049 1 *59488 1.57236 1 *54331 1'47457 1 '4 0596 1.38857 1 *32691 1,36759 1.18630 1.10413 0.99717 1.72287 85 Viscosity.0.78099 0.60272 0'74084 0.67228 057396 0.53603 0.40095 0'36450 032322 0.28042 0.20568 0'15370 0 '14706 0.11293 0.09239 0*07119 0.05851 0-00891 0w52 Percentuge H,SO,.86 DUNSTAN AND WILSON : In a useful summary of work done on the question of the molecular constitution of solutions of sulphuric acid, Burt (Trans., 1904, 85, 1351) points out that the conclusion that combination takes place in such solutions with the formation of complexes had been arrived a t mainly by cryoscopic methods. Pickering (Trans., 1890, 57, 64, 331), in his classical investigation on this subject, brings forward indisputable evidence as to the exist- ence of such complexes, an existence which in the case of some he proves by their actual isolation. With respect to density determina- tions, Pickering quotes Bfendel6eff’s experimental curves (Zeit.physikal. Chem., 1887, 1, 275 ; see also Crompton, Trans., 1888, 53, 116) in which after differentiation the following hydrates were deduced : H,SO,,H,O, H2S0,,2H20, H2S04,6H20, H2S0,,1 5OH,O. Pickering’s own curve after a similar process afforded seventeen straight lines equivalent to a complex first curve of seventeen parabolic components, which the author considered as the density curve of seventeen hydrates in solution. From the contractions on mixing, similar discontinuous sections identical with the above were found. H e investigated Kohlrausch’s conductivity curves, which gave five hydrates, and obtained the same results. Jones (J. Amer. Chem. Soc., 1894, 16, l), by investigating the lower- ing of the freezing point of acetic acid by sulphuric acid, claimed to have proved the existence of H,SO,,H,O and H2S0,,2H20 in solution.That the former hydrate is capable of existence and isolation is no longer doubted. Pictet (Compt. rend., 1894, 119, 642) obtained, by the crposcopic method, maximum and minimum points corresponding with H2S0,,H20, H2S0,,2H,0, and others. Ramsay and Shields (Trans., 1894,65, 179) found that the constant boiling liquid 1 2H2S0,,H20 had an abnormally high molecular weight and concluded that complexes had been formed. Graham’s work (PM. Ikans., 1846, A , 513 ; 1861, 373) on solutions of sulphuric acid and water brought out quite clearly the maximum at 85.1 per cent. of the acid corresponding with H2S04,H20; the remainder of the curve on both sides of this point is quite normal.Burt’s own conclusions (Zoc. cit.) drawn from his results on the vapour pressures of sulphuric acid solutions are of great interest ; he points out that : (1) The molecular weights calculated from the vapour pressures never rise above 32.7. (2) The molecular weights usually lie below 32.7, increase with temperature, and decrease with greater concentration. (3) Inversion points are of frequent occurrence in the curves ofTHE VISCOSITY OF LIQUID MIXTURES. 87 molecular weight x temperature. H e concludes t h a t complexes are formed, but finds no evidence for the existence of definite hydrates. Knietsch (Be?.., 1901, 34, 4069) made a n elaborate investigation of these mixtures, using not only determinations of viscosity, but also of the melting points, conductivities, and surface tensions.From the melting-point curve, he deduced the existence of H,SO,,H,O, and H,SO,,SO, at maxima, and OF BR,S0,,H20, 4H,SO,,SO,, and H2S0,,2S0, at minima. From the conductivity numbers, he found discontinuities at points corresponding with H2SO4,H20, and 2H,S0,,H20, and at 15 per cent. free SO,. The viscosity data show that the effect of adding sulphuric acid to water in gradually increasing amount is to cause a n equally gradual increase in the viscosity. The first maximum point is attained at 85 per cent., that is, the “monohydrate,” but i t is to be noticed that the increase in the viscosity is by no means commensurate with the simple addition of H,O to H,SO, or of H2S0, to H,O. So far as can be seen from the previous work on aqueous solutions, these maxima would more probably correspond t o aggregates such a s (H,SO,,H,O),,, where ‘‘ n ” may be of considerable magnitude.As will be noticed in the sequel, a very rough approximation for the addition of CH, in an homologous series is 0.001 unit of viscosity. Thus toluene to xylene, methyl to ethyl iodide, hexane t o heptane, ethyl bromide to propyl bromide give such increments. Larger increments are found in the alcohol and acid series, but in the case we are considering, the minimum point viscosity is O.OS3255, an3 the maximum point 10 per cent. from it is 0.094794, whilst water is 0.00891. From this maximum, further addition of water reduces the viscosity to rz minimum which is located at about 95 per cent.; after this point the viscosity again steadily increases through H,SO, until the second maximum at 50 per cent.free SO, (Knietsch, Zoc. cit.), both maxima corresponding with the two maxima of density. It will be noticed that in the appended curve there is a minimum point at 95 per cent. corresponding with 3H2S0,,H20. A similar minimum point was obtained with mixtures of benzaldehyde and alcohol and with benzene and alcohol. Such a point can be inter- preted as being the final result of the fission of sulphuric acid complexes by the water, the fission being complete when the water reaches the above concentration. The addition of more water causes more complex formation until this culminates in the building up of the monohydrate, which, at any rate in solution, may be the first anhydride of ortho- sulphuric acid.The position of this well-known compound is clearly indicated at 85 per cent. No further well-marked discontinuity occurs, at any rate, of the same order as the maximum already qucjtecl.88 DUNSTAN AND WILSON : Possibly more delicate apparatus would indicate such complexes of the ‘‘ second order.” The position of sulphuric acid and its “ monohydrate ” on the viscosity-molecular weight curves (v.s.) indicates the high degree of association it possesses. It will be readily seen from what has gone before that little obedience to the mixture law can be expected from two components like sulphuric acid and water, alcohol and benzene, or, in brief, wherever we deal with associated substances, and it is because of this reciprocal action of one on the other that all attempts to investigate these effects have failed.The formula given by Lees (Phil. Mag., 1901, [vi], 1, 12S), q n = ~ ~ q ~ ) t + w.,q2n, where “n” is a constant for the liquid pair, 7, qL, and y2 the viscosity coefficients for the mixture, and the two components respectively, and v102 the relative volume of the two components, fits in most closely with observed facts; at the same time it should be noticed thnt this can scarcely be described as a mixture law which has to be qualified in each case. Several regularities have been met with in the course of this investigation, especially in connexion with unimolecular liquids. A. Connexion between Moleculur WeigJLt and Angle between Tcmgent to Cuwe and Axis of Viscosity. I n any of the previously given curves (Trans., 1904, 85, 81 7 ; 1905, 87, 11) let tangents be drawn at the point where the curve meets the viscosity axis. Let a be the angle between the tangent and the viscosity axis.Then a is connected with the molecular weight of the liquid in question, as follows : TABLE I. Solution in benzene. Mol. wt. a. Product. Carbon tctraciiloride.154 52 7.9 Toluene .............. 92 93 8.55 Ethyl acetate ........ 88 94 8.27 Carbon disulphide ... 76 105 7.98 Ethyl ether ............ i4 102 7-55 Solution in alcohol. Mol. wt. a. Product. Carbon disulphide. 76 128 9-73 Mercaptan ......... 62 148 9.17 Acetone ............... 58 100 5 . 8 Eenzene ........... 78 48 3,72 Benzaldehyde ...... 106 62 6.57 It is to bo noticed that the last three alcoholic solutions give abnormal experimental results, in t h a t minima or exceptionally sbgged curves are shown.If such behaviour indicates dissociation, then the associated benzalde- hyde and benzene having a greater molecular mass than normal would, as shown in the sequel, give a steeper curve and a smaller angle a. I n all cases examined, the viscosity concentration curves are parabolic, and can be fairly represented by x = ay2 + by + c,THE VISCOSITY OF LIQUID MIXTURES. 89 dx therefore __- = Ky + iW, d?r hence a relation exists between the tangent of a and y, that is, the viscosity coefficient, or, as is shown here, between a and molecular weight. B. Connexion between iwolecular Weight and Viscosity, The following table (Dunstan, Zeit.phylsikal. Chent., 1905, 51, 738) further shows the close connexion between molecular weight and viscosity, and also illnstrates the great abnormality of the hydroxyl- ated liquids (see Thorpe and Rodger, I‘M. Trccns., 1897, 185, A , 397) : Liquid. v1M.V. x lo6. Benzene .................... 65 Ethyl acetate ............ 60 Ethyl iodide ............. 69 Ethyl bromide ............ 51 Chloroform ............... 67 Acetone .................... 43 Liquid. 7/M.V. x lo6. Watcr .................... 493 Methyl alcohol ......... 138 Ethyl ,, ......... 189 Propyl ,, ......... 262 Ally1 ,, ......... 180 1 Glycol .................... 2750 Benzaldehgde ............ 14 3 Acetic acid .............. 195 ~ Lactic ,, .............. 5410 A further relationship may be deduccd from the viscosity concentra- tion curves given in previous communications (Zoc.cit.). Taking again tangents to these curves a t the vertical axes and calling the angles between the curve and tangent “ b ” and “ c ” respectively, then the following statement holds good. The product of the molecular weight of each liquid with the angle ‘ ‘ c ” or “ 6 ” is constant, for the effect of liquid A on liquid B is measured by the angle “ b ” and vice uersb, the effect of B on A is measured by the angle ‘‘ c ’’ : Liquid A . Ethyl mercaptan . , . , , . Toluene ................ Carboii disnlphiJe.. .... Ethyl ether ............ Carbon disulpltide.. ... Ethyl acetate.. .......... - 62 92 76 i 4 76 88 - TABLE 11. -__ Ethyl alcohol ......... 46 13 Beiizene ............... 78 2 Methyl iodide .........142 4 Benzene ............... 78 15 Benzene ............... 78 3 Benzc-ne .............. 78 1290 DUNSTAN AND WILSON : C . Relation between MoZecuZu~ Teight aizd t'iscosity of Series of Compounds. A n important connexion between these quantities is evidenced when they are plotted as in Fig. 2, log. viscosity against nioleculsr weight. It mill be seen that the various menibe1.s of a chemical series lie on the same curve. The viscosity-molecular weight curves are parabolic. The FIG. 2. 60 so 100 120 140 160 simple esters lie closely together, and there is a similar proximity between the symmetrical and asymmetrical ketones. Chloroform is placed near the paraffins. The paraEns investigated by Thorpe and Rodger lie almost on a straight line; other available determinations show a considerable want of agreement with these and with themselves, It is to be noticed that the first members of each series diverge more or less from the logarithmic line and behave as though they had aTHE VISCOSITY OF LIQUID MIXTURES.91 larger molecular weight than normal (see also, for this association of the early members of homologous series, Ramsay and Shields, Trans., 1893,53, 1101). Benzene also occupies an anomalous position, giving evidence of considerable association (nearly 110 mol. wt.). Fig. 3 shows the logarithmic curves for the acids and alcohols. The two curves are very similar and indicate the same inconsistent be- haviour of the earliest members; from the points given by water and formic acid the curves follow almost parallel to each other. A con- FIG. 3. so0 600 400 200 sideration of these curves will show that water behaves as a liquid of molecular weight nearly 50, that is, (H20)3, and formic acid nearly 100, that is, (H*CO,H),, assuming that the other members are normal. Hence we may deduce the general law : where y is the molecular weight, A and B are constants depending on the particular series to which the liquid belongs, and y is the viscosity coefficient . It will be noticed that B, which measures the slope of the curves, is almost the same in the various series, and has therefore a general nature, A being the specific constant for each family. The authors desire to thank Prof. Trouton for his interest in this y = A + B log. r], investigation. EAST HAM TECIINICAL COLLEGE. UNIVERSITY COLLEGE.