Journal o f Solution Chemistry, Vol. 5, No. 10, 1976

The Ionization of Aqueous Ammonia to 300~ in K CI Media B. F. Hitch and R. E. Mesmer Received April 26, 1976; revised M a y 11, 1976 A potentiometrie technique using a hydrogen electrode concentration cell with flowing solutions was employed to study the ionization o f ammonia over the temperature range 50-295~ in KCI media from 0.04 to 3.3 m. The isothermal pressure coefficient o f the ionization reaction was obtained at pressures up to 100 bars and temperatures to 250~ in these same media, and was found to vary as the square root o f the ionic strength within the experimental error. Smoothing functions have been presented which also fit selected published data on the ammonia ionization reaction with a standard error o f fit o f 1.8 times the assigned uncertainties. Thermodynamic parameters for the reaction have been tabulated at rounded temperatures, and ionic strengths at the saturation vapor pressure. A limit is given for the association quotient o f HCl at 300~ in 3 m KCI based on these data.

KEY WORDS: Ammonia; ionization; dissociation; equilibrium constant; thermodynamics; pressure effect; salt effect; high temperature. 1. I N T R O D U C T I O N A m m o n i a is one o f the i m p o r t a n t bases o f interest as a buffer o f acidity in n at u ral an d l a b o r a t o r y systems. Because o f its high volatility, it also finds application as a source o f alkalinity in condensates at elevated temperatures. T h e simple i o n i z a t i o n e q u i l i b r i u m reaction NH3(aq.) + H 2 0 ~ N H g + O H -

(1)

has been extensively studied by precise p o t e n t i o m e t r y between 0 and 50~ in dilute salt solutions. Bates and P i n c h i n g <1) studied the alternative acidic dissociation equilibrium, i.e., N H + ~ NH3(aq.) + H +

(2)

z Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830. 667 9 1976PlenumPublishingCorporation,227 West 17thStreet,NewYork. N.Y. 1O011.No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical,photocopying,microfilming,recording,or otherwise,without writtenpermissionof the publisher.

668

Hitch and Mesmer

with the classical AgCI/Ag and H +/H2,Pt electrodes in the cell without liquid junction H2,Pt/NH4OH(m~), NH4CI(m2)/AgC1,Ag making corrections for loss of ammonia in presaturators, the solubility of AgC1 in ammoniacal solutions, and the vapor pressure of NH3 in the conversion to unit pressure of H2. In addition, these authors (2~ have used the method of "partial hydrolysis" of the ammonium salt of p-phenolsulfonic acid. The results of the two approaches are in agreement to 0.001 log units for the dissociation constants and are within 0.01 log units of the results of measurements by Everett and Landsman (a~ using a concentration cell with hydrogen electrodes. The ionization equilibrium has also been studied by conductance measurements in dilute ammonia solutions by Quist and Marshall (~) up to 700~ and 4000 bars and by Wright e t al. (5) to 290~ and Noyes e t al. (6~ to 218~ In 1972 Fisher and Barnes (~ selected values of the ionization constant at the saturation pressure from all the conductance data to 350~ and assigned errors for values above 50~ at between 0.05 and 0.10 log units. More recently Olofsson (8~ determined calorimetrically the heat of protonation of ammonia at infinite dilution from 5 to 145~ These latter data provide an avenue for calculating the equilibrium constant for the reaction as a function of temperature if one value is chosen at a reference temperature, as was done by Olofsson. It is clear from present information that the molal ionization constant for ammonia passes through a maximum between 50 and 100~ and decreases with temperature beyond 100~ in a manner remarkably similar to acetic acid. Unlike most of the other common weak acids and bases, there is little information on the salt effect of the ionization of ammonia even at ordinary temperatures. Using the same potentiometric techniques presented earlier by Sweeton e t al. (9~ for a comprehensive investigation of the ionization of water, we are able to determine the equilibrium quotients for ammonia as well as the pressure coefficients to 300~ as the salt concentration is varied widely. The technique is particularly suited to such studies on ammonia because of the absence of a gas phase in the ceil. This study provides another occasion for testing models for fitting precise equilibrium data where temperature, pressure, and salt concentration are varied, as was the case for the ionization of water. Ammonium ion is expected to exhibit weaker complexing than the proton for chloride ions. If, indeed, the association of HC1 is appreciable at the higher temperatures, it should be reflected in differences in the thermodynamic parameters for the ionization equilibrium of water and ammonia.

The Ionization of Aqueous Ammonia to 300~ in KCI Media

669

2. M A T E R I A L S

Reagent grade chemicals were used throughout this work. Carbon dioxide was stripped from a concentrated stock solution of KC1 by acidification and sparging with nitrogen followed by neutralization with C02-free base. Potassium hydroxide was stored in polyethylene-lined glass containers under hydrogen gas, and transfers were made in the absence of air. Carbonate-free ammonia was stored as a 1 M solution, and transfers were made by syringe. The water used in this work was purified by recycling distilled water through columns of thallium metal to remove oxygen and through an ion exchanger to remove the thallous hydroxide. The hydrogen gas was purified by passage through a palladium alloy in a Serfass H2 Purifier. 3. A P P A R A T U S

AND

PROCEDURES

The potentiometric apparatus described previously ~1~ consists of a hydrogen electrode concentration cell through which are pumped two solutions presaturated with hydrogen. Within the cell the solutions contact only Teflon before seeing the separated platinized platinum electrodes. Ultimately, the streams mix and exit through a flow control valve. The cell representation is as follows:

H2,Pt/NH3(2ml),HCI(rnl),KCI(m2)//KCI(rn2),KOH(rnl)/Pt,H2

II

The nominal molalities of NHa and N H i ~ were nearly equal, and account was taken of the free hydroxide concentration present at the temperature in the calculation of the ionization quotient (the free hydrogen ion concentration was usually less than a few percent of the total base present but was also included in the calculations). Thus, [NHa] = mob - [ O H - ] + [H +]

(3)

The measurements were made in a thermostated oil bath, the temperature of which was determined to + 0.1 ~ with a platinum resistance thermometer. In each run emf readings were taken (1) at two flow rates at a pressure slightly above the vapor pressure at the temperature, (2) at the higher-flow rate at a pressure about 70 bars greater than the previous pressure, and (3) again at the lower pressure and the higher flow rate. By this sequence of measurements, data were obtained for making a small correction to the cell potential to give the potential at infinite flow rate. The small correction, usually less than 1 mV, is believed to be due to extraneous currents and to conditioning of the Teflon channels. The solutions were presaturated with hydrogen gas by sparging. A correction was made for the loss of NHa from the solutions in this operation.

670

Hitch and Mesmer

Generally about 17o of the NH3 was lost from a solution buffered at the [NH~ ]/[NHa] ratio of unity. The cell potential is given by

RT [OH]t E = --if- In [OH]r

~l DI([Xll,r - [Xlt)

(4)

where [OH]t is the observed free hydroxide concentration in the left compartment of cell II and [OH]~ is that in the reference compartment. The DI are the liquid junction coefficients ~9~as given by the Henderson equation, and the summation is over all the ionic species present [X]I. For the values of rn2/rnl used herein, the maximum liquid junction potential calculated by the above expression was - 0 . 6 mV. The ionization quotient for reaction (1) is given by the relationship lnQ =~

E+~D~([X]~,~-

[X D

+ln[OH]~-ln

[NHs] [NH~]

(5)

4. R E S U L T S

The log Q values derived from Eq. (5) are summarized in Table I and are plotted in Fig. 1 for KC1 concentrations from 0.04 to 3.3 m and at temperatures from 50 ~ to 295~ (corrected to the saturation pressure of water). The experimental error is estimated to be 0.02 log units t~p to 250~ and 0.04 log units at 300~ The ionization quotient shows the least temperature dependence at the highest salt concentration, having a value in 3.3 m KC1 of - 4 . 2 7 at 50~ and a value of - 4 . 8 3 at 295~ Table I. Summary of log Q in KC1 Media at the Saturation Pressure -log Q~ I 0.0399 0.1026 0.2109 0.4056 1.000 1.001 1.9511 1.9695 3.342

50~

100~

150~

200~

250~

295~

4.543 4.502 4.453 4.383 4.317 4.305 4.256 4.256 4.262

4.655 4.599 4.547 4.473 4.392 4.388 4.292 4.294 4.294

4.901 4.839 4.755 4.693 4.558 4.561 4.421 4.429 4.406

5.246 5.164 5.047 4.949 4.804 4.818 4.605 4.609 4.508

5.688 5.588 5.442 5.299 5.118 5.129 4.822 4.810 4.704

6.210 5.886 5.730 5.068 4.844

Uncertainties estimated to be 0.02 log units up to 250~ and 0.04 log units at the highest temperature.

The Ionization of Aqueous Ammonia to 300~

6-0 , ~ 6,5

1

1

I

I

in KCl Media

I

671

t

5.5 ,

295~

5.0

4 . 5 ~ 4.0 0

I 0.5

I 1.0

50 ~ I 1.5

I 2.0

~-~ ~ 2.5

I 5.0

3.5

i (m)

Fig. 1. The variation of log Q for the ionization of ammonia as a function of ionic strength in KC1 media at the saturation vapor pressure. Pressure coefficients o f log Q in bar-1 are given in Fig. 2, with their estimated errors, as a function o f the square r o o t o f the salt concentration. The isothermal pressure coefficient (A log Q/2xP)Tis independent o f pressure at the pressures attained in these experiments ( < 70 bar). The magnitude o f the coefficient increases f r o m 5.0 x 10 -~ bar -1 at 50~ to 8.8 x 10 -~ bar -1

E, 91

0

0.5

1.0

t.5

2.0

77-

Fig. 2. The dependence of the isothermal pressure coefficient of log Q on the square root of ionic strength. The lines were calculated using the parameters for Model I in Table II.

672

Hitch and Mesmer

at 250~ in pure water and from 3.8 x 10 -4 bar -~ at 50~ at 250~ at I = 3 m.

5. M O D E L I N G

OF E Q U I L I B R I U M

to 4.6 x 10 -~

QUOTIENTS

It is to be expected that interpolations and extrapolations of data of this kind will depend somewhat on the form of the mathematical model used to fit the data. Here, as in a related previous paper on the dissociation of water, (9) we have used two approaches. The first, Model I in Table II, is based on an expression for the ionization quotient of ammonia containing three terms: one for (log K)p =v~, one for - log [(yNa~+YoH-)/(YNu~au~o)]v= P~ at the saturation pressure (P~), and one for (~ log Q/OP)r. Model II in Table II was derived from the temperature dependence of molal volumes and includes the Table lI. Two Models for the Temperature, Salt, and Pressure Dependence of the Ionization Quotient for A m m o n i a ~ I [ ~ log A Q

log

\ YNHaaH20 ]P=Ps

p

PD

PX P4 Iog(K)P=Ps = --~ + P2 In T + paT + "-~ + P5

,

/7NH,+Yoa-'l I \ errr~3a:-:2o /P=P~

-rag/'--

2S~/1 [ 4_p11 ] + Plo + p l z T 2 + plaF(1) I - 0.0157(I)1 1 + ~I ---T

A log Q~ - ' - - - ~ f f - - ] r = /~(P6 + pTT + p s ~ ? T + pgVTIT 2) II

- R T l n K{T, p} = (q6 + qTT + qsTln T) + qz(P - P~ - q 2 l n p + 18.015(qa -- 1)[A(P - P~ + B(1/p -- 1) + P/,o - po]

_ R T ( \ -aln - ~ - -Q~ ]r

= [ql - q2/3 + (qa - 1)V~] - [q, -b 3.55 - (qs + 1.05 x 105)/3]'V'7

-0.018(3.55 - 1.05 x 105fl)I al2 , /Y'a4+YOH-\ 2S "~/' [ Pn ] - l o g / '\- - YNuaarIzo /P=Vs / = 1- + a/7 + Plo + "-f" + PJ.2T= + plaF(I) I -- 0.0157q)I

Units and definitions: P, pressure ( b a r ) ; / , ionic strength (m); T, absolute t e m p e r a t u r e (~ Ps, saturation pressure o f water ( b a r - 1) ; p, density o f water ( g - c m - a) ; p o, pressure at unit density (bar); /3, compressibility coefficient; S, D e b y e - H t i c k e l coefficient; R, gas c o n s t a n t (units o f terms in q6, q7, qs, c a l - m o l e - I ~ for all other terms units are l i t e r s - b a r - m o l e - l ~ - 1); ~ , osmotic coefficient o f the solution (use data on NaC1 f r o m ref. 11).

The Ionization of Aqueous Ammonia to 300~

in KCI Media

673

following: terms for log K as a function of temperature and density; terms for (Olog Q/OP)T as a function of the molar volume of water (Vg), the compressibility coefficient of water (fl), and the ionic strength; and the same expression for the activity coefficient ratio as in Model I. In Model I the expression for (log K)p=v~ is that resulting from the assumed temperature dependence of the change in heat capacity at saturation pressure (a + b T + c/T2). The expression for the activity coefficient quotient is based on the form derived from the Bronsted-Guggenheim (B-G) formulation for ionic activity coefficients in electrolyte mixtures. A simple model for the ionic strength dependence of the interaction coefficients in the B - G treatment was proposed by Pitzer ( ~ for single electrolyte solutions ~ and was used in an approximate form for activity coefficients in mixtures by Baes and Mesmer. (13) In the present case log 7Na~+7~

~

7>m3an2o =

2SWQ

1 + V Q + B1 + 0.0157~I

(6)

where B

=

- [P~o +

p~/T + p~2T 2 + p~3F(1)]l

(7)

and F(I) = [1 - (1 + 2I 1/2 - 2I)exp(--2Pl2)]/4I

the function suggested by Pitzer. Lastly, the pressure coefficient of log Q has the form suggested by the observations of Marshall and Quist (1~) and by Franck, (15) i.e., (0 log K/O log p) is a constant at constant temperature and therefore (~ log K'~

----g-F-/T = ~

(s)

By inspection of the data, the dependence of k on temperature and salt concentration was found to be k = P6 + pTT + p ~ V ~ T + p g X / I T 2

(9)

In Model II, expressions for the partial molal volumes of components are the basis for the mathematical formulation of log Q. Relationships for the partial molal volumes of ions V~, the apparent molal volume v~, and the salt coefficient si derived (9) principally from Ellis' data <~6~are given below: = A, -- Bfl + CiF,~

(10)

~, = -v;- o + s , ~ m

(11)

s~ = O~ + Eifi

(12)

2 Pitzer(12) used a slightly different leading term in the expression for log 7~:.

674

Hitch and Mesmer Table III. Coefficients for Two Smoothing Functions for log Q Parameter (p, q)

I

1 2 3 4 5 6 7 8 9 10 11 12 13

2.74967 x 104 81.2824 -0.0905795 -1.71772 x 106 -513.761 19.3750 -0.0251761 -8.3565 x 10 -a 9.76089 x 10 -6 -0.376232 78.7733 1.01406 x 10 -6 -0.268869

II 75.6709 5.11457 x -3.50085 6.23709 2.00795 x 5.43080 x -60.5168 11.2130 0 -0.200167 33.6375 6.71694 x -0.267888

105

105 10a

10 -v

Expressions ~ for//, S, and F(I): *fl = A / [ ( B + P)vw]; vw = 1 + A ln[(B + P ~ + e)] A = 0.1400 B = 2.59922 x 1011T -a - 4.69505 x 109T -2 + 2.38585 x 107T -1 - 3.98294 x 104 + 19.7392T **P~ = --2.63078 x 1013T -4 + 3.14559 x 1011T -a - 8.02139 x 10ST -2 - 5469.93 + 20.1951T S = --2.97627 + 4.80688 x 1 0 - 2 T - 2.69280 x 10-4T 2 + 7.49524 x 10-7T 3 1.02352 x 10-gT 4 + 5.58004 x 10-13T 5 F ( 1 ) = [1 - (1 + 2 D t2 - 21)exp(-2Dt2)]/4I -

The expression for/~ in ref. 9 has an error (P~ should be replaced by P). The expression for P ~ in ref. 9 has an error in the fourth term. The correct value is - 5469.93. T h e s e e q u a t i o n s h a v e b e e n s h o w n (9) t o l e a d t o t h e f o l l o w i n g e x p r e s s i o n a:

-Rr

~--Tff-] ~ = [ql -

q~/~ + ( q s -

-0.018(3.55-

1)Vgl -

[q4 + 3 . 5 5 -

1.05 x 10~/3)I s/2

(q5 + 1.05 x 1 0 5 ) N ~ / ? (13)

A t c o n s t a n t t e m p e r a t u r e E q . (13) p r e d i c t s d e p e n d e n c e o n t h e s q u a r e r o o t o f t h e i o n i c s t r e n g t h , as e v i d e n c e d i n F i g . 2 h e r e ( s i n c e t h e t e r m i n I aI2 is s m a l l ) a The details of the derivation of these relationships for the ionization of water are given in ref. 9. Exactly the same form of the equations is found if one assumes the partial molal volume of ammonia is proportional to the molal volume of water. The qa in this paper is related to the analogous quantity in ref. 9 (q~) by the relationship 9

o

qa = qa V~'aa/Vaso.

The Ionization of Aqueous Ammonia to 300~

in KCl Media

675

and also in Fig. 3 in refi 9. Likewise, from this model the behavior of the ionization constant is given by (see footnote 3 on page 674) - R T In K{T, p} = (q6 + q7 + q s T l n T) + q l ( P - P ~ - q2 In p

+ 18.015(qa- 1 ) [ A ( P - P ~

+ B(llp-

1) + P i p - P ~

(14)

where P~ is the pressure at unit density (p) and A and B are constants in the Tait equation of state for water. The first parentheses on the right of Eq. (14) enclose the three terms that originate from the assumption of a temperatureindependent AC~ for the process and give the value of log K at unit density. The coefficients P l . . . P l s and ql...qz3, obtained from a least-squares analysis by fitting the two Models to selected data, are listed in Table III. The data to which the models were fitted included, in addition to those reported here, (1) the low-temperature potentiometric data of Bates and Pinching (1'2) and of Everett and Landsman, (3) (2) the conductance data of Quist and Marshall (4) and Hamann and Strauss, (17) and (3) the calorimetric data in dilute solutions by Vanderzee et al. ~8) at 25~ and Olofsson (8) from 5 to 145~ 6. D I S C U S S I O N

Figure 3 shows the deviations of log K at saturation pressure calculated from the parameters of Model II from those of Model I as well as the deviations of various experimental values from this same result. The two models give essentially the same fit to all the experimental data described previously

0.3

r

T

50

400

]

r

H 0.2

o~0.t i

0

t50

200

250

300

t ~

Fig. 3. The deviation from smoothed values of log K for the ionization of ammonia based on Model I in Table II. The curve labeled II represents the deviation of the smoothed values given by Model Ii, and the points represent experiental measurements.

676

Hitch and M e s m e r

Table IV. Values of (8 In K/OIn p)~ Given by the Two Models t, ~

Model I

M o d e l II

Lit. values

0 50 100 150 200 250 300

29 + 2 26 23 20 17 14 + 1.5 --

27 + 2 24 22 20.5 18.6 16 + 1.5 --

30 ~ 25.93 ~ 24 ~ 20 ~ 17 ~

a Q u i s t a n d M a r s h a l l (1972). b Stokes (1975) at 25~

as expressed in terms of the variance of fit. The small but systematic differences between the results from the two models have maximum values of -0.03 log units at 175~ and of + 0.03 log units at 275~ The larger systematic deviations of the curves I and II from the plotted experimental points originates from the influence of the new precise calorimetric data and our own potentiometric values at low salt concentrations. The pressure coefficient of the equilibrium constant is strongly dependent on the partial derivative (8 In KIOIn p)~.. This latter quantity is significantly greater for the ionization of ammonia than for the ionization of water, as is I

o -2 o

I

I

I

I

4 12 t0

"~

-4

-6 -6 ~1,o - 8 n- - 1 0 <3 -12

2

-~4

0

-16

-2 I

50

I

t00

I

t50

I

200

I'k~

:>50

f, ~ Fig. 4. T h e A H for t h e i o n i z a t i o n o f a m m o n i a (solid c u r v e s - - l e f t ordinate) a n d t h e i o n i z a t i o n o f w a t e r ( d a s h e d c u r v e s - - r i g h t o r d i n a t e ) in KC1 m e d i a . Values for t h e ionizat i o n o f a m m o n i a were calculated f r o m M o d e l I, a n d t h o s e for t h e i o n i z a t i o n of water were t a k e n f r o m ref. 9.

The Ionization of Aqueous A m m o n i a to 300~

in KCI Media

677

Table V. Thermodynamic Quantities for the Ionization of Ammonia at Rounded Temperatures from Model I in Table IT at the Saturation Pressure in KC1 Media l

log O

~

AG

AH ~ "1

cal mole -I

cal mole -t

AS

~,C

AV

~a[ mole -t ~ -~

cal mole -I[ ~ K -~

cm 3 mole -j

I=0,0 0 25 50 75 100 125 150 175 200 225 250 275 300

-4.864 -4.752 -4.732 -4,772 4.856 -4.976 -5.128 -5.311 -5.525 -5,770 -6.047 -6,355 -6.694

~ ,006 ~ .003 z .004 -* .009 ~ .014 ~ .019 ~ .024 ~ .028 • .031 t .031 *- .032 • .039 • .058

6079. 6483. 6997. 7602. 8291. 9065. 9929. 10891. 11962. 13153. 14474. 15938. 17556.

-'8. ~ 4. *-6. 9 14. ~ 24. -* 35. • 46. ~ 58. • 66. • 71. • 76. -*97. ~ 152.

2400. 950. -270. -1420. -2630. -3980. 5550. -7410. 9610. -I2230. -15360. -19200. -24300,

~ 250. • 40. ~ 100. ~ 140. ~ 170. • 220. ~ 240. • 250. • 290. ~*480. • 830. • 1330. • 2000.

0 25 50 75 100 125 150 175 200 225 250 275 300

--4.648 -+ .007 -4.526• 4.495 *- .004 4.521 • .008 - 4 . 5 8 7 • .013 - 4 . 6 8 5 • .017 - 4 . 8 1 4 + .022 - 4 . 9 6 9 • .026 -5.151 • .028 - 5 . 3 5 7 • ,028 -5.584 • .029 - 5 , 8 2 7 ~ .037 6.079 • .056

5809. 6175. 6646. 7201. 7831. 8536. 9320. 10190. 11152. ! 2211. 13366. 14614. 15941.

• 9. • 4. • 6. • 13. -* 22. • 31. • 42. + 53. ~ 61. -* 68. + 70. • 92. • 148.

2520. 1120. -20. -1060. 2130. 3320. -4710. -6310. -8150. -10220. -12470. -14940. 17850.

• 250. ~ 50. ~+100. • 130. * 160. • 210. + 240. • 240. • 280. -* 460. • 800. t 1300. • 1970.

0 25 50 75 100 125 150 175 20~ 225 250 275 300

-4.517 -4.392 -4.353 -4.368 -4.420 -4.502 -4.610 -4.741 -4.895 -5,067 5.252 -5.441 -5.622

• .021 • .011 • .008 • .011 • .014 • .016 -* .019 + .022 • .024 • .025 • ,025 ~ .032 • .051

5645. 5991. 6437. 6959. 7547. 8202. 8925. 9723. 10598. I1550. 12572. 13646, 14743,

t 26. • 15. ~ 12. • 17. • 24. • 30. ~*37. ~ 46. -* 53. • 56. ~ 60. .*80. ~ 133.

~50~ 1210. 150. -790. -1740. -2780. -3980. -5360. -4890. -8490. -10040. -I 1410. -12590.

~ 300. • 160. • 150. • 130. ~ 180. -* 190. • 230. • 230. • 250. • 400. * 720. • 1190. ~ 1840.

0 25 50 75 I00 125 150 175 200 228 250 275 300

-4,460 -4.336 -4.296 -4,306 -4.351 -4.422 -4.516 -4.633 -4.768 -4.918 -5,077 -5.233 -5.371

• .046 * .026 • .015 • ,014 * ,017 • .018 *- .020 -* .022 • .023 • .023 • .023 + .029 * ,047

5574. 5916. 6352. 6860. 7428. 8055. 8745. 9800. 10323, 11211. 12152. 13124. 14086.

~ 58, ~* 36. -* 22. ~ 22. ~*28. • 34. ~ 39, *. 45. ~ 5 I. -* 53. ~. 55. ~ 73, :~ 123.

2510. 1210. 220. -650. -1500. -2440. -3520. -4740. -6070. -7390. -8530. -9280. -9490.

* 420. • 310. • 260. -* 200. • 170. • 200. • 230. ~ 240. -* 250. • 380. • 670, • 1120. • 1760

0 25 50 75 100 125 150 175 200 225 250 275 300

-4.401 -4.291 -4.253 4.286 -4.284 -4.330 -4,393 -4.470 --4.559 -4.654 -4,747 -4.825 -4.870

-+ .163 ~ .104 • .066 • ,048 ~ .044 • .044 ~ .044 • .042 * .040 • .039 -* .043 • .054 ~* .075

5500. 5854. 6289. 6780. 7314. 7889. 8505. 9166. 9869. 10608. 11364. 12103, 12771.

-* 204. • 142. • 97. • 76. • 75. • 81. • 85. • 86. • 86. * 89. • 102, -* 135. ~ 195.

2240. 1080. 270. -380. -990. -1640. -2380. -3200. -4020. -4680. -4930. --4400. 2700.

• 1040. • 910. -* 780. • 620. • 460. • 360. • 350. ~ 420. § 550. ~ 740. -* I020. • 1440. • 2140.

1347 18.55 -22.48 25.92 -29.26 -32.77 -36.59 40.84 -45.60 -50.95 -57,02 -64~09 -72.98

~ 0.88 ~ 0.14 -* 0.34 • 0.42 *- 0.51 -* 0.60 • 0-85 • 0.63 ~ 0.66 § 0.97 ~ 1.61 ~* 2.53 • 3.77

-65.2 -52.1 -46.5 -46.5 -50,7 -58,1 -682 -80.8 -95.9 - I 14,0 -137.3 -173.0 -242.1

t 17.8 ~ 7.2 t 3.7 -* [,6 ~ 1,8 ~ 3,1 • 3.8 -* 4.8 • 7.5 ~ 14.I ~ 24.4 ~ 27.6 ~ 37.1

-33.3 -31.4 -30.8 -31.6 -33.8 -37.7 -43.0 -50.0 -58.7 -70.2 -87.1 -I 16,3 ~174.2

t 2.9 ~ 2.5 ! 2.3 ~ 2.1 ~ 2.1 ~ 2.2 ~ 2.5 ~ 3.l ~ 4.3 ~ 6.5 ~ 10.3 • 17.7 ~ 34.4

-12.05 -16.95 -20.62 -23.73 -26.70 -29.80 -33.15 -36.83 --40.80 -'45.02 -49.40 -53.92 -58.96

• 0.88 • 0.17 • 0.33 • 0.39 ~ 0.47 ~ 0.58 + 0,63 + 0.61 • 0,63 9 0,93 • 1,56 • 2,46 -* 3,64

-63.9 -49.4 -42.7 -41.6 -44.8 -81.2 -59.5 -68.9 -78.3 -86.6 -94.0 -104-5 -133.9

• 17.8 -* 7.2 ~ 3.8 • 1.6 ~ 1.8 • 3.l • 3.6 ~ 4.7 • 7.2 • 13.8 • 24.1 -* 26.8 • 32.7

-32.0 -30.I -29.3 -29.9 -32.0 -35.4 -40.3 -46-5 -$4.3 ~64.6 -79.6 -105.5 -156.6

~ 2.4 ~ 2A ~ 1.8 ~ 1.7 • 1.6 ~ 1.7 • 1.9 ~ 2.3 • 3.2 ~ 4.8 t 7.5 ~ 12.8 • 24.6

-11.34 -16,05 -19.46 22.25 -24.88 -27.59 -30.51 -33.65 -36.95 -40.22 -43.22 -45.71 -47.70

-+ 1.02 • OA9 -~0.46 • 0.40 • 0.42 9 0.52 -* 0.59 • 0.57 • 0.56 • 0.81 • 1.40 • 2.27 ~ 3.40

-62.2 -46.7 -38.9 -37.0 -39.4 ~4.7 --51.6 -58.4 -63.2 -64.0 -59.2 -50.2 -47.4

~ 17.7 • 7.3 • 4.3 9 1.8 ~ 2.1 • 3,1 ~* 3.2 -*4,2 • 6,5 • 13.1 * 23.3 • 25.8 +~ 31.0

-11.22 -15,78 -18.99 -21.56 -23.93 -26.37 -28.98 -31.78 -34.64 -37.33 -39.53 -40.86 -41.13

• 1.35 • 0.93 • 0.78 ~ 0,59 • 0.48 + 0,52 • 0.58 • 0,57 • 0.55 • 0.75 • 1.30 -* 2.13 • 3.25

-60.8 ~4.5 -36.2 -33.7 -35.5 -40.2 -46,1 -51.4 -53.8 -50.5 -39.2 ~19.6 1.3

• • • •

17.7 7.4 5,0 2.6 * 2,9 • 3.7 • 3.4 -* 4.3 • 6,1 • 12.4 • 22.6 • 25.3 • 33.1

-29.2 -27.1 -26.2 -26A -27.9 -30.5 -34.2 -39.0 -44.8 -52.4 -63.3 -81.9 -118.5

~ 2.0 • 1,8 • 1.7 ~ 1.6 • 1,6 -* 1,7 ~ 1.7 • 1.9 • 2.3 • 3.5 ~ 6,2 ~* 12.1 • 26.4

-11.93 -16.00 -18,64 ~20.58 -22.25 -23.93 -25.72 -27-58 -29.34 -30.69 -31.14 -30.11 -26.98

~+3.13 • 2.65 + 2.20 ~ 1.71 ~ 1.26 • 0.94 * 0.84 • 0.93 • 1.14 • 1.49 * 2.02 • 2.78 • 3.97

-56.0 -38.2 -28.4 -24.4 -24.6 -27.6 -31.4 -33.5 -31.1 20.3 2,8 41.8 97:3

• 17.9 9 8.8 • 8.1 • 6A • 7.3 • 8.2 • 8.0 ~ 9.1 • 9.6 • 13.5 • 22.4 ~ 27.0 • 48.5

-26.2 -24.0 -22.8 -22,7 -233 -25.3 -27.8 -30.9 -34.6 -39.3 -45.8 -56.8 -77.6

• 2.9 -* 2.8 *- 2.8 • 2.8 • 2.9 • 3,1 • 3.2 -+ 3.5 • 4.5 ~ 6,9 ~ 12.4 -* 24.4 + 53,4

I=0.1

1=0.5 ~30.4 • 2.0 -28.4 • 1.8 -27.8 -* 1,6 - 2 7 . 9 -* 1-5 - 2 9 , 6 • 1.4 - 3 2 . 6 -+ I A - 3 6 . 8 • 1-5 -42..2 -+ 1.8 - 4 8 . 9 • 2.3 -57.9 -* 3.4 - 7 0 . 3 ~ 5.7 -92.0 • I0.I 134.8 • 20.7

I = 1.0

1=3.0

678

Hitch and Mesmer

also the change in volume for the process. Table IV gives values at 50~ intervals for the density coefficient calculated by the two models along with estimated uncertainties and the values reported by Quist and Marshall C~>and by Stokes. <19>Model I provides a slightly better fit at the lower temperatures, and Model II at the higher temperatures. The thermodynamic parameters AG, AH, AS, ACp, and AV were calculated at 25~ intervals from 0 to 300~ at five different ionic strengths using Model I. These values are listed in Table V. The uncertainties in the quantities were computed by propagation of the errors assigned for individual measurements and are expressed as 3or to allow for the probable effect of the choice of model on these quantities. The trends of A H and A V with temperature and ionic strength are shown in Figs. 4 and 5. The dashed curves represent the values for the ionization of water. It is evident that the differences between the two ionization processes are relatively small. We believe that these differences could be interpreted in terms o f ionic activity coefficient differences rather than in terms of ion association. The change of log Q with ionic strength and temperature might be an indication of increasing association of either K O H or NH~C1. We may alternatively consider the quotient for reaction (2) and define a quotient Q~ in which actual concentrations of the species are used rather than stoichiometric or total concentrations,

Q = Qo i-(1 +_ [ (1 + QHm[CI-]) J [ .__...I .....

J.__

I

-~o~-: . . . . . . . . . -. ----.,:~.

I

I /

., ----....

-,ot-

,, ~

-t

I

\ ,,x,, ,,y=3 \ ' , \ z . ',k

-zo I-

\ ', \-

/

\

\",, X

/ 0

50

100

t50 f, ~

ZOO

(15)

250

Fig. 5. The A V for the ionization of ammonia (solid curves) and the ionization of water (dashed curves) in KCI media. Values for the ionization of ammonia were taken from Model I, and those for the ionization of water were taken from ref. 9.

The Ionization of Aqueous Ammonia to 300~

in KCI Media

679

where QNa4cl and Qacl are the respective ion association quotients for NH~CI and HC1. The magnitude of the bracketed ratio can be estimated if some assumption is made regarding the effect of ionic strength and temperature on the quotient gH +gr~E3/g~r~4 § (the activity coefficients excluding ion association). Furthermore, if we assume QNH4cl[C1-] << 1, an estimate can be given for Qi~cl. It is generally agreed that the association of HCI is insignificant at low temperatures. If the change in log ~'H+TNHJyNa4+ between 200 and 300~ at 3 m KC1 were assigned to increased association of HC1, then QHcl at 300~ is < 0.2. This limit suggests a small amount of association, and such weak association obviously cannot be determined unambiguously. Association of either or both NH4C1 and HC1 leads to the following possible net reactions under the appropriate conditions: NH~- + C1- ~ NH3(aq.) + HCl(aq.) NH4CI(aq.) ~ NHa(aq.) + HCl(aq.) NH~CI(aq.) ~ NHa(aq.) + H + + C1-

Az 2 = --2 Az 2 = 0 Az 2 = + 2

(a) (b) (c)

The effect o f ionic strength on the quotient for reaction (2) at the higher temperatures is too small to be attributable to either (a) or (c) above. Likewise, the observed 2xV is nearly independent of temperature and ionic strength within the experimental error. This result is also inconsistent with either (a) or (c). Hence, it seems likely that there is little if any association of either NH4C1 or HC1 under these conditions and that the principal net reaction is reaction (2) in Sec. 1.

ACKNOWLEDGMENTS

This research was sponsored by the Energy Research and Development Administration under contract with Union Carbide Corporation. The authors wish to acknowledge the helpful discussions with C. F. Baes, Jr., regarding this work.

REFERENCES

1. 2. 3. 4. 5.

R. G. Bates and G. D. Pinching, J. Res. Nat. Bur. Stand. 42, 419 (1949). R. G. Bates and G. D. Pinching, J. Am. Chem. Soe. 72, 1393 (1950). D. H. Everett and D. A. Landsman, Trans. Faraday Soe. 50, 1221 (1954). A. S. Quist and W. L. Marshall, J. Phys. Chem. 72, 3122 (1968). J. M. Wright, W. T. Lindsay, Jr., and T. R. Druga, The behavior of electrolytic solutions at elevated temperatures as derived from conductance measurements, Bettis Atomic Power Laboratory Report WAPD-TM-204, June 1961. 6. A. A. Noyes, Y. Kato, and R. B. Sosman, Publ. Carnegie Inst. 63, 153, 193 (1907). 7. J. R. Fisher and H. L. Barnes, J. Phys. Chem. 76, 90 (1972~. 8. G. Olofsson, J. Chem. Thermodyn. 7, 507 (1975).

680

9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19.

Hitch and Mesmer

F. H. Sweeton, R. E. Mesmer, and C. F. Baes, Jr., J. Solution Chem. 3, 191 (1974). F. H. Sweeton, R. E. Mesmer, and C. F. Baes, Jr., J. Phys. E6, 165 (1973). Chia-tsun Liu and W. T. Lindsay, Jr., J. Solution Chem. 1, 45 (1972). K. S. Pitzer, J. Phys. Chem. 77, 268 (1973). C. F. Baes, Jr., and R. E. Mesmer, The Hydrolysis of Cations (Wiley-Interscience, New York, 1976, in press). W. L. Marshall and A. S. Quist, Proc. Nat. Acad. Sci. U.S.A. 58, 901 (1967); A. S. Quist and W. L. Marshall, J. Phys. Chem. 72, 1536, 1545 (1968); W. L. Marshall, Rec. Chem. Prog. 30, No. 2, 61 (1969); A. S. Quist, J. Phys. Chem. 74, 3396 (1970). E. U. Franck, Z. Phys. Chem. (Frankfurt am Main) 8, 92, 107, 192 (1956); Angew. Chem. 73, 309 (1961). A. J. Ellis, J. Chem. Soc. (A), 1579 (1966). S. D. Hamann and W. Strauss, Trans. Faraday Soc. 51, 1684 (1955). C. E. Vanderzee, D. L. King, and I. Wads6, J. Chem. Thermodyn. 4, 685 (1972). R. H. Stokes, Aust. J. Chem. 28, 2109 (1975).