Journal of Solution Chemistry, Vol. 11, No. 9, 1982
Ionization Constants of Aqueous Ammonia from 25 to 250~ and to 2000 Bar A. I. Read 1 Received June 15, 1982; revised September 29, 1982 The ionization constant of ammonia has been determined by conductivity measurements and found to vary from 1.77x 10-5 at 25~ to 1.3x lO6mol-kg 1 at 250~ The pressure effect to 2000 bar has been measured and the ratio K2ooo/K 1 is 6.8 at 25~ and 11 at 250~ The standard molar volume change for the ionization at 1 bar, & V~, changes from -28.8 at 25~ to -67 cm3-mol 1 at 250~
KEY WORDS: Ionization constant; ammonium hydroxide; ammonia; conductivity; volume of ionization; thermodynamics; high temperature; high pressure,
1. I N T R O D U C T I O N
Few acid or base ionization constants have been measured to moderate temperatures as a function of pressure. As part of a program for determining the behavior of solutions in natural geothermal systems, this paper reports the temperature effect to 250~ and the pressure effect to 2000 bar on the ionization of ammonia NH3(aq) + H20 = NH~- + OH-
where NH3(aq) refers to the total of unionized forms of dissolved ammonia. The investigations of reaction (1) to 50~ by Bates and Pinching, (1'2) who used an EMF method, provide t h e m o s t reliable figures for the ionization constant at low temperatures. Everett and Landsman, (3) who used a concentration cell with liquid junction, obtain-
lChemistry Division, Department of Scientific and Industrial Research, Private Bag, Petone, New Zealand.
ed results in close agreement with these values. Reaction (1) has also been studied by conductivity measurements of dilute solutions by Noyes (4~ at saturation water vapor pressure (s.w.v.p.) to 306~ by Wright et al. ~5) at 2000 psi to 290~ and by Quist and Marshall ~6~ with moderate precision to 700~ and 4000 bar. Another approach has been the calorimetric investigation to 145~ by Olofsson, (7~ while more recently, Hitch and Mesmer ~8~ studied the ionization reaction from 50~ to 295~ using a potentiometric technique. While the pressure effect on Reaction (1) has been studied to 3000 bar at 25~ by Buchanan and Hamann (9~ and for small increments of P (-----70 bar) to 295~ by Hitch and Mesmer, (8~ this report presents the first precise study of the effect of pressure to 2000 bar at temperatures to 250~ 2. EXPERIMENTAL
The construction of the conductivity cell and of the pressure vessel and details of the procedure for recording a series of measurements have already been described. (1~ Temperatures were monitored with mercury-in-glass thermometers. These were calibrated with a standard platinum resistance thermometer. Temperatures are considered accurate to better than ---0.02~ at 25~ and to better than - 0 . 1 ~ at all other points. Conductivities for 0.001m solutions of NaC1, NH4C1, NaOH and 0.066m NH4OH were measured with a Wayne-Kerr B641 conductivity bridge. The NaCI and NHaC1 were of analytical reagent quality (B.D.H.-AnalaR) and triply distilled water was used for all solutions. The NH4OH (Merck Suprapur) and carbonate-free NaOH (13) solutions were stored in P.T.F.E. containers and standardized against HC1 by weight titration. Dissolved CO2 (and 02) in the triply distilled water was removed by bubbling with N2 (several hours is necessary as monitored by conductivity) prior to solution preparation. Separate NH4CI solutions, to which has been added sufficient NH4OH to supress hydrolysis of the ammonium ion, were prepared for measurement at each temperature. The concentration of ammonium hydroxide required to give a neutral solution at the measurement temperature was calculated from the temperature dependence of the hydrolysis constant for the ammonium ion obtained from the ionization constants of ammonia and of water tabulated by Fisher and Barnes. ~4) The effect of pressure on the hydrolysis constant was ignored. In contrast to the behavior at lower temperatures, the conductivities of NaOH solutions at 200 and 250~ were not stable but
Ionization Constants of Aqueous Ammonia
Table I. The Product Ap for 0.001m Aqueous NHaC1 Solutions to 250~ and 2000 bar a p (bar)
decreased slowly with time. Apparently, the polycrystalline alumina insulator was being slowly attacked by OH- ions which were being replaced in solution by a less mobile aluminum species accounting for the decrease in conductivity with time. Quist and Marshall ~6~reported that reliable conductivity measurements with NaOH solutions could only be obtained below 300~ due to reaction between NaOH and their A1203 insulator tube. On the other hand, it has been found here that the conductivity of NH4OH solutions at 250~ increased with time. In this case the reaction of OH- allows further ionization of the weak electrolyte which leads to a net increase in conductivity with time, an observation not previously reported. After cooling the pressure vessel, the cell solutions were analyzed for aluminium by atomic absorption spectrophotometry. The aluminum co,ltent of the cooled solutions does not wholly account for the change in conductivity of the cell solutions at high temperatures. In view of the difficulty in obtaining reliable conductivity values for NH4OH (at 250~ and for NaOH solutions (at 200 and 250~ measurements were recorded at only three pressures (near 2000, 1200 and 200 bar). Plots of conductivity against time at each pressure were closely linear and extrapolations were made to eliminate the effect of the drift in conductivity with time. Hence, the accuracy of the conductivity values for NaOH (at 200 and 250~ and NH4OH (at 250~ solutions is lower than other conductivity values and errors from this pro-
Table II. Ap for 0.001m Aqueous NaOH Solutions to 250~ and 2000 bar p (bar)
cedure (at constant T and decreasing P) are cumulative, resulting in greater uncertainty at lower pressures. Thus, at 200 and particularly at 250~ K at 1 bar is likely to be less accurate than K at 2000 bar. However, the error in K at 1 bar from this source is expected to be less than 1%. Solvent corrections were made in a manner similar to that described earlier. (11~The total solvent blank is considered to be the sum of the contributions due to stray ions of strong electrolytes and to the dissociation of water. At each temperature the conductivity of pure water (~5~ was subtracted from the measured water blank at s.w.v.p, to give the contribution due to stray ions of strong electrolytes (considered independent of pressure). As the ionization of NaOH and NH4OH repress the ionization of water, only the contribution to the water blank due to stray strong electrolyte ions need be subtracted from the conductivities for NaOH and NH4OH solutions. However, for the neutral NaCI and NH4C1 solutions the total solvent blank must be subtracted. For 0.001m neutral salt solutions the correction at 200~ ranged from about 1.1% at 1 bar to about 2.3% at 2000 bar, while for 0.066m NH4OH at 200~ the correction was 2%.
Ionization Constants of Aqueous Ammonia
Table III. Ap for 0.066m Aqueous Ammonia as a Function of Temperature and Pressure p(bar)
Isothermal solution resistances were obtained at integral values of the pressure by interpolation on a large scale plot. Values at 1 bar for temperatures other than 25~ were obtained by a short extrapolation. Corrections for lead resistance and the effect of frequency (m were applied. As noted previously, (1~ the cell requires dismantling and cleaning after each run and the cell constant varies about 2%. Therefore, for measurements with 0.001m NaOH, NaCI and NH4CI the cell constant was obtained at 25~ using literature conductivity values:(~618) The presence of excess NH4OH to prevent hydrolysis of NH4C1 solutions at high temperature was allowed for in the calibration. For NH4OH solutions, the cell was calibrated using the measurement at 25~C and 1 bar, the NH4OH concentration (0.066m) and taking the ionization constant as K = 1.77 x 10 .5 on the molal scale. With this system of individual run calibration, the agreement between (AP)r.J(AP)2soc, l bar for repeat runs was often better than 0.2%. Here A is the molar conductivity and p is the solution density taken to be equal to that of pure water at the salt concentrations used. No correction was applied for the change of cell constant with temperature. Using these cell constant values, Ap was calculated from Ap = k/mlq where m is the molality, k is the cell constant and ~ the resist-
Table IV. T h e r m o d y n a m i c Ionization Constants (105K) for Aqueous A m m o n i a to 250~ p(bar)
ance. Specific water volumes were taken from Kell et al.(~9) in conjunction with the recent data of Hilbert. (2~ W h e r e there is overlap, values agree closely with the data of Grindley and Lind. (21) At9 for NH4C1 and NaOH at r o u n d values o f T and p and for NH4OH at the temperature of each experiment are shown in Tables I, II, and III. AO for NaCI have already been published. (12~ In deriving the K values listed in Table IV the degree of dissociation a is approximated by the ratio A/A o where A, the molar conductivity at infinite dilution, is given by A~
This is ref'med by successive approxomations to give a = A / A ' where A' is the molar conductivity o f the hypothetically completely ionized electrolyte at the ion concentration a m. To estimate A~ (for NH4C1, NaOH, and NaC1) and A' (for ammonia) the limiting Onsager equation was used in the forms Ap = A~ A'p
- SO a/2 ( m ) v~ - So 3/2 ( a m ) '~'
where S, the Onsager limiting slope, was evaluated from the known properties of the solvent. (22-~4)T h e equilibrium constant on the molality
Ionization Constants of Aqueous Ammonia
Bates and Pinching 6
Hitch and Mesmer a X
t/*C Fig. 1. A comparison of the pK for aqueous ammonia from this work with literature data at the vapor pressure of the system.
scale is given by K = [a2m/(l~)h,~ in which the activity coefficient of the undissociated molecule is taken as unity, and y_+ is estimated from log 3'• = - - 4 ( o t r t l P ) 1/2 where A = 1.8246x 106/(eT) 3/2, 9 is the dielectric constant and T is in degrees Kelvin. Below 200~ the accuracy of the pK values is estimated to be better than ---0.03 unit; however, in view of the difficulty in measuring conductivities of alkali solutions mentioned earlier, the corresponding pK at 200 and 250~ are less reliable but are accurate to better than --0.04. On the other hand, as shown by A V ~ derived from repeat runs (at constant T) the pressure effect may be obtained with much greater precision (see Fig. 3). The present pK values for aqueous ammonia at s.w.v.p, listed in Table V are compared with published results in Fig. 1. The results of Noyes (4) recalculated by Fisher <~5)show good agreement with the present pK values but it should be noted that A~ derived from the measurements of Noyes <4) differ from those of this work by up to 6%. The data of Wright, Lindsay and Druga <5) were based on the A~ values of Noyes. ~4) Further, Wright et al. ~5) pressurized
Fig, 2. Evaluation o f the standard molar volume and compressibility changes for the ionization of aqueous ammonia at 200~
their apparatus to 2000 psi. When considering the data of Wright et al., Fisher t25) (also see Fisher and Barnes ~4)) did not make allowance for the pressure effect on A ~ and on the ionization constant data, which thus apply to 2000 psi. Hence, these data are not included in Fig. 1. The data of Quist and Marshall, C6) extrapolated to the s.w.v.p. curve by Fisher t25) are in good agreement with the present work with the exception of the one point at 200~ From calorimetric measurements of the dissociation of NH~- to 145~ and from pK~~ values, Oloffson (7) has obtained pK values which agree closely with those from this study. A comparison with the data of Hitch and Mesmer ~8) is difficult. These authors curve fitted their own experimental data simultaneously with selected literature data to models based on semi-empirical equations describing heat capacity, activity coefficient and pressure coefficient behavior and have then derived ionization constant values at infinite dilution. As a result, their Fig. 3 presents a comparison of these values with the previous literature which is biased by published values. However, their data at I = 0 from their Table V offers an important comparison between pK values derived from potentiometric and conductimetric measurements at high T. As seen from the figure,
Ionization Constants of Aqueous Ammonia
t/*C 25-0 99,7 99.8 150-2 150.2
20 "6 E
60 l 500
Fig. 3. Isothermal pressure dependence of the standard molar volume change on ionization of aqueous ammonia in water. there is a discrepancy between the pK's from the two sets of measurements which increases with temperature to 0.17 unit at 250~ This is rather large and is not accounted for by the uncertainty of the individual pK determinations. The effect of association on this discrepancy is not known, but at the low concentrations used in the conductivity measurements, ion-pairing is expected to be minor, and further, the correction for activity coefficients is expected to be adequately described by the method used. On the other hand, the potentiometric data were obtained at much higher ionic strengths so that the contribution of ion-pairing and of activity coefficients is much less certain. By assuming the standard molar compressibility change is independent of pressure, the standard molar volume change at 1 bar may be calculated using the expression derived by Harned and Owen (26) [RT/(p- 1)] In (K/K1) = - A V~ + [(p- 1)~2lax ~
where the standard molar compressibility change is defined by ax
o = _ (~a
The plot for 200~ is shown in Fig. 2. At low p the left-hand side of Eq. (2) is strongly dependent on the value chosen for K1. The value of V~~ at 25~ obtained in this work is compared with literature values for Reaction (1) in Table VI. It is clear that both precise density and conductivity measurements lead to closely similar results.
Table V. pK for the Ionization of Aqueous Ammonia at the System Vapor Pressure at Several Temperatures ~
150.2 200.3 250.6
5.098 5.429 5.876
Table VI. Standard Molar Volume Change for the Ionization of Aqueous Ammonia at 25~ and 1 bar A Vl~ a
Buchanan and Hamannb Results of Buchanan and Hamann recalculated by Lown e t al. c Stokesd This work
(3A G ~ Eq. (2)
Density Eq. (2)
aUnits: cm3-mol"1. bRef. 9. CRef. 29. dRef. 27.
The standard molar volume change at each temperature and for a range of pressures (1-2000 bar) were also calculated from values of K by an empirical equation of the form logK=
ap 2 + bp + c
The form of this equation is consistent with the standard molar compressibility change being independent of the pressure [see Eq. (2)]. In using Eq. (2) above 100~ a subjective extrapolation to obtain the resistance at 1 bar and hence K1 values is required, so the use of Eq. (4) may be preferred. In practice, the difference between A V1~ values from Eq. (2) and by differentiation of Eq. (4) varies from 0.4 cm3-moll (1.4%) at 25~ to 1.2 cm3-mol1 (1.9%) at 250~ The agreement between Ax ~ from these equations is poorer, with differences of 0.5 X 10 .3 cm3-molLbar "1 (10%) at 25~ and 1.6 x 10 "3 cm3-molLbar 1 (11%) at 250~ These diferences are not significant and the use of Eq.
Ionization Constants of Aqueous Ammonia
Table VII. Standard Molar Volume and Compressibility Changes for the Ionization of Aqueous Ammonia from 25 to 250~ and to 2000 bar a
-A V~ 103Ax ~
1 1000 2000 1-2000
28.8 23.6 18.4 5.2
31.7 26.3 21.0 5.3
39.5 32.7 26.0 6.8
47.7 39.4 31.1 8.3
67 52 38 15
a Derived using Eq. (4). dx V~ cm3-moll; Ax ~ cm3.moll-bar q. Excepting 250~ values are the mean of two experiments adjusted to rounded temperatures.
(2) is preferred. Table VII summarizes the data obtained by the use of Eq. (2). In Fig. 3, A V o is plotted against p for temperatures from 25 to 250~ As seen from the figure, A V ~ becomes more negative both with increasing temperature and decreasing pressure. The standard molar volume changes determined by Hitch and Mesmer (8) do not agree well with those of the present study. For example, at 200~ they obtained -58.7 which is somewhat higher than the value o f - 4 7 . 2 cm3-mol1 obtained here. The temperature dependence of the standard molar compressibility change for Reaction (1) is shown in Fig. 4. The rapidly changing slope at high T represents typical behavior for ionization reactions in aqueous solutions. "1'12'29) The variation of 2~ V ~ with temperature at constant pressures of 1, 1000 and 2000 bar is shown in Fig. 5. The slope of these curves (3A Vo/3 T)p, gives the standard isobaric molar expansibility change for Reaction (1). As seen from the figure, the expansibility change becomes more negative with an increase in temperature and decrease in pressure. In Fig. 6, A V~~ is plotted against the standard molar compressibility change for Reaction (1). The trend is similar to that obtained with earlier studies. (~1'~2'29) The thermodynamic functions at constant pressure were obtained by fitting the ionization constant data to an equation of the type InK = d + B / T + C l n T +
DT + ET 2
where T is in Kelvin. A H ~ and ACp~ were then obtained by differen-
t/~ Fig. 4. Temperature dependence of the standard molar compressibility change on ionization of aqueous ammonia in water at 1 bar. I
~/oc Fig, 5, Isobaric temperature dependence of the standard molar volume change on ionization of aqueous ammonia in water at 1, 1000 and 2000 bar.
tiation of Eq. (5) AH ~
R ( - B + CT + D T 2 + 2ET 3)
A C ; = R ( C + 2DT + 6ET 2)
Ionization Constants of Aqueous Ammonia
5 103 Ax~
10 3 motqbar -I
Fig. 6. Relationship between the standard molar volume and compressibility changes on ionization of aqueous ammonia in water at 1 bar.
where The molar free energy and entropy changes were obtained from AG ~ = - R T l n K
= AH ~
The data fitted the equation with residuals always less and generally much less than the estimated experimental error. However, the use of Eq. (5) for extrapolation purposes is not recommended, for it may readily be shown, by using different equations to describe A Cpo as a function of temperature, that the corresponding expressions for InK can lead to wide variations in the prediction of pK, AG ~ A H ~ AS ~ and especially of A Cp~ outside the experimental temperature range. Values for AG ~ A H ~ ACp~ and AS ~ as a function of temperature and at 1 bar are listed in Table VIII. The agreement with the A H ~ obtained by Oloffson (7) is reasonable. No useful comparison can be made with the A H ~ listed by Hitch and Mesmer (8) in their Table V as they have already been weighted with the data of Olofsson.(7) As expected, A Cp~ from this study agree less well with the heat capacity (7) measurements (see Table VIII) and the accuracy of the A Cp~ values at the extremes of the experimental temperature range is estimated to be only about 50% but to be 15% in the middle of the range.
Table VIII. Thermodynamic Values for the Ionization of Ammonia to 350~
at Selected Pressures ~
j.K l . m o l d
AC; j.Kl.mol 1
p = 1 bar 0 25 50 75 100 125 150 175 200 225 250 300 350
26.0 b 27.1 29.1 31.6 34.6 37.8 41.3 45.1 49.2 53.8 59.0 71.9 b 89.5 b
19.3b(11.2) 7.8 (3.94) -0.6 (-1.28) -6.8 (-5.96) -11.5 (-10.70) -15.7 (-15.7) -20.1 (-21.05) -25.7 -33.2 (-36 b) -43.5 -57.4 (-57 b) -99.5b(-90 b) -166.3 b
-24 b -65 -92 -110 -124 -134 -145 -158 -174 -195 -222 -299 b -410 b
-530b(-362) -390 (-236) -290 (-191) -210 (-186) -170 (-194) -170 (-206) -190 (-237) -260 -350 ( ~ 3 5 0 b) -480 -640 (~-500 b) -1070 b -1630 b
p = 1000 bar 0 25 50 75 100 125 150 175 200 225 250
a Based on fit of K values from Table IV to Eq. (5). Parameters are given in Table IX. b Values outside the experimental range, c The values in parentheses are from Olfsson, Ref. 7.
Ionization Constants of Aqueous Ammonia
Table IX. Equation (5) Parameters For Fit of K from Table IV p (bar)
1 1000 2000
2814.03 -597.128 -2261.90
-70047.7 12554.9 53816.9
-512.21 109.042 410.757
1.262 -0.285577 -1.01705
-5.39132 1.01215 3.96863
A maximum (or minimum) is to be expected from Eq. (7) and it occurs at approximately 118~ This is to be compared with the maximum in ACp~ at about 70~ from the data of Olofsson. (7) As the maximum in the present work will occur where d S C ; / d T = 0 i.e. at T = - D / 6 E , an error in this ratio of only 15% can account for the discrepancy with Olofsson's value. Eliminating the quadratic term in Eq. (5), which is equvalent to A Cp~ being a linear function of 7", leads to only a marginally inferior fit of In K as a function of T but this is incompatible with the maximum found experimentally in A Cp~ as a function of temperature. The similarity in magnitude and position of the maxima indicates that for the ionization of ammonia in water, the quadratic function for A Cp~ is the simplest description consistent with both the precise heat capacity (7) and pK data presently available. Maxima below 100~ in A Cp~ with T have also been recorded for benzoic (3~ and for formic, acetic and propionic acids (31) in water. In contrast to the maximum at 1 bar, A C~~ shows a minimum with increasing T at both 1000 and 2000 bar. Obviously, direct measurements are required to accurately resolve the heat capacity behavior of electrolytes at high T and p. The trends in the thermodynamic functions at 1 bar are similar to those for benzoic acid. ~12) Once again, the change in entropy is the property dominating the free energy change at high T. Although A H ~ rapidly becomes large and negative, the magnitude of the T A S ~ term ensures A G o becomes more positive i.e. the weak electrolyte becomes progressively weaker, with rise in temperature. This behavior is the result of the very strong ordering of H20 molecules around ions from the low density bulk solvent at high temperatures resulting in both a large decrease in volume and a dominant negative entropy change for the ionization process.
ACKNOWLEDGMENT T h e a u t h o r t h a n k s W. A. S i n g e r s for assistance with the c o m p u t a tions.
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