T H E DIFFUSION O F SODIUM CHLORIDE IN AQUEOUS SOLUTIONS BY L. J. BURRAGE
I. Introduction The main object of the present investigation was to test the accuracy with which the diffusion coefficients of electrolytes could be measured as a preliminary to work on the diffusion of mixtures. Comparison was made with the results of Oholm, which form the most accurate and extensive work on the subject so far available. The experimental comparison was carried out on sodium chloride, partly in order to ascertain whether there was a definite minimum in the diffusion coefficient-concentration curve similar to those found in the cases of HC1, KCl and LiCl. Whereas Oholm' found such minima to be well marked with these electrolytes, the curve for sodium chloride was practically linear between I M and 6 M, and parallel to the concentration axis, exhibiting no upward movement. Its course in this concentration region was, however, determined by two points only, at 2.8 M and 5.5 M, and these are scarcely sufficient for so large a concentration range. In the experiments recorded below the diffusion coefficient has been determined for six solutions falling within the same range; the curve can consequently be drawn with greater accuracy. Figures have also been obtained for the diffusion coefficient of 0.1 M HCl in water and these have been made use of in a later paper where experiments on the rate of diffusion of 0.I M HCl in solutions of alkali metal halides are described. 11. Experimental An examination of the previous workers' methods and the difficulties which they experienced, shows that there are three important factors which must be taken into account to ensure the success of the practical work. (a) Temperature Variation. (b) Vibration Effects. (e) Mixing during the filling or emptying of the apparatus. Although, strictly speaking, these three factors come under the one category, since they all cause a false movement of the diffusing substance, it will be advantageous to consider them separately and to show what precautions have been observed to eliminate each. ( a ) Temperature Variatzon. A sudden rise or fall in the temperature tends to cause mixing of the solution even though that variation be comparatively small. A much greater temperature change will be far less serious if it takes place over a long period of time. 1
Z. phyaik. Churn., 50, ,-j(~y( i y q ) .
DIFFUSION OF SODIUM CHLORIDE IN AQUEOUS SOLUTIONS
2167
I n order to reduce this temperature effect to a minimum the experiments were carried out in a large vault, the door of which was felted to prevent any possibility of draughts. The vault itself had a fairly constant temperature, the maximum range covered being IzOC. in Winter to 18' in Summer. The vault was lit by a single electric lamp which was used as little as possible during the experiments, an electric torch also being used when a strong local illumination was needed. The author remained in the vault for as short a time as possible during an experiment. Inside this vault, whose only outlet was the door, was a large wooden box six feet in height and three feet square in cross-section, papered throughout internally and then painted, thus ensuring that all cracks and pinholes were covered. The parts of the box which opened were felted, both inside and outside, to prevent any slight external temperature change from being communicated. The box was provided with maximum and minimum thermometers.
( b ) Vibration E$ects. I n order to ensure that the vibration effects should be reduced to a minimum the following precautions were taken. A vibration-free concrete block was constructed which stood about 3 feet above the ground level and was 2 % ft. square in cross-section. On this a stout wooden platform was securely bolted and so arranged as to be exactly horizontal. This block was entirely encased by the constant temperature box to which reference has already been made. A portion of the front, the whole width and 18 inches high, was hinged at its lower end and thus allowed of access to the apparatus when emptying the latter. I n order to avoid opening this door unnecessarily it was fitted with a long mica inspection window about 3 inches in height and running the whole length near the bottom. Convection effects during the filling or emptying of the apparatus. A full description of the apparatus employed will be given at this point, as the design is a matter of importance when discussing convection effects during filling or emptying. An examination of previous workers' apparatus has brought to notice the following points: ( I ) That a very accurate control of the rate of flow of the liquid is necessary when filling or emptying, and (2) That it is preferable to fill from above and empty from below. The method employed in this investigation was based upon that of Graham as modified by Svedberg and Uholm. I n general outline it consisted of placing a certain volume of solution below three times that volume of pure water and allowing diffusion to take place. At the close of the experiment the liquid was separated into four equal portions which were referred to as layers. These were analysed and the distribution of substance in each of the layers obtained. The apparatus used in these experiments was essentislly that of Uholrn.' It consisted of a diffusion cylinder D about 2 0 cms. long nnd j . 5 cms. in cross(c)
'8.physik. Chem., 50, 309 (1904).
2168
L. J. BURRAGE
section, fitted with a ground glass joint at the upper end and a capillary tube, 1.5 mm. in diameter, with t,ap, at the lower. d is a pipette of about 2 0 ccs. capacity between the marks x and y, and fitted with taps above and below these points. Below the lower tap was a ground glass joint B, which fitted into the diffusion cylinder. I n t,his ground glass joint there was a small hole C to allow of the free passage of air during filling or emptying. The length of capillary tubing below E was O. j mm. in diameter. This was an improvement on previous designs, which did not employ a sufficiently narrow capillary. A second point, of difference between this apparatus and that used by oholm was the incorporation of a t a p a t the top of the pipette. This tap was so adjusted as t,o let air pass very slowly indeed. Both these improvements were designed t o minimize mixing of the solution when the diffusing liquid first entered the diffusion cylinder. Unless very careful control is exercised when the lower tap is first turned the diffusing liquid will run down into the cylinder too rapidly and convection will result. (d)
X e t h o d of Operntz'on. ( I ) Filling. Four pieces of apparatus viere arranged side by
side near the front of the box and mercury poured into each unt,il it was 0.5 mm. - 1 . 0 mm. below the end of the pipette. E:acli pipet,te was then filled t o thc upper mark with distilled water placed in t,he apparatus, and allowed to run in until the liquid reached the lower mark. This was repeated twice. The diffusion cylinders were now corked and the pipettes put, on a stand at the back of the box,which n'as closed and left for about 24 hours to allow of t,emperature FIG.I equalisation. Each pipette was then rinsed out with the solution whose diffusion coefficient was about to be determined, filled to the top mark, the stem being carefully dried with a dry cloth, and inserted in the apparatus. The door of the box was closed and the apparatus left for 3 hours to allow the disturbing effects of slight change of temperature, due to opening the door of the box, and liquid disturbances, caused by the withdrawal of the pipette, to disappear. After a three-hour interval the door of the box was opened and the lower tap turned very slowly, the time being simultaneously noted, for diffusion starts from this moment. The speed of running-in was such that the total 2 0 ccs. should t'ake about z hours. The rate was noted by the movement of the liquid column, observation being made through the upper of the mica windows. When the liquid had reached t,he lower mark the tap was turned and the door of the box closed. The vault was not entered again until the time for the wit'hdrawal of the liquid had arrived. The length of a single run varied from case t'o case, but generally fell between one and seven days. (2) Withdrawal of the L i p i d . A narrow platform, fitted inside the box, ran parallel to the front, underneath the exit tubes at the bottom of each piece of apparatus. I t was attached to the sides of t,he box, was quite independent
DIFFUSION OF SODIUM CHLORIDE I N AQUEOUS SOLUTIONS
2 169
of the concrete block, and served as a tray to carry the flasks which were filled with liquid during emptying. The liquid was drawn off into flasks of similar design to those used by ()holm, each one having a graduation mark on the neck corresponding to the volume of the pipette, between the marks x and y. I n this way the liquid column could be separated into four equal portions, which were subsequently analysed. The time was noted when each flask was filled, the period of diffusion being counted up to this point. It was most essential that the four layers should be separated as accurately as possible, since a very slight error at this point caused a large variation in the determined value of the diffusion coefficient. The rate at which the withdrawal of the liquid was carried out was approximately I cc. per I O mins., although considerably longer times have been taken in some cases.
( e ) Materials employed. The following chemicals were involved in this investigation:( I ) Potassium and Sodium Chlorides. These were of A.R. quality and were used as such after heating strongly until all decrepitation had ceased. (2) Hydrochloric Acid. Analytically pure acid was distilled under constant boiling conditions. This was then diluted until a concentration of exactly 0.1M was obtained. (3) Lithium Chloride. This was not obtainable as A.R. quality. The impurities, other than water, were, however, only a few hundredths of I%, the chief being ferric chloride. Calibration of the Apparatus. The calibration of each portion of the apparatus was carried out with water, by weighing in the case of the pipette and volume measurements for the cylinder. For the success of the experiments it is essential that the diffusion column should be as nearly as possible of constant cross-section. This means that the diffusion cylinder must be of constant cross-section as must also be the external dimensions of the capillary of the pipette. The cylinder was calibrated in the following manner. It was set up in the stand, as for an experiment, mercury being run in until there was about a millimetre gap between this and the end of the pipette. The height of this mercury level was read off, the measurements being made to I/IOO mm. by a cathetometer. A known volume of water - 9.94 ccs. - was then added and the level of the water measured with the pipette in position and when it had been removed. This was carried out eight times successively. The results showed that in every case, the condition of constancy of cross-section was sufficiently fulfilled. (f)
L. J. BURRAGE
2170
111. Results The diffusion coefficient has been calculated for each of the four layers from the tables of Kawalki and Stefan.' In Table I a few results are given showing the agreement between the coefficients for the four layers for sodium chloride solutions. The vertical columns have the following significance:I.
Concentration of sodium chloride.
Temperature of experiment. 3. The Diffusion coefficient for the lowest layer. 4. The Diffusion coefficient for the next layer and similarly for 5 and 6. 2.
j . The average diffusion coefficient of all four layers. Each horizontal set of figures shows the complete results for one single experiment.
TABLE I 7
1
2
3
4
5
6
Conc.
T
K1
Ka
K3
K4
0 . 4 9 8 M.
13.6'
0.936
0.931
0.933
0.932
0.933
0,937
0.917
0.948
0.945
0.937
0.931
0.943
0.938
0.930
0.935
0.935
0.946
0.943
0.927
0.938
0.952
0.945
0.953
0.949
0.950
5.810 M.
13.5'
av
K
0.954
0.960
0.952
0.949
0.954
0.951
0,952
0.952
0.946
0.950
0.954
0.955
0.952
0.955
0.952
Table I1 comprises the full results and the symbols have the following significance.
M. A. T. At. K. K1.
Weight molality. Apparatus used. The temperature of the experiment "C. The extreme temperature variation. The average diffusion coefficient for the four layers. The average diffusion coefficient for a given concentration at a definite temperature.
Wied. Ann., 52, 166 (1894).
DIFFUSION OF SODIUM CHLORIDE IN AQUEOUS SOLUTIONS
2171
TABLEI1 K'
M
T
0.1012
14.7 14.7 14.7 14.7
-
.7 '7 .7 .7
D A C F B
13.6 13.6
'5 .5 '5 '5 .5
D F A B
13.6 13.6
-
c
13.6 13.6 13.6
0.198
0.498
I ,005
F B A I .so1
14.4 14.4
14.4
13.6 13.6
13 .o
At
-
.2 .2
.3 .3 .3 .3
f .o f .o
A D
c
B 2.072
D E F A D F
c D A
c
D F
c
B
15.0 15.0 15.0 1 5 .o
12.8 12.8
+ .4 + .4 + .4 - .6 + + .I .I
13,s 13.5 13.8 13.8
+ +
13.3 I3 e3 13.3 13.3
+ .3 + .3 + .3 + .3
f .o f .o .I .I
0.986
0.944
0.968 0.933 0.937 0.935 0.938
0.936
0.927 0.926 0.929 0.912
0.927 0.912
0.930 0.928 0.937 0.926
0.930
0.972 0,974 0.954 0.992 0.897 0.913 0.917 0.918 0.954 0.947 0.930 0.920 0.947 0.925
0.973 0,905 0.918 0.950
0 * 930
L. J. BURRAGE
2172
Table I1 (continued) M
A
T
5 ' 503
A
16.0
B D F
13.3
B
16.2
A
16.2
17 .o 13.3
K
At
+ .3
+ .6 + .os + .05
I ,026
1,075 0.940 0.939
0.940
5.810
0.1004
B C F
Hydrochloric Acid - .I
16.2
16.2
16.6
+ 3 .3 .5 - '3
+ +
2
'
I53
2.157 2.1j6 2.148
2 . I53
2.166
2.166
The variation in the temperature during the course of the experiment (At) only amounted to 0.1- o.z0C.,the increase above this value being caused by the opening of the box at the close of the experiment, thereby exposing the apparatus to the change in the temperature of the vault. The 4t values quoted in the table represent the change which had occurred a t the close of each experiment and that amount due to the opening of the box cannot affect the result t o any serious extent as the diffusion had already proceeded for a period varying from I to 7 days, and the gradient must be small, hence there is little danger of any sudden connection effect due to this cause, since it only occurs during the withdrawal of the liquid.
IV. Discussion Discusszon of Sources of Errors affecting the Results. (a) The first possibility is that the amount of diffusing substance in the column may be increased during a run by diffusion out of the end of the pipette. This, however, does not take place since the lowest section of the bottom layer in the diffusion column does not change in concentration during the course of the experiment, and there is therefore no tendency for the pipette contents to diffuse outwards. However, if any did diffuse, it would not cause serious error since the volume of liquid contained in the pipette below the lower tap is exceedingly small. (b) It will be noted that the value of 41 derived from the second layer of an experiment sometimes appears high. This is undoubtedly due to a very slight amount of mixing. A reference to Kawalki's figures will show how serious is the effect of a slight error in the determination of the amount of
DIFFUGION OF SODIUM CHLORIDE IN AQUEOUS SOLUTIONS
2173
diffusing substance in this particular layer. There will be seen that the value of VI, the amount of substance expressed as parts per 10,000,for the second layer very slowly increases and then falls just as slowly. This gives a very flat curve corresponding to a large range of x values, where x = hI2/K T = 4 height of a layer squared, divided by the diffusion coefficient multiplied by the time. It is thus easy to see that a very slight error in v' may give rise to a very serious error in the value of x and thus cause the value of K to be somewhat inaccurate. (c) In some cases the value of the K for the fourth layer is somewhat uncertain. This happens when the experiment has only proceeded for a short space of time and there is an insufficient amount of diffusing substance in the top layer to give a really accurate analysis.
Comparison of Results at 18' The results in Table I1 have been calculated to 18Oc. by means of the temperature coefficients given by Oholrnl and these final figures are collected in Table I11 together with those obtained by Oholm. Fig. 2 contains the data (circles) for NaCl plotted in the form of diffusion coefficient against molality. Oholm's data are shown by crosses.
TABLE I11 Substance
M
K 18"
NaCl
0.101
0.198
1.094 I ,086
0.498
I
,078
1,077
1.005
I
,069
1.074
I . 501
I ,067
2.072
I ,071
2.936
1.074 I .083
I .064
5.503 5.810
1.097
I .065
I . 100
-
0 . IO0
2.227
2.229
4.259
HC1
oholm K 18" 1.117 I ,089
-
Agreement with Oholm is seen to be moderate thmughout the whole concentration range. In contrast to his results, however, the present curve shows a distinct minimum a t a concentration of 1.5 M.
L. J. BURRAGE
2174
, o ' 0 0
10
0
0
0-
1. 0 5
summary I. A detailed account has been given of the precautions taken to prevent vibration and mixing. 11. The diffusion coefficient of NaCl has been measured over a large concentration range. 111. The diffusion coefficient of 0.1M HC1 has been measured. IV. Comparisons have been made with existing data. The author desires to express his thanks to Prof. A. J. Allmand, under whose direction this work has been carried out. King's College, University of London. March 17. 1938.
