DIFFUSION COEFFICIENTS OF ORTHOPHOSPHATE SOLUTIONS
2555
Diffusion Coefficients of Aqueous Solutions of Ammonium and Potassium Orthophosphates at 2501
by J. D. Hatfield, 0. W. Edwards, and R. L. Dunn Division of Chemical Development, Tennessee Valley Authority, Muscle Shoals, Alabama (Received February 86, 1966)
~
~~
Diffusion coefficients for mono- and dibasic ammonium and potassium orthophosphate solutions at 25” were measured by the Gouy method and calculated by the Airy optical method. The diffusion coefficients, in cm2/sec, X lo6, decreased from extrapolated values a t infinite dilution of about 12 for NH4H2P04 and KHzP04and 13 for (NH4)2HP04 and K2HP04to values near the saturation points of 5.3 for NH4H2P04,6.5 for KH2P04, 3.2 for (NH4)2HP04,and 5.3 for K2HP04. The deflection constants C, were determined by extrapolating plots of Y / e - r a us. Z”3 for the lower fringes and by averaging the seven lowest fringes. When the number of fringes was less than 40, diffusion coefficients were calculated also by the “saddle-point” method; results agreed with those of the Airy method within experimental error.
Ammonium and potassium orthophosphates are important constituents of mixed fertilizers and of the solutions that are formed when the fertilizers dissolve in the soil solution.2 Knowledge of the physicochemical properties of the solutions of these salts is useful in interpreting their behavior in supplying nutrients to plants. Measurements were made of the diffusion coefficients in aqueous solutions of each of four of these salts; in the course of the measurements the densities and refractive indices of the solutions were determined also. Measurements have been reported of the density, viscosity, pH, electrical conductivity, and vapor pressure of solutJions in the system NH3-H2O4-Hz0 a t 250j3 as have measurements of the conductivity of monoammonium phosphate4 and (while this study was being made) of the diffusion coefficients and viscosities of solutions of monoammonium phosphate.6 Physicochemical data for the system K20-HZ04-H20, on the other hand, are sparse and at least 50 years old.6
Experimental Section Apparatus. The Gouy interferometer and accessory equipment were modified slightly? from Costing’s assembly.* The optical lever arm (b distance) was redetermined by calibration with potassium chloride solutions of known diffusion coefficientsgJOand by
measurement of the diffraction pattern produced by an accurate Ronchi ruling placed in the system, similar to the use of a wire grating.7811 The b distance, 232.25 0.23 cm, was practically the same as that reported previo~sly.~*12 The a distances of the two tall-form Tiselius cells were 2.5027 and 2.4983 cm, respectively; the first cell was used for the ammonium phosphate (1) Presented before the Physical Chemistry Division at the 148th National Meeting of the American Chemical Society, Chicago, Ill., Sept 1964. (2) A. W. Taylor and E. L. Gurney, J . Agr. Food Chem., 13, 92,95
(1965). (3) F. A. Lenfesty and J. C. Brosheer, J . Chem. Eng. Data, 5 , 152 (1960). (4) C. Watkins and H. C. Jones, J . Am. Chem. Soc., 37,2626 (1915). (5) J. W. Mullin and T. P. Cook, J . Appl. Chem., 13, 423 (1963). (6) (a) C. Forch, Ann. Phys. Chem., 5 5 , 100 (1895); (b) H. H. Hosford and H. C. Jones, Am. Chem. J., 46,240 (1911);(0) B. E.Moore, Phys. Rev., 3, 321 (1896); (d) L. G. Winston and H. C. Jones, Am. Chem. J., 46, 368 (1911). (7) 0. W. Edwards and E. 0. Huffman, J . Phys. Chem., 63, 1830 (1959). (8) L. J. Gosting, E. M. Hanson, G. Kegeles, and M. S. Morris, Rev. Sci. Instr., 20, 209 (1949). (9) L. J. Gosting, J . Am. Chem. SOC.,72, 4418 (1950). (10) L. A. Woolf, D. G. Miller, and L. J. Gosting, {bid., 84, 317 (1962). (11) E. Leibhardt, J . Opt. SOC.Am., 43, 1220 (1953). (12) 0.W. Edwards, R. L. Dunn, J. D. Hatfield, E. 0. Huffman, and K. L. Elmore, J . Phys. Chem., 70,217 (1966).
Volume 70, Number 8 August 1966
J. D. HATFIELD,0. W. EDWARDS, AND R. L. DUNN
2556
solutions and the three lowest concentrations of KHZPO4; the second cell was used for the rest of the solutions. Preparation of Solutions. The solutions were prepared with distilled water which had been passed through a mixed-bed ion exchanger and had a specific ohm-1 cm-l. Reagent conductance less than 2 X grade NH4H2P04,(NH4)2HP04,and KH2P04were recrystallized at 0” from solutions saturated at 25 to 50”. Solutions of (NH4)2HP04were adjusted with ammonium hydroxide to pH 7.5 to 8.0 before crystallization. The recrystallized salts were free of extraneous crystalline phases; spectrographic and petrographic examinations showed negligible amounts of metallic impurities. Chemical analyses of the recrystallized salts showed atomic ratios N : P or K : P correct within the estimated standard analytical error of 0.01. Reagent grade KzHP04 was used without further recrystallization because of the difficulty of obtaining a stable hydrate. The salt was homogeneous, and its atomic ratio PI :P was correct within analytical error, but spectrographic analysis showed about 0.3% metallic impurities. The moisture contents, determined by the Karl Fischer method, of the recrystallized salts ranged from 0.01 to 0.31%; that of the reagent grade KzHPO4 was 1.2%. The molecular weights were based on 12C. All solutions were prepared from weighed amounts of salt and water; concentrations (C) were expressed in moles per liter ( M ) . Densities of the solutions were determined at 25” with modified Gay-Lussac pycnometers; duplicate determinations agreed to within 1 part in lo4. All weights were corrected for buoyancy of air. Procedure. The cell was filled, the boundary was sharpened, and correction and Gouy patterns were photographed in the usual The displacements of fringe minima were measured with a Gaertner Linear Comparator, Model 1201-30B. The whole number of fringes was determined with a high-precision Rayleigh interferometer (Zeiss No. 321005). Calculations. The diffusion coefficients were calculated by Airy optical theory13 and, when j, (the total number of fringes) was less than 40, by the “saddle-point” equations14 also. The deflection constant, C,, for each Gouy pattern was determined by two methods: in the “average” method C, was taken as the average of the normalized fringe displacements, Y,/e-{”, for the seven lowest fringes, and in the “extrapolated” method, as the intercept of the rei* tion Yj/e-r’*= C , BZz’a. In the latter method the extrapolation was made with the seven lowest fringes
+
The Journal of Physical Chemistry
-
2.628 -
2.630
oo \ t = I100 SEC.‘
-
2.626
,
-
o \ -
1.3681
l.205[
0’0
----4
,
,o
4
6
*-J-0 t = 5300 SEC.
1.204
0
2
213
8
Figure 1 , Representative plots for determining Ct. KzHPOa, = 0.98276. AC = 0.06938.
when j , was less than 40, and with fringe numbers 0, 1, 2, 3, 4,5 , 6, 10, 15, and 20 when j , was more than 40. Typical plots for three patterns of one run are shown in Figure 1. When the refractive index gradient was gaussian about the boundary, as when t = 4100 and 5300 sec in Figure 1, Y,/e-l.2
-
:
c
I
0
I 2 CONCENTRATION, M
Figure 4. Density of ammonium and potassium phosphate solutions.
Table I11 : Densit'y and Refractive Index Functions
n
- no
P
-
PO =
NH~IIzPOI a1
a2 a3 S( p )
bi bz b3 ba
s(n)
PO = a#
+ b2p0
=
blC
+ anCa/, + a8C2
+ bzp + bsCp + baC2
0.997075; no = 1.333977 (SH~)ZHPOI
KHzP04
KzHPOd
0.0670220 0,0884262 0,0969262 0.152202 -0.0069233 -0.0129366 -0.0062164 -0.014315 0.0006389 0.0005167 0.0 0.0 0.00005 0.00004 0.00011 0.00009 0.0351175 -0.0229942 0.0240131 0.0289903 0.247542 0 4654452 0.0251213 0.189237 -0.0350313 0.0103853 -0.0109121 -0.0301610 0.0018714 0.0 0.0 0.0028018 0.000013 0.000015 0.000018 0.000008
tions makes the refractive index gradients for NH4HzP04, (T\"J2HPO4, and KH2PO4 less gaussian and the gradients for K2HP04 more gaussian; the slope of the line for K2HP04 then is almost zero. The data are not sufficiently extensive or accurate to test the concentration-gradient effect, but it is apparent from Figure 3 that the dependence of D on concentration may introduce significant errors in the diffusion coefficients, particularly when the concentration gradient is large. The uncertainties in determinations of j , and Y, are serious sources of error in D. A sufficiently large error in j , c:tuses a drift in Y , / e - c l aeven though the boundary is gaussian; it may make the boundary appear gaussian when it is not. Errors in Y,, if normally distributed, affect only the precision of C,, regardThe Journal of Physical Chemistry
1.33
r
0
I
I
I 2 CONCENTRATION, M
1
3
Figure 5. Refractive index of ammonium and potassium phosphate solutions.
less of the method used to evaluate C,; a bias in Y,, however, causes a drift similar to an erroneous j,. The standard errors of duplicate measurements were 0.24 fringe inj, and 0.004 mm in Y,; these are precision rather than accuracy errors. The change in the diffusion coefficient with the fringe number, dD/dj,, is greater with the average method of computing C, than with the Z"/" extrapolation; dD/dj, also varies with concentration, from salt to salt, and with the number of fringes, j,. The precision error of 106D ranged from 0.002 to 0.018 for the data in Table I and from 0.004 to 0.027 for those in Table 11. The average accuracy errors are estimated to be about 0.014 in Table I and 0.04 in Table 11, as determined by analysis of variance of the data. The precision error varied more with the salt concentration and among the salts than with the method of evaluating C,. These results imply that the best
DIFFUSIONCOEFFICIENTS OF ORTHOPHOSPHATE SOLUTIONS
estimate of the diffusion coefficient is the average of the two C, methods. Regression equations of the form
D - Do
=
AiC”’
+ AzC + A3Ca’/’+ A4C2
(6)
where Do is the limiting diffusion coefficient at C = 0, were fitted to the data in Table I for both D,, and Dext. The parameters of eq 6 are given in Table IV. The standard errors of predicting D , s(D), by these equations are of the same order of magnitude as the estimated accuracy of the data for all salts except K2HP04. The rather poor fit for K2HP04may be due to impurities, to its wider solubility range covered by the data, or to other factors that affect the accuracy of determining the diffusion coefficients. Table IV: Equation for Diffusion Coefficients 106D = Do
+ AiC1/2 + AzC + A,C’/? +
N H ~ H I P O ~(NH~)zHPOI
Do Al Az AS A4
0)
12.13 -6.302 4.324 -4.206 1.431 0.035
12.82 -9.770 2.165 1.114 -0.549 0.040
A4C2
KHzPOi
K?HPO4
12.14 -8.161 12.761 -14.996 5.683 0.013
12.83 -11.829 12.870 -7.819 1.703 0.133
The results in Table I1 show that the Airy integral method gives the same values of D as does the more elaborate saddle-point method. It is important, however, that only the lower fringes be used in the evaluation of C, when the fringe number is small. Since the accuracy of D is more dependent on the accuracy of j , in runs with small concentration gradients than in those with large concentration gradients, extrapolations become less accurate as the concentration gradient is decreased. The densities of solutions in the system ”3H3P04-H20at 25” reported by Lenfesty and Brosheer3 were expressed as functions of the concentrations of NH3 and H3P04 in a power series equation; densities calculated from the equation agreed with those measured on the solutions of NH4H2P04and (NH4)2HP04
2561
used in this work. The densities of aqueous KHzP04 solutions reported in the “International Critical Tables”lg agree with those measured in this study for the lower part of the concentration range, but a t higher concentrations the plot of density vs. concentration for the older data is concave upward, whereas that for the solutions used in this study is concave downward (Figure 4). Mullin and Cook5 expressed the diffusion coefficient of NH4H2P04solutions a t temperatures of 15 to 40” by the equation
lo8& = 4.7
+ 0.16t
(7)
where t is temperature in degrees centigrade and is the viscosity in centipoises. These viscosity data are related to the concentration and temperature by the expression 7 =
+ 0 . 4 5 6 8 ~- 0.03616s 0.01256mt + 0.07525m2 + 0.000308t2 0.001106m2t + 0.000131mt2
1.611
(8)
where m is the concentration, molality, of NH4HzP04. Each term in the equation is significant, and the standard deviation is 0.008 cp. The results of the present work are compared in Table V with those calculated from the equation of Mullin and Cook.
~ Table V : Diffusion Coefficients of N H ~ H z P OSolutions
C,av concn of
a
106D, cm?/sec-----
c
NHIH~POI,M
This work
0.04983 0.49814 0.99585 1.9907 2.4988
10.88 8.75 7.35 5.73 5.28
Mullin and Cooka
9.6 8.5
7.3 5.3 4.4
See ref 5.
(19) “International Critical Tables,” Vol. 111, McGraw-Hill Book Co., Inc., New York, N. Y., 1928, p 90.
Volume 70,h’umber 8 August 1966
