TEMPERATURE OF MAXIMUM DENSITY O F AQUEOUS SOLUTIONS. DEVIATIONS FROM THE LAW OF DESPRETZ BY NORA GREGG-WILSON AND ROBERT WRIGHT
The generally accepted explanation of the phenomenon of the temperature of maximum density of water is derived from the fact that the density of water is greater than that of ice. I n common with other liquids the density of water increases with fall of temperature, but as it approaches the freezing point ice molecules are supposed to form and their smaller density to counteract the increasing density of the water. At 4 O , the temperature of maximum density (t.m.d.) of water, these two effects just balance, and between 4' and the freezing point the preponderance of ice molecules causes an increasing lowering of the total density. The t.m.d. of aqueous solutions has been frequently investigated, and the most important generalisation put forward is that due to Despretz,' who found that the t.m.d. of water was lowered by the addition of a solute and that the lowering was directly proportional to the concentration of the dissolved substance. The lowering of the t.m.d. by a solute does not depend, like the lowering of the freezing point, solely on the molecular concentration, but varies also with the nature of the dissolved substance. De Coppet* has measured the molecular lowering of the t.m.d., that is the lowering produced by a gram molecule of solute in a litre of solution, for a number of substances and found the result to vary greatly with the nature of the solute employed. I n the solutions of simple binary electrolytes it would seem that each ion has its specific effect on the t.m.d., and that the molecular lowering of a salt solution can be calculated from the observed effects of other salts.a All salt solutions which have been investigated, and the great majority of solutions of organic substances, obey the law of Despretz. The important exceptions are the dilute solutions of the lower alcohols;4 of these ethyl alcohol is the most interesting. With dilute solutions thls substance causes a rise of the t.m.d., but with greater concentrations a depression is produced. Solutions of ethyl ether also deviate from the law of Despretzb but they do not give an elevation of the t.m.d. In considering the effect of a solute on the t.m.d. of water three factors should receive attention. The lowering of the temperature of production of ice molecules-1.e. of the freezing point, the temperature coefficient of expansion of the solution, and the density of the solution. 'Ann. Chirn. Phys., 70 j , 49 (1839); 73 296 (1840). *Ann. Chirn. Phys., 3,k46,268 (1894);kornpt. rend., 125,533 (1897); 128, I559 (1899); 131, 178;132, 1218 (1900). 134, 1208 (1902). a Wright: J. Chem. Sod. 115 119 (1919). 4DeCoppet: Cornpt. rmd., lis, 6 2 j (1892);J. P. McHutcheson: J. Chem. SOC., 129, 1899 (1926). 6 Nort: Landolt and Bornstein Tabellen.
TEMPERATURE OF MAXIMUM DENSITY OF AQUEOUS SOLUTIONS
6 25
Since the lowering of the freezing point depends only on the molecular concentration of the solute, it should be the same for all solutions of organic compounds of equal molecular concentration, though for salt solutions the effect will be greater owing to ionisation of the solute. I n all cases the lowering of the freezing point will produce a corresponding lowering in the t.m.d. of the solution. The coefficient of cubical expansion of any aqueous solution is greater than that of pure water. It therefore follows that the contraction caused by the fall of temperature, which has to be balanced by the formation of ice molecules before the t.m.d. is reached, is greater for a solution than for water, hence the increase in the coefficient of expansion will cause a lowering in the t.m.d. The effect on the t.m.d. due to the density of the solution depends on whether that density is greater or less than that of water. If the solution has a density greater than that of water, then the separation of ice molecules in the neighbourhood of the t.m.d. will increase the concentration of the remaining solution and the resulting increase of density will have to be balanced by the further production of ice molecules before the t.m.d. is reached. That is, the t.m.d. will be lower on account of the solution being more dense than water. On the other hand if the density of the solution is less than that of water, then the removal of solvent by the formation of ice molecules will still further decrease the density of the remaining solution, and thus help the action of the ice molecules and tend to raise the t.m.d. of the solution. We thus come to the conclusion that for solutions of greater density than water, all three contributary causes tend to lower the t.m.d.; whilst for other solutions, the lowering of the freezing point and the greater coefficient of expansion, will be to some extent balanced by the smaller density of the solution. For dilute solutions all three factors, lowering of the freezing point, increase in the coefficient of expansion, and the density of the solution, will be proportional to the concentration of the solute, and therefore their combined effect will also be proportional to the solute concentration and hence the solution will obey the law of Despreta. As a rule with electrolytes all three contributary factors are relatively great, so that only dilute solutions, such as might be expected to obey the law of Despreta, have been investigated. With more concentrated solutionsthe t.m.d. isin generallower thanthe freezing point. Solutions of hydrochloric acid and lithium chloride are however exceptions to the general class of electrolytes, since the molecular lowering of the t.m.d. (as calculated from dilute solutions) is in the neighbourhood of six degrees. These solutions were therefore examined up to a concentration of 2 s with the result shown in the table:
.u
Hydrochloric acid lowering o f t . m. d.
N 0.;
I
2
.o
16.4
2
.o .o
Lithium chloride lowenng o f t . m. d. 2 . 7
5.9 12.5
626
NORA GREGG-WILSON AND ROBERT WRIGHT
I t is at once obvious that at high concentrations the law of Despretz is not obeyed. This result is probably related to the well-known phenomenon of the excessive lowering of the freezing point which occurs with concentrated electrolyte solutions.' With solutions of organic compounds the coefficient of expansion is generally less than that of salt solutions of a corresponding molecular concentration, and the depression of the freezing point owing to the absence of ionisation) will also be less. Further, if we confine our attention to those substances which give solutions of less density than that of water, we are dealing with a class of solution of which the molecular lowering of the t.m.d. will be the smallest possible. As a consequence we should be able to employ fairly concentrated solutions and have a good opportunity of observing deviations from the law of Despretz. The number of organic compounds less dense than water, and at the same time sufficiently soluble, is considerably restricted. Apart from the alcohols, which have already been investigated, the most important group is that of the fatty amines. The values of the t.m.d. for a number of amines have been determined and the resalts are tabulated along with those obtained for a few other substances. It will be seen that in general there is a deviation from the law of Despretz for the stronger solutions, and that the deviation is in the direction of excessive lowering of the t.m.d. The relative densities at 5' have also been tabulated and so have the coefficients of expansion between the temperatures 12.5' and 15'. The densities when plotted against the concentrations give approximately linear graphs, but the coefficients of expansion as a rule show excessive increases with increase of concentration. This abnormal increase in the coefficient of expansion is made clear by the table of "Molecular increase of coefficient of a - aa expansion", in which is given the values for where a. is the coefficient N of expansion of the solution, awthat of pure water and N the concentration of the solute in gram molecules per litre. If the change in the coefficient of expansion was directly proportional to the concentration, then the value of as - a, should be constant. It will be seen however that for most solutions it tends to increase, and it is to this excessive increase in the coefficient of expansion with the more concentrated solutions that the excessive lowering of the t.m.d. is to be attributed. Three substances among those investigated call for special mention. Ethyl alcohol, as already pointed out, first raises the t.m.d. and then lowers it. The coefficients of expansion of the alcoholic solutions are very near those for pure water in the case of solutions up to N / z strength. So that for this substance the factor due to the small density of the solution outweighs the others in the case of dilute solutions, but at higher concentrations the increasing coefficient of expansion causes a lowering of the t.m.d. For aceto-nitrile, up Biltz: 2. physik. Chem., 40, 185 (1902); Jones: Carnegie SOC.Reprint 60 (1907.)
TEMPERATURE OF MAXIMUM DENSITY OF AQUEOUS SOLUTIONS
m
b
N
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s:
0
0
0
0
0
0
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627
628
NOR.4 GREGG-WILSOK AND ROBERT WRIGHT
to Z X concentration, the coefficient of expansion is directly proportional to the concentration, and hence this substance obeys the law of Despretz. The same is true for ammonia but only up to ?i concentration. The above results indicate clearly that the law of Despretz, like so many other generalisations, only holds in the case of dilute solutions and breaks down as soon as the solutions become concentrated. Experimental. The determinations of the t.m.d. were carried out by means of a compensated dilatometer in the manner already described by one of US.^ The coefficients of expansion were made with the same instrument, the stem being calibrated for the purpose. The choice of the temperature range I 2 . j oto I j ois an arbitrary one, but it was considered to be sufficiently removed from the t.m.d. to be free from the complication of the formation of VlS - V I 2 5 ice molecules. The coefficient was calculated from the expression a = ____ 2.5
x viz.5
where V I S and V,,., are the volumes a t I S and 12.5 respectively. I n conclusion it should be recalled that the t.m.d. is not capable of exact determination and hence the above data are only approximate. Iievertheless there can be no doubt that the conclusion that the law of Despretz only holds for dilute solutions is correct. Physical Chemistry Laboratory, Unzuerslty of Glasguw. J u l y 1, 1930.
Wright: J. Chem. SOC.,115, 1x9 (1919)
