212
A. G. KEENANAND W. H. DUEWER
Silver and Sodium Ion Transport Numbers into Pyrex from Binary Nitrate Melts’
by A. G. Keenan and W. H. Duewer Department of Chemistry, University of Miami, Coral Gables, Florida $8184 (Received August 6 , 1968)
The cation transport numbers of sodium and silver ion from mixed melts of the nitrates into a Pyrex membrane at 318’ are found to be accurately equal to the corresponding cation mole fractions in the melt over the whole range of compositions. This result is explainable on the basis of a simple liquid-junction model without surface exchange for the membrane. This is in contrast with the previous equilibrium membrane potential studies whicrh required an ion-exchange model. The reasons for this are discussed. Ionic mobilities in glass are of interest from many points of view. I n two recent publications2sa it has been demonstrated that the ion-exchange equation4 statisfactorily fits Pyrex membrane potential data in fused salts. The selectivity constants so determined involve mobility ratios. Mobilities in glasses and fused salts may be measured in a variety of known ways, such as conductance, diffusion, tracer diffusion, and transport experiment^.^ The coefficients so determined are not necessarily equivalent. No systematic study seems to have been made of macroscopic electric transport of cations into glass from fused salts since the very early work of SchultEe6 and Kraus and Darby.’ Their results were largely qualitative, although they are still much quoted. We have now found that over the whole range of composition from pure silver nitrate to sodium nitrate, the cation transport fractions into a Pyrex glass membrane are equal to their mole fractions in the melt. This somewhat startling result can be explained on the basis of a liquid-junction model for the membrane in contradiction to the equilibrium emf data.
Experimental Section The transport experiments mere carried out in a direct manner by measuring the weight change of a Pyrex bulb containing, and immersed in, silver nitrate-sodium nitrate melts through which a measured current was passed for a measured time. The Pyrex bulbs were about 20 mm in diameter and 0.2 mm thick, blown on the end of 10-mm tubing. Their dc resistances varied from 2 to 15 kohms. A cathode of pure silver wire was immersed in the internal solution, which was an equimolar mixture of analytical reagent grade silver and sodium nitrates. The external solution was a similar melt of variable composition. It contained a massive pure silver anode of several square centimeters in surface area. The external melt was held in a 30-mm Pyrex test tube, which in turn was immersed in a constant-temperature bath, Temperature control and measurement have been previously described.2sa The Journal of Physical Chemistry
The dc voltage was obtained from a 110-V ac supply through a constant-voltage transformer followed by a Variac and was rectified with a 1.8-A full-wave silicon bridge rectifier. A 10.5-H choke and a 30 MFdual-section capacitor were used as a T filter, followed by a 100-ohm power resistor. Up to 74 V (dc) were available with an ac ripple of less than 0.1% as measured on an oscilloscope. The charge passed through the transport cell was obtained by integrating the potential across a 1-ohm standard series resistor as a function of time. This was done by means of an electronic potentiometric recorder of 5-mV full-scale sensitivity provided with a ball-and-disk integrator. Runs ranged from 2 to 24 hr. The current was usually about 10 mA and remained constant within a few per cent after the first 5 min. The salt mixtures were melted before a run and were sparged with pure nitrogen for 2 hr to remove water. The inner bulb containing the salt and electrode was carefully weighed with all the usual precautions before and after the electrolysis. Blank runs indicated that weighing errors were no more than 2%. The weight changes were taken to result solely from passage of sodium and silver ions into the glass, since it is well establisheds.9 that current in the glass phase is carried only by cations. From the data, the si1ver:sodium ratio and hence the transference numbers could be calculated. The experimental method obviously gives the electrical transport fractions passing from the melt (1) This work was supported by the Office of Naval Research, Power Program, under Contract Nonr-4008(07). (2) K. Not5 and A. G. Keenan, J . Phys. Chem., 70,662 (1966). (3) A. G.Keenan, K. Nota, and F. L. Wiloox, ibid., 72, 1085 (1968). (4) F. Conti and G . Eisenman, Biophys. J., 5, 247, 511 (1965). (5) R. W.Laity and M. P. Miller, J . Phys. Chem., 68,2145 (1964). (6) G. Schultae, Ann. Physik, 40, 335 (1913). (7) C. A. Kraus and E. H. Darby, J. Amer. Chem. Soc., 44, 2783 (1922). (8) G. Eisenman, Advan. Anal. Chem. Instr., 4, 213 (1965). (9) J. 0. hard in “Glass Electrodes for Hydrogen and Other Cations,” G . Eisenman, Ed., Marcel Deklrer, Inc., New York, N. Y., 1967, p 51.
213
SILVER AND SODIUM ION TRANSPORT NUMBERS Table I: Transport Data into Pyrex Glass for Nitrate-Sodium Nitrate Melt at 318" Mole fraction of AgNOs in melt
Q,
0 * 000 0.100 0.100 0.222 0.222 0.350 0.350 0.358 0.500 0.506 0.700 0.700 0,900 0,900 0 * 900 1.000 1 * 000
1.0 ti
Silver
C
Awe mg
tAg
100.0 79.1 75.2 124.2 89.5 128.9 58.9 71.6 106.0 128.0 96.8 143.5 113.9 51.8 51.9 96.5 162 5
23.9 29.8 24.3 59.0 37.9 68.5 33.3 42.0 71.0 89.9 83.2 118.7 123.5 51.5 51.4 108.0 184.6
0 I002 0.157 0.097 0.269 0.211 0.333 0.372 0.396 0.491 0.528 0.706 0.669 0.962 0 859 0.855 1.001 1.020
I
O* 8
ri
0.6
'ji u-
c
i E
I
l-
into the glass. Blank experiments with zero current showed that ion exchange and thermal diffusion contributed negligible weight changes. I n some cases the glass of the bulbs after electrolysis was ground in a stainless steel mill, was dissolved in hydrofluoric and nitric acids, and was analyzed for sodium, potassium, and silver with an atomic absorption spectrometer.1o
0.4
012
0
Results The transport data for the silver-sodium system are given in Table I. A graph of average values of tAg against rounded concentrations is shown in Figure 1. The standard deviation from the line tAg = X A is~ 0.034 and the average deviation from the line is +0.007. The optimum fit of third order or less as determined by a least-squares computer program is t a g = 0.956X~, 0.027 and has a standard deviation of 0.031, so that no statistical justification exists for an attempt to fit the data with any other type of curve. No significant correlation between the amount of charge transported or the duration of a run and the mag~ nitude or sign of the deviations from tAg = X Aexists. Transport numbers of sodium and silver ion into Pyrex are thus equal to their respective mole fractions in the binary-nitrate melt. No attempt was made to carry out systematic analyses of glass composition changes for all runs, but the data obtained showed that, as expected,? replacement of sodium by silver was on an equivalent basis. Up to 50% replacement occurred in the longer runs. The glass changed color but did not appear to lose appreciable mechanical strength.
+
Discussion The general flux equation for ion transport i~43~'-1* Jt = -Ciuc(dVt/dx)
(1)
Mole fraction of silver nitrate.
Figure 1. Transport number of silver ion into Pyrex membrane vs. mole fraction of silver nitrate in a NaNOa-AgNOa melt at 318".
where J , is the flux, in mol sec-l, of component i in the x: direction; C,is the concentration, in mol cm-S; V , is the electrochemical potential, in volts; and ut is the mobility in the glass. The electrochemical potential is given by
Vi = pP
+ RT In a( + x,F$
(2)
where the first two terms are the chemical potential, xi is the charge, F is the faraday, and $ is the electrical potential. I n the present system the electrical potential was of the order of 70 V. The chemical potential is equal to the equilibrium membrane potential in emf measurements and is therefore of the order of millivolts* and is negligible. Thus the gradient of the electrochemical potential in the flux equation is the same for both univalent cations and cancels out below. (10) We are indebted to Mr. 0. Joensuu of the Institute of Marine Science for these analyses. (11) R. W. Laity, J. Phys. Chem., 67, 671 (1963). (12) R. W. Laity, J. Chem. Phys., 30, 682 (1969). (13) L. Onsager, Trans. N . Y.Acad. Sci., 46, 241 (1946).
Volume 78, Number 1 January 1969
214
A. G. KEENANAND W. H. DUEWER
From its definition,14the transport number ti may then be written
- -_ CiU 1
ti = &J
