The Journal of
Registered i n
Physical Chemistry
US.Patent Office 0 Copyright, 1981, by the American Chemical Society
VOLUME 85, NUMBER 19
SEPTEMBER 17,1981
LETTERS Acid-Base Dissociation Constant of Water in Liquid Ammonia U. Schindewolf * and H. Schwab Instltut fur Physikalische Chemle und Elektrochemie der Universitat Karlsruhe, 7500 Karlsruhe, West Germany (Received: May 11, 198 1; In Final Form: June 1, 1981)
In an electrochemical cell (without diffusion potential) responding reversibly to Na+ ions and solvated electrons e- (or alternately to hydrogen) we determined the thermodynamics of the reaction HzO + e- (+Na+) F= l/zHz + OH- (+Na+) in liquid ammonia. The combination of data with those for the reaction NH4++ e- * l/zHz + NH3 also in ammonia yields the thermodynamics of the dissociation reaction NH3 + HzO* NH4++ OH-. (-40 "C, dimensionless) and AH = 21 f 6 kJ/mol. K is by almost 10 powers of ten We obtain K = 6 X smaller than reported on the basis of conduction experiments, but well within the range of data estimated from the partial molar thermodynamic quantities of species involved in the equilibrium. The very small dissociation constant of NH3 + HzO in ammonia as compared to that of the same reaction in water (3 X lo-' at 25 "C) is mainly due to the differences of entropies of the species in both solvents.
The reaction of solvated electrons with water in ammonia is assumed to proceed via ammonium ions1g2formed by the reaction NH3 + HzO
NH4+ + OH-
(1)
Their concentration should be known for the evaluation of rate data. However, the dissociation constant K, of reaction 1,used for the calculation of the ammonium ion concentration, is known only with poor data between and have been reported. Therefore we reinvestigated by emf measurements the thermodynamics of the dissociation reaction with the cell (1)W.L. Jolly in "Solvated Electron", American Chemical Society, Washington, D.C., 1965,Adu. Chern. Ser., No. 50, p 27. (2)R. R. Dewald and R. V. Tsina, J.Phys. Chern.,72,4520(1968);R. R. Dewald, Ber. Bunsenges. Phys. Chem., 75, 686 (1971). 0022-3654/81/2085-2707$01.25/0
Pt/Na(solid)/NaP-alumina/Na+,0H-,H20,H2in ammonia/Pt (2) the left part of which with the Na+ ion conducting P-alumina membrane responds reversibly to Na+ ions and the right part of which with the platinized Pt electrode responds to solvated electrons (alternately, the Pt electrode with molecular hydrogen can be refered to as a hydrogen electrode). The emf of the cell3 is E = E " - -RT In [a(e-)a(Na+)] (3) F with a(i) the activities of Na+ ions and of solvated electrons, and E" the standard potential of the cell a t the (3) U. Schindewolf and M. Werner, J. Phys. Chern., 84,1123 (1980);
M.Werner and U. Schindewolf, Ber. Bunsenges. Phys. Chern., 84,547 (1980);U.Schindewolf, ibid., submitted for publication. 62 1981 American Chemical Society
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Letters
The Journal of Physical Chemistry, Vol. 85, No. 19, 1981
hypothetical ideal standard concentration of 1 M Na+ ions and solvated electrons (E" = -0.0837 V; dEo/dT = 6.4 X V/K at 233 K)? In a solution of hydroxide ions and molecular hydrogen the reaction OH- + 1/2H2 H 2 0 + e(4) will proceed in analogy to the corresponding reaction with NH2- ions, which is so favorable1 that solvated electrons can be optically observed in From the measured emf the equilibrium activity of solvated electrons according to eq 4 can be obtained, and from this its equilibrium constant K4, if the activities or concentrations of the other reaction partners are known. The experiments were carried out in the following way. Highly purified ammonia (200 cm3,kept over sodium) was distilled into the electrochemical cell. A known amount of dilute sodium-ammonia solution from a buret was added to the ammonia. The faint blue color of the solution remained for many hours indicating that the system is free of reacting impurities. With a syringe 10 HL of triply distilled and degassed water was added under an inert gas M). After stream (water concentration up to 3.75 X evacuation the system was filled with 100 torr of hydrogen. It took several hours until the sodium had completely reacted with the excess water (reverse of reaction 4) and a stable emf was established. Then the emf and its temperature dependence were recorded by raising and lowering the temperature between -35 and -65 "C (1 "C in 10 min). Data were discarded if the emf could not be reproduced within 1 mV in subsequent heating and cooling cycles. The measurements were repeated two to three times after adding further aliquots of the sodium-ammonia solution to the cell. Four experiments with new fillings of the cell have been carried out with altogether ten different and 2 X M. sodium concentrations between 2 X Slight turbidity of the solutions after adding water and sodium indicated that the solubility of sodium hydroxide was exceeded. To obtain its solubility limit we studied the electrical conductivity of the same cell with the same method of solution preparation. Above M NaOH we found, independent of temperature, no change in conductivity with concentration, i.e., the solubility of sodium hydroxide is about (1 f 0.1) x 10" M in the temperature range between -35 and -65 OC. Thislimit also follows from the specific conductivity of the saturated solution ( K = 3 X lo4 Q-l cm-l at -35 "C) together with the conductivities of Na+ and OH- ions (125 and 170 3-1cm2mol-l at -35 "C); it is assumed that OH- ions have the same mobility as other simple monovalent anions in ammonia. In the older literature6 the solubility of NaOH is given as 4 X M at -40 "C.From the equivalent point of the potentiometric ~~
(4) E. J. Kirschke and W.L. Jolly, Science, 147, 45 (1965); Inorg. Chem., 6 , 855 (1967). (5) U. Schindewolf, R. Vogelsgesang, and K. W.Biiddeker, Angew. Chem., 79, 1064 (1967);Angew. Chem., Int. Ed. Engl., 6, 1076 (1967). (6) M. Skossarewsky and N. Tchitchinadzg, J. Chim. Phys., 14, 153 (1916).
titration of water in ammonia with Na-ammonia solution it can be unambiguously concluded that solid NaOH contains no water, as also assumed by Jolly7 in his thermodynamic calculations. With the Na+ and OH- concentrations known, and the water concentration corrected for the amount of water that reacted with added sodium, we calculate from the measured emf (E = 1.18-1.26 V depending on conditions) and its temperature dependence V/K) the following equi(average dE/T = -0.52 X librium data for reaction 4 at -40 OC: AG4" = 93 f 3 kJ/mol; AH40 = 158 f 5 kJ/mol; AS4"= 276 f 20 J/(mol M/bar1/2. K); K 4 = 1.3 X We combine these data with those for the electron reaction with ammonium ions, also from emf measurements3 at 40 "C HN4++ e- l/zHz + NH3 (5)
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AG5" = -185 f 5 kJ/mol; AHH,"= -179 f 4 kJ/mol; AS5" = 27 f 10 J/(mol K); K5 = 1.3 X loa bar1/2/mol,to obtain those of the desired equilibrium (the sum of reactions 4 and 5 gives the reverse of reaction 1). For -40 "Cwe obtain AGIO = 92 f 6 kJ/mol; AHl0 = 21 f 6 kJ/mol; ASl" = -303 f 22 J/(mol K); K1= 6.3 X (dimensionless constant with the ammonia concentration 40 M; the error in K1follows the uncertainty of AGIO). Thus the equilibrium constant at -40 "C is about 2.6 powers of ten smaller than previously reported for 25 "C on the basis of thermodynamic estimati0ns.l One power of ten is due to the temperature difference; the missing factor should be due to the uncertainty between our and the other thermodynamic data. In water the same reaction is known with K1,w= 3 X lo-' at 25 "C (dimensionless with water concentration 55 M), = -77 J/(mol K)6 (AS was = 4.5 kJ/mol, and calculated from AG = -RT In K and AH differs from the A S values given here by R In c 30 kJ/(mol K); c is the concentration of the solvent ammonia or water respectively in mol/L). This large solvent effect in dissociation reaction 1 is only 20% due to the difference of the reaction enthalpy and 80% to the difference of the reaction entropy in both solvents. Further evaluation3 of the data by an HaberBorn cycle leads to results in agreement with the general observation' that the solvation enthalpies of simple salts are only slightly more negative but the solvation entropy is more negative by about 200 J/ (mol K) in ammonia as compared to water. A consequence of the small dissociation constant of water in ammonia is that at equilibrium the ammonium ion concentration is very small and therefore the electron-water reaction in ammonia very likely does not proceeds via ammonium ions.
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Acknowledgment. We are grateful to the Deutsche Forschungsgemeinschaft for financial support. (7) W.L. Jolly, J . Phys. Chem., 58, 250 (1954). (8) L. V. Coulter, J.Phys. Chem., 57, 553 (1953).
