Enthalpy of dilution and the thermodynamics of ammonium chloride

J . Phys. Chem. 1990, 94. 7794-7800

7794

Enthalpy of Dilution and the Thermodynamics of NH,Cl(aq) to 523 K and 35 MPa W. E. Thiessen and J. M. Simonson* Chemistry Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (Received: December 12, I9891

Downloaded by UNIV OF NEBRASKA-LINCOLN on September 14, 2015 | http://pubs.acs.org Publication Date: October 1, 1990 | doi: 10.1021/j100383a011

Enthalpies of dilution of NH,Cl(aq) were measured from 6.039 to 0.007 mol-kg-' at temperatures from 298 to 523 K and at pressures near 7.0 and 34.5 MPa. The hydrolysis of aqueous ammonium ion is not negligible over the complete range of conditions investigated here. The measured values have been represented quantitatively with the ion interaction treatment of Pitzer, with explicit consideration of the hydrolysis equilibrium, assuming ideal mixing behavior for aqueous ammonia. Activity and osmotic coefficients and relative apparent enthalpies are tabulated at smooth intervals in pressure, temperature, and composition. The implications of the present results in prediction of ammonium salt volatility at high temperatures are discussed.

Introduction Aqueous ammonium salts have received relatively little attention in recent studies of the thermodynamic properties of electrolytes to high temperatures and pressures. The relatively high volatility of ammonium salts at elevated temperatures makes it difficult to apply techniques in which a vapor phase is present, including direct vapor pressure or isopiestic measurements. Also, the hydrolysis of ammonium ion at high temperature in aqueous solution significantly complicates the quantitative representation of experimental results. The volatility of ammonium salts makes information on their thermodynamic properties at high temperatures of interest in practical applications, including the problem of material transport and solid deposition in all-volatile-treated (ammonia and hydrazine) steam generator systems. Of more basic interest is the thermodynamic behavior of a polyatomic cation of relatively low charge density in aqueous solution at high temperatures. Previous studies of enthalpies of dilution of electrolytes in this have demonstrated the increasing tendency of "strongn electrolytes to form ion pairs at high temperatures; one goal of this study is to investigate the behavior at high temperatures of an electrolyte which might, through electrostatic considerations, be expected to show less ion association than those investigated previously. In the present study the enthalpy of dilution of NH,Cl(aq) is reported from 6.039 to 0.007 mo1.kg-I at temperatures from 298 to 523 K and pressures near 7 and 34.5 MPa. Corrections to the results for hydrolysis of ammonium ion are made, based on the measurements of the ionization of ammonia of Hitch and Mesmer6 and Quist and Marshall,' and the equation for the thermodynamics of ionization of water developed by Marshall and Franck.8 It is found that the observed enthalpies of dilution are consistent with the assumption of an unhydrolyzed, strong electrolyte to 523 K, but that the application of the correction of the results for solute hydrolysis makes it necessary to treat the dilution enthalpies in terms of a weak association to NH,Cl(aq) at the highest temperatures considered here. Experimental Section The equipment and measurement techniques used to measure enthalpies of dilution reported here have been described in detail previously.' I n brief, the calorimeter is a high-temperature ( I ) Busey, R. H.; Holmes, H. F.; Mesmer, R. E. J . Chem. Thermodyn. 1984, 16, 343. (2) Holmes, H. F.; Busey, R. H.; Simonson, J. M.; Mesmer, R. E.; Archer, D. G.; Wood, R. H. J . Chem. Thermodyn. 1987, 19, 863. ( 3 ) Simonson,J. M.; Busey, R. H.; Holmes, H. F.; Mesmer, R. E.; Archer,

D.G.;Wood, R. H. J . Phys. Chem., in press. (4) Simonson. J. M.; Busey, R. H.; Mesmer, R. E. J . Phys. Chem. 1985, 89.. 557. -( 5 ) Simonson, J . M.; Mesmer, R. E.; Rogers, P. S. Z. J . Chem. Them" dyn. 1989, 21, 561. (6) Hitch, B. F.; Mesmer, R. E. J . Solution Chem. 1976, 5 , 667. (7) Quist, A. S.; Marshall, W. L. J . Phys. Chem. 1968, 7 2 , 3122. (8) Marshall, W . L.; Franck, E. U. J . Phys Chem. ReJ Data 1981, IO, 295 ~

0022-3654/90/2094-7794$02.50/0

TABLE I: Densities of NHACl(aa)at 299.65 K m/(mol.kg-')

p(7.0 MPa)

0 0.0442 0.2022 1.014 6.039

0.999 7 1 1.000 39 1.00296 1.01526 1.069 05

p(34.5

MPa)

1.011 67 1.012 39 1.014 88 1.026 69 1.078 8 1

heat-flux instrument (SETARAM) equipped with matched PtPt/Rh thermopiles. Water is delivered against a constant back-pressure of argon from high-pressure positive-displacement pumps (Ruska Instrument Corp.). Solutions are delivered from Teflon isolator bags contained in thermostated high-pressure reservoirs through platinum capillary tubing. The stock (initial) solutions are diluted with water in a platinum capillary heat exchanger located within the calorimeter thermopile. The effluent stream from the sample heat exchanger flowed through a matched reference heat exchanger located in a second thermopile before release to the effluent reservoir to minimize the magnitude of the calorimeter base-line signal; the calorimetric signal is the difference in output voltage of the two thermopiles. The calorimeter was electrically calibrated at two total flow rates at each temperature with a small heater located near the mixing region of the sample heat exchanger. A stock solution of NH,Cl(aq) was prepared from reagent grade crystalline material (EM Science) and diluted by mass with degassed, deionized water to the desired initial solution molalities. All stock solutions were stored under argon. Initial solution molalities were determined gravimetrically to be 6.039, 1.014, 0.2022, and 0.0442 mol-kg-' by precipitation as AgCI. Values of the density of the four stock solutions used were needed to calculate final molalities of the diluted solutions and the enthalpy of dilution as detailed below. As reliable values of the density of NH,Cl(aq) are not available at elevated pressures, these densities were measured with a vibrating-tube densimeter (Mettler-Paar Model 502) at 299.65 K and 0.6, 6.9, 19.8, and 34.8 MPa. Water and 5.505 mol-kg-' NaCl(aq) were used to calibrate the densimeter; the density of water at experimental conditions was calculated from the equation of state of Haar, Gallagher, and Ke11,9 and that for NaCl(aq) was calculated from the equations of Rogers and Pitzer.Io Measured densities for the stock solutions are listed in Table 1.

Results Initial and final solution molalities and enthalpies of dilution of NH,Cl(aq) at temperatures from 298 to 523 and at pressures near 7.0 and 34.5 MPa are listed in Table 11. The dilution enthalpies were calculated from the observed calorimetric signal with the relation (9) Haar, L.; Gallagher, J. S.; Kell, G. S. NBSINRC Steam Tables; Hemisphere: Washington, DC, 1984. ( I O ) Rogers, P. S. 2.; Pitzer, K. S. J . Phys. Chem. Rex Data 1982, I I , 15.

0 1990 American Chemical Society

The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 7795

Thermodynamics of NH4Cl(aq)


TABLE 11: Enthalpies of Dilution of NH,Cl(aq) TIK DIMPa m; tnr

TI K

R/MPa

7.36 7.36 7.36 7.36 7.34 7.36 7.36 7.36

6.039 6.039 6.039 1.014 1.014 1.014 0.2022 0.2022

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007 0.0335

-9 1.6 -136.1 -186.8 19.7 42.3 211.4 102.9 235.8

297.96 297.97 297.98 297.96 297.97 297.98 297.96

7.36 7.36 7.36 7.36 7.36 7.36 7.34

6.039 6.039 6.039 1.014 1.014 1.014 0.2022

mr 2.699 1.738 0.8404 0.4975 0.3296 0.1638 0.1007

-G;,H,

297.97 297.98 297.96 297.97 297.96 298. I4 297.96 297.98 320.38 320.40 320.40 320.43 320.40 320.40 320.43

7.05 7.05 7.02 6.92 7.05 7.02 6.90

6.039 6.039 6.039 6.039 1.014 1.014 1.014

4.841 2.699 1.738 0.8404 0.4975 0.3296 0.1638

112.7 352.8 501.6 727.4 228.2 322.2 507.8

320.40 320.43 320.38 320.40 320.43 320.38 320.43

7.02 6.92 7.05 7.02 6.92 7.05 6.92

6.039 6.039 6.039 1.014 1.014 1.014 0.2022

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007

226.3 353.1 718.3 132.9 218.2 579.2 171.5

344.47 344.41 344.50 344.46 344.4 I 344.50 344.46 344.46

6.88 6.90 6.84 6.92 6.90 6.84 6.92 6.92

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022

4.841 2.699 1.738 0.8404 0.4975 0.3296 0.1638 0.0335

263.0 823.9 1 I67 1610 405.5 597.1 865.8 627.2

344.50 344.35 344.47 344.50 344.35 344.47 344.41

6.84 7.01 6.88 6.84 7.01 6.88 6.90

6.039 6.039 6.039 1.014 1.014 1.014 0.2022

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007

536.4 826.1 1615 254.8 403.9 873.8 250.6

371.33 371.37 37 1.29 371.32 371.37 37 I .29 371.32 37 1.33 371.31 371.31 371.33 371.31

7.03 7.02 6.98 6.97 7.02 6.98 6.97 7.03 34.7 I 34.7 1 34.61 34.61

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022 6.039 6.039 1.014 0.2022

4.841 2.699 1.738 0.8404 0.4975 0.3296 0.1638 0.0335 3.727 1.734 0.4974 0.0335

431.7 1358 1920 2620 631.2 942.8 1360 888.9 837.4 1839 604.2 803.7

37 1.29 371.32 371.33 371.29 371.32 371.33 371.37 371.32 371.33 37 1.33 371.33

6.98 6.97 7.03 6.98 6.97 7.03 7.02 6.97 34.61 34.61 34.61

6.039 6.039 6.039 1.014 1.014 1.014 0.2022 0.2022 6.039 6.039 1.014

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007 0.0335 2.695 0.8377 0.1637

873.2 1361 2657 400.5 642.1 1360 438.9 907.8 1297 2530 1268

422.38 422.54 422.46 422.39 422.5 I 422.39 422.38 422.54 422.41 422.41 422.42 422.42

7.01 7.03 7.07 7.08 6.99 7.08 7.01 7.03 34.28 34.28 34.17 34.17

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022 6.039 6.039 1.014 0.2022

4.841 2.699 1.738 0.8404 0.6675 0.4975 0.1638 0. I007 3.727 1.734 0.4973 0.0335

778.5 2529 3623 51 I5 787.8 1208 2582 743 1516 3392 1106 I404

422.46 422.39 422.38 422.46 422.54 422.51 422.39 422.46 422.42 422.42 422.42

7.07 7.08 7.01 7.07 7.03 6.99 7.08 7.07 34.17 34.17 34.17

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022 6.039 6.039 1.014

3.731 2.699 0.8404 0.8404 0.4975 0.3296 0.1638 0.0335 2.695 0.8377 0.1637

1661 2515 5053 5182 1250 1746 2604 1621 226 1 4719 2309

472.80 472.84 472.8 1 472.80 472.84 472.8 I 472.81 472.80 472.85 472.85 472.8 1 472.8 1

7.12 7.17 7.08 7.12 7.17 7.08 7.08 7.12 34.48 34.48 34.44 34.44

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022 6.039 6.039 1.014 0.2022

4.841 2.699 1.738 0.8404 0.4975 0.3296 0.1638 0.0335 3.727 1.734 0.4974 0.0335

1226 41 22 5831 8545 2089 3067 4546 2843 1476 5541 1979 2577

472.81 472.80 472.84 472.81 472.80 472.80 472.84 472.8 1 472.81 472.81 472.81

7.08 7.12 7.17 7.08 7.12 7.12 7.17 7.08 34.44 34.44 34.44

6.039 6.039 6.039 1.014 1.014 1.014 0.2022 0.2022 6.039 6.039 1.014

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007 0.0335 2.695 0.8377 0.1637

2576 4121 8267 1273 2093 4546 1289 2806 4113 7744 3987

523.30 523.28 523.28 523.27 523.28 523.30 523.27 523.30 523.28 523.32 523.32 523.3 I 523.3 I

7.10 7.10 7.10

6.039 6.039 6.039 6.039 1.014 1.014 1.014 0.2022 0.0442 6.039 6.039 1.014 0.2022

4.841 2.699 1.738 0.8404 0.4975 0.3296 0.1638 0.0335 0.0221 3.727 1.734 0.4975 0.0335

1872 6706 10215 14610 4048 6246 8796 5622 1214 3608 8516 3230 4701

523.28 523.27 523.30 523.30 523.27 523.30 523.28 523.27 523.28 523.31 523.31 523.31

7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.24 34.24 34.24 34.24

6.039 6.039 6.039 1.014 1.014 1.014 0.2022 0.2022 0.0442 6.039 6.039 1.014

3.731 2.699 0.8404 0.6675 0.4975 0.1638 0.1007 0.0335 0.0074 2.695 0.8377 0.1638

4140 6710 14457 2589 400 1 8866 2576 5550 2950 5785 12187 7102

7.10

7.10 7.10 7.10 7.10 7.24 34.23 34.23 34.24 34.24

-&dim

m;

-132.9 -1 76.5 -186.0 77.5 126.8 198.2 85.7

7796 The Journal of Physical Chemistry, Vol. 94, No. 20, 1990 (l) AdilHm = A c / C i p f F In eq 1, A6 is the observed electrical signal, Ciis the number of moles of NH,Cl(aq) per kilogram of stock solution,f, is the stock solution flow rate, F is the electrically determined calibration factor, and p is the solution density at the temperature and pressure of the reservoir vessels. All final molalities given in Table 11 are calculated for stoichiometric NH,Cl(aq); that is, the hydrolysis of ammonium ion NH,+(aq) = NH3(aq) + H+(aq) (2) has been neglected. The tabulated AdilHmare differences i n effective apparent molar enthalpies L,e at final and initial molalities m f and m,


AdilHm = L,’(mf) - L@e(mi)

2mNH,mCI[BNH4CI

+ zcNH&il

-P = ( - A , / b ) [ b l l / z / ( l + b I ’ / z )+ 2 In (1 + b l i / z ) ] (14) The relative enthalpy is related to the temperature derivative of the excess Gibbs free energy through -L/ (n,RTZ) = d [Gex/(nwRT )] /a T

+ (4)

where

+ b1’I2) In eq 5, b = 1.2, I is the ionic strength, Z = ?nH + “HI, f(r) = -(41A,/b) In (1

(5)

and A, is the limiting slope for the osmotic coefficient as defined by Bradley and Pitzer.’, The mixing parameters 8 and are covariant with the unknown values of BNH4Ci and CNH4Ci and have been set equal to zero at all temperatures in this work. The second virial coefficients B, are dependent on ionic strength

+

B,, = 0): + p g g ( a l I q + pgg(azI’/2) g(x) = 2[ 1 - ( 1 + x) exp(-x)] / x 2

(6) (7)

where a l = 2.0 and cuz = 8.0 independent of temperature and pressure; this extension of the usual Pitzer treatment for strong electrolytes is the same as that used for NaOH (as) by Simonson et aL5 In expressions for the activity coefficient of a component in a mixed electrolyte solution the following definition of B i a is useful:

+ P$f’g’(az1’/2)]/I + x + x2/2) exp(-x)] /xz

Wca = [ p g ) g ’ ( c u p )

The apparent molar enthalpy L, for the hypothetical unhydrolyzed NH,Cl(aq), based on the reference state of NH,+(aq) and Cl-(aq) at infinite dilution, includes only those terms of eq 15 for NH,Cl(aq). The effective apparent molar enthalpy L,e includes contributions from the enthalpy of dilution of all ionic species in their equilibrium ratios and the enthalpy of hydrolysis of N H,CI( aq): LGe=

(8) (9)

+ p:fr) exp(-cu2P/2) +

+ mNH4mCI(B’NH4CI + Z c N H 4 C I ) I (12)

and for the mean ionic activity coefficient In

=f’

+ ~ N H ~ ( B N+HZCNH,CJ ~CI + ~~(BH +C ZCHCI) I + ~CI[~NH,(B’NH,CI +C

YNH~CI

mH(B’HCl

+cHCl)l

+ ZCLHCll + mNH4[BLNH4CI + zcLNH,CIIt

Due to the contribution from the hydrolysis equilibrium and the reference state of L, = 0 for NH,Cl(aq) at m = 0, the intercept is nonzero for L,e at m = 0. Values are needed for the equilibrium constant for eq 2, and for the activity coefficients of the ionic species at the experimental conditions, to calculate equilibrium molalities of all species present. Hitch and Mesmer6 and Quist and Marshall’ report values of K for the ionization of ammonia NH3(aq)

N H , ~+ + mCl(BNH,CI + zCNH,Cl) (13)

log K = k1

(17)

+ k , / T + k 3 / P + k 4 / T 3 + log p(k5 + k , / T ) (18)

This form was originally applied to the full range of results to 1073 K by Mesmer et a k i 5 application of eq 18 over the more limited temperature range considered here gives a slightly more precise representation of K in the temperature range of interest. Values of the parameters ki are listed in Table 111. The equilibrium constant for the hydrolysis reaction (eq 2) was calculated from eq 18 by using values for the ionization of water taken from Marshall and Franck.* Equilibrium molalities were calculated from =

(~NH3mH/mNH,)(rHClz/rNH4Clz)

(19)

where it has been assumed that yNH,= 1. In terms of the parameters of eq 13 the ratio of the activity coefficients is

In

(YHCI/YNH4CI)

=

mCl[BHCl

-

BNH4Cl

+ mCI(CHCl - CNH,CI)I (20)

Parameters for HCl(aq) were taken from model I of Holmes et aL2 At very low molalities, the hydrolysis is buffered by the ionization of water HzO = H+(aq) + OH-(aq) KW =

Pitzer, K. S. J. Phys. Chem. 1973, 77, 268. (12) Pitzer, K. S.; Kim, J. J. J. Am. Chem. SOC.1974, 96, 5701. (13) Peiper, J. C.; Pitzer, K. S . J. Chem. Thermodyn. 1982, 14, 613. (14)Bradley, D.J.: Pitzer. K . S. J . P h y s . Chem. 1979. 83, 1599.

+ HzO = NH4+ + OH-

from 273 to 1073 K. The values of K below 773 K were represented with the expression

KH

(10) (1 1)

2~Z,Za~~~~C,,

Then in the particular case of interest here 4 - 1 = (2/&i)[-A,$13/Z/( 1 + bIi12)+ mHmcl(B’HC1 zcmHCl)

+ ( A L / ~In) (1 + b1’/’) -

(”H,/n?,-l)Argm

2RTZ1mH[BLHCI

For the osmotic coefficient, Cca@ =

(15)

(16)

+mHmNH4[28H.NH4

Bca, = pit) + pi!) exp(-a,l’/z)

~~

The expression for the activity coefficient for HCl(aq) in the mixed solution is the same as eq 13 with the parameters for HCI substituted in the last term on the right hand side. In eq 13

+ ZCHCll + mCI+H.NH,.CII

g’(x) = -2[ 1 - ( 1

TABLE 111: Values of the Parameters of Ea 18 i k, I k, 1 -5.94455 4 6.84111 X IO’ 2 1993.64 5 2.18971 3 -7 I4031 X IOs 6 8226.45

(3)

The relation between Lde and the apparent molar enthalpy L, is described in more detail below. The explicit consideration of reaction 2 in the analysis forces the application of treatments appropriate for mixed electrolytes. The ion interaction treatment developed by Pitzer,” and applied to mixed electrolytes by Pitzer and Kim,Iz has been shown to be applicable to dilution enthalpies of reacting systems by Peiper and PitzerI3 and by Simonson et al.3 Neglecting the contribution of the low levels of electrically neutral NH3(aq) present in these solutions to the excess thermodynamic properties, the excess Gibbs free energy may be written as

G C X / ( n w R T=) f(1) + 2mHmCl[BHCl

Thiessen and Simonson

Z

MHmOHYHCI’YNH4OH /YNH,C?

(21 1 (22)

( 1 1)

( 1 5 ) Mesmer, R. E.; Marshall, W. L.; Palmer, D. A,; Simonson, J. M.; Holmes, H. F.J . Solution Chem. 1988, 17, 699.

Thermodynamics of NH,Cl(aq)


II

1

0

I -1

h

7-

: e

-2

-7

-3

@Q-

d -4

-5

~

-6


0.0

0.5

LO

1.5

2.5

2.0

Im/(mol.kg-')iy2

Figure 1. Enthalpies of dilution of NHaCl(aq) near 7.0 MPa: 0, 298.0 K; A, 320.4 K; 0,344.5 K; V, 371.4 K; 0 , 422.5 K; 0 , 472.8 K;

K - Curves calcuiated from eq 16. This ratio of activity coefficients has been approximated here by yNHICI2, as the values of the hydroxide activity coefficients are not known as functions of temperature. Values of the parameters of eq 16 needed to represent the measured enthalpies of dilution were obtained by an iterative least-squares fit of the results of Table 11. Values of the osmotic coefficient for NH4Cl(aq) at 298.15 K and saturation vapor pressure were taken from Wishaw and Stokes;I6 reference values of I$ at 7.0 MPa were calculated from those results by using the appropriate relation from Rogers and PitzerIo and a pressure coefficient for the parameter @& cI determined through fits of the apparent molar volume at 298.13 K calculated from the density equation of Novotny and Sohne1.I' It should be noted that only the pC0) parameter was found to depend on pressure in fits of the density data to 6.0 mol-kg-I. Reference values of @(O), @ ( I ) , and 0'at 298.15 K and 7.0 MPa were determined by fitting to the corrected isopiestic results. The dilution enthalpy results were then treated as a function of temperature at 7.0 MPa, with the necessary values of the free-energy parameters calculated at the temperature of interest by integration of the empirically chosen form of the enthalpy parameters. I n a preliminary analysis of the enthalpy results in which the hydrolysis of NH4+(aq)was neglected, it was found that the data of Table I1 were consistent with the assumption of complete dissociation of the solute at all temperatures to 523 K. However, the inclusion of the hydrolysis correction resulted in poor fits to the experimental values at the highest temperatures, with the measured dilution enthalpies more exothermic than the calculated values. Assuming that this deviation is due to the onset of ion association at the highest temperatures considered here, an additional term in p(*)for NH4Cl(aq) was used to more accurately represent the observed enthalpies. As in a previous study on NaOH(aq),5 it was considered desirable that @(2) and its temperature derivatives be negligibly small over a wide range in temperature, with a finite contribution from this term at the highest temperatures. The temperature dependence of @(2) developed in the earlier work5 is again adopted here

.,

523.3

separately from those near 34.5 MPa, following the assignment of reference values of the free-energy parameters at 298.1 5 K and 7.0 MPa as described above. The temperature-invariant parameters of this fit were taken as input to a fit of the dilution enthal ies near 34.5 MPa. In this latter fit, it was found that only /3fi[,cl is dependent on pressure over the temperature range of this study. It was assumed that a@(O)/r3pis independent of pressure over the range considered here. Values of a @ ( o ) / ~and p a2@(o)/r3p r3T near 298.15 K calculated from the representation of volumetric properties given by Novotny and Sohnel" were used to constrain the values of the pressure coefficients of the enthalpy of dilution near 298.15 K and to calculate the corresponding pressure dependence of the free-energy parameters. The form chosen for the @(O), @ ( l ) , and CY parameters is

f(T)= ql + q2 In T + q,T + q4p+ q 5 / ( T- 227) + q6/(648 71 + (P -pr)[q7 + 9s In T + q9T+ 41071 + 411/(648 - 771 (24) where pr = 7.0 MPa. Values of the parameters of eq 24 are listed in Table IV. Values of the activity and osmotic coefficients, the contribution of the hydrolysis of ammonium ion to the relative apparent enthalpy A,H,, and the relative apparent enthalpy are listed in Table V at regular intervals of temperature and molality at saturation pressure and 35.0 MPa. The quality of the fit of eq 26 to the measured enthalpies near 7.0 MPa is illustrated in Figure 1, where the observed and fitted dilution enthalpies are shown as functions of the square root of the final stoichiometric molality. Observed and calculated values of the pressure coeffficient of the enthalpy of dilution, jA(AL+e)]/Ap, are plotted against the square root of the final stoichiometric molality in Figure 2.

As in the case of NaOH(aq), zl = -0.195 54, z2 = -7.4581 X z3 = 4.534, and z4 = 3.505 X only zo = -171.41 was determined by fitting to the results of this study. In order to remove the complication of an explicit dependence of the parameters on pressure, the results near 7.0 MPa were fitted

Discussion It is often the case that a large body of experimental results for a particular aqueous electrolyte can be brought together in a consistent analysis over wide ranges of temperature, pressure, and composition. Unfortunately, the available data for NH4Cl(aq) are limited, both in scope and in apparent precision. The most direct comparison of the results of the present study with values available in the literature is with the enthalpies of solution of NH4CI reported over a range of molalities at 0.1 MPa and 298.15, 323.15, and 348.1 5 K by Mishchenko and Ponomareva.18 These authors also report specific heat capacities over the same tem-

(16) Wishaw, B. F.; Stokes, R. H . Trans. Faraday SOC.1953, 49, 27. (17) Novotny. P.; Sohnel, 0. J . Chem. Eng. Data 1988, 33, 49.

(18) Mishchenko, K . P.; Ponomareva, A. M. J . Gen. Chem. USSR 1956, 26, 1465.

p(2)= zolzl + z2T + z , / T

+ z4 In T + 1/(647

- T)]

(23)

Thiessen and Simonson

7798 The Journal of Physical Chemistry, Vol. 94, No. 20, I990 TABLE IV: Values of the Parameters of Eq 24 4.

8‘1) 613.399 -1.42555 1093.95

B(0)

-929.689 2.20237 -1033.06 5.49192 -91.5057

1

c“

I

I

!

I

1.0

1.5

I

I

-2.19772 -1.41 416 0.8

9.09242 2.12221

4.88766 -1.09552 5.61713 -3.628 17 1.93572

+

0.6

0.4 200

l75


n

0.2

7-

:

-

0.0

0.5

2.0

2.5

{m/(rnol+kg-1){v2

150

Figure 3. Activity coefficients of NH,Cl(aq) calculated from eq 13 (solid curves),NaCl(aq), from ref 22 (chain-dashed curves), and KCl(aq), from ref 23 (dashed curves), at saturation pressure and 298.15 K (upper set) and 523.15 K (lower set).

125

4

.3 2 too 2 75

50

25

0

0.0

0.5

1.0

1.5 -1 r/2

2.0

2.5

I

lm/(mol*kg Figure 2. Pressure coefficients of the enthalpy of dilution of NH,Cl(aq): V, 371.4 K; 0 , 4 2 2 . 5 K; 0, 472.8 K; 0,523.3 K. Curves calculated from the pressure derivative of eq 16.

perature range. There is some inconsistency between Mishchenko and Ponomareva’s enthalpy measurements as functions of temperature and their reported specific heat capacities: however, the disagreement is not large in comparison with the experimental uncertainties in the two sets of measurements. Calculated values of L; from the equations of this work are in good agreement with those calculated from the enthalpies of solution given by Mishchenko and Ponomareva at 323.15 K and 0.1 MPa: less satisfactory agreement is observed at 298.1 5 K, where 15: of the present work are systematically higher by as much as 200 J-mol-’ at molalities near 1.0 mol-kg-I. The results of Mishchenko and Ponamareva are badly scattered at 348.15 K, indicating some difficulty in measuring enthalpies of solution with their apparatus at this temperature. Enthalpies of dilution of NH,Cl(aq) and of substituted methylammonium chlorides were measured to very low dilutions at 298.15 K and 0.1 MPa by Streeck.I9 Direct comparison of the measured bilHmat molalities to the minimum studied by Streeck mo1.kg-l) with values calculated with the present (1.9 X equations gives unacceptably poor agreement: the measured values at very low molalities do not show the upward concave trend with m’i2predicted by the fit equations, and the limiting dependence of the measured values on m1I2at the lowest experimental molalities does not approach the theoretical limiting slope. Doehlemann and LangeZ0showed that significant corrections were introduced into the results of Streeck if i t is assumed that the (19) Streeck, H. 2.Phys. Chem. A 1934, 169, 103. (20) Doehlemann, E.; Lange. E. Z . Phys. Chem A 1934. 170. 391

dilution water is contaminated with small amounts of protolytic impurity. Using the value of the equilibrium constant for the first ionization of carbonic acid from Patterson, Slocum, Busey, and Mesmer,2’ KI = 4.477 X lo-’, and solving for the degree of hydrolysis of NH,+(aq) on the assumption of 10” mo1.kg-l C02(aq) present in the dilution water gives values of AdilHm at low molalities in good agreement with those reported by Streeck. It should be noted that this calculation i s very sensitive to the level of assumed contamination; if C02(aq) is assumed present at the 0.1 MPa atmospheric saturation value ( mol.kg-l), the calculated L,e remain concave down with m i l 2 , in qualitative agreement with the observed values, but the slope with m 1 i 2is significantly steeper than the measured values over the molality range of interest. Due to the uncertain assumptions involved in calculating enthalpies based on a low level of protolytic contamination, no attempt has been made to include a quantitative representation of the results of StreeckI9 in the analysis reported here. N o measured values of activity or osmotic coefficients at elevated temperatures are available for NH,Cl(aq). Activity coefficients at saturation pressure calculated from the results of this study at 298.1 5 and 523.15 K are compared in Figure 3 with values for NaCl(aq) taken from Pitzer, Peiper, and Busey22and for KCl(aq) as tabulated by Holmes and M e ~ m e r .At ~ ~298.15 K, -y(KCI) is nearly equal to -y(NH,CI), with y(NaCI) significantly higher at high molalities. This comparative behavior is consistent with the assignment of the primary differences in y to differences in cation size, as discussed for the alkali metal chlorides by Holmes and Mesmer.23 At 523.15 K, while the relative trend in y (NaCI > KCI > NH,CI) is maintained, y(KCI) is a significantly poorer model for -y(NH,CI) than at 298.15 K. The low levels of ion association assumed for NH,Cl(aq) at 523.15 K, implicit in the use of the @c2) term to describe the dilution enthalpy results at high temperature, are not large enough to give the lowered values of y relative to KCl(aq) observed at this temperature. Holmes and M e ~ m e showed r ~ ~ that the osmotic coefficients of the alkali metal chlorides could be represented with fair accuracy with an extended Debye-Huckel limiting law expression in which (21) Patterson, C. S.; Slocum, G. H.; Busey, R. H.; Mesmer, R. E. Georhim. Cosmochim. Acra 1982, 46, 1653. (22) Pitzer, K . S.; Peiper, J. C.; Busey, R. H . J . Phys. Chem. Ref. Data 1984, 13, I . (23) Holmes, H. F.; Mesmer, R. E. J . Phys. Chem. 1983, 87, 1242.


Thermodynamics of NH,Cl(aq) TABLE V: Thermodynamic Properties of NH,Cl(aq)

P = Psst

m.t

Q

Y

4H

0.01 0.10 0.50 1 .oo 2.00 4.00 6.00

0.967 0.925 0.899 0.897 0.910 0.945 0.970

0.901 0.766 0.646 0.600 0.568 0.559 0.563

0.01 0.10 0.50

0.966 0.922 0.895 0.894 0.908 0.944 0.966

0.013 0.004 0.002 0.001 0.001 0.000 0.000

LA' 298.15 K 0.189 0.443 0.667 0.717 0.687 0.544 0.441

0.968 0.927 0.902 0.901 0.916 0.954 0.981

0.902 0.770 0.652 0.609 0.579 0.574 0.582

0.012 0.004 0.002 0.001 0.001 0.000 0.000

0.180 0.427 0.669 0.757 0.816 0.865 0.962

0.896 0.757 0.635 0.589 0.557 0.548 0.550

0.028 0.009 0.004 0.002 0.002 0.001 0.001

323.15 K 0.290 0.693 1.165 1.397 1.638 1.900 2.115

0.966 0.924 0.898 0.898 0.912 0.948 0.970

0.898 0.761 0.64 1 0.597 0.566 0.558 0.561

0.027 0.008 0.003 0.002 0.001 0.001 0.000

0.274 0.655 1.110 1.349 1.622 1.973 2.288

2.00 4.00 6.00

0.961 0.913 0.88 1 0.878 0.889 0.917 0.931

0.884 0.732 0.599 0.549 0.51 1 0.492 0.483

0.102 0.032 0.014 0.009 0.006 0.003 0.002

373.15 K 0.605 1.390 2.469 3.106 3.891 4.91 1 5.701

0.962 0.915 0.885 0.882 0.893 0.921 0.933

0.887 0.738 0.608 0.559 0.522 0.503 0.494

0.098 0.03 1 0.013 0.009 0.006 0.003 0.002

0.562 1.277 2.255 2.832 3.541 4.488 5.229

0.01 0.10 0.50 I .oo 2.00 4.00 6.00

0.956 0.899 0.859 0.851 0.855 0.872 0.873

0.868 0.697 0.550 0.493 0.446 0.413 0.393

0.28 1 0.088 0.038 0.025 0.017 0.010 0.007

423.15 K 1.174 2.543 4.548 5.759 7.262 9.185 10.065

0.957 0.903 0.865 0.858 0.862 0.879 0.880

0.872 0.706 0.563 0.507 0.462 0.429 0.409

0.270 0.085 0.036 0.024 0.01 6 0.009 0.007

1.068 2.266 4.026 5.092 6.427 8.162 9.467

0.01 0.10 0.50

0.948 0.879 0.827 0.8 12 0.807 0.81 1 0.802

0.846 0.651 0.487 0.423 0.368 0.324 0.297

0.6 17 0.195 0.085 0.058 0.039 0.024 0.017

473.15 K 2.200 4.613 8.212 10.363 12.983 16.195 18.419

0.950 0.886 0.838 0.824 0.8 19 0.823 0.812

0.852 0.656 0.506 0.444 0.390 0.346 0.3 18

0.595 0.187 0.08 1 0.055 0.036 0.023 0.016

1.934 3.918 6.925 8.745 11.014 13.900 15.980

0.936 0.850 0.782 0.757 0.740 0.732 0.7 I6

0.814 0.588 0.407 0.338 0.279 0.23 1 0.203

1.118 0.356 0.159 0.1 1 1 0.076 0.050 0.037

523.15 K 4.134 8.941 15.855 19.878 24.651 30.197 33.727

0.940 0.861 0.800 0.778 0.762 0.751 0.731

0.826 0.61 1 0.437 0.369 0.309 0.258 0.228

1.076 0.341 0.150 0.104 0.070 0.046 0.034

3.405 6.989 12.223 15.304 19.065 23.644 26.714

1 .oo

2.00 4.00 6.00 Downloaded by UNIV OF NEBRASKA-LINCOLN on September 14, 2015 | http://pubs.acs.org Publication Date: October 1, 1990 | doi: 10.1021/j100383a011

6

p = 35.0 MPa Y AJI

0.01 0.10 0.50 1

.oo

1 .oo

2.00 4.00 6.00

0.0 1 0.10 0.50 1

.oo

2.00 4.00 6.00

the hydrated ion-size parameter was the only parameter adjusted. They calculated effective ionic radii r which varied with temperature and cation type, following the pattern rLiCl> rNaCl> rKcl > rGClat all temperatures. As the activity and osmotic coefficients at high temperature calculated here for NH,Cl(aq) lie below those for the alkali metal chlorides, rNH,Cl is smaller, in this model, than the corresponding radii of the other chlorides. It can be argued that the smaller hydrated radius of NH,+(aq) must reflect weaker hydration of NH,+(aq) compared with K+(aq), although the implications of this assumed weaker hydration of NH,Cl(aq) for ion pairing at high temperatures are unclear. Mesmer et aI.l5 have shown that the ion-pairing reaction at high temperatures is driven by entropy considerations, with waters of hydration released to the bulk due to the charge neutralization of ion-pair formation. Assuming that water is less strongly bound to ammonium ion than to any of the alkali metal ions, the net entropy increase should be less for formation of the NH,Cl(aq) ion pair than for the corresponding alkali metal salts, with a correspondingly lower association constant for the reaction. The approximate ion-pairing parameter p(2)was required for an improved fit of the results of this study at high temperatures and low molalities, although the

LAe

value of the parameter is not large; none of the alkali metal chlorides were found by Holmes and MesmerI5 or by Pitzer, Peiper, and BuseyZZto require this parameter for satisfactory representation of the results in the temperature range considered here. As the values of the p(2)parameter are small and noting that relatively small errors in the thermodynamic quantities for the hydrolysis reaction could change significantly the values of the hydrolysis contribution to the observed enthalpy at low molalities and high temperature, an explicit treatment of the present results on the basis of the assumed formation of ion pairs is not warranted. Volatility of ammonium salts has been proposed as a mechanism for the transport of anions in all-volatile-treated steam generators. If it is assumed that the salt partitions to the vapor phase as ion pairs and given the very low levels of ion pairing of NH4Cl(aq) implied by the present measurements, it seems unlikely that the transport of anions would be enhanced significantly in NH,Cl(aq) over other simple chloride salts. On the other hand, if the partition of the solute to the vapor phase occurs as simultaneous volatilization of NH,(aq) and HCl(aq), both of which are known to be quite volatile and to exist in solution through the hydrolysis

J . Phys. Chem. 1990,94, 7800-7805

7800

equilibrium, then the transport of chloride could be enhanced significantly over that observed for alkali metal chloride solutions at comparable temperatures and molalities. Acknowledgment. This research was sponsored by the Division

of Chemical Sciences, Office of Basic Energy Sciences of the U.S. Department of Energy, under Contract DE-AC05-840R2 1400 with Martin Marietta Energy Systems, Inc. Registry No. NH,CI, 12125-02-9.

Isopiestic Studles of Aqueous Solutions at Elevated Temperatures. 10. {(l - y)NaCI yCsCI](aq)+

+

H. F. Holmes* and R. E. Mesmer


Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (Received: December 18, 1989)

The mixed electrolyte system I( 1 - y)NaCI + yCsClJ(aq) has been studied with the isopiestic technique over the temperature range 383.19-523.17 K. NaCl(aq) served as the reference electrolyte. The ion-interactionmodel, as applied to mixed electrolytes, gave an excellent description of the experimental results, requiring only a binary mixing parameter in addition to the pure electrolyte properties. As with previously studied mixtures of the alkali metal chlorides, the excess thermodynamic properties are relatively simple in that the mixing parameter is a linear function of reciprocal temperature. Relative behavior of the alkali metal chloride mixtures is independent of temperatures over the range of 298-523 K. All of the results are qualitatively consistent with the relative strength of the cation-water interaction involved.

Introduction Trends in the properties of mixed electrolyte systems are best determined from studies of ternary common-ion mixtures, e.g., two cations with a single anion. Previous work with ((1 - y)NaCl yKCIJ(aq)lJ and {(1 - y)NaCI yLiCl)(aq)3-Shas demonstrated that mixing contributions have the opposite temperature dependence in these two systems with mixing effects for Na-K being more important at low temperatures and for Na-Li at high temperatures. In terms of size, Li’ is smaller than Na+ while K+ is larger than Na+ and the hydration energies have an inverse correlation with ion size. It thus seemed desirable to include [( 1 - y)NaCl + yCsCl)(aq) in our studies of mixtures of alkali metal cations. Additional support for the present study comes from the fact that cesium is an important fission product of nuclear fuel and the properties of its water-soluble compounds are of considerable interest in studies related to waste disposal and for reprocessing of spent nuclear fuel. Analysis and interpretation of experimental results for mixed-electrolyte systems generally require the thermodynamic properties of the pure components at the same ionic strength as the mixture. In the case of NaCl(aq), the required quantities were calculated from the formulation of Pitzer, Peiper, and Busey.6 Our mathematical model’ was used to compute the thermodynamic properties of CsCl(aq). There are three ~ t u d i e s ~ of - * the .~ present system at 298.1 5 K which are available for comparison with our results at elevated temperatures.

+

+

Experimental Section Description of the O R N L high-temperature isopiestic facility and subsequent minor modifications have appeared in previous p u b l i c a t i ~ n s ~I ~from ~ * ~this ~ J laboratory. The present set of results were obtained in conjunction with those for { ( I - y)NaCl yLiCl(aq)l,3 using the same NaCl(aq) reference solutions. CsCl used in these experiments was the same ‘ultrapure” sample used in the earlier studyI2 of pure CsCl(aq). In essence, the experiment consists of determining, by means of in situ weighting, the molalities of solutions which are in isopiestic equilibrium at constant temperature and pressure.

+

‘This paper is dedicated to Professor Kenneth S . Pitzer on the occasion of his 75th birthday.

0022-3654f9Qf 2094-78Q0$02.50f Q

Results and Discussion Equilibrium isopiestic molalities of the reference solution NaCl(aq) and of the compositions of {(1 - y)NaCl + CsCIJ(aq) used in the present work are listed in Table I. At temperatures greater than 473 K, molalities for the composition y = 0.5518 were, for an unknown reason, clearly not compatible with the other results and were excluded from further consideration. The last digit of most of the molalities listed in Table I is not significant and is given for consistency. Accuracy of the results in Table I is estimated to be about 0.2% based on our operating experience. Osmotic coefficients 4 were computed from the isopiestic molalities of Table I by means of the relation 4 x = ~ ~ ( ~ , ) s / X ( ~ , ) x=1R4s 4s I

(1)

I

where mi is the molality of ion i, R is the frequently used isopiestic ratio, and subscripts s and x refer respectively to the standard solution and the solution whose properties are unknown. The model of Pitzer, Peiper, and Busey6 was used to calculate osmotic coefficients of the standard solutions, NaCl(aq) in the present case. We have selected, as in the case of ((1 - y ) yLiCl)(aq)3and also with earlier work,’ the ion-interaction model of Pitzer et al.’3J4

+

(1) Holmes, H. F.; Baes, C. F., Jr.; Mesmer, R. E. J . Chem. Thermodyn. 1979, 11, 1035. (2) Robinson, R. A. J . Phys. Chem. 1961, 65, 651-662. (3) Holmes, H. F.; Mesmer, R. E. J . Chem. Thermodyn. 1988, 20, 1049. (4) Robinson, R. A.; Wood, R. H.; Reilly, P. J. J. Chem. Thermodyn. 1971, 3, 461. ( 5 ) Kirgintsev, A . N.; Luk’yanov, A. V . Russ. J . Phys. Chem. 1963, 37, 1501. (6) Pitzer, K. S.; Peiper, J. C.; Busey, R. H. J . Phys. Chem. Ref. Data 1984, 13, 1. (7) Holmes, H. F.; Mesmer, R. E. J . Phys. Chem. 1983, 87, 1242. (8) Robinson, R. A. J . Am. Chem. SOC.1952, 74, 6035. (9) Rard, J. A.; Miller, D. G. J . Chem. Eng. Data 1982, 27, 169. (IO) Braunstein, H.;Braunstein, J. J . Chem. Thermodyn. 1971, 3, 419. ( 1 I ) Holmes, H. F.; Baes, C. F., Jr.; Mesmer, R. E. J . Chem. Thermodyn. 1978, IO, 983. (12) Holmes, H. F.; Mesmer, R. E. J. Chem. Thermodyn. 1981,13, 1035. ( 1 3) Pitzer, K. S. J . Phys. Chem. 1973, 77, 268. (14) Pitzer, K. S.; Kim, J . J. J . Am. Chem. SOC.1973, 96, 5701.

0 1990 American Chemical Society

Enthalpy of dilution and the thermodynamics of ammonium chloride

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