PARTIAL MOLAL VOLUMEOF POTASSIUM SALTS
Jlec., 3!)3i
Summary The solubilities of citric and tartaric acids in water have been determined a t loo intervals (including 250) Over the range of temperature
0-looo.
below this transition temperature citric acid monohydrate exists, while above anhydrous citric acid is the stable phase. The solubility curve for tartaric acid is a straight line representing solutions in equilibrium with the anhydrous form of the acid.
The solubility curve for citric acid consists of two straight line curves which intersect at 35.8' ; BROOKLYN, N. Y.
[CONTRIBUTION FROM
THE
2549
RECEIVED JUNE 23, 1937
DEPARTMENT OF CHEMISTRY, NORTHDAKOTA AGRICULTURALCOLLEGE]
The Partial Molal Volumes of Potassium Chloride, Potassium Bromide and Potassium Sulfate in Sodium Chloride Solutions BY HENRYE. WIRTH Since the discovery by Masson' that the apparent molal volume of a dissolved salt is a linear function of the square root of the volume concentration, several investigator^"^ have made exhaustive tests of the applicability of this relationship. It was found valid for a number of salts over a surprisingly large coiicentration range. Root4 derived from Masson's rule a simple equation relding density and volume concentration which has found wide application. Redlich and Rosenfeld5 derived from the Debye-Hiickel theory a linear relationship between the square root of the volume concentration and the partial molal volume of a dissolved salt. This gave a partial theoretical basis to Masson's rule as the apparent molal volume is closely related to the partial molal volume. The expression obtained was --
-
/I =
v; + qw%" C','?
(1)
I.; is the partial molal volume of the salt in a solution of concentration c; 't;," is the partial molal volume at infinite dilution; q is a complex factor involving the temperature, compressibility, the type of electrolyte, the dielectric constant and its change with pressure; and o is one-half the summation of the number of ions times the square of the valence of the ion. When considering a solutioii containing two or more electrolytes the last term in Eq. 1 becomes p ' ( Z . ~ c ) ~ ~ ~ . The factor ZWCcorresponds to the ionic strength 0x1a volume basis, so that the partial molal volume of a salt in solution should be a linear function of the square root of the volume ionic strength. This 11) Mas.-on, Phil. Ma:.: [ 7 ] 8, 218 (1929). J . P h y s . Chem., 35, 2316 (1931). (3) Geffcken, Z . physik. Chem., A166, 1 (1931). (4) Root, THISJOURNAL, 55, 850 (1933). (6) Redlich and Rosenfeld, Z . physik. C h e m . , AlSS, 65 (1931). 12) Scott,
relationship was tested by determining the partial molal volumes of potassium chloride, potassium bromide and potassium sulfate in sodium chloride solutions of different concentrations. Methods Preparation of Solutions.-The salts used were either Baker Analyzed or Mallinckrodt Reagent quality and were not further purified. Salts to be weighed were dried a t 350-400". Solutions for the density determinations were prepared by adding a weighed amount of the dried salt (potassium chloride, potassium bromide or potassium sulfate) to a weighed amount of water or sodiuni chloride solution. The volume concentration of the added salt could then be calculated using the observed density. Enough sodium chloride solution for each series was prepared and its concentration determined from the density. This concentration was corrected fot: the change caused by the addition of another salt. The concentrations reported are expressed as moles per liter of solution. The sodium chloride solutions used were approximately 0.04, 0.16, 0.36, 0.64 and 1.0 normal. To each of these solutions was added sufficient potassium chloride, potassium bromide or potassium sulfate to make the volume ionic strength of the added salt approximately 0.04, 0.16, 0.36 and 0.64. Solutions in water of the latter salts of volume ionic strength 0.04, 0.16, 0.36, 0.64 and 1.0 were also prepared. Density Determination.-The density of each of the above solutions was determined by means of the sinker method. The solutions whose densities were to be measured were placed in heavily silver plated copper cans immersed in a thermostat a t 25'. Metallic containers were used to decrease the time required to attain temperature equilibrium. The temperature was maintained constant to *O.O0lo. The sinker was suspended in the solution by means of a fine platinum wire which was coated with platinum black where it passed through the liquid surface. This wire could be fastened to a pan of a balance which was supported over the thermostat. DiEerences in density were calculated directly using the equation d, - d, = (m, - ~ J / v (2)
HENRYE. WIRTH
2550
VOl. 59
where de is the density of the sodium chloride solution, d~ is the density of the solution of sodium chloride plus the added salt, m2 and maare the weights required to balance
vent, and a2 is the apparent molal volume of the second component in a solution containing nl moles of solvent and na moles of solute only. the sinker when immersed in the respective solutions and The quantity Fa = -(d3-&)/c3 was found to v is the volume of the sinker. When using this equation it is necessary to know the volume of the sinker only to be a linear function of the square root of the the accuracy desired for the density differences. volume ionic strength, pv = oZc2 w3c3. The In practice two sinkers were used so that duplicate experimental data were therefore represented determinations could be made successively. Three hundred-cc. floats were used, and as ma and ma by equations of the form d3-& = ac3 - bc3 - c;'/') repwere determined to 0.1 mg. the method was sensitive to (p;l2 - c ~ ' / ' ) where the term (&I2 dserences of 0.8 parts per million in the density. The resents the increase in volume ionic strength due accuracy as determined by duplicate measurements on to the addition of n3moles of the third component.
+
identical solutions was about 2 parts per million with a maximum deviation of 5 parts per million.
47.0
140
1.5
-P
-
d
ti
P LOi
246.5
rr; 135 I
M
d
ri
I
I
130
1.5
0.4
0.8
- cyz.
1.2
/.l"'/'
0.4
0.8
pvvs
.-
- cyz.
1.2
Fig. 1 - F us. increase in the square root of the volume ionic strength for potassium chloride (0) and potassium bromide ( 8 ) : curve 1, water solution; curves 2, 3, 4, 5 and 6 are for 0.04, 0.16, 0.36, 0.62 and 0.97 normal sodium chloride solutions, respectively; temperature, 25'.
Calculation of Results.-In general the methods of Guckers were used with those modifications necessary due to the presence of a third component. The apparent molal volume (%) of a salt in a solution containing another salt may be defined by @'3
= [
- (%IF; -k nz@'z)I/%8
(3)
where V is the total volume of solution containing n l moles of solvent and n2 and n3 moles of solutes, V! is the volume occupied by a mole of pure sol(ti) (:ticker, J . P ' l i y ~ .C h c ~ i, 38, :307 (1934).
Fig. 2.- - F us. increase in the square root of the volume ionic strength for potassium sulfate; curve 1, water solution; curves 2, 3, 4, 5 and 6 are for 0.04, 0.16, 0.35, 0.62 and 0.97 normal sodium chloride solutions, respectively; 0 , Jones and Ray; temperature, 25'.
This form of the equation was selected since, as pointed out by Gibson,' less weight is given to the quantity F. The constants a and b were determined by the method of least squares. a is the value of - fl in the sodium chloride solution containing no other salt and b is bF3/b&'. @ was calculated from the relation = (fl Ma)/&, where MS is the molecular weight of the added salt. Values of Qa at other concentrations were then obtained using the slope = (bR/ &-?') /dz. If nl and nzare kept constant and only n3 varied
+
(7) Gibson, i b i d , 38, 319 (1934).
Dec., 1937
PARTIAL
MOLALVOLUME
as was done in this work the equation derived by Guckere
may be used to calculate the partial molal volume. Using AIzas the variable the equation becomes =
*’
G8[w(h/dCa) +
20oop:/2
+ ~ l ( 1 0 0 0-
c&s)(&/&&”)
+ c;[wz(iwaca) + oai(as/ap:/9 (5)
Throughout this article the subscript 1refers to the solvent, 2 to the sodium chloride or sodium chloride solution and 3 to the added salt (potassium chloride, potassium bromide or potassium sulfate) or its solution. The superscript 0 refers to infinite dilution (ca = 0).
2551
OF POTASSIUM SALTS
For KC1: d264= 0.997074 For KBr: dZs4 = 0.997074 For &Sod: dZ64= 0.997074
+ 0.047896~- 0.002069c8/? + 0.085141~- 0.001842ca/2
+ 0.142068~- O.O06987cp;’2
The apparent molal volumes (Table I, Figs. 3 and 4) were calculated from the constants in these equations. The value 26.74 ml. found for the limiting apparent molal volume of potassium chloride is slightly less than that (26.81 ml.) reported by Geffcken and Price.s However, the equation given by Jones and Rayg leads to the value 26.57 ml. for @ and to values of the apparent molal volume a t higher concentrations that are in essential agreement with the results obtained by KruislO (Fig. 3).
I
30.5
-
-a6.0
.o
A‘ d
d m
9
529.0
-34.56
P
e
w
M
M
6
6
27.5
-88.0 I
I
I
I
0.4
0.8
1.2
I
pV=/2.
Fig. 4.-Apparent molal volume us. square root of the I volume ionic strength for potassium sulfate in water 0.4 0.8 1.2 (curve 1) and in solutions of sodium chloride (curves pv=/p. 2, 3, 4, 5 and 6); temperature, 25’. Fig. 3.-Apparent molal volume vs. square root of the volume ionic strength for potassium chloride and potassium The discrepancy between the three sets of bromide in water (curve 1) and in sodium chloride soluvalues may be due to differences in temperature tions (curves 2, 3, 4, 5 and 6): 8 , Geffcken and Price; or to impurities in the salts used. In either case (3, Kruis; --- calculated from equation of Jones and Ray; temperature, 25’. the results reported here are comparable as the
Results The experimental values for the densities of potassium chloride, potassium bromide and potassium sulfate in water solution are expressed by equations of the form suggested by Root.‘
temperature was maintained at the same constant value and the same lots of salts were used except in the one instance noted below. The value of the limiting apparent molal vol(8) Geffcken and Price, 2. physik. Chem., B26,81 (1934). Jones and Ray, Tms JOURNAL, S9, 187 (1957). ClU) Kruis, 2. phrsik. Chcm., B34, I (1936). (Y)
2552
HENRYE. WIRTII
Vol. 5!)
TABLE I with those reported here (see Fig. 2) and give APPARENTAND PARTIALMOLALVOLUMES OF POTASSIUM 32.36 ml. as the limiting apparent molal volume POTASSIUM BROMIDE AND POTASSIUM SULFATE CHLORIDE, of potassium sulfate in water solution. IN WATERSOLUTION
0 0.03986 .03950 .15838 .15906 .35623 ,36072 .64525 .64621 .99498 .99662
(ds-di)lOOO
P?
c3
-
-F3
Potassium Chloride 0 (47.90) 0.19963 1.888 47.38 ,19875 1.869 47.31 .39797 7.455 47.07 .39883 7.482 47.04 .59685 16.620 46.66 .6OO60 16.828 46.65 .SO327 29.839 46.244 .SO387 29.883 46.243 .99749 45.602 46.832 .99831 45.671 45,826
0
0.03983 .04048 .16112 .15986 .36555 .35846 ,65991 .62782 1.00809 1.00555
Potassium Bromide 0 0 (85.14) 0.19957 3.373 84.68 .20120 3.424 84.58 .40140 13.602 84.42 .39982 13.484 84.35 ,60461 30.719 84.04 ,59872 30.116 84.01 .SI235 65.212 83.666 .7923j 52.536 83.680 1.00404 83.970 83.296 1.00277 83.747 83.285
0 0.014833 ,014795 .058643 .05910$ ,13534 ,13292 .23815 .23219 ,33290 .33874
Potassium Sulfate 0 0 (142.07) 0.21095 2.088 140. $7 .21068 2.081 140.65 .41944 8.164 139.22 .4211() 8.221 139.09 ,63719 18.628 137.64 ,63147 18.296 137.65 .84525 32.427 136.16 .83461 31.632 136.23 .99934 44.934 134.98 1.0080g 45.775 136.13
0
(T3
T 'a
26.74 26.74 27.15 27.36 27.56 27.97 27.97
28.59
28.40
29.22
28.81 29.81
33.97 34.34
33.97 34.52
34.71 36.08
0.04 N XaC1: ds - d2 = 0.04735~3- 0.00209C3(p$' 0.15 N NaCl: ds - dz = 0.04657~3- 0.00183c3(p:'f 0.35 N NaCl: ds - dz = 0.04578C3 - 0.00191~3(/~:/2 0.62 N NaCl: d3 - d2 = 0 . 0 4 4 7 3 ~-~ U 00144c3(p: ? 0.97 A7 NaCl: d3 - d, = c).o$3$oC3 - 0.00184~3(p(:" -
35.09
35.64
35.47 36.20 35.83 36.72
32.28 32.28 33.76 34.50 35.22
36.69
36.75 38.99
c: 0.03849 ,03845 .03845 .03832 ,03832 .03810 .03810 .03779
+
(11 1 Jones and Bickford, THIS JOURNAL, 66,605 (1934).
0.3936) 0.5890) 0.78il)
0.9859)
w;b
c3
0 0.03967 ,03979 ,13904 ,13922 ,36074 .35642 .I33849
(dr-dd
1000 --F3 = 0.03849, dz = 0.998672 0.19619 0 (47.33) 47.06 .27949 1.867 1.876 47.15 .27970 7.446 46.81 .44425 7.448 46.78 .44446 .63151 16.759 46.46 ,82811 16.557 46.45 ,82236 29.393 46.04
0 3
L.8
27.24 27.42
27.24 27.56
27.76
28.14
28.13
28.74
28.55
29.33
(4
0.1648 .1547 ,1547 .1541 ,1541 .1533 .I633 ,1520
38.21 41.14
39.39 42.74
0.1962)
TABLE I1 APPARENTAND PARTIAL MOLAL VOLUMES OF POTASSlUM CHLORIDE IN SODIUM CHLORIDE SOLUTIONS cy
ume of potassium bromide in water (33.97 ml.) is about 0.8yohigher than that obtained from the results of Geffcken and Prices for potassium chloride, sodium bromide and sodium chloride by the following calculation : @gBr = &a = 26.81 23.48 - 16.60 = 33.69rnl. This latter value is in agreement with the less accurately determined value of 33.56 ml. calculated from the results of Jones and Bickford." Similarly, the value of for potassium sulfate in water as calculated from the results of these authors for sodium sulfate, potassium chloride and sodium chloride is 31.94 ml. as compared with 33.28 m!. found in the present work. The data of Jones and Rayg are in excellent agreement
+
The equations representing the experimental results for potassium chloride in sodium chloride solutions are :
0.1548, di = 1.003447 (46.57) 0.39347 0 0 ,44048 1.826 46.38 0.03937 1.837 46.47 ,03990 .4411j 46.2(i .'l5870 ,35931 7.341 46.25 ,65929 7.339 .I.5868 45.99 ,71336 16.356 ,33565 .36 = 1.022113 0 (44.73) 0.78713
0 0.039.56 ,03970 .l5980 ,15947 .:35790
.88100
1.769 1.778 7.131 7.107
.98537
13.B08
.81144 .SI154 .88119
44.72 44.71 44.62 44.X 44.43
c! = 0.9719. d: = 1.035984 0 (43.70) 0.98683 0 1.734 43.66 0,03972 1.00622 1.727 43.61 ,03960 1.00516 6.927 43.55 .15906 1.06128 43.57 .15867 1.06111 6.913 .35906 1.14911 15.581 43.39
28.93 29.32 29.21
29.80
29.18 29.21
29.18 29.24
29.31
29.48
29.46
29.70
29.79 29.82
29.79 38.84
29.92
30.01
30.08 30.34
The apparent molal volumes calculated from the constants in these equations are uniformly
PARTIAL MOLAL VOLUMEOF POTASSIUM SALTS
Dec., 193i
greater than those in water solution (Fig. 3). The equation T3 = 26.735 3.086~:' which represents the partial molal volumes of potassium chloride in water solution can also be used to calculate the partial molal volumes in sodium chloride solutions. Omitting the values of 7; (CQ = 0) which depend on the method used to extrapolate to infinite dilution the average deviatioii between the observed and calculated values is 0.036 ml. The maximum deviation which occurs three times is 0.075 ml. This is within the experimental error which, although difficult to estimate, averages about 0.04 ml. The equations representing the experimental data for potassium bromide in sodium chloride solutions are
+
0.04 N NaCl: d3 - (Ep = 0.16 N NaCl: d3 - d? = 0.36 N NaCl: d3 - dz = 0.62 N NaCl: d3 - da =
0.6170 .fill31 .e161 ,6134 ,6130 .6089 .eo90 .6020
c: = 0.6170, dr = 1.032007 0 (82.11) 0.78649 0 0.03980 .80970 3.241 82.05 .80992 3.273 82.13 .03985 1
