U. S. Department of Commerce Research Paper RP1982 Nationa l Bureau of Standards Volume 42, May 1949 Part of the Journa l of Research of the Nationa l Bureau of Sta ndards

Acidic Dissociation Constant of Ammonium Ion at 0 ° to 500 C, and the Base Strength of Ammonia By Roger G . Bates and Gladys D. Pinching

The acidic dissociation of many acids has been studied in detail, but weak bases have generally been neglected because of the experimental difficulties encountered in the investiga­ tion of some of their buffer solutions by electromotiye-force methods. These difficulties may arise from volatility of the free base or the existence of extraneous electrode reactions such as the formation of ammine complexes at the silver- silver-chloride electrode. In this study of ammonia, special saturators were used to prevent, insofar as possible, t he removal of ammonia from the solutions by the hydrogen gas. A co rrection was applied for the amou nt of diam­ mine silver complex formed at the sil ver-silver-chloride electrode, a nd t his silver ion was pre­ vented by mechanical means from reaching the platinum electrodes. With these precautions, the acidic dissociation constant of ammonium ion at 0° to 50° C was determined from electromotive-force measurements on 19 buffer solutions containing equal molalities of ammonia and ammonium chloride. The changes of free energy, heat con­ tent, entropy, and heat capacity that accompany the dissociation processes in the standard state were derived from the temperature coefficients of the acidic dissociation constant of ammonium ion and of the basic dissociation constant of ammonia. The activity coefficient o[ ammonium chloride in equimolal buffer solutions at 25° C was calculated.

I. Introduction to drift at the rate of about 0.1 mv every 5 min In principle, the thermodynamic dissociation after apparent equilibrium had been attained. constants of weak bases in aqueous solution can They concluded that ". . . the method seems be determined by the same electromotive-force to lack the precision and reproducibility . .. which methods [1, 2, 3]1 that have been used successfully it enjoys in the study of acid solutions". to study the acidic dissociation of a large number The hydrogen-silver-chloride cell is well suited of weak acids. The high solubility of silver to a determination of the basic dissociation con­ chloride in solutions of the ammonia bases led stants of- many ampholytes [6] which neither Owen to suggest [4] that the silver-silver-iodide react appreciably with silver chloride nor are electrode be employed. The latter electrode is removed from the solution by bubbling hydrogen. not, however, as reproducible as the silver-silver­ In solutions of sodium glycinate and sodium chloride electrode, and its potential is consider­ chloride, a dilute sodium-amalgam electrode has ably more sensitive to traces of oxygen in th e been found to give results comparable with solutions. Furthermore, special precautions must those obtained with the silver-silver-chloride be taken, when the base is volatile, in the use of electrode [7] . There is no theoretical r eason why the hydrogen electrode. In an investigation of the sodium electrode should not prove applicable solutions of methylamine and its hydroiodide to other bases as well. In practice, however, the by means of hydrogen-silver-iodide cells, Kalming dropping amalgam electrode is inconvenient at and Schmelzle [5] found the electromotive force best. The suggestion of Roberts [8] that a thallium amalgam electrode be employed in buffer I Figures in brackets indicate the literature references at the end of this paper. solutions to which a soluble thallous salt has been

419 added appears never to have been subjected to in which m is molality, were obtained. Each emf experimental test. value, E, corrected to a partial pressure of 1 atm Our information concerning the thermodynam­ of hydrogen, can be converted to the corresponding ics of basic dissociation consists principally of the value of the acidity function, pwH [14], by the results of studies of ammonium ion and the mono­ equation methyl-, dimethyl-, and trimethyl-ammonium ions _ F (E-EO) by Everet~ B,nd Wynne-Jones [9, 10, 11] and of pwH= - log (JHfc lmH) = 2.3026RT+log mCb (1) anilinium and chloroanilinium ions by Pedersen in which EO is the standard potential of the cell ; [12, 13]. In the work on ammonium and sub­ stituted ammonium ions, two hydrogen-electrode F is the faraday, 96,496 abs coulombs per equiva­ half cells, one filled with a mixture of buffer lent [15]; R is the gas constant, 8.3144 abs j pel' solution and potassium chloride and the second degree per mole [15]; T is the absolute tempera­ with a solution that differed from the first only ture, to C + 273.16; and f is the activity coefficient by replacement of the buffer by hydrochloric acid, on the molal scale. The values of EO and of were connected by a bridge of 3.5-N potassium 2.3026 RTIF in absolute volts are given in table l. chloride. The liquid-junction potential was elim­ The former were obtained by multiplication of thc inated by an extrapolation method and the ther­ standard potentials in international volts [16, 17] modynamic dissociation constants obtained by an by the conversion factor, l.00033 [181.

extrapolation to infinite dilution of data for TABLE 1. rallles of EO, 2.3026 RT/F, and K ,v/Kr different ionic strengths. Glass electrodes were 2.3026 RT used by Pedersen in the study of anilinium and t EO (K ••I K r) X IO' F chloroanilinium ions. ------Inasmuch as our present knowledge of the °C abs I) abs I' thermodynamics of weak acids and ampholytes 0 0.23652 0.05419, 2.8 5 .23404 .05518, 2.9 is based chiefly upon the cell with hydrogen and 10 .23140 . 05617, 2.9 silver- silver-chloride electrodes, it seems desir­ 15 .22854 . 057170 2.9 20 . 225,\; . 05816, 3. 0 able that studies of weak bases should relate, in­ I sofar as possible, also to this cell. This paper 25 .22245 . 05915, 2. 9 30 . 21918 . 00014, 2. 9 reports a determination of the acidic dissociation 35 . 21571 . 06113, 2.8 constant of ammonium ion from 0° to 50° C by 40 . 21214 .062130 2.8 45 . 20829 . 06312, 2. 7 electromotive-force measurements of hydrogen­ silver-chloride cells. Suitable precautions were 50 .20439 . 06411, •? • -I 55 . 20040 . 06510, taken to retard the removal of ammonia from the 00 . 19625 . 06009, solution and to prevent silver ion from reaching , the hydrogen electrodes. Corrections were ap­ The concentration of hydrogcn (hydronium) plied for the solubility of silver chloride in the ion, mH, is determined by the extent to which the buffer solutions. The standard changes of frec dissociation reaction, energy, heat content, entropy, and heat capacity for the dissociation of 1 gram ion of ammonium NHt+H 20 = NH3 + H 30 +, (2) were evaluated . In agreement with Everett and proceeds. The dissociation constant IS formu­ Wynne-Jones [9 , 10], log Ka was found to be a lated linear function of l i T , within experimental error, where Ka and T are the dissociation constant (3) and absolute temperature, respectively. The ac­ tivity coefficient of ammonium chloride in equi­ where the molalities, mi, represent the total molal molal buffer solutions at 25 ° C was calculated. concentrations of the species i, hydrated or other­ wise, and a w is the activity of water. If mHfH II. Method from eq 3 is substituted in eq 1, an expression lor Electromotive-force data for cells of the type - log K a is obtained: 'Ilh:H+ f"H +f cl- aw - log K«= pwH+ log ' _ 4 + log' -' - ' --. (4) Pt; H 2(g) , NH4CI (m), NHa (m), AgCI (8) ; Ag, 1r1 N H:J f"H3

420 Journal of Research The last term of eq 4 disappears at zero ionic strength. Consequently, - log Ka is evaluated in the usual way by plotting the right side of eq 4, computed with a reasonable estimate of the , , activity coefficients, as a function of ionic strength ( ,--- , : ,i and extrapolating to infinite dilution where each I , :, I , activity coefficient becomes unity. I.... "I , ".) , , , 1. Correction for Volatility of Ammonia , , a , b The gas that surrounds the platinum electrodes '~~: of the cells is a mi."ture of hydrogen, ammonia, v and water vapor, and its composition depends upon the temperature and composition of the solution with which it is in eq lIi librium. H ence, E, the electromotive force of the cell when the partial pressure of hydrogen is 760 mm Hg, is A obtained from E', the unrorrccted electromotive force, by

where P is the total pressure, u,nd PH20 and PNH3 arc the partial pressures of water vapor and ammonia, respectively. Inasmuch as an error of 1 mm in the partial pressm e of hydrogen changes E by less than 0.02 mv, it is possible to use the vapor pressure of pure water at the appropriate temperature for PH20 in eq 5, with it resultant elTor at 50 ° C of less than 0.05 mv at an ionic strength of 0.5. Similar­ ly, the partial pressure of ammonia is altered so slightly by the presence of ammonium chloride [19 , 20) tha t a negligible uncertainty is introduced in E if P N H 3 is taken to be the partial press ure of ammonia vapor in equilibrium with a pure aq lIeo us B solution of the same ammonia concentration as that in the buffer solution in question. H emy's F I GURE 1. Cell vessel and exira satumtor. law, (6) ities exceeding 0.59 is given at several tempera­ tm es by Sherwood [24). From the data for solu­ appears to be yalid for solutions of ammonia in tions in the range m = 0.59 to m = LIS, the H emy's­ water and ih salt solutions of constant ionic la.w constant is found to be 16.3 a.t 30°, 25.5 to strength, at least at anunonia concentrations of 26.2 at 40°, and 37.S at 50 ° C. At 0°, it appears a few tenths of a mole per liter or below [19, 21, to be 3.8 to 4.0. 22, 23) . The H enry's law constant, k, for partial No determination of the Henry' -law cQnstant pressures in mm H g, appears to be about 12.9 for dilute ammonia solu tions seems to have been to 13.4 at 25 ° C [19, 23). The maximum COITeC­ made at temperatmes above 25 ° C. Conse­ tion at 25 ° C, that for the most concentrated buffer quently, the partial pressure of the gas in equilib­ solution, amounts to 0.02 my. The partial pres­ rium with a 0.16-m aqueous solution at 50 0 C sure of ammonia from aqueous solutions of molal- was determined by measurement of the amount

Dissociation Constant of Ammonia 421 of ammonia removed by a definite volume of The extent to which reaction 7 proceeds at 25° C hydrogen. The solution was contained in a satu­ is readily calculated from the known values of rator of the type shown at B, figure 1. The satu­ K .v [27, 28] and KI [26, 29]. The increase in rator was attached by a standard-taper joint to an chloride molality, IlmCl, will equal the molality of absorption cell containing O.Ol -M hydrochloric silver-ammonia complex at equilibrium: acid, which in turn led to a wet-test meter that K sll X (m-2/::"mClrj~ registered the volume of hydrogen passed through AmCl = mAg (NHa)t = KI (m+ Amcl)fi' (8) the system. The absorber was designed with two three-way stopcocks to permit the flow of gas where fu is the activity coefficient of uncharged emerging from the saturator to bypass the acid ammonia molecules andf± is the mean ionic activ­ solution until air had been swept out of the entire ity coefficient of silver-ammonia chloride. Inas­ system and equilibrium attained. Then, by a much as AmCI is a correction that amounts to less suitable adjustment of the stopcocks, the gas was than 0.5 percent of m for buffer solutions contain­ admitted to the absorption cell through a perfo­ ing ammonia and ammonium chloride at the same rated disk at the bottom. After passage of 0.6 molality (m), where m does not exceed 0.1, it is to 1.5 liters of hydrogen, at a rate of about 5 ml evident that the actual value need not be estab­ per minute, a sample of the acid solution was lished with great accuracy. Indeed, an error of titrated with 0.008-M sodium hydroxide to the 20 percent in IlmCI corresponds in the most un­ methyl-red endpoint. 'fhe accuracy of the method favorable case (m=0.1,20°C) to less than 0.03 was ascertained by a control measurement of the mv in the electromotive force. This error is less partial pressure at 25° C. The result, 2.18 mm, than the uncertainty in EO and the reproducibility compared favorably with 2.06 and 2.14 mm com­ of the experimental data. Hence, Amcl can be puted from published data [19 , 23]. Duplicate omitted from the right side of eq 8, ju can be con­ measurements at 50° C gave 5.90 and 5.99 mm sidered to be unity, and i± set equal to the mean for the 0.16-m solution, or a value of 37.2 for k, stoichiometric activity coefficient of hydrochloric the Henry's-law constant . at this temperature. acid, fHC!) at the concentration m [6, 16]. With This result can be compared with 37.8 derived these simplifications, eq 8 becomes from the measurements of Sherwood [24]. (9) 2. Correction for Solubility of Silver Chloride for the special case of equimolal buffer solutions, The molality of chloride ion at the silver-silver­ and eq 1 can be written chloride electrode is needed to calculate pwH by eq 1. As a result of the appreciable solubility of F ~-~ ), 2 pwH= 2.3026RTT log m+ log [1 + (Ksp/K N f Hel]' silver chloride in the buffer solutions, this chloride­ (10) ion concentration is somewhat greater than m, the stoichiometric molality of ammonium chloride. At 25° C, the correction for solubility, represented Chloride ion and silver enter the solution, the by the last term of eq 10, contributes 0,0020 to latter principally in the form of the univalent pwH for m = O.l and 0.0015 for m = O.01. Thus diammine complex ion [25, 26]: the percentage increase in chloride concentration resulting from solution of silver chloride in the AgCl+ 2 NHa=Ag (NHa);-+ CL (7) buffer solutions is practically independent of m, The equilibrium constant for reaction 7 is K sv/KI, provided that the ammonia and ammonium chlor­ where Ksp is the solubility-product constant for ide are present at equal molalities . . It should be silver chloride, and KI is the instability constant remembered that the decrease in ammonia con­ for the diammine silver ion. The correction for centration resulting from the formation of complex solubility is made by evaluating the true molality ion according to reaction 7 is confined to the vicin­ of chloride ion at the silver-chloride electrode for ity of the silver-silver-chloride electrode and, use in eq 1. A secondary effect, the potential consequently, does not influence the activity of gradient through the cell resulting from the small hydronium iOIl at the hydrogen electrode. difference of composition between the solutions For temperatures other than 25° C, K,P was surrounding the two electrodes, is negligible. taken from the paper of Owen and Brinkley [28] .

422 Journal of Research

'-- - - vi Their equation for the variation with temperature cation such as ammonium, however, this is not of the logarithm of the solubility-product constant the case. The la t term of cq 4 is approximately between 5° and 45° C was used to calculate the twice the common logarithm of the mean activity constant for 0° and 50° C as well as for the inter­ coefficient of ammonium chloride, or about mediate temperatures. By assuming that the - 0.08 for m = 0.005 at 0° C [32]. Unfortunately, heat of formation of the diammine complex from sil­ the activity coefficient of ammonium chloride in ver ion and ammonia is constant over the range these buffer solutions has not been determined. 0° to 50° C and equal to - 13.2 kcal, as found by In order to evaluate log K a, therefore, the activity­ Berthelot and D elepine [30] , KT can be calculated coefficient term in the experimental range of con­ at the other temperatures from its valu e at 25° C. centrations must be expre sed as some function This procedure is justified by the low degree of of ionic strength, so that an accurate extrapola­ precision required. The values of K .p/KI ob­ tion can be made to zero ionic strength. The tained in this manner are given in the last column two-parameter equation of Huckel [33] was found of table 1. to be well suited to this purpo e. This same equation successfully represents the correspond­ 3. Correction for Hydrolysis ing activity-coefficient terms in buffer systems of The base strength of ammonia exceeds the acid acid anions. strength of ammonium ion. Consequently, these If each ionic activity coefficient is expressed by two constituents of equimolal buffer solutions will the Huckel equation, the last term of eq 4 become react with the amphoteric water solvent to differ­ ent extents, with the net result that a part of the (14) ammonia is converted into ammonium ion:

where A and B arc constants at a particular tem­ perature in the water medium [34], a* and {3 are The concentration of hydroxide ion at equilib­ adjustable parameters, and Jl. , the ionic strength, rium evidently indicates the extent to which is, for the purpose at hand, negligibly different reaction 11 takes place, that is, the number of from the molality of ammonium chloride. Thi moles of ammonium ion formed at the eA'Pense of an difference was Ie s than 0.6 percent in all cases. equal amount of ammonia. Hydrolysis is greatest The complete equation can now be written in a at the highest temperature. However, the cor­ form for extrapolation by making the appropriate rection to log Ka is only 0.0024 in the most unfavor­ substitutions in eq 4: able case. The molality of hydroxide ion IS readily obtained by the approximation [31] - log K~=- - log Ka- {3 m=pwH+

log mOH= log K w+ pwH, (12) 1og m+mOH (15) m-mOH where Kw represents the ionization constant of water [6]. If m is the stoichiometric molality of The a* parameter governs the curvature of the ammonia and of ammonium chloride, the second extrapolation plots. When too large a value of term on the right of eq 4 is given by a* is used, a plot of the right side of eq 15 with respect to m is concave downward; if a* is too mNH: m+mOH. (13) small, the curves are concave upward. A value mNH3 m -mOH of 2.0 at each temperature was found to yield 4 . The Extrapolation straight lines that could be extended with little uncertainty to zero concentration, as shown in When this electromotive-force method is ap­ figure 2. The slopes of these lines are - {3. From plied to a determination of the dissociation con­ the measured slopes, {3 was found to have the stant of an uncharged monobasic acid [3], the term following values, for a*= 2.0: 0.22 at 0°, 0.27 at containing activity coefficients is nearly zero in 5°, 0.28 at 10° to 40°, inclusive, 0.30 at 45°, and dilute solutions. When the acid is a univalent 0.31 at 50° C.

Dissociation Constant of Ammonia 423 10.09 The intermediate stopcock, open only at the time of measurement, appea.red to be essential to constancy of electromotive force. Three cells, 10.07 two with separation of the electrode compartments and one without, were filled with an equimolal buffer solution of 0.05- m ammonium chloride and 10.05 0.05- m ammonia. All three were provided with 9.25 the extra saturator. Over a period of 48 hr, the electromotive force of the cells with stopcocks d dropped by 0.14 and 0.05 mv, whereas that of the C>"" 0 9.23 ~ one without a stopcock fell 1 mv, in spite of the I fact that It gray cast on the edges of the platinum electrodes was scarcely perceptible. This result 9 .21 was surprising in view of the small effect that 8.54 visible deposits of silver have been found to exert on the potentials of hydrogen electrodes in certain basic buffer solutions. 8 .5,2 Solutions of ammonia, about O.l- AI, were pre­ pared in paraffin-lined flasks by absorption of ammonia gas in conductivity water from which 0 .05 0.10 dissolved oxygen had previously been removed by m passage of a stream of nitrogen. A stream of FIGU RB 2. Plot of - log f{~ , the right side of eq 15, as] a function of In at 0°, 25°, and 50° C. nitrogen gas was also used to remove ammonia from a concentrated chemically pure solution, III. Experimental Details contained in a gas-washing bottle, and to conduct From fLll experimental point of view, it is not it into tIle flask of water. The concentration of sufficient that corrections be made for hydrolysis, ammonia was determined by weight titration, for for the solubility of silver chloride, and for the which a O.l- .JI solution of distilled hydrochloric partial pressure of ammonia. If the cells arc to acid, standardized by gravimetric determina­ maintain constant values for periods of 2 to 3 tion of its chloride concentration, was used, with days, two precautions must be observed. First, methyl red as indicator. Although the color silver ion must be prevented from reaching th e change was quite sharp, a color standard com­ hydrogen electrodes and ammonia from diffu sing posed of ammonium chloride solution and indica­ in th e opposite direction to equalize the small tor aided in establishing the endpoint. The titra­ difference in concentration between the two elec­ tions were performed by addition of the ammonia trode solutions. Secondly, removal of ammonia solution to the standard solution of hydrochloric by the bubbling hydrogen must be eliminated, acid. Sufficient pure ammonium chloride to insofar as possible. Both of these clifficul ties ('qual the molality of the ammonia was added to were surmounted by use of the cell shown in this stock solution. Ammonium chloride of figure 1. The solution in the vicini ty of the reagent grade was purified by a single r ecrystal­ hydrogen-electrode compartment, a, is separated lization from water. It was dried at 110° C and from that in the sil ver-silver chloride electrode analyzed by gravimetric determination of chloride. comprutment, b, by a stopcock (c) having a Three analyses gave a result of 100.03 ± 0.01 bore approximately 4 mm in diameter. Part B percen t. is a triple saturator containing some of the same In order Lo avoicl loss of ammonia and at the buffer solution as the cell. In it the hydrogen same time exclucle atmospheric oxygen and car­ gas becomes charged with sufficient ammonia bon dioxide, the buffer solutions were prepared in and water vapor to preclude a change in com­ the following manner. The proper quantity of position of the solu tion in the hydrogen-electrode pure water was placed in the weighed solutioll compartment. Part B is attached to ' part A flasks and 11itrogen passed through for 2 hI' to at the standard-taper joint at the left of the figure. remove oxygen. The flasks were weighed again,

424 Journal of Research the stock solution added with the aid of a modi­ by eq 16, a maximum error of 0.09 mv, at the fi cation of the apparatus described by Bates and extreme temperatures of 0° and 50° C., would be Acree [35], and a final weight obtained. Inas­ introduced. much as the solution flasks were already fillpd with nitrogen, however , it ,,-as considered un­ T A RLE 2. Electromotive J01'ce 0/ the cell: P t; Hz, N H 3 ( m ), XH,CI ( m ), Agel, Ag; con stants 0/ eq 16 necessary to risk loss of ammonia by passing nitrogen into them during addition of the stock I l'f (,HIl solution. "High-vacuum" silicone lubricant ap­ m E 25 a X LO' bX 1Q6 d E peared to be little affected by the buffer solutions, ------abs v rnv and a thin film of it was used to luhricate the stop­ O. 10 77~ 0. 84000 3. 6.3 3. 05 0. 03 cocks in th e cells and solution flasks. . 09635 . 84321 3.55 3. 0~ . 03 . 08613 . 84548 LIO 3. 15 . 01 About 6 hr was allowed for the cells to attain . 07620 .84817 3.39 3. 0·1 .03 th eir initial equilibrium values of electromotive . 06499 . 85 139 3.30 3. 08 . 02

force at 25 ° C, although no more than 4 hI' was '. 0546.3 .85514 3. 15 3. 20 · Or. usually necessary. The temperature was lowered . 0~ 354 . 86004 3. 08 3. 16 . 06 . 04272 . 86053 3. 02 3. 20 . 03 to near 0° overnight. ~1 e a s urem e nt s at 0° to . 0:33 72 . 86559 2.84 3. 08 . 02 2.5° were madp on th c sccond day and at 25 ° to . 03:J0 1 . 866 13 2.84 3. 20 . 05

50° on thc third day, when final value at 25 ° . 03017 . 86798 2. 78 3. 12 . 0 1 were also obtained. A comparison of the four &. 02540 . 871 80 2. 6·1 3. 16 . 03 . 02 124 .87585 2.52 3.24 . ().! electromotive-force values for each cell at 25° C . 02069 .87625 2. 54 2. 9C, · U4 revealed a slow decrease in potential, roughly b. 0170 15 . 'l8077 2. 40 3. 05 .0(;

linear with Lime, during the 48-lu' course of the . 015834 . 88243 2. 34 3. 12 . 07 experiments. ~{o s t of the results obt ained near . 012598 . 88755 2. 16 3. 08 . 0·1 '. 011842 . 88897 2. 16 3. 00 . 03 the end of the series , that is, at 25° to 50°, were &. 008569 .89649 1. 94 3. 02 · O~ increased by small amounts in order to compen­

sate for this slow change. No change was made a For the range 5° to 50° C, incl. in the data for three cells, t wel ve were increase d b Ji"or tbe ra nge 25° to 50° C, in c!. by 0.04 to 0.10 m v, and three by 0.10 to 0.1 5 mv. The mean values of - log K a derived by the The electromotive force of the cell co ntaining the methods described in the foregoing section are most dilute solution (0.008569 m) decreased listed in table 3. These were obtained by averag­ abnormally, and 0.23 and 0.40 mv were added to ing the results from the measurement of each th e low- and high-temperature data, respectively, for this cell. individual solution by the equation IV. Results - log K a=-log K 'a+ fJm , (15a)

The correc ted electromotive-force data for pach where - log K'a represen ts the numerical value of solution over the range 0° to 50° C ,,-ere fitted to the righ t side of eq 15 when a*= 2. The values the quadratic equation, of fJ have been given in the previous section . The basic dissociation constan t of ammonia, K b, is the equilibrium constant for reaction 11. The constan t K b is eviden tly K w/K a. H ence, by the graphical method described by Harned and Nims [36). The constants of eq 16 are given in t able 2. The average differences between the " observed" elec tromotive force at the 11 tempera­ Values of - log K b compu ted from - log K a and tures and that calculated by eq 16 are given in log K w[6) are given in the next to the last column the last column. It is apparent from the figures of table 3. The third and last columns list K a in the next to the last column that there is no and K b , respec tively. significant trend of the constan t b with change of By another electromotive-force method, Everett m. If the m ean value of b, 3.1 X 10- 6, were and Wynne-Jones [9) found 9.215 for - log K a at chosen for the computation of E t for each solution 25 0 C. This r esult is appreciably lower than

Dissociation Constant of Ammonia 425 829788- 49--::1

I . TABLE 3. Acidic dissociation constant of ammonium ion, where t..Cp , the change of heat capacity for the K a, and the basic dissociation constant of ammonia, K b given process, is assumed to be a constant over the temperature range in question [10, 42]. For t I - log K. I K.XlOIO - logK. K.X105 the dissociation of ammonium ion, these authors found p to be zero. Equation 18 can also be °C t..C 0 10. 0813±0. 0009 0.829 4.862 1. 37 regarded as a special case of the equation 5 9. 904O±0. 0010 1. 247 4.830 1. 48 10 9. 7306±0. 0010 1.860 4.804 1.57 A 15 9. 5641±0. ooI[ 2. i3 4. 782 1. 65 - log (20) 20 9. 4oo2±0. 0007 3. 98 4. 767 1.71 Ka = r+B+ CT,

25 9. 2449±0. 0010 ~. 69 4. 751 1. 77 30 9. 0926±0. 0012 8. 08 4.740 1. 82 which is of the form suggested by Harned and 35 8. 9466±0. 0009 11. 31 4. i33 1. 85 Robinson [43]. By application of the usual ther­ 40 8. 8047±0: OOO7 · _ 15.68 4.730 1. 86 45 8. 67oo±0. 0008 21. 4 4.726 1.88 modynamic formulas, it becomes evident that eq 8. 5387±0. 0011 28.9 4.723 1. 89 50 20 requires t..Cp for the dissociation process to be directly proportional to T, rather than a constant.

The discovery that p for the dissociation of 9.244, recorded in table 3. Hence, their value of t..C ammoniulll ion is zero was not surprising, in view K b, 1.65 X 10- 5, is also lower than that (1.77 X 10- 5) of the isoelectric character of process 2. Nor found in this investigation. Owen's determination with the silver-silver-iodide electrode [4] gave would it have been surprising if t..Cp for the disso­ ciation of other hydrogen acids with a single posi­ 1. 7 5 X 10- 5• This corresponds to 9.239 for -log tive charge were also zero. This expectation has Ka. In earlier work, Harned and Owen [1] clllcu­ not been fulfilled, however, for studies of the lated 1.79 X 1 0-5 for Kb from electromotive-force mono-, di-, and trimethylammonium ions have measurements of unbuffered cells [37]. The yielded rather large positive values of p [10, 11]. medium effect amounted, however, to about 20 t..C The proper equation for the calculation of the percent of K b , and some uncertainty was intro­ duced in correcting for it. Determinations of K b thermodynamic functions must be presumed to be the equation that best represents the individual by the conductance method display a somewhat greater uniformity than do the electromotive­ Ka values. Unfortunately, the range of temper­ atures over which measurements are made rarely force studies, namely, LSI X 10- 5 (Kanolt, 1907 exceeds 60° C, and experimental errors usually [3S]) , 1.S7 X lO- 5 (Lunden, 1907 [39]), 1.S1 X 10-5 (interpolated; Noyes, , Kato, and Sosman, 1910 preclude an aecuracy greater than ±0.002 in -log K. Hence, it is sometimes found that each [40]), and 1.S2X10- 5 (Lewis and Schutz, 1934 of two equations representing two different means [41]), all at 25° C. of smoothing the experimental results reproduces V. Thermodynamic Functions for the Dis­ the data equally well. In such a case, there is no sociation of Ammonia and Ammonium way to choose between two different values of the Ion temperature coefficient of log K, and, hence, be­ tween different values of the heat content and Everett and Wynne-Jones [9] were able to rep­ entropy changes for the dissociation. The differ­

resent their values of - log Ka from 5 ° to 45 ° C by ences in the second derivative, upon which t.. Cp the simple equation depends, will be still larger. A -log Ka ='J'+B, (IS) The values of -log K. given in table 3 can be represented either by eq 18 or by eq 20 with a where T is temperature in OK and A and Bare, mean deviation of 0.0011. The constants of these respectively, 2,706 and 0.139. The general equa­ equations were obtained by the method of least tion, of which eq IS is a special case, can be squares and are given in table 4. Harned and written Owen [6, 44] examined four determinations of the A t..C ionization constant of water and found that - log - In K = - +B-- P In T (19) T R ' KID between 0° and 60° C can be expressed by or A 4470.99 - log Ka = 'J'+B+ C log T, (19a) - I og K w= T 6.0875+ 0.017060T, (21 )

426 Journal of Research ------

with an average deviation of 0.0005. As eq 17 TABLE 5. Thermodynamic functions for the acidic dissocia­ indicates, an expression for - log Kb is found by tion of ammonium ion: NHt= NHa+H+ subtracting eq 18 from eq 21. The resulting tlFO tl1l0 tlSO tlCO equation, the constants of which are also given Equation p in table 4, is in the form of eq 20. I I I I 0° e 'fABLE 4. Change of K a and K b with temperature: constants of eq 18 and 20 (lb. j deo-I ab. j (/'0- 1 abs j mole-I ab. j mole-1 mole- I mole- 1 18 ______52,725 52,216 -1.86 0 20 ______•• ____ ._ 52,733 52,540 -0.70 -13 A B C

25° [{G, eQ 18 ______2727. 42 0. 0973 e [{G, eq 20 ______2835. 76 -.6322 0.001225 [{" eQ 20 ______17<13. 57 -6. 1848 . 017060 52, 771 52, 216 - 1.86 0 20IL ___ •______------1__ 52, 765 52,205 - 1.87 - 14 1 1 Thc thermodynamic functions for the two dis­ 50°C sociations (processes 2 and 11) in the hypothetical standard state of unit activity are computed by 18 ______._. 52, 818 52, 216 -1.86 0 20 _____ ••• ______52,827 51,841 -3.06 -15 the equations 1 1 1 !!.FO= 2.3026R(A+ BT+CT 2) (22) TABLE 6. Thermodynamic quantities for the acidic dis­ sociation of ammonium ion at 25° C compared with the M-l°= 2.3026R(A- CT2), (23) results of Everett and Wynne-Jones !!.so=2.3026R( - B - 2CT), (24) tlFO tlHO tlSO tlC· p !!. C;=2.3026R( - 2CT), (25) ------cal (/'0- 1 cal

The four thermodynamic quantities for the t tlFO tlN° ~ ° tlCO ~ acidic dissociation of ammonium ion at 0°, 25°, -- abs j d'O-1 abs j (/eo- 1 and 50° C are given in table 5. Two sets of 1 1 °C ab. j mol.-' abs j 71101.-' mole 111ole- values, computed from the constants of eq 18 and 0 25,407 9,010 -60. 0 178 25 27, III 4,345 -76. 4 195 20, respectively, are included. At 0° and 50° C, the 50 29, 225 -728 - 92.7 211 extremes of the experimental range, the uncertain­ ty in Mr, !!.8°, and !!.C; is large, as the differ­ ences between the two methods of computation Jones [9, 10], the thermodynamic quantItIes in indicate. In the centcr of the experimental range, joules were converted to numbers of calories by however, the temperature coefficient is established dividing by 4.1840. Table 6 demonstrates the with much greater certainty, and only the values essential agreement between the two investiga­ of !!.C; differ appreciably at 25° C. The differ­ tions. Only in the case of !!.Fo are the differences ences at 0° and 50° C serve as a warning against as large as the combined errors of. the two de- pla;cing undue reliance on the temperature co­ tm;minations. \ ' efficient at the extremes of the temperature span. The thermodynamic constants for the basic It is thought that Mr is accuratc within 300 j dissociation of ammonia are given in table 7. mole- 1 at 25 ° C and that th e uncertainty in The value of !!.Ho (1,040 cal mole-I) can be com­ !!.So is less than 1 j deg- 1 mole-I. For comparison pared with 855 cal given by Thomsen [45], with with the results obtained by Everett and Wynne- 835 cal found by Muller and Bauer [46], and

Dissociation Constant of Ammonia 427 with 1,157 cal computed by Lunden [39] from his T ABLE 8. Values of f±.vawlfN H3 in six buffer solutions values of Kb obtained by the conductance method. containing equal molalities of ammonia and ammonium , chloride VI. Activity Coefficients Molali ty of ammonia and ammonium chloride It is evident from eq 4 that the activity-coeffi­ t 0.005 0.01 0.02 0.05 0.0, 0. 1 ci ent term i NH+icl- Caw/f 3) can be obtained from 4 NH ------the experimental data when K a is known . This °C is probably accomplished most conveniently by 0 0.928 0. 002 0.869 0.813 O. , 90 0, 764 5 . 928 . 002 . 869 . 814 . 791 . 765 eq 14. The first part of this term, iNH.+l ci -, is 10 . 927 . 00 1 . 868 . 813 . 700 . 7 6~ the square of the mean ionic activity coeffi cient, 15 . 927 .001 . 867 . 812 . 789 . 764 20 . 926 . 900 . 866 . 810 . 787 . 762 f±, of ammonium chloride in the mL"Xtures con­ taining equal molalities of ammonia and ammoni­ 25 . 925 . 899 . 865 . S09 .786 .760 30 . 925 . 898 .864 · SO i . 784 . 758 um chloride, and the part enclosed in parentheses 35 .924 . 897 .86.3 · S06 . i 82 . 756 is the ratio of the activity of water to the activity 40 .923 . 896 . 862 · S04 . 7SO . 754 45 .923 . 896 . 86 1 · S03 . 7SO . 752 coeffi cient of the uncharged ammonia molecules. 50 .922 .895 ' . 859 · SO l . 7i8 .,750 I It must be remembered, however , that . i 1N H.. + , i NH3 ' and a w in eq 14 relate to the solution a t the hydrogen electrode where the activity of hydroaen buffer solutions containing equal molalities (m) • • b of ammonia and ammonium chloride at 0° to ~on , wInch they influence according to eq 3, exerts Its effect upon the potential of the cell. Yet l C1, 50° C. These values were computed by eq 26. as already indicated, is the activity coeffi cient of Matthews and Davies [20] determined the chloride ion in the solution immediately surround­ activity coefficient of ammonia in solutions con­ ing the silver-silver chloride electrode, where taining ammonium chloride by measurement of chloride exer ts its primary effect. H ence, eq 14 the distribution of ammonia between water and should most properly be separated into two parts chloroform at 25° C. From their data it is possible or, for small, differen ces of composition, mean to calculate -JiNH3 in t.wo equimolal buffer solutions. values of J.L and J.L 1/2 used in the equ ation as written . For 0.02 m, -JiNH3 is 0.999, and for 0.2 m, 1.007. The differences of composition diminish as the Inasmuch as the change of the activity coefficient ionic strength ' of the equimolal buffer solutions with change of m is so small, NH3 can doubtless becomes smaller. For this reason it was permis­ .vi be estimated in the range of molality 0 to 0.1 sible, for purposes of extrapolation, to substitute wi th an error no greater than ± 0.002. The limit­ m for J.L Ceq 15). The ionic strength at the hydro­ ing value at m= O is, of course, unity. gen electrode is m + mOH and at the silver-silver Stokes [47] has calculated the activity of water chloride elec trode m + moH+ LlmCI. The differ­ in solutions of potassium chloride fron~ the elec­ ence, LlmcI, is greatest for the most concentrated tromotive-force data of H arned and Cook [48]. buffer solution (0.10773 m) and at 0° C. If m For molalities of po tassium chloride from 0 to were used in place of the average J.L to calculate 0.2 , - log -Jaw is 0.0072 m. The nonelectrolyte log (i N H t l cl-awIiNH) for this most unfavorable ...... , ammoma, IS presumed to have a much smaller case, an error of only 0.0004 would result. This eff ect on the activity of ,vater in these buffer figure corresponds to 0.03 mv, or less than the solutions than do es the ionized ammonium experimental error . H ence the use of m in place of chloride. Fmthermore, the water activi ty de­ ionic strength to compute activity coeffi cients in parts so slightly from unity that it can be con­ the rang;e 0 to 0.1 m involves no compromise of sidered, for the purpose at hand, equ'al to that in accuracy. Inasmuch as a is 2.0 at each tempera­ * a solution of potassium chloride of the same t ure, eq 14 can be rewritten molality. The values of -Ja wlAu3 given in the second column of table 9 were accordingly evalu­ log (J±.,/awlfNl1) ated from the activity coeffi cient of ammonia found by Matthe\ys and D avies and from the Table gives this activity-coefficient term in six activity of water in solutions of potassium chloride,

428 Journal of Research as givcn by Stokes. The m ean ionic activity three times as great as the medium effect of O.I - M cocfficient of ammonium chloride in thesc equi­ acetic acid lIpon the activity coefficient of 0.1- 1\1 lTl.olal buffer solutions at 25° C, cl erived from hydrochloric acid [50] . .JaW/jNH3 and the data of tablc 8, is given i~ the third column. VII. References The activity coefficients of ammO! ium chloride (1] H. S. Harned and B. B. Owen, J . Am. Chem . Soc. 52, in its pure aqueous solution a t the freezing point 5079 ( 1930). were determined by Scatchard and Prentiss [32]. [2] E . J. Roberts, J. Am. Chern. Soc. 52, 3877 (1930). In order to make a comparison at 25 ° C, thesc (3] H. S. Harned and R. W. E hl ers, J. Am. Chem . Soc. 540, values have been corrccted from 0° to 25 °. It. 1350 ( 1932). [4] B . B. Owen, J. Am. Chem. Soc. 56, 2785 ( 1934). was assumcd for the computation that 2, thc L [5] E. W. Kanning and A. F . Schmelzle, Proc. Indiana relative partial molal heat content of ammonium Acad. Sci. 51, 150 ( 1941). chloride, is constant for each concentration in this [6] H. S. Harned and B. B. Owen, The pliysical chemistry range of tempera ture and equal to that listed in of electrolytic solutions ( Reinhold Publishing the last column of table 9 [6 , 49]. Inasmuch as Corporation, New York, N . Y., 1943). [7] H . S. Harned and B. B. Owen, J. Am. Chem. Soc. 52, log C.Jaw/fNH:) is so nearly zero, dlog C.Jaw7j ;;H3)/dT 5091 ( 1930). is' probably also small and, hencc, as an apprOXl­ [8] E . J. Roberts, J. Am. Chem . Soc. 56,878 (193,1.). mation, [9] D. H. Everett a nd W. F. K . Wy nn e-J ones, Proc. R oy. Soc. ( London) 169A, 190 (1938). [10] D. H. Everett and W. F. E . Wynne-Jones, Trans. Faraday Soc. 35, 1380 (1939). [11] D . H . Everett and W. F. Ie Wy nn e-Jones, Proc. Roy. The valu es of L2, the relative partial molal heat Soc. ( London) 177A, 499 (1941) . content of ammonium chloride in the buffer [12] 1\: . J . Pedersen, Kg!. Danske videnskab. sclskab., solutions, were computed by eq 27 and are listed Math.-fys. Medd. H, No.9 (1937). in the fifth column of table 9. [13] K. J. Pedersen, Kg!. Danske videnskab. selskab., Mat h A ys. Medd. 15, No. 3 ( 1937). [14] R. G. Bates, Chem. Rev. 42, 1 ( 1948). T A BLE 9. JIl ean ionic activity coeffi cient, f ±, and relative [1.5] J. W. DuMond and E. R. Cohen, R ev. Modern Phys. pU1·tial molal heat content L2, of ammonium chloride i n 20, 82 (1948). equimolal buffer solutions compU1'ed with corresponding [16] H . S. Harned and R. W. Ehlers, J . Am. Chem . Soc. valves in pure aqueous solutions of the salt at 25° C 55,2179 ( 1933). [17] W. J. Hamer, J. O. Burton, and S. F . Acree, J . Re­ f* in- L 2 in- search NBS 240, 269 ( 1940) RP1284. 711 ,ja w/lS Il , [18] Announcement of changes in electrical and photo­ Buffer ,,'ater ButTeI' \Vater metric units. NBS Circular C459 ( May 15, 1947). I I ------_. ------_. [19] P. E. C. Scheffer and H . J . J)e Wijs, R ec. t rav. chim. cal cal 44, 655 (1925). 0. 00 5 1. 000 0. 925 0.908 49 42 . 01 1. 001 .898 .877 G5 56 [20] H . E. Matthews and C. W . Da\'ies, .r . Chem . Soc., . 02 1. 001 .864 .841 89 72 1435 ( 1933). . 05 0. 998 .810 .784 138 98 [21] E . Klarmann, Z. anorg. Chem . 132,289 ( 1924). . 07 .997 . 788 -- -- _.- 155 109 [22] M. Randall and C. F. Failey, Chem. Rev. 40,271 ( 1927) . . 1 . 995 .764 . 735 179 12l [23] G. X . Lewis and lVL Randall, Thermodynamics and the free energy of chemical substances, p. 558 (McGraw-Hill Book Co., Inc., X ew York, N . Y., The difference between L2 for alllmonium 1923) . chloride in water and in an aqueous solution of [24] T . K. Sherwood, Ind. E ng. Chem. 17,745 (1925). , ammonia are not large. The activ ity coefficient [25] J . BjeITum, Metal ammine formation in aqueous in the buffer solution appears to be somcwhat solut ions, p. 133 ( P. Haase and SOil , Copenhagen, greater than in LIte pu re aq ueous solu lion. This 1941). [26] W. C. Vosburgh and R. S. LVIc CJurc, J. Am. Chem . difference, except for the part that can be attrib­ Soc. 65, 1060 ( 1943). uted to e1'["ors in the tl\·O determinations, is a [27] A. S. Brown and D . A. MacI nnes, J. Am. Chem . Soc. measure of the m edium eff ect of ammonia upon 57, 459 ( 1935). the activity coe ffi cienL of ammonium chloride. [28] B. B. Owen and S. R. Brinkley, Jr., J . Am. Chem. Soc. However, the obsC'l"y cd in c["cfl s(' aL 0.1 m is about 60, 2233 ( 1938).

I Dissociation Constant of Ammonia 429 [29] P. F. Den, R . M. Stockdale, and W. C. Vosburgh, (40) A. A. Noyes, Y. Kato, and R. B. Sosman, Z. physik. J. Am. Chem. Soc. 63, 2670 (1941). Chem. 73, 1 (1910). (30) M . Berthelot and M. Delepine, Cornpt. rend. 129, (41) G. N. Lewis and P . W. Schutz, J . Am. Chem. Soc. 56, 326 (1899). 1913 (1934). (31) R. G. Bates, G. L. Siegel, and S. F. Acree, J. Research (42) K. S. Pitzer, J. Am. Chern. Soc. 59,2365 ( 1937). NBS :U, 205 (1943) RP1559. (43) H . S. Harned and R. A. Robinson, Trans. Faraday (32) G. Scatchard and S. S. Prentiss, J. Am. Chem. Soc. Soc. 36, 973 (1940). S!, 2696 (1932). (44) H . S. Harned, J. Franklin lnst . 225, 623 (1938). (33) E. Huckel, Physik. Z. 26, 93 (1925). (45) J. Thomsen, Thermochemische Untersuchungen (J . A. (34) G. G. Manov, R. G. Bates, W. J. Hamer, and S. F. Barth, Leipzig, 1882). Acree, J . Am. Chem. Soc. 65, 1765 (1943). (46) P. T . Muller and E. Bauer, J. chim. phys. 2, 457 (1904). (35) R . G. Bates and S. F . Acree, J. Research NBS 30, [47] R . H. Stokes, J. Am. Chern. Soc. 67, 1686 ( 1945). 129 (1943) RP1524. (48) H. S. Harned and M. A. Cook, J . Am. Chem. Soc. (36) H. S. Harned and L. F. Nims, J . Am. Chem. Soc. 54, 59, 1290 ( 1937). 423 (1932). [49] H . Streeck, Z. physik. Chem. 169A, 103 (1934). (37) H. S. Harned and R . A. Robinson, J. Am. Chern. Soc. [50] B. B. Owen, J. Am. Chern. Soc. 54, 1758 ( 1932). 50, 3157 (1928). (38) C. W. Kanolt, J. Am. Chern. Soc. 29, 1402 (1907). (39) H. Lunden, J . chirn. phys. 5, 574 (1907). WASHINGTON, February 1, 1949.

1 430 Journal of Research