116 CROMPTON AN EXTfiENSION OF VK-An Extension of MendelLefs Theory of Solution to the Discw-sion of the Electrical Conducti?;ity of Aqueous Solutions. By HOLLAND CROMPTON Student in the Chemical Department of the City and Guilds of London Central Institution. AS a consequence of MendelBeffs original treatment of the subject, our conceptions of the constitution of solutions have suddenly acquirctl a degree of precision which is- altogether remarkable when the nature of the problein is considered. Fellows of the Chemical Society have had the privilege to be put in direct possession of the views of the renowned Russian chemist his method of treating the problem being briefly indicated in a paper on “ The Compounds of Ethyl Alcohol with Water” in the October number of the Transactions (1887 p.778). By discussing the dependence of change of relative density on percentage composition Mendelheff arrives at t’he conclusion that three distinct hydrates of alcohol may exist in solution in a disso-ciated condition-~,H60*120Hz CzH60*30Hz and 3C,H60*OH ; and the reliability of his method is established to demonstration by his success in isolating the first and second of these. Discussing the data f o r sulphuric acid in a similar manner (Ostwald and Van’t Xoff’s Zeit. phys. Chem. 1887 273) he concludes that this acid forms the hydrates-H2S 04.OH2 HZS 04.2 0 Hz HZS O4.60H HZS 0 4 . 1 500H2 * the existence of two of which is already reoognised by chemists. It is evident and was pointed out by MendelBeff in the paper in which he first advanced his views of solution (Ber.1886 379) that tha presence of the hydrates thus indicated must influence other physical properties as well as that of density and the problem there-fore is one of determining in what manner and to what extent this * See Dr. Armstrag’s remarks regarding this “ hydrate. Joum. C k . S o c . Jia. 1888-POLARIZATION OF COPPER BY 001 OF ZINC. LAURIE. Flak 1 E. M. F OF ALLOYS (A) IN STANNOUS CHLORIDE. (B) IN STANNOUS SULPHATE. LAUR I E Plate 2 ' 3 A t i R 9 U313 W VllO CURVE SHOWING THE ELECTROMOTIVE FORCES OF THE ZINC*COPPER ALLOYS IN THE CUPROUS IODIDE CELL. LAURIE Plate 4.k Ihrnson % Sons. Lith. S' M~~UDE La*. k MENDELEEFF’S THEORY OF SOLUTION. 11 7 influence may be rendered evident in different cases. At Dr.Arm-strong’s suggestion I have therefore investigated the dependence of change in electrical conductivity on composition in the case of sul-phuric acid and of a number of other typical solutions in the hope of throwing further light on this question. The number of excellent determinations given by F. Kohlrausch (Arm Phys. Chem. 1 8 i 5 , 154 215; 1876 159 233; 1879 6 l) and the extension of the numbers for sulphuric acid from H2S04 t o H,S,O by W. Kohlrausch (ibid. 1882 17 69) rendered t h i s a comparatively easy task. Taking the curves which show the relation between electrical con-ductivity and percentage composition one peculiarity will be noticed as common to nearly all that they rise from zero and after attaining a maximum more or less gradually fall back again to zero.To all appearances the curve between the two zero points is absolutely con-tinuous. The curve for sulphnric acid differs however in a re-markable manner from the rest in having two maxima the one at a point intermediate between the compound H,SO and the first hydrate H,SO,.OH, and the second beyold the point where the hexahydrnte is situated. It was a question of much interest whether by treating the electrical conductivity as a function of the per-centage composition and differentiating in Mendelbeff’s manner this curve could not be broken up so as to give evidence of the definite hydrates before mentioned. This is therefore what has been done the result being shown in the appended curves. It will be seen at once that the result thus far has beeu disappointing inasmuch as the curve obtained by plotting the differential expressing the change of conductivity with percentage composition E against the percentage composition does not give the broken curve expected but one which is to all appearance con-tinuous.The form of this curve excluded the idea which I at first elltertained that the conductivity might be a parabolic non-ccntinuous function of the percentage composition. There was however obviously a possibilit,y that the function might be of the third order and in this case if-dP K = A + Bp + Cp2 + Dp3, we should have-.’?- = EC + GDp, dP2 that is the second differential coefficient would between certain limits, be a rectilinear function of the percentage composition. On taking the second differential coefficient this was found to actually be the case it is indeed evident that the resulting curve consists of a serie 118 CROMPTON AN EXTENSION OF of rectilinear curves showing breaks and what is most important that these breaks occur at points corresponding with the composition of the hydrates discovered by MendelBeff with the addition of one other, namely HzSOa.240Hz.The numbers by means of which the curves for the conductivity and first and second differential coefficients of sulphuric acid have been drawn are given below. The differential coeficients have been I. Sulphuric Acid. P-1 -03 2 -51 5 '02 10.05 15 '33 19.95 24 -89 29 *98 34.87 39 *39 49 *6L 59 *95 66.16 71 -46 75 -00 78-70 82 -06 84.49 86 *lo 87 -52 90 -50 92 .go 95 -20 96 -87 98 -42 99.08 99 -44 100 * 14 100 *21 100 '40 1OC * 63 101.12 101 * 30 102.08 103 *53 105 -61 107 -61 108 '19 108 *70 109 -20 109 - '74 110 *38 K.443 1026 1944 3679 5168 6100 6701 6911 6784 6383 5112 3494 2554 1823 1421 1109 945 914 927 954 1014 1025 948 790 553 337 -4 199 *o 175 185 *6 202'2 222 *2 251 - 8 2 57 270 253 179 86 *8 60 *5 43'2 33 *2 23-6 13 *05 Pa -0.51 1-77 3 *76 7 *55 12.69 17 *64 22 *42 27 *4Q 32.39 37 -13 M. 50 54 9 8 63 -05 68.81 73 *23 76 *85 80.38 83.27 85 -29 86.82 89.01 91.7 94 -05 96 -03 67'14 98 7 5 99 *26 100 *17 100 '30 100 -51 100 -87 101 * 21 101 *69 102 80 104.57 106 -61 107.90 108 *44 108.95 109 -47 110 '06 I 430 393 366 339 282 202 122 - 25.6 - 88.5 -124.3 - 156 '4 - 151 *3 - 138 '1 -112.5 - 84.3 - 48'8 - 12.7 8 18.3 20 -1 4 * 5 - 33.9 - 95-4 - 152 -9 - 387 - 384 41.7 151 '4 87 -4 86.9 60.4 28-7 16-6 - 11.7 - 35.6 - 46.1 - 45.3 - 33.9 - 20 - 17.9 - 16.5 1 *14 2 -76 5 -65 10 *12 15 -16 20.03 24 -91 29 *89 34 -76 40.81 49.64 59 *01 65 -93 71 -02 75 *04 78'61 81 '82 84 -40 86.05 88 -21 90 -3.5 92-87 95 *04 96 -58 97 *94 99 *oo 100 -23 100 -40 100 .69 101.04 101'45 102 - 24 103 -68 105 '59 107 *25 108.17 108 -69 109.21 109 *76 - 29.3 - 13.6 - 7.1 - 11.1 - 16.2 - 16.9 - 16.2 - 13.5 - 13.2 - 4 '8 - 3 *1 0.6 2 '3 3.5 7.8 10.5 12 *5 10 -2 6.7 0.8 - 5'8 - 16.1 - 48.2 - 51.8 -108.1 - 112 - 492 - 2.4 - 73.6 - 93.2 - 25'2 - 25.5 - 13.6 - 5.1 0.6 21 '1 27 '2 4.1 2.MENDELEEFF'S TBEORY OF SOLUTION. 119 calculated by taking the differences between consecutive observations and dividing by the differences of the corresponding percentages ; although thiH does not give true differentials yet where the observa-tions are accurate the errors thus introduced are small and this method has the advantage of employing only the actual observed values so ihat the curves may be said to b e deduced directly from experiment. This most important concurrence mith Mendelkeff 'a result besides helping to confirm the latter proves that the electrical conductivity of sulphuric acid if not wholly due to is very largely influenced by, the formation of definite hydrates in solution ; and that the rectilinear character of the second differential coefficient curve gives us the means of ascertaining what hydrates there arc which exercise this influence.That this is true for other solutions besides that of sul-phuric acid has been likewise ascertained and in each case it has been found that the points where breaks occur on the - carve exactly correspond with those which occur on MendelBeff's curve for the as change of density with percentage composition -. From the form of the second differential coefficient curve it can easily be seen where breaks in the continuity of the conductivity curve may be expected and equations of the €oFm K = A + Bp + Cp' f Dp3 may be constructed for the various continuous portions of the conductivity curve.Thus the conductivity at 18" of a solution H,sO~WZOH~ is expressed by means of the following equations :-d2k d2J2 4P to r l b = 1 1 From m = - 12 I( = - 34396 - 758.97~ - 3.878~' - G.00205p3 . . (1) From m = 1 t o m = 2. K = - 860 + 617.5;~ - 13.88@ + 0*0807p3 . . . . (a) From m = 2 to 97% = 6. K = 5321 + 252-9p - 7.38~' + O*O&+' . . . . . (3) From m = 6 to m = 24. K = - 1456 + 624.58~ - 14.194~' + 0*c/866p3. . . (4) From m = 24 to m = 150. K = 69.3 + 386.22~ - 1.494~' - 0.1418~~ . . . . ( 5 ) where p is the percentage of acid in the solution. These equations are only applicable strictly between the limits stated.The values deduced by their application agree most satisfactorily with the ob-served values iu the case of (3) but in no case does the averag 120 CROJlPTON AN EXTENSIOS OF difference between the calculated and observed values exceed 1 per cent. Reverting to the sulphuric acid curT-e I would call attention to the following points :-The addition to the acid of any quantity of water up to about 2 per cent. does not appear to influence the electrical conductivity in any regular manner the second differential curve changing its direction in totally irregular fashion. But when the acid is of such a strength that it coiitains about 98 per cent. H2S04 the conductivity is iufluenced perfectly regularly by further dilution ixp t o H2SOI.0Hz the second differential curve between these limits being a continuous straight line.It is specially noteworthy that no change takes place in the differential coefficient curve between these points corresponding with the maximum attained by the conduc-tivity curve. The maximum is evidently due to some influence exerted by both the compounds H,S04 and H,SOa.OH on the con-ductivity in such a way that a t this point the sum of the influence of each becomes a maximum. It will be noticed that the second maxi-mum on the conductivity curve is also in no way indicated on the second differential curve but that it lies between the hydrates 'H2SOa.60Hz and HzSOa*240K? and this is to be explained in a similar manner. On passing the last " hydrate " indicated namely, H,SOa* 1500H, the second differential curve assumes again a per-fectly irregular form just as at the commencement and this irregu-larity continues up to the end.This irregularity a t each end of the curve is a poiiit of special interest. If we st4art again from the compound H,SOa and proceed in the opposite direction towards H2Sz07 we find in this case an exact parallel to what formerly happened. Up to a point corresponding with about 102 per cent. HzSOa the second differential coefticient curve is absolutely irregular; it then takes the form of a straight line and proceeds regularly till the composition 2H2SOa SOs is reached where a break occurs and the direction of the curve changes slightly. It still proceeds regularly however until the point HzSz07 is very nearly reached ; and here again it suddenly becomes irregular.The irregularity in fact always occurs and the same is true for every solution besides that of sulphuric acid that has been ex-amined as yet when the pure compound begins to undergo dilution. I t may be taken as representing an initiative stage during which the action of the compounds that are just beginning to be formed has not come fully into play and the conductivity varies with a series of physical actions which here probably take place and does not assume that regularity which it afterwards attains when depend-ing solely on the influence of the hydrates formed. It is on the case of sulpliuric acid as offeririg the greater range C ROMPTON. -700 & 4m NITBXC ACID SULPEURIC ACID.C KOM PTO N. I?QTASSI’,”M HYDROXIDE. ‘ O I i NENDELEEFF’S THEORY OF SOLUTIOY. 121 and the one for which tbe largest number of determinations have been made that we may a t present rest the hypothesis that electrical conductivity of aqueous solutions is due to the formation and owing to the influence of certain definite hydrates. The sulphuric acid curve is in fact typical of all others that have been examined. In the case of nitric acid for instance on taking the second differential coefficient there is evidence of the formation of two compounds, HN0,*150H2 and HN0,-40H2 and the presence of the same com-pounds is indicated by MendelBeff’s curve for change of density. It is unfortunate that the numbers for the electrical conductivity do not extend beyond an acid containing 62 per cent.of HNO.I so that the presence of hydrates richer in iiit>ric acid than the one indicated by HNO3*4OH cannot be ascertained. Phosphoric acid gives a very characteristic curve for the second differential coefficient and breaks corresponding exactly with those which occur on Mendel6eff’s curve occiir for the hydrates H,PO,.iOH, and H3POa-20H2. In this case also the observations do not extend far enough to enable i t to be ascertained whether a hydrate richer in phosphoric acid exists. Potassium and sodium hjdroxides have likewise been examined, b u t the numbers in these cases are altogether insufficient for any-thing like an adequate investigation. It is of interest that in this case the evideiice as far as.it goes tends to prove that potassium and sodium hydroxides form the same hydrates namely one with 6 mols.H,O and one with 10 to 11 mols. Acetic acid a compound with very low conductivity gives distinct evidence of the formation of two hydrates C,H,O,*OH and C2H402*30H2 and a tlhird hydrate is indicated most probably having the constitution C,H,O2*9OH?. The following are the numbers from which the curves in each case have been constructed :-IT. Nitric Acid. 6 - 2 12.4 18 -6 31 *O 3’7.2 43 *4 49 *6 55 *a 62 -0 24 -a 2924 5072 6460 7185 7319 7062 6550 5935 5290 4646 3 -1 9 *3 15.5 21.7 27 -9 34 -1 40 ‘3 48 -5 52 *7 58.9 - 4’71 343 224 117 21 -6 - 39.8 - 82.6 - 99’2 -104 - 104 6 ‘2 12.4 18.6 24.8 31 -0 37 - 2 43 -4 49 -6 55 -8 62 -0 d‘k.dy“’ -__. - 126 - 121 - 107 - 95.4 - 61’4 - 42.8 - 16.6 - 4.8 122 CROMPTON A S ESTESSION OF 4 '92 10 -25 20.05 30.52 36-90 49 -80 67.80 78 -93 87 *07 P-0.3 1 .o 5 10 15 20 25 30 35 40 45 50 55 60 ti5 70 75 80 99.7 K. 288 54.4 1061 1574 1804 1945 1436 962 660 K. 2 *98 5.48 11 '47 14.30 15.18 15.04 14 *24 13'12 11 -72 10 *13 8-49 6'93 5 -52 4 -28 3 -17 3'20 1 '37 0.76 0 -0004 IIT. Phosp7~0w'c Acid. P. 2 -46 7 -58 15 -15 25.31 33 -71 43 a35 58.80 73 -36 83 *00 dk -dP' 58 *5 48 '1 52'7 49.0 36.0 10 -9 - 28 '2 -42.6 -3'7.1 IV. Acetic Atid.0.15 0 *65 3 7.5 12 -5 1'7.5 22 *5 27 -5 32 '5 37'5 42 -5 47 -5 52-5 57 *5 62 -5 67 *5 72 *5 77.5 90 9 *9 3 -5 1.467 0 -5660 0 * 176 -0.028 -0.160 -0.224 - 0.280 -0.318 - 0 '328 - 0 '312 - 0 -288 - 0 '248 - 0 *222 - 0.194 -0 -166 -0 *122 - 0 '038 5 -00 11 *36 20 *23 29-51 38.53 61 *07 66-08 78.18 io. -0 *4 1-82 5.25 10 15 20 25 30 35 40 45 50 55 60 65 70 75 83 -7 -20'3 - 3.6 -15.5 -27'3 -25.3 - 9.8 + 5 . 7 6.1 - 901 - 390 - 204 - 132 - 64 - 56 - 22 - 10 16 30 34 26 28 28 44 8 MENDELEEFF'S THEORY O F SOLUTION. V. Potassium Hydroxide. 123 4.2 8.4 12.6 16.8 21.0 25.2 29.4 33.6 37.8 42.0 1372 2552 3526 4271 4784 5061 5090 4890 3344 4484 --2-1 6-3 10.5 14.7 18-9 23-1 27-3 31-5 35'7 39.9 2.5 5 10 15 20 25 30 35 40 42 E.1019 1845 2927 3244 3062 2543 1892 1409 1088 995 dk d/p -. -326.6 281 232 179 122 66 7 - 48 - 97 - 129 VI. Sodiunr Hydroxide. P. 1-25 3-75 7'5 12.5 17'5 22-5 27.5 36'5 37.6 41 4.2 8.4 12.6 16.8 21.0 25-2 29.4 33.6 37.8 -45.6 - 49 - 53 - 57 - 56 - 59 - 55 - 49 - 32 dk dp' -4Q7-6 330.4 216.4 63.4 - 36.4 -103.8 -130.2 - 96.6 - 64.2 - 46.5 2.5 5.62 10 15 20 25 30 35 39'25 -3o.ao -30'12 -10'60 -19.96 -13'48 - 5.28 - 6.72 - 6'48 - 5-06 The values for the conductivity which have been used in investi-gating the above cases are those given by Kohlrausch for the t,em-perature of 18".It has not been possible owing to the want of full experimental data to ascertain what effect change of temperature would have on the second differential curye. According to Mende-18eff's theory the only effect which a rise or fall of temperature could have on the solution would be to alter the amounts of the products of dissociation but as the compounds formed would be the same for the same concentrations no change would take place in the position of the points where breaks occur on the second differential coefficient curve although the direction of the lines joining those points might be altered. That is the same hydrates would be formed provided the concentrat'ion were kept constant whatever tihe tempera-ture mightl be as long as it were short of that which would produc 124 AN EXTENSION OF MENDELdEFF'S THEORY OF SOLUTIOY.total decomposition in the hydrates. Proof of this is brought forward by Mendel6eff in his paper on the change of density of sulphuric acid (Zon. cit.). This statement as t o the effect of temperature is fully verified by the electrical data in the case of nitric acid the conductivity of which has been determined hp Kohlrausch at O" 18" and 40° and working out the second differential from the numbers given for these tempera-tures the direction of the straight lines representing the various portions of the second differential curve is found to alter perfectly regularly as the temperature rises or falls but the breaks occur a t the same points for all temperatures.This being the case such experimeiits as those of Heim (Ann. Phys. Chem. 27 643) on change of conductivity with change of tempera-ture and of Nicol (Trans. 1887,389) on change of specific viscosity with change of temperature for saturated solutions cannot be accepted as proving that the composition cf sat'urated and non-saturated solutions is necessarily the same since where the concentration of the solution undergoes no change the composition must of necessity remain the same. It is only by investigating the change of the physical pro-perties with the concentration that change of composition a t the saturation point might be shown to take place and as far as can be ascertained from the few experiments quoted by Nicol (Zoc.cit.) on the rel;tt,ion of specific viscosity to concentration such a change at the saturation point does actually take place. Heim's experiments on the other hand niay be taken as affording additional support to Mende-16effs views of the influence of temperature on solutions. Assuming Mendeldeff's theory to be true and that what we really have in a solution of two substances a t any point is a mixture of two dissociable and dissociating compounds formed from these substances in different proportions we may deduce an expression for the electrical conductivity of such a solution in the following rcaiiner :-If K is the conductivity of the solution we may suppose a certain proportion of this to be borne by each constituent of the solution and if p is the percentage of one constituent and pl the percentage of the othei- and a quantity a of the first is combined with a quantity 7 of the second the remainders representing the products of dissociation, we have-K = ( p - a)k + ( p l - b ) h + ( n + b ) h , where 76 k and k are the conductivities of unit amounts of the components present under the conditions of experiment.But it is obvious that the amount a of p which will remain combinsd will be proportional t o the total amount'p of t'he constituent present all other things remaining constant.; and that in like manner the amount b o ARJISTRONU ON ELECTROLYTIC CONDUCTION. 125 pl remaining combined will be proportional to p . equation becomes-Hence the above K = kcp + klCIp1 + (c2p + c3pJk2, where c cl c2 and cj are constants.But now since neither con-stituent when alone and in a pure condition has any conducting power it is clear that the conductivity of any one constituent must in some way be influenced by the presence of the others and I cannot but think that it is not only the simplest but also a fair assumption to make that this influence will be directly porportional to the amounts of the other constituents present. If this is so k becomes equal to 100 - y multiplied by some constant and k becomes equal to 100 - pl multiplied by some other constant ; or since 100 - p l = p , to p multiplied by a constant. The quantity Tc in the same way is proportional to p since the amounts combined czp and c.p, depend on p andp or 100 - p . But k represents the conductivity of a mixture of two compounds and the influence of each of the compounds on the other must here also be considered. This influence, as will easily be seen is likewise porportional to p . Therefore kz as representing the conductivity of the combined amounts becomes proportional to p and as representing the influence of one compound on the other is also proportional to p ; in this way kz becomes proportional to p2. If we now substitute the values for k kl and k , in the above equation and for p write 100 - p we should find that it would eventually simplify down to K = Bp + Cpa + Dp3, B C and D being constants. The conductivity would thus be represented as a function of the third order of the percentage coin-position a relation which as has been shown is rendered extremely probable by the nature of the second differential coefficient