CONDUCTIVITY OF MOLTEN PHOSPHORIC ACID
3245
The Influence of Ionic Solutes upon the Conductivity of Molten Phosphoric Acid
by Ronald A. Munson and Michael E. Lazarus General Electric Research and Development Center, Schenectady, New York
(Received March 13, 1967)
The electrical conductivity of phosphoric acid is believed to result from a protonic chain conduction mechanism since the high viscosity of the phosphoric acid effectively hinders the Stokesian or normal conduction. The introduction of an ionizing solute other than water into phosphoric acid results in a linear decrease in the conductivity of the phosphoric acid. The conductivity decrease is ascribed to a breaking of the hydrogen-bonded structure of the phosphoric acid by the ions which inhibits the formation of the structures necessary for proton jumps. A comparison of the conductivity decreases produced by acids and bases in phosphoric acid permits an estimation of the mobilities of the H4P04+ and HzPo4- ions. Activation energies for the proton-jump mobilities in phosphoric acid are very close to those for the proton-jump mechanism in water although the mobilities themselves are about a factor of 4 lower in phosphoric acid. The oxonium ion is anomalous in its influence on the conductivity of phosphoric acid and may itself participate to a limited extent in the protonic conduction.
Owing to the high viscosity (725 = 178 cp) of molten 100% phosphoric acid, ordinary Stokesian migration of its ions is much too small to account for its remarkably high electrical conductivity (U25 = 0.04596 ohm-' cm-l) . Greenwood and Thompson' interpreted this as evidence for the presence of a protonic chain conduction mechanism utilizing the movement of H4P04+ or HzP04- ions through the highly hydrogen-bonded structure. Indeed, they found that the transport number for potassium ion (which must conduct by Stokesian migration) was less than 0.002. The equilibria present in phosphoric acid may be represented by 2H3P04
H4P04'
2H3P04 )c H30'
+ H2P04+ HsPz0,-
(1)
(2)
It is now believed that pyrophosphoric acid is essentially a monoprotic acid behaving as indicated in (2) although some additional protolysis cannot be ruled out. The equilibrium concentrations of these ions can be determined2r3from cryoscopic ([H80+]0 = [HsPZO7-]O= 0.28 m at 38') and electromotive force ([H4PO4+I0= [H2P04-I0 = 0.50 m at 38') measurements. From the temperature dependencies293 we estimate [HaP207-]0=
0.39 m and [H4PO4+I0= 0.51 m at 80' and [H4PO4+I0 = 0.58 m at 150'.
Experimental Section The preparation of the phosphoric acid solutions has been described previ~usly.~The conductivity of the phosphoric acid solutions was measured in either of two thin, sealable Pyrex conductivity cells of standard design which had been placed in a silicone oil constanttemperature bath. The cell constants, which were determined by standard method^,^ were 92.23 and 223.56 cm-' at 25' (92.18 and 223.45 cm-' at 150'). Temperatures were established by the use of Beckmann thermometers, which had been standarized to *0.005' with a National Bureau of Standards calibrated resistance thermometer. After pyrophosphate equilibrium had been reached the conductance was measured with a Jones bridge with Wagner earth at 1000 sec-l. (1) N.N.Greenwood and A. Thompson, J . Chem. SOC.,3485 (1959). (2) R.A. Munson, J. Phgs. Chem., 68, 3374 (1964). (3) R.A. Munson, ibid., 69, 1761 (1965). (4) R. A. Munson and M. E. Lazarus, ibid., 71, 3242 (1907). (5) G. Jones and B. C. Bradshaw, J . A m . Chem. SOC., 5 5 , 1780 (1933).
Volume 7 1 , Number 10 September 1967
RONALD A. MUNSON AND MICHAEL E. LAZARUS
3246
Table I : The Initial Slope of Conductivity os. Solute Concentration in Hap04 Slope a t 80,00~, ohm-1 cm-1
Slope a t 150.O O O , ohm-1 om-'
m -1
m -1
Solute
I
.2
.J
- .4
SOLUTE CONCENTRATION
.3
(do!)
- 0.0169 -0,0191 - 0.0628"
HC10a (NHn)JE"a KHzPOi LiHzP04 Mg(HePO4)z NH4HSOa NHaC10n KHSOa LiClOa HzO a
-0.0416 -0.0704
...
- 0.0808
-0.0848 - 0.0976 -0.262
, . .
...
...
-0.0814
- 0.0838
...
-0.1013 ... 0.0258
-0.1172 - 0.1736
...
Expressed for NHdHzP04.
Figure 1. The specific conductivity of phosphoric acid solutions at 80": 0 , H20; 0, HClOa; 0, NHaHSOa.
t
.43 .42[
0
I
,I
\o I
1
.2
.3
tions have limited significance. It seems more productive to concern ourselves with those factors which produce linear changes in the conductivity either by changing the concentrations of the conducting species or by acting on their mobilities by effectively withdrawing solvent molecules from t,he conduction process. Although higher power terms in the concentrations become predominant above l m, we shall not deal with them here. The addition to phosphoric acid of salts which cannot influence equilibria 1 or 2, and which do not effectively contribute to the conductivity themselves because of the high viscosity, can affect the conductivity ( u ) by altering the charge carrier mobilities. I
.4
I
.5
SOLUTE CONCENTRATION (molall
Figure 2. The specific conductivity of phosphoric acid solutions a t 150': 0 , HzS04; 0, KHzPOI; 0,KHSO4; A, Mg(HzP04)z.
Results Figures 1 and 2 illustrate the effect of several solutes on the conductivity of phosphoric acid. Water is the only solute which has been found to increase the conductivity. The conductivity-concentration plots are all quite linear to a t least 0.4 m for the solutes, except water, for which linearity disappears a t lower concentrations. Table I lists the initial slopes of these linear plots.
Discussion The intrinsic ionic concentrations in phosphoric acid are so large that even the extensions of the limiting laws for mobilities in dilute solutions to higher concentraThe Journal of Physical Chemistry
Ussit
=
CA'WA'[~
+ (sa + s ~ ) x+]
+ + ~ d z l(3)
C B ' ~ B ~ [ ~(sa
CA', WA', CB', W B O are intrinsic charge concentrations and mobilities of H4P04+and H2PO4-, respectively, without solute addition; x is the molal concentration of added solute; and sa and so represent the relative effect of the added anion and cation on the mobilities. I n the case of acid or base addition to phosphoric acid, an additional term is required to represent the change in
CONDUCTIVITY OF MOLTEN PHOSPHORIC ACID
3247
charge carrier concentrations (Ao = [H4PO4+I0 = [HZPO4-]O). When a and b are the relative effects of changes in (H4P04+]and [HpP04-] upon the charge carrier mobilities, then Sa [ = sa '/z(u b) ] and So[ = so - '/z(u - b)] are the relative changes in mobility per molal produced by acid and base addition. I n eq 4 and 5, the cross quadratic terms with coefficients Sa/ 2A0), etc., have been neglected since at low solute concentration these terms will be very small compared with the linear terms. The factor x/Ao is halved in eq 4 and 5 since so long as x/A O is small, half the added acid will react with phosphoric acid to produce H4P04+ and half will react with H2P04- to form phosphoric acid. If base is added, the reverse occurs. From eq 3 , 4 , and 5, we find
+
duaoid
-
dubast: += U0(Sa+ SC)= dx
-
dx
."(sa
+ sc) = du.ait dx
(6)
If the postulated linear influences on the phosphoric acid conductivity are independent of each other, then eq 6 requires that the sum of the conductivity slopes from acid and base addition must equal that obtained from the addition of their salt. Table I1 contains a comparison of such data, and the equality of eq 6 is verified within experimental error. The mechanism of protonjump conduction consists of two steps.6 The first is the orientation of the solvent molecules so that hydrogen bonds are formed through which a proton jump may occur. The second step, which is generally considered to be the fast process in water and is probably the fast one in phosphoric acid also since both processes involve a proton transfer between oxygen atoms, is the proton movement within the hydrogen bridge. The effect of the presence of ions on the mobility of the proton can be ascribed to a modification of the solvent structure so that the protons find themselves in an environment in which the hydrogen-bond orientations are, on the average, less conducive to proton transfer. It is not possible to separate the values given in Table I1 into anion (8,) and cation (8,) components. For the purposes of this paper, we will assume that the sc's are very nearly equal to the sa's for monovalent ions, which is quite reasonable if for a first approximation these effects are largely determined by the magnitude of the charge on the ion. It is of interest to compare the conductivity decreases with those expected from the presence of nonconducting spheres of volume v in a total volume Trr u =
-
3); 2,
=
2 X 103(sa
3p0N
+ sc)
(7)
Table 11: The Effect of the Addition of Acid and Base Compared with the Effect of the Addition of the Salt of the Acid and Base on the Conductivity of Phosphoric Acid Number of molea of Hap04 excluded
Salt added
Temp, O C
m -1
m-1
mole-'
solute
KHSO4 "4C104 NH4HS04 KHSOa LiC104
SO 80 SO 150 150
-0.494 -0.414 -0.403 -0.270 -0.358
-0.512 -0.424 -0.412 -0.250 -0.370
179 149 145 97 136
2.2 1.8 1.7 0.7 1.5
where p o is the phosphoric acid density and N is Avogadro's number. It has been suggested4that the addition of electrolytes to phosphoric acid does not result in appreciable electrostriction; nevertheless, on the average (Table 11) 1 mole (at 150') to 2 (at SO") moles of phosphoric acid, in addition to the volume taken up by the electrolyte, are effectively removed from the conduction process by the presence of 1mole of electrolyte. I n sulfuric acid: "solvation numbers" of the order of ten times larger were needed to account for the observed protonic mobility decreases. Since the intrinsic ionic concentration in sulfuric acid is some 30-fold smaller than it is in phosphoric acid, there is considerably less shielding of each ion by nearby ions which means that each ion in sulfuric acid has a much more sizeable volume of solvent molecules whose structure it can affect. To the extent that one may speak of ion atmospheres in these intrinsically concentrated ionic solutions, one may say that the radius of the ion atmosphere in sulfuric acid is relatively large, which gives each ion a sizeable sphere of influence on the average, whereas in phosphoric acid this radius is indeed small and correspondingly the number of solvent molecules whose orientation can be affected is much reduced. By subtracting the slope of eq 5 from that of eq 4,we find
-
-~
(6) G. 3. Hills, P. 3. Ovenden, and D.R. Whitehouse, Discussions Faraday SOC., 39, 207 (1965),and references therein. (7) J. W. Rayleigh, Phil. Mag., 34, 481 (1892). (8) R.H.Flowers, R. J. Gillespie, E. A. Robinson, and C. Solomons, J. Chem. Soc., 4327 (1960).
Volume 7 1 , Number 10
September 1967
RONALDA. MUNSONAND MICHAEL E. LAZARUS
3248
Since we are assuming that an ion's influence on the mobility is related only to the magnitude of its charge, then (8, S &), the first term on the right-hand side of eq 8 can be neglected. I n that case, eq 8 and 9 can be UO
CAOWAO
+
(9)
CBOWBO
solved simultaneously to determine the H4P04+and pP04- mobilities. The values so obtained, which are listed in Table 111, are just about a factor of 4 lower than is found for hydroxyl and hydronium ion chain conduction mobilities in water a t 80'. The lower protonic mobilities in phosphoric acid may result from the disruption of its hydrogen-bonded structure caused by its substantial self-ionization. The apparent "activation energy" for protonic mobility in phosphoric acid is 1.2 kcal mole-' for H4P04+and 1.6 kcal mole-' for H2P04-. These values are close to those found in liquid water.g As in other protonic Table I11 : Protonic Mobilities in Phosphoric Acid WAOl
OB0,
OC
crna v-1 8ec -1
cml v-1 8ec -1
80 80 150 150
1.28 X 1 . 2 3 x 10-3 2.48 x 10-3 2.46 x
Electrolytes employed
Temp,
H2SO4, KHiPOa HClOI, NHaHzPOa HzSOa, KHzPO4 HClO4, LiHzPOa
The Journal of Physical Chemistry
0.92 X
conductors, the movement of positive charge takes place with greater ease than that of negative charge (i.e., @A0
>
WBO).
I n the exceptional case of the H3P207-and the oxonium ion, it turns out that separate sa and se values can be obtained. From the decrease in conductivity which occurs when orthophosphoric acid, which initially contains no pyrophosphate, self-dissociates to establish equilibrium 2, we find3S H ~ P ~ O , - S H ~ O+ = -0.235; from the addition of water to equilibrated phosphoric acid = 0.0258/ (Table I) we find 1 / 2 ( - s ~ I ~ I ~ , SH~O':) 0.198 = 0.130 m-l. At 80' then, S H ~ P % O = ~ - -0.248 and S H ~ O += 0.013. The s value for the pyrophosphate is about half the (8, E,) values listed in Table 11, so that its influence upon the protonic mobility is in line with what has been suggested above, namely that anions and cations of the same charge have nearly the same influence on the mobility. Oxonium ion, H30+, is unusual in that it appears to increase the conductivity slightly. Its presence may tend to facilitate proton jumps or it may take part in the conduction process itself, although to a much more limited degree than H4P04+and H2P04-. A similar facilitation of proton conduction by the oxonium ion was found in sulfuric acid.&
+
+
+
0.98 x 10-3
2 . 2 3 x 10-3 2.25 x 10-s
(9) E. U. Franck, D. Hartmann, and F. Hensel, Discussions Faraday SOC.,39, 200 (1965).
