RONALD A. MUNSON AND MICHAEL E. LAZARUS
3242
in carrying out the radiolyses is gratefully acknowledged as well as the assistance received from the Florida
State University Institute of Molecular Biophysics in the form of access to the esr spectrometer.
Densities and Apparent Molal Volumes of Molten Phosphoric Acid Solutions
by Ronald A. Munmi and Michael E. Lazarus General Electric Research ccnd Development Center, Schenectady, New York (Recewed March IS, 1967)
The densities of a number of electrolyte solutions in phosphoric acid at 80" and a few a t 150" are reported. Most of the 1-1 electrolytes investigated have apparent molal volumes which are quite close to the molar volume of phosphoric acid. This indicates that these electrolytes enter inko the solvent structure with very little over-all electrostriction of the phosphoric acid. Apparent molal ionic volumes of a number of ions have been calculated on the basis of the assumption of equality of volumes of the lyonium and Lhe lyate ions. It is suggested that this assumption is of value in comparing electrostrictive influences in different solvents.
The densities of ionic solutions may be used to obtain information concerning ion-solvent interactions. The apparent volume changes observed may result from general influences of the ion on the solvent structure or from the displacement of solvent equilibria. In phosphoric acid, two self-dissociative equilibria are of importance, both of which produce extensive ionization. loa
+ HzPO42HaP04 _r H3of + H3P207.-
2H3P04
H4P04'
(1) (2)
Experimental Section Chemical Preparation. Phosphoric acid was prepared from analytical reagent 85% phosphoric scid by water removal under v a ~ u u m . ~It was adjusbed to 100.0% by the crystalline melting point technique used previously.' Sulfuric acid (100.0%) was prepared from analytical reagent fuming sulfuric acid and distilled water. A solution 19.0% by weight perchloric acid and 80.8% phosphoric acid was prepared a t 120° by stirring analytical reagent phosphorus pentoxide with analytical reagent 70% perchloric acid. Lithium perchlorate was prepared by neutralizing lithium carbonate The Journal of Physkcal Chemistry
with analytical reagent perchloric acid. To remove the last trace of water, it was necessary to heat it to 300' just prior to use. It analyzed 92.9'G (expected 93.5%) perchlorate. Lithium dihydrogen phosphate (99.0%) was also prepared from lithium carbonate. Mg(H2P04)2,which was prepared firom magnesium oxide and phosphoric acid, contained 11.2y0 (expected 11.1%) magnesium. Reagent potassium bisulfate (100.1%) and potassium dihydrogen phosphate (99.4%)) which were analyzed by acid-base titration, as well as the other salts, were stored in a vacuum desiccator at 100'. Solutions were made up by weight and all open manipulations were performed in a drybox furnished with dry Nzand Pz05. Procedure. The dilatometer (18 cc) was constructed from a small erlenmeyer flrtsk into which was fitted by means of a ground-glass joint a graduated glass tube with a terminal constriction. The volume of the dilatometer was calibrated with doubly distilled water. Temperature in the oven remained constant to k0.2O. (1) R. A. Munson, J. Phys. Chem., 68, 3374 (1964). (2) R. A. Munson, ibid., 69, 1761 (1965). (3) Inorg. Sun., 1, 101 (1960).
DENSITIESOF MOLTEN PHOSPHORIC ACID SOLUTIONS
MNSITY
TEMPERATURE FOR DO'/. H, PO,
VS.
3243
Table I : Apparent Molal Volumes of Some Solutes in Phosphoric Acid a t 80'
o PRESENT WORK A I.C.T. VALUES
1.86
1.771
0
I
I
I
20
40
60
I
I
80 100 TEYPEAATURE- 'C
I
I
1
120
140
160
Figure 1. The density of 100.0% phosphoric acid. Data at the lower temperatures are from the "International Critical Tables."
WdX,
9VP
g 1. -1 m -1
om8 mole-'
0.028 0.050 0.054 0,050 0.022 0,001 -0.002 0.108 -0.025
48.6 50.8 57.8 59.1 51.8 54.7 54.4 87.1 17.4
where M z is the molecular weight of the solute, po is the density of the pure solvent, and X is the molal concentration of the solute. Notice that for most solutes the apparent molal volume is very close to the molar volume of the phosphoric acid (53.6 cc mole-' a t 80') so that these electrolytes must fit into the phosphoric acid structure with very little over-all electrostriction. Figure 2 presents some of the data obtained. The straight lines are not lines of best fit but represent the density changes which would be expected if each mole of solute replaced one mole of phosphoric acid. Self-
The sample was allowed to reach chemical and temperature equilibrium in 2 hr during which the loss or gain of water was not found to be significant. Measurements were made at 80 and 150' in order to avoid the long wait required for the establishment of equilibrium 2 close to room temperature.
Results and Discussion The density of phosphoric acid is a linear function of temperature (Figure 1) and may be approximated very closely by pg = pso
+ 6.94 X 1OW4(80- t )
(3)
where pso = 1.827 is the density a t 80' and t is the temperature in degrees centigrade. The densities in phosphoric acid solutions are very nearly linear functions of the solute concent,rations to 0.4 m. Freezing point depression measurements indicate these solutes to be essentially fully dissociated. Table I lists the limitingdensity-concentration slope for a number of solutes. The apparent molal volumes were calculated by means of the expression 4 -----+2 lo3 dp M v po2 d X PO
(4)
v
''770
0.1 0.2 0.3 0.4 0.5 SOLUTE CONCENTRATION (MOLALITY)
0.6
Figure 2. Density dependence on solute concentration for 100.0% phosphoric acid.
Volume 71, Number 10 September 1967
RONALDA. MUNSONAND MICHAEL E. LAZARUS
3244
dissociation according to eq 1 and 2 is extensive enough so that the electrolyte concentrations used in these solutions are much smaller than the intrinsic ionic concentrations. The addition of 1 mole of base to phosphoric acid shifts the position of equilibrium 1according to MH8O.j '/2&P04+ + M+ H s P 0 4 '/2H2P04-. Similar equilibrium shifts occur in phosphoric acid solutions containing acid or water. The volume changes contributing to the apparent molal volume are
+
+
4V(bas4
=
vM
+It
+
1
I
2[VHaO+
Phosphoric acid a t SO0, om* mole-1
+
+
~ [ V H S P O ~
'/2VHzPO4-
4V(H@)=
Table I1 : Apparent Molal Ionic Volumes
-
VHSPZOI-1
VHsPOi
+
-
'/ZVH4PO4+]
(5)
-
(7)
+
'/2[VHzPO4-
VHIPOI+I
Since the H2P04-and the H4P04+ions are derived from phosphoric acid by the addition or subtraction of only a proton they must be quite close to the same size, and as their charge magnitude is identical, they should have very similar electrostrictive influences on the solvent. ~ - to It therefore is reasonable to set V H ~ P Oequal V H ~ P ~ , + . Table I1 lists the apparent molal ionic volumes of a number of ions in phosphoric acid and in water4 calculated using the equality of the apparent molal volumes of the lyonium and lyate ions. The general similarity of the data suggests that the prin-
The Journal of Physical Chemhtry
Water at 2 5 O ,
cma mole-:
-5 -3 4 -20 56 55 -72
-3.6 -4.1 6.1 -23.5 [45)=
...
-2.6
...
Estimated.
ciple of the equality of the volumes of the lyate and lyonium ions provides a rational basis for the comparison of ionic volumes in different solvents. From eq 7 only the difference between ionic volumes of the oxonium and the pyrophosphate ions can be obtained. However, if a reasonable value of -3 cm3 mole-' is assigned to the oxonium ion, then the volume obtained for the pyrophosphate monoanion (69 cm3 mole-') is consistent with the expectation of a somewhat larger volume than that found for the other anions listed in Table 11. (4) B. B. Owen and S. R. Brinkley, Jr., Chem. Rev., 29, 461 (1941)
