Fch., 1962
3ii
NOTES
MOIAR IiEBRACTlONS OF AQUEOUS SOLUTIONS OF SOME CONDENSED PIIOSPTTATES'
soliit,r or molecular weight df, For thc solvcnt, watw, v:ilrics of thc rrfractive index no and thc! dciisity do ~vcrcdcfinod tis 710
BY ~ ~ O B J C RC.T BRASTED AND ARTHUR K. NELSON T h e SchooL of Chemistry. Uniyera'ty of Minnesota. Mznneapol?s,
Minnesota Recerved Saplember 11, 1061
It is well known that the molar rcfravtion is an additive function of the atoms or groups of atoms within a molecule. Exact, additivity is not always realized since the property also is constitutive. Since the condensed phosphates are formcd by the sharing of oxygen atoms a t the corners of PO4 tetrahedra, the molar refraction of a condensed phosphate may be expected to be a furiction of the number and kind of POI tetrahedra present. This study involves the determination of the apparent molar refractions of aqueous solutions of the crystalline condensed phosphates of sodium. These include the pyrophosphate NadP207, the tripolyphosphiLte Na5P30i0,the trimetaphosphate XaJ'309, and the tetrametaphosphate ;l\ia4P4012. Experimental Compounds.-Samples of sodium tripolyphosphate, sodium trimetaphosphate and sodium tetrametaphosphate were obtained from the Victor Chemical Worlcs and the RiIonRanto Chemical Company. These phosphates were purified by repeated recrystallization from water by methods essentially the same as those given in the literature.2 In addition, anhydrous sodium pyro hosphate was prepared by ignition of reagent NadPzO,.lOHzf; at 1000". Preparation of Solutions.-A series of several solutions of each phosphate was made up by weight from conductivity water using ground-glass stoppered bottles. All weighings were made with calibrated weights and tares and buoyancy corrections were applied using the density of air from the recorded temperature, barometric pressure and relative humidity for each weighing. Density Measurements.-A modified Sprengel (bicapillary type) pycnometer with a capacity of approximately 10 ml. was used for all density measurements. Solutions to be measured were transferred to the pycnometer by means of suction and then held a t 25.00 f 0.02" for 20 to 30 min. The pycnometer then was removed from the constant-temperatrire bath, wiped dry and weighed after equilibration with the air in the balance. This process w~tsrepeated and the density obtained aa an average of two or three fillings and weighings. Vacuum corrections were applied to all weighings. Refractive Index Measurements.-The refractive index was determined for a separate portion of each solution using a Dausch and Lomb Dipping Refractometer. White light was used as a source. Measurements were taken in a trou h designed for use with the instrument held at 25.00 f 0.02 with a constant temperature circulating system purchased from Precision Scientific Company.
Q
Results Apparent molar refractions, R a p p , were calculated using the equation given by Kohner3
where n and d refer t o the solution and no and do refer to the solvent while m is the molality of the (1) Taken from the Ph.D. thesis of Arthur IC. Nelson, 1959. (2) (a) 0. T.Quimby, J . Phys. Chcm.. 5 8 , 603 (1964); (b) L. F. Audrieth, "Inorganio Syntheses," Vol. 111, McGraw-Hill Book Co., Now York, N. Y.,1950. p. 104. (3) H. Kolmer, Z . physik. Chem., Bl,427 (1928).
do =
=
71'k
d2a4 =
= 1.33252 0,99708 g. rnl.-I
Thc associated error in each valuc of Rappwas cstimat,cd by means of the approximate equation of K o h ~ i e r . ~The results arc listed in Table I. TABLE I APPARENTMor,an REFRACTIONS OF AQUEOUSSOLUTIONS OF SODIUMPIIOSPIIATES Phosptirrte
Molality
d%
X;n4PlO7 0.21931
1.05125 .I6772 1.03805 .lo177 1.02286 .048348 1.00959
n%
RaDp,ml. mole-'
1.34245 1.34023 1.33734 1.33486 Av.
29.03 f 0.11 28.93 f . I 4 2 9 . 0 1 f .24 28.49 f .50" 29.0 i O . 1
NabP3010 0.31623 .26330 .17631 .lo052 .040446
1.09585 1.08007 1.05366 1.03005 1.01067
1,34941 1.34681 1.34240 1.33834 1.33495 Av.
40.58 f 0.08 40.61 i .09 40.63 i .14 40.37 f .24 40.08 f .60" 40.6 f O . 1
NajPaOo 0.46393 .37815 ,26837 ,15006 .091918
1.09594 1.07876 1.05609 1.03078 1.01786
1.34657 1.34420 1.34102 1.33743 1.33560 Av.
34.90 f 0.04 34.85 f .06 34.76 f .09 34.67 f .16 34.94 f .26 34.8 f O . 1
NaiP'01z 0.26576 .21940 .16071 .11458 .056595
1.07661 1.06326 1.04610 1.03245 1.01488
1.34442 1.34248 1.33997 1.33793 1.33528 Av. Values not used in computing average
46.31 f 0.09 46.35 f .I1 46.43 f -15 46.35 f .21 46.23 f .42" 46.4 i 0.1
Rap,,.
From Table I it can be seen that the apparent molar refraction is constant within the limits of experimental error over the concentration range available. Any extrapolation to infinite dilution here would yield a straight-line relationship within experimental error. The average value can be considered equal to the value a t infinite dilution. Certain values indicated by a in Table I were not used in computing the average because of unfavorable experiment)al error a t higher dilutions. At infinite dilution the molar refraction of an electrolyte may be considered as the sum of individual ionic refractions. The accepted value of R N a + a t 25' and for the D-line of sodium is 0.200 ml. rn~le-'.~J Using this value and neglecting the possible existence of NaPx09-2 and NaP4012-athe ionic refractions may be determined for each phosphate anion Phosphs te
Renu
NaIPzOT NaBPJOlo NasPSOo Na,P,012
29.0 40.6 34.8 46.4
Anion
PZG-~
R.nlon
28.2 Pe010-6 39.6 PaOe-' 34.2 ~ , 0 ~ ~ - - 4 45.6
(4) W. Ceffcken, ibid.. B5,81 (1929). (5) R. Luhdemsnn, rbid., B19, 133 (1935).
378
NOTSB
Discussion The condensed phosphates are formed by the sharing of oxygen atoms at the corners of POq tetrahedra. Since the two known ring phosphates, trimetaphosphate and tetrametaphosphate, contain only middle groups of POetetrahedra, the refraction due to a middle group may be calculated RP~oQ-’ = 34.2;
Rmiddle
RP~o= ~ -45.6; ~ Rmiddle =
34’2 = 11.4 3 45.6
phosphates at two chosen concentrations, 50.0 and 100.0 g/l. The results of Griffith differ markedly from those quoted here. Griffith provides sufficient data for a recalculation of Rap,. This was done for NaeP3010 at 100.0 g./l. and a value of 39.1 was obtained, compared with his reported value of 71.49 and the value 40.6 reported here as an average Rap?. The value 71.49 apparently was obtained by the incorrect use of the equation
= 11.4
4 The pyrophosphate and tripolyphosphate are the first two members of a family of chain phosphates. Pyrophosphate contains two end groups ~
Vol. 66
where n and d refer to the solution, illl is the molecular weight of the solute, ro the specific refraction of water and w o the weight of solvent containing one mole of solute. The definition of Woaccording 28.2 Rp,~.r-~ = 28.2; Rend = - = 14.1 to Kohner is not that used by Griffith, who ap2 parently substituted the weight of solvent taken Tripolyphosphate contains two end groups and rather than the weight of solvent containing one one middle group. Hence, the expected ionic re- mole of solute. In order to obtain a value of 71.49 fraction of tripolyphosphate may be calculated Womust be taken as approximately 101 g. Actually, using Griffith’s data, 3,623.1 g. of water would RPaOlo-‘ = %end Emiddie = 2 x 14.1 + 11.4 = 39.6 This is exactly equal to the experimentally-dcter- contain one mole or 367.9 g. of Na6P3OI0. The apparent molar refraction of a solute genmined ionic refraction. The ionic refraction of condensed phosphate erally changes very little with concentration. Beanions is an additive function of the number of end cause R a p p changes only slightly with concentration and middle groups present. This result further and because the accuracy in R a p p is greatly dedemonstrates the equivalence of middle groups in creased in very dilute solutions, apparent molar rings and chains. A nuclear magnetic resonance refractions have largely been obtained for concenstudy of phosphorus compounds6 also has shown trated solutions. Common practice has involved this equivalence. An extension of the present work extrapolation of R a p p values obtained at solute con?~ would involve the ionic refractions of the long-chain centrations above 1 N to infinite d i l u t i ~ n . ~The of the crystalline sodium phoslimited solubilities glassy phosphates. An end group contributes more to the ionic re- phates negate this procedure. Hence, when considered in terms of Rapp, the fraction than a middle group. If the shared oxygen atoms are considered, an end group “owns” 3.5 concentration interval used by Griffith is very small. oxygen atoms while a middle group “owns” 3 oxy- Yet, many conclusions concerning polarizabilities of gen atoms. The environment of an end group ob- crystalline and glassy phosphates were drawn on the viously differs from that of a middle group. In the basis of the change in Rapp, ARapp, observed. In corresponding acids, middle group hydrogens are this work, Rapphas been shown to be practically invariably strongly ionized while end group hydro- constant in this concentration range. The conclusions of Griffith based on his calculations would gens are only weakly ionized. Griffith’ previously has reported values of R a p p at seem to have no credence. I n order to detect any 25’ and for the D-line for these same condensed change in R a p p over this concentration interval, more precise measurements would be necessary. (6) J. R. van Wazer, C. F. Callis and J. N . Shoolery, J . Ant. C h e w Ac&,wledgment.-An academic-year fellowship Soe., 77,4945(1955): J. R.Van Wazer, c. F. Callis, J . N. Shoolery and extended to Arthur E(.Nelson by the Dow ChemiR. C. Jones, zbid., 78,5715 (1956). cal Company is gratefully acknowledged. (7) E J. Griffith. ibid.. 79, 509 (1957).
+
