discussed for defocused metastables (8). Direct ensemble averaging of the peak envelopes appears to be advantageous; if the peak scan is 20 data points wide, 20 buffer tables are set up in computer memory, and points from each peak scan which correspond in mass are added to the previous total to prepare an averaged peak envelope. Although our present instrumentation and computer programs are relatively unsophisticated, our preliminary results at normal scan rates indicate that this not only gives the statisticallyexpected accuracy improvement for both the abundance and exact mass values, but that it greatly facilitates the deconvolution of overlapping ion multiplets (11). We are also investigating peak rescanning by offsetting the ion accelerating potential. Although this requires
greater sophistication of both the hardware and software, it makes possible refocusing of a peak over a much wider mass range. More rescans of a peak should thus be achievable, especially for members of a mass multiplet. Higher mass measuring accuracy may also be achievable by alternative focusing of unknown and reference peaks, i.e., dynamic peak matching. F. W. MCLAFFERTY R. VENKATARAGHAVAN J. E. COUTANT B. G. GIESSNER
(11) R. Venkataraghavan, F. W. McLafferty, and J. W. Amy, ANAL.CHEM.,39, 179 (1967).
RECEIVED for review November 30, 1970. Accepted March 16,1971. Work supported by NIH Grant G M 16609.
~~~
Department of Chemistry Cornel1 University Ithaca, N. Y. 14850
~~
Dissociation Constant of Hydrochloric Acid from Partial Vapor Pressures over Hyd rogen Chloride-L it hium Chloride So I ut ions SIR: The fact that concentrated aqueous hydrochloric acid solutions have a measurable partial vapor pressure of hydrogen chloride ( I ) indicates the presence of small, but finite, amounts of undissociated hydrochloric acid molecules in these solutions. Hydrochloric acid has, therefore, a dissociation constant K, (molal scale) which has been estimated to be 2.5 x lo7 mole kg-' at 0 "C (2) and 1.3 X lo6 mole kg-1 at 25 "C (3). These values were derived from the partial pressures of hydrogen chloride over concentrated aqueous solutions of hydrochloric acid. A recent paper by Scarano, Gay, and Forina ( 4 ) reports the partial vapor pressure of hydrogen chloride at 25 "C over solutions dilute with respect to hydrochloric acid (m,from about 1.3 X loua to 1.3 X lod2 mole kg-') and concentrated with respect to lithium chloride (mz about 15.5 to 19.8 mole kg-I). It is of interest to ascertain whether the values of the dissociation constant of hydrochloric acid derived from these data are consistent with those obtained from the vapor pressures of concentrated aqueous solutions of the acid. If so, they provide strong support for the validity of the dissociation constant obtained by this method. The dissociation constant of hydrochloric acid in aqueous solutions can be calculated in the following manner. If p is the partial vapor pressure of hydrogen chloride over a solution of hydrochloric acid and p" is the vapor pressure of liquid hydrogen chloride at the same temperature, the activity and the mole fraction XHC I of undissociated hydrochloric acid in the solution are given by aHCl
=
XHClfHCl
=p/p"
(11
Table I. Dissociation Constant of Hydrochloric Acid at "C from Measurements of the Partial Pressure of HCl over Aqueous Solutions
25
Wt %HC1
30 32 11.76 12.91 15.1 32.5 4.26 9.16 x H C ~ x 104 log Km 6.19 6.17 Mean value of log K, = 6.19.
Molality/mole kg-l plmm Hg
34 14.14 68.5 19.30 6.17
36 15.43 142 40.01 6.17
38 16.82 277 78.05 6.23
where fHcl is the activity coefficient of the undissociated acid on the mole fraction scale. If f H c l is taken to be unity, the molality m H c 1 of the undissociated acid is given by
where ml is the stoichiometric molality of hydrochloric acid in the solution. From data given in International Critical Tables (5), p" = 46.7 atm at 25 "C. The dissociation constant on the molality scale is given by (3) In Equation 3, YHCI
= (1
+ 0.036m1)-~
(4)
as f & l has been taken to be unity. The values of log K, given in Table I have been calculated from the partial vapor pressure of hydrogen chloride over concentrated solutions of hydrochloric acid together with the mean ionic activity coefficients 7%of hydrochloric acid in these solutions (7).
(a,
(1) S. J. Bates and H. D. Kirschman, J . Amer. Chem. SOC.,41,1991
(1919). (2) W. F. K. Wynne-Jones, J. Chem. SOC., 1930,1064. (3) R. A. Robinson, Trans. Faraday SOC., 32,743 (1936). (4) E. Scarano, G. Gay, and M. Forina, ANAL.CHEM., 43, 206 (1971).
( 5 ) "International Critical Tables," McGraw-Hill, New York, N. Y.,1928, Vol. 111, p 228. (6) Zbid.,p 301. (7) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed. revised, Butterworth, London, 1970, p 504. ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
969
Table 11. Dissociation Constant of Hydrochloric Acid a t 25 "C from Measurements in Lithium Chloride Solutions of Molality about 15.5 mole kg-1 (ml/mole kg-l)a mz/mole P/mm XHCl 1% x 103 kgHg x 106 K, 1.330 15.58 0.0207 0.582 6.13 15.56 0,0451 1,271 6.18 2.660 3.974 15.54 0.0683 1,924 6.19 5.289 15.52 2.55 6.19 0.0904 15.50 6.605 0.1135 3.20 6.20 7.915 15.48 0.1341 3.78 6.19 9.230 15.46 0.1548 4.36 6.19 10.54 15.43 5.06 6.17 0.1794 Mean value of log K, = 6.18. a Molalities of acid in the first column were calculated from volume concentrations given in ( 4 ) . Table 111. Dissociation Constants of Hydrochloric Acid a t 25 "C from Measurements in Concentrated Lithium Chloride Solutions (ml/mole kg-1)" mg/mole plmm XHCl log x 103 kg-1 Hg x 106 K, 1.366 17.27 0.0363 1.023 6.35 6.29 2.732 17.25 0.0825 2.32 6.27 4.081 17.22 0.1289 3.63 17.20 0.1717 4.84 6.26 5.433 6.28 6.779 17.17 0.2142 6.04 4.061 19.75 0.2718 7.66 6.34 6.36 8.080 19.75 0.5660 15.95 6.36 13.40 19.75 0.9471 26.68 Mean value of log K, = 6.31. a Molalities of acid in the first column were calculated from volume concentrations given in (4).
Equation 1 also applies t o the hydrochloric acid-lithium chloride solutions studied by Scarano, Gay, and Forina (4, but Equation 2 becomes
+
r n m = ~ ( 5 5 . 5 1 2rn2>/p0
since rnl
