Dec., 1928
WEAK ELECTROLYTES I N SALT SOLUTIONS
3157
equation of state extrapolates to low pressures with a high degree of accuracy. The values a t 0" of the ratio of the pV product at one atmosphere to that a t zero pressure, and the weights of a normal liter of CO and N20 are calculated from their molecular weights and the values of the constants of the equation of state of their isosteres, namely N2 and COZ. The agreement with the observed values is very good, and indicates that for many thermodynamic calculations the constants of N2 and COZ can be used for CO and N20, respectively. CAMBRIDGE, ~IASSACHUSETTS [CONTRIBUTION FROM THE
JOHN HARRISON LABORATORY OF CHEMISTRY OF THE VERSITY OF PENNSVLVANIA]
UNI-
THE IONIC CONCENTRATIONS AND ACTIVITY COEFFICIENTS O F WEAK ELECTROLYTES I N CERTAIN SALT SOLUTIONS BY HERBERT S. HARNEDAND ROBERT A. ROBINSON' RECEIVED JUNE 15, 1928
PUBLISHED DECEMBER 10, 1928
The electromotive forces of cells of the types Ag I AgX I H X m o ) , MWm) I H z I HX(mo) I AgX I Ag and Hz I MOH(mo), MX(m) I MxHg I MOH(mo) I HZ
have proved very useful in determining the activity coefficients of some strong acids and hydroxides in certain salt solutions.2 I n the cases so far considered, this method has been applied to the class of strong acids and hydroxides. The question naturally arises as to whether measurements of this kind cannot be extended so as to determine the activity coefficients of weak acids and hydroxides in salt solutions of varying strengths as well as the hydrogen and hydroxyl ion concentrations of weak acids and hydroxides in these solutions. It is the purpose of this study to show that this information may be acquired by measurements of cells without liquid junction potentials. Furthermore, this result can be accomplished with cells which contain easily reproducible electrodes such as the hydrogen and silver-silver chloride electrodes. The limitations of the method are for the most part experimental and depend on the difficulty of obtaining the reversible electroCommonwealth Fund Fellow, 1927-1929. (a) Harned, THISJOURNAL, 38, 1986 (1916); (b) 42, 1808 (1920); (c) 47, 684 (1925); (d) 48, 326 (1926); (e) Loomis, Essex and Meacham, ibid., 39, 1133 (1917); ( f ) Chow, {bid., 42, 497 (1920); (9) Harned and Brumbaugh, ibid., 44, 2729 (1922), (h) Akerlof, ibid., 48, 1160 (1926); (i) Harned and Swindells, ibid., 48, 126 (1926); (j) Harned and James, J . Phys. Chem., 30, 1060 (1926); (k) Harned and h e r l o f , Physik. Z.,27, 411 (1926); (1) Giintelberg, 2. pkysik. Chem., 123, 199 (1926); (m) Randall and Breckenridge, THISJOURNAL, 49, 1435 (1927). 2
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HERBERT S. HARNED AND ROBERT A. ROBINSON
motive force of the hydrogen electrode in solutions containing hydrogen or hydroxyl ion a t very low concentrations and salts a t high concentrations. This opens up a wide field for investigation, since we shall be able to study the effect of the powerful fields of electrolytic solutions upon the characteristic potentials of the organic cations and anions, and make preliminary attempts to parallel this property with the ion constitution. Further, these results may be compared with results obtained from catalytic data by Harned and Hawltins7 and the 1-alues of the ionic activity coefficients of water in salt s o l ~ t i o n s . ~ ~ ~ ’ ~ j Outline of the Method The activity coefficient of a weak electrolyte may be defined in two ways. Assuming that the activity product, aCaA, of the ions of a uniunivalent weak electrolyte has been determined, we may define an activity coefficient bv either
I n (a) mC and n z ~are the stoichiometrical molalities of the ion groups of the electrolyte which would be computed in just the same way as in the case of a strong electrolyte. Thus, in a solution of HAc(ml) ITa4c(m2), UZC equals ml and mA equals (vzl m),and in a solution of HAc(m1) ITaCl(m2),nzc equals mA equals ixl. I n (b), nz+ and nz- are the true molal concentrations of the ionic species. It is the second of these quantities which is the subject of the present study. In fact, the second is the more important since this quantity is directly comparable to the activity coeficients of strong electrolytes and to the potentials of ionic solutions in general. I n the first place, we shall consider the determination of the activity coefficients of a weak acid in a salt solution. Let us consider the simple cells
+
+
Hz I HAc(n?i), hlX(NZ2) I AgX 1 -4g H P I HX(VZ~), hfX(f1~3) I AgX 1 Ag
+
(1) (2)
where HACis a weak acid and HX is a strong acid. Subtract ( 2 ) from (1) and obtain Ag I AgX I HX(mo), hIX(vza) I Ha [ HAc(m), klX(mz) 1 AgX [ Ag
(3)
The cell reaction of (3) represents the transfer of H X from the solution containing H X to the solution containing HAC. The electromotive force of (3) is therefore given by
where YH(2) Yx(2) is the activity coefficient product of the ions in the solution 3 Harned and Hawkins, THIS JOURNAL, 50, 85 (1928). Harned, ibid.,47, 930 (1925).
Dec., 1928
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WEAK ELECTROLYTES I N SALT SOLUTIONS
containing HX only and YH(I)YX(l) the same in the solution containing HAC; ?r$H is the stoichiometrical molality of the hydrogen ion. We shall now consider the conditions under which YH(l)YX(l) may be taken equal to YII(2) Yx(2). Throughout this discussion, let i t be understood that the total ionic strengths of the two solutions are equal. Thus, nz3
+ nto = mE + ma
Assume that the molality of the weak acid is low enough so that the presence of the uiidissociated molecule of the acid causes no appreciable change in Y H ( l ) Y X ( l ) . I t has been shown for mixtures of strong electrolytes of these types that a constant total molality of the ions log
YEIX = DlmHX
+ log
(5)
70
where a is a constant, Y H equals ~ d w xand Y O equals YHX when m H X equals The values of the constants a for the different salt solutions are such that YHX practically becomes independent of the acid concentration in solutions containing less than 0.01 Ad HX. This is illustrated
-
4
-
2
3
Log
Fig 1 -?-log
i
0
0.5
mHC1.
m plot of hydrochloric acid in potassium chloride solutions at a constant total molality of 3.
in Fig. 1 in which in a potassium chloride solution is plotted against the logarithm of the acid concentration. The total concentration of the acid and the salt is 3 M . Thus a t concentrations below 0.01 M hydrochloric acid, the plot becomes parallel t o the abscissa. To be exact, at 0.01 MI YHCl equals 0.860, and a t 0.001 M i t equals 0.S59, corresponding t o a difference of less than 0.1 mv. Thus, if mH(l) and mo are 0.01 M or less, Y H ( ~ ) Y c ~ may ( ~ ) be taken equal to YH(2)YC1(2) without introducing an error greater than the experimental. Equation 4 becomes
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HERBERT S. HARNED AND ROBERT A. ROBINSON
Vol. 50
and since mo, m2 and m3 are known, mK may be computed. After having computed mH by Equation 4 or Equation 6, the calculation of YHYAcIYHAc becomes a simple matter since the thermodynamic equation for the dissociation of HAC is K - yElY.4~ mi Y H A ~ml
-
(7)
and K , rrtl and m H are known. That exactly similar considerations will apply to the determination of the activity coefficient products of weak hydroxides in salt solutions from measurements of cells of the type HzI MOH(mo), MX(md I M,Hg I BOH(mJ, MX(m2) I HZ (34 where MOH is a strong and BOH a weak hydroxide, may readily be shown. For this case, the equation corresponding to Equation 4 will be
where the subscript (2) refers to the solution containing the strong, and (1) to that containing the weak hydroxide. Since the ratio of the activity of water in the two solutions will be unity, and since for low concentrations of the weak base we may take the activity coefficient ratio in the two solutions as unity, we obtain
which corresponds to Equation 6. I n many cases i t may be simpler from the point of view of experiment to measure cells with salt bridges such as Hz I HX(mo), MX(m3) I sat. KCl I HAc(mJ, MX(m2) I Hz
HzI MOH(mo), MX(m3) I sat. KCl I BOH(m1), MX(m2) I HI I n the case of the latter cells, the difference in the two liquid junction potentials will be very small provided that the hydrogen-ion concentrations in the first and the hydroxyl-ion concentrations in the second are the same on both sides of the salt bridge. If we apply the above considerations to these cells, then a t small concentrations of HAC and BOH (not above 0.5 M ) , the electromotive force is a measure of the ratio of the hydrogen or hydroxyl-ion concentrations in the two electrode compartments. So far we have assumed that the concentration of the undissociated molecule, HAC, is so low that i t has only a negligible effect on YH(I) Yx(1). At higher concentrations of HAC, the absolute value of Y H ( ~ )Yx(1) relative to pure aqueous solution will increase with increasing concentration of the undissociated molecule. Thus, Harned and Fleysher6 have found that 5
Harned and Fleysher, THISJOURNAL, 47, 82 (1925).
Dec., 1928
WEAK ELECTROLYTES IN SALT SOLUTIONS
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YHYCl in a 0.01 M acid solution in water increases 3 1 times its initial value on the addition of 25 mole per cent. of ethyl alcohol. From the nature of the plot of their results, the presence of 0.1 M ethyl alcohol would ). cause an increase of somewhat less than 0.5% in Y H ( I ~ Y ~ ( ~ Consequently, Equation 6 is only exactly valid a t zero concentration of HAC, but is valid to within less than 1.2% for solutions containing 0.2 M HL4cor less, if we presume that the effect of undissociated acetic acid upon the activity coefficient is not greater than that of ethyl alcohol. Equation 6 will be strictly valid in the case of the cells
Ag I AgCl I HX(mo), M(m4), MX(m3) I Hz I HAc(mi), M X ( 4 I AgCl I Ag provided that M is an undissociated molecule a t a concentration m4 =
(ml - m ~ which ) produces the same effect on YH(l)YX(l) as does the undissociated acetic acid. Since the present study contains extensive determinations of YHYAc/YHAc and YBYOH/YBOH in aqueous solutions, we have not thoroughly investigated the above effect a t this time. We have, however, obtained a few series of results with acetic acid a t high concentrations in sodium chloride solutions which we shall use to illustrate the magnitude of this effect. Part 1. The Ionic Concentrations and Activity Coefficients of Acetic Acid in Salt Solutions Experimental Results and Method of Numerical Calculation.-The cells measured were of the type Hz I HAc(mi), MX(W) I AgCl I Ag (8) Extended series of measurements of cells containing 0.1, 0.2, 0.5, 1.0, 5.0 and 10 M acetic acid were made in each of which sodium chloride.was varied over a concentration range of 0.02 to 3 M . Further, a series of determinations of cells containing acetic acid a t a concentration of 0 2 M and potassium, lithium and barium chlorides of varying strengths was made, as well as a series of cells with 0.1 M acetic acid and potassium chloride. The acetic acid and salts were of a high grade of purity. The potassium and sodium salts were dried a t a suitable temperature, barium chloride was used in the form of the dihydrate and the lithium chloride solutions were made by dilution of an analyzed concentrated solution. The silver-silver chloride electrodes were of the spiral type. The silver oxide paste was heated at 500' on the platinum spiral. No electrolytic silver was deposited on the spiral previous to this operation. Electrodes made in this way have the same potential as those made by the Noyes and Ellis method. The hydrogen electrodes were of the usual platinum foil type and were found to give reproducible results in all cases except those of the cells containing 0.1 M acetic acid. In the latter case, with cells containing either sodium or potassium chlorides, it was found impossible to obtain electromotive
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HERBERT S. HARNED AND ROBERT A . ROBINSON
Vol. 50
forces corresponding to reasonable values of the activity coefficient of acetic acid unless the platinum foils were coated with an extremely thin film of platinum black. With this additional precaution, potential readings were obtained which are thought to be reasonably close to the correct ones, but a high degree of accuracy is not claimed. This source of error is in accord with the experiments of Harned.ld He found that in solutions containing hydrochloric acid and sodium or potassium chlorides (of constant total molality) the hydrogen electrode as usually prepared was unreliable a t acid concentrations below 0.002 M to 0.003 M . He showed that very thinly coated electrodes improved the situation but did not completely eliminate the error when the salt to acid ratio was very high. Our observations agreed with his, since the error was found to be the greater. the higher the salt concentrations. In the cells containing acetic acid a t 0.2 M or higher, the reproducibility was approximately 1 0 . 2 mv. if the salt concentrations were a t 0.05 M or higher. Attempts were made to obtain results in solutions of 0.02 M salt but they were siuccessful in only a few cases. Instead of comparing the electromotive force of the cell containing acetic acid with that of the cell containing hydrochloric acid in salt solution of the same total molality according to the Scheme 3 and Equation 4 i t was found more convenient to proceed as follows. If the cell Ag 1 AgCl I HCl(Wo), hICl(ma) I I-& I HCl(O.01) I AgCl I Ag (9) be subtracted from (3) for the case where X equals chlorine, the cell Ag 1 AgCl I HCl(O.01) 1 Hz I HBc(mi), MCl(mz) 1 AgCl I Ag
(10)
is obtained. But this cell is also obtained by subtracting Ha I HCl(0.01) I AgCl I Ag
(11)
from the cells measured, namely Hz 1 HAc(ml), iV.Cl(mz) I -4gCl [ Ag
(12)
Let E' equal the electromotive force of cells (12)*',' and 0.4644 be the electromotive force of (ll), then E' - 0.4044
=
0.06915 log
(0.902)2(0.01) Y H ( l ) Y X ( I ) MHmZ
if 0.902 be taken as the activity coefficient of hydrochloric acid in water a t 0.01 M . Equation 13 reduces to E'
- 0.2325 =
-0.05915 log
Y ~ ( i ) Y c i ( i T) E H ~ Z Z
(14)
Keglecting for the present any correction involving the change in solvent caused by the presence of undissociated acetic acid, we let YH(l)YC1(1) equal Yfi(2)YcI(2), which latter data were obtained from cells of the type ( 2 ) containing hydrochloric acid and a chloride. The experimental data as well as the calculated hydrogen-ion concentrations and activity coefficients are given in Table I ; nzl is the molal
Dec., 1928
3 163
WEAK ELECTROLYTES IN SALT SOLUTIONS
concentration of the acetic acid, m2 the molal concentration of added salt and E' the measured values of the electromotive forces. The values of YH(2)Yc1(2! or YH(l)YC1(l) were read off plots of the data taken from the tables of Harned and .&kerlof.2" m~ is the hydrogen or acetate-ion concentration calculated by Equation 14. The next column gives the values of fi computed by Equation 8 from the values of mH. The value employed for the dissociation constant of acetic acid6was 1.85 x lop5. All measurements were made a t 2.5'. Since nzli was unknown in the most dilute solutions, TABLE I HYDROGEX OR ACETATE-ION COXCENTRATIONS AiXD ACTIVITYCOEFFICIENTS O F A C E T I C ACID IN CHLORIDESOLUTIOXS A. Potassium Chloride (1) m, = 0.1005 M HAC. Correction for E' = +O.OOOl (0.445) E'
mz
0.05 .1
.2 .5 1.5 2.0 3.0 0.05 .1 ,194 .5 1.0 1.5 2.0 3.0
mi
.781 .747 .711 ,736 ,777 ,859
0.001616 ,001652 .001723 .001771 ,001582 ,001442 ,001260
0.837 ,818 . 785 ,763 ,855 ,939 1.075
"H(corr
)
0.001609 ,001645 ,001716 ,001763 ,001575 ,001436 ,001255
d
