Journal of Solution Chemistry, Vol. 21, No. 8, 1992

Thermodynamic Quantities for the Ionization of Nitric Acid in Aqueous Solution from 250 to 319~ 1 J. L. Oscarson, 2 S. E. Gillespie, 2 R. M. Izatt, 2 X. Chen, 2 and C. Pando 3 Received March 2, 1992 The aqueous reaction, HNOa(aq) = H § + NO~ was studied as a function o f ionic strength I at 250, 275, 300 and 319~ using a flow calorimeter and the equilibrium constant K and enthalpy change (AH) at I = 0 were determined. Using these experimental values, equations describing log K, All, the entropy change AS and the heat capacity change ACp of reaction at I = 0 and temperatures from 250 to 319~ were derived. The increasing importance of ion association as temperature rises was discussed. The use of an equation containing identical numbers o f positive and identical numbers of negative charges on both sides o f the equal sign (isocoulombic reaction principle) was applied to the logK values reported here and to those determined by others. The resulting plot of log K for the isocoulombic reaction vs. l I T was fairly linear which supports the postulate that the principle is a useful technique for the extrapolation of logK values from low to high temperatures.

KEY WORDS: Equilibrium constant; enthalpy change; entropy change; heat capacity change; flow calorimetry; high temperature; nitric acid; ion association; isocoulombic reaction.

1. Introduction Understanding various geochemical processes and industrial problems requires a thorough knowledge of the thermodynamic properties of aqueous electrolyte solutions and of reactions occurring in these solutions at high temperatures. Many studies of these solutions and the determination of equilibrium constants K, and enthalpy changes 1presented at the Second International Symposium on Chemistry in High Temperature Water, Provo, UT, August 1991. 2Departments of Chemistry and Chemical Engineering, Brigham Young University, Provo, LIT 84602. 3

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Departamento Quumca Flmca I, Umversldad Complutense, E-28040 Madrid, Spain. 789 0095-9782/92/0800-0789506.50/09 1992PlenumPublishingCorporation

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Oscarson et al.

AH for the reactions taking place therein have been made near room temperature and pressure. The need for accurate K and AH values at elevated temperatures becomes apparent when one recognizes that the behavior of chemical species toward the solvent and toward each other differs markedly from that at room temperature. The purpose of this paper is to provide logK and A/-/values for the ionization of nitric acid, (1)

HNO3(aq) = H + + N 0 ;

in aqueous solution from 250 to 319~ To this end, enthalpies of dilution of HNO3 (aq) have been measured by means of a high-temperature flow calorimeter. The dilution reaction may be written as

(2)

HNO3 (aq,mi) = HNO3 (aq,mf)

where mi and mr are the initial and final molalities, respectively. Values of log K, AH, the entropy change (AS), and the heat capacity change (ACp) for reaction (1) may be calculated by analyzing calorimetric data for reaction (2). Reaction (1) has been the subject of several previous investigations. Krawetz (1) obtained values for the ionization constant at 0, 25 and 50~ from Raman spectra. Young e t al. (z) evaluated the electrical conductance measurements of Noyes and obtained K values at 218 and 306~ Marshall and Slusher(4'5) reported values for logK from 100 to 350~ obtained from solubility measurements of calcium sulfate in nitric acid aqueous solutions. Values of AH and other related thermodynamic quantities were also obtained from the variation of K with temperature. (as) Clegg and Brimblecombe(6) combined Henry's law constants and activity coefficients for HNO3 at 25~ with apparent molar enthalpy and heat capacity data to describe measured solubilities of I-INO3 in aqueous solutions from -60 to 120~ The activity coefficient equation of Pitzer and Simonson(7'8) was used in this calculation. To the best of our knowledge, enthalpies for the ionization of nitric acid at high temperature obtained directly from calorimetric measurements have not been reported to date. 9

(3)

~

2. E x p e r i m e n t a l 2.1. Materials

Nitric acid (Maninckrodt, Analytical reagent) was used. The solutions were prepared using distilled, deionized water. Before use in the calorimeter, the solutions were sparged with argon for 20 minutes to remove excess dissolved oxygen. The solutions were standardized by

Ionization of Nitric Acid in Aqueous Solution

791

titration using a known basic solution after the argon treatment. 2.2. P r o c e d u r e The calorimetric determinations were made using a hightemperature flow calorimeter described elsewherefl '1~ The measurements were made in a steady-state, fixed composition mode. Five sets of data were obtained at 250~ and 10.3 MPa. Three of these sets were obtained keeping the flow rate of the nitric acid solution constant at 8.3x10 -3 cm3-s 1 and varying the flow rate of water in 0.5x10 a cm3-s-1 increments. Values of mi were 0.2744, 0.5064, and 1.025 mol-kg -t. Two sets of data were obtained keeping the total flow rate constant at 16.7x10 -3 cm3-s -1 and with values of mi of 0.5071 and 1.549m. Two sets of data were obtained at 275~ and 11.0 MPa keeping the flow rate of the nitric acid solution constant at 8.3x10 -3 cma-s -t and varying the flow rate of water in 1.0xl0 -3 cm3-s -1 increments. Values of mi were 0.5481 and 1.106m. The two sets of data taken at 300~ and 11.0 MPa and the two sets of data taken at 319~ and 12.8 MPa were obtained keeping the flow rate of the nitric acid solution constant at 8.3x10 -3 cma-s -~ and varying the flow rate of water in 0.5• -3 cm3-s -1 increments. Values of mi were 0.2195, 0.4384, 0.1919, and 0.3986m. The values of pressure were chosen to be above the saturation pressure of the solutions studied. Details of the data reduction method are available. Cn) Nitric acid s01ution densities were calculated from data given elsewhere/~2'~3) 2.3. Calculations Table I gives the calorimetric data at each temperature and pressure. The heat of dilution is exothermic at all of the temperatures and pressures studied. The heat of dilution vs. the total mass flow of solvent data were analyzed by a computer program to derive the l o g K and AH values of the ionization reaction at null ionic strength (I = 0). The volumetric flow rates were converted to molar flow rates using the densities and molalities of the solutions. Activity coefficients y based on Lindsay's modified Meissner model ~4"~8~were calculated in the program and were used to extrapolate logK values at the I values of the experiments to the l o g K values at I = 0 and to account for the heats of dilution due to changes in ionic strength. This model is based on NaC1 data to 350~ and includes three assumptions. First, at high temperatures the ~, values of all 1:1 electrolytes approach each other and can be asssumed to be a function only of I, temperature, species charge, and dielectric constant. Second, sodium chloride is an acceptable model for all 1:1 electrolytes, especially at high temperature. Third, the y value for

Oscarson et al.

792

Table I. Calorimetric Data Obtained by Mixing HNO3 Solution with Water a HNO 3 Flow A

HzO Flow B

Exp. Heat of Dilution

Calc. Heat of Dilution

HNO 3 Flow A

HzO Flow B

Exp. Heat of Dilution

Calc. Heat of Dilution

250~ 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571 0.4571

10.3 MPa 0.2008 0.2771 0.3069 0.3476 0.3785 0.4222 0.45(X) 0.4912 0.5211 0.5608 0.5870 0.6325 0.7041

0.2744m -0.466 -0.619 -0.694 -0.763 -0.806 -0.873 -0.917 -0.979 -1.008 -1.063 -1.119 -1.159 -1.244

-0.497 -0.646 -0.698 -0.768 -0.819 -0.887 -0.928 -0.987 -1.028 -1.081 -1,114 -1.170 -1,253

250~ 0.4543 0.4543 0.4543 0.4543 0.4543 0.4543 0,4543 0.4543 0.4543 0.4543 0.4543 0.4543 0.4543

10.3 MPa 0.2008 0.2777 0.3069 0.3476 0.3785 0.4222 0,4500 0.4912 0.521t 0.5608 0.5870 0.6325 0,7041

0.5064m -0.979 -1.273 -1.377 -1.522 -1.558 -1,689 -1.766 -1,922 -1.921 -2.085 -2.227 -2.289 -2.455

-0.919 -1.198 -1.296 -1.427 -I .522 -1.651 -1.729 -1,841 -1.919 -2.019 -2,082 -2.189 -2.348

250~ 0.7912 0.7253 0.6594 0.5769 0.4945 0.4121 0.3297 0.2637 0.1978

10.3 M P a 0.2005 0.2673 0.3342 0.4177 0.5012 0.5848 0.6683 0.7352 0.8020

0.5071m -0.821 -1.037 -1.251 -1.455 -1.608 -I.712 -1.738 -1,591 -t.462

-0.988 -1.259 -1.496 -1.739 -1.916 -2.013 -2.015 -1,932 -1.751

250~ 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478 0.4478

10.3 M P a 0.2008 0.2777 0.3069 0.3476 0.3785 0.4222 0.4500 0.4912 0.5211 0.5608 0.5870 0.6325 0.7041

1.2046m -1.957 -2.487 -2,711 -2.948 -3.181 -3.397 -3.508 -3.720 -4,012 -4.164 -4,261 -4,389 -4.649

-I.825 -2.381 -2.577 -2.839 -3,029 -3.286 -3.443 -3.667 -3.824 -4.025 -4.153 -4.368 -4,690

250~ 0.7686 0.7206 0.7046 0.6405 0.5604 0.4804 0.4003 0.3203 0.2562 0.2402 0.1922

10.3 MPa 0.2005 0.2506 0.2673 0.3342 0.4177 0.5012 0.5848 0,6683 0.7352 0.7519 0.8020

1.5495m -2.898 -3,504 -3,621 -4.347 -5.072 -5.592 -5.899 -5.852 -5.555 -5.511 -5.106

-2,909 -3.516 -3,707 -4.409 -5,131 -5.660 -5,962 -5.992 -5,772 -5,676 -5.274

275~ 0.4539 0.4539 0.4539 0.4539 0,4539 0.4539 0.4539

11.0 MPa 0.2009 0.2778 0.3477 0.4223 0.4913 0.5610 0.6327

0.5481m -0,946 -1,241 -1.504 -1.789 -2,049 -2.219 -2,380

-0,975 -1.283 -1.540 -I .793 -2.012 -2.220 -2.421

Ionization of Nitric Acid in Aqueous Solution

793

Table I. Continued HNO 3 Flow A

H20 Flow B

Experi. Heat o f Dilution

Calc. Heat o f Dilution

275~ 0.4469 0.4469 0.4469 0.4469 0.4469 0.4469 0.4469

11.0 MPa 0.2009 0.2778 0.3477 0.4223 0.4913 0.5610 0.6327

1.1057m -1.950 -2.572 -3.069 -3,577 -3.994 -4.418 -4.750

-1.746 -2.295 -2.754 -3.208 -3.600 -3.972 -4.333

300~ 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552 0.4552

11.0 MPa 0.2009 0.2778 0.3070 0.3477 0.3786 0.4223 0.4502 0.4913 0.5212 0.5610 0.5872 0.6327 0.7043

0.4384m -1.137 -1.412 -1.547 -1.726 -1.802 -1.939 -2.007 -2.180 -2.203 -2.344 -2.492 -2.531 -2.654

-0.872 -1,155 -1.257 -1.395 -1.496 -1.635 -1.721 -1.845 -1,932 -2.045 -2.118 -2.241 -2.428

319~ 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878 0.4878

12.8 MPa 0.1837 0.2505 0.2772 0.3236 0.3481 0.3949 0.4221 0.4701 0.5003 0.5399 0.5729 0.6155 0.6837

0.3986m -0.886 -1.289 -1.440 -1.671 -1,800 -2.000 -2,114 -2.288 -2.399 -2.558 -2.655 -2.810 -3.005

-0.795 -1.051 -1,149 -1.314 -1.400 -1.558 -1.647 -1.801 -1.896 -2.017 -2.116 -2.240 -2.433

a Units: flow, g H20-mina; heats, J-min "1.

HNO 3 Flow A

HzO Flow B

Experi. Heat of Dilution

Calc. Heat o f Dilution

300~ 0.4579 0.4579 0.4579 0.4579 0.4579 0.4579 0.4579 0.4579 0.4579 0,4579 0.4579 0.4579 0.4579

11.OMPa 0.2009 0.2778 0.3070 0.3477 0.3786 0.4223 0.4502 0.4913 0.5212 0.5610 0.5872 0.6327 0.7043

0.2194m -0,620 -0.788 -0.812 -0.929 -0,953 -1.036 -1.066 -1.179 -1.167 -1.267 -1.261 -1.346 -1.406

-0.533 -0.705 -0.767 -0.850 -0.911 -0.995 -1.047 -1.121 -1.174 -1.242 -1.285 -1.359 -1.471

319~ 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905 0.4905

12,8 MPa 0.1837 0.2505 0.2772 0.3236 0.3481 0.3949 0.4221 0.4701 0.5003 0.5399 0.5729 0.6155 0.6837

0.1919m -0.639 -0,846 -0.922 -1.018 -1.078 -1.179 -1.235 -1.326 -1.377 -1,462 -1.505 -1.583 -1.684

-0.504 -0.666 -0.727 -0.832 -0.885 -0.984 -1.041 -1.137 -1.196 -1.272 -1.333 -1.411 -1.531

794

O s c a r s o n et al.

multiply-charged species can be approximated by the following equation 2

~ = (~,z=l)" (3) where n is the charge of the ion. The third assumption does not apply in the case of the nitric acid solutions. A multivariate Newton method (OPTDES.BYU optimization routine~19~)was used to find the logK and AH values which gave the best agreement between the predicted and measured heats. Using this program, water formation is taken into account(2~ and the operator may input other reactions which are believed to be significant in the calculations. The correct selection of these reactions is crucial to the success of the calculation procedure. In this study, the ionization of nitric acid and the ionization of water were considered the significant reactions occurring. The calorimetric data collected over an appreciable ionic strength range at each of four temperatures spanning a wide temperature range were used to calculate a satisfactory set of logK and AH values for the ionization reaction. A satisfactory set of logK and AH values is obtained when the following criteria are met. First, at each ionic strength and at each temperature the experimental heat of dilution data are fitted well by a curve constructed using the calculated logK and AH values. Second, a knowledge of AH as a function of temperature and of logK at a given temperature allows one to calculate logK as a function of temperature by integration of the Van't Hoff equation. Agreement of these calculated logK values with those determined calorimetrically provides a stringent test of consistency. Third, the plot of logK vs. the inverse of temperature is approximately linear for the reaction written in its isocoulombic form, i.e., equal numbers of positive and negative charges are present on each side of the reaction. A good fit of the five sets of data taken at 250~ is obtained for a value of -1.00 for logK and a value of -91.23 kJ-mo1-1 for AH of reaction (1). A value of 0.0013 J-min-1 was obtained for the standard deviation between calculated and experimental heats of dilution. This value for logK is in excellent agreement with those reported previously at this temperature(4,s) Hence, the values of AH obtained at each of the four temperatures studied and the value o f - 1 . 0 0 for logK at 250~ were used to apply the Van't Hoff equation.

Ionization of Nitric Acid in Aqueous Solution

795

Table II. Values as a Function of Temperature for the Reaction HNO3(aq) = H + + NO~a ~

logK

AH

AS

ACp

Methodb

Ref.

218 250

-0.78 -1.00 -1.01 -0.99 -1.42 -1.35 -1.92 -1.82 -1.79 -1.67 -2.39 -2.35 -3.05 -3.37 -3.73

-52.8 -91.2 -60.3 -67.0 -102.6 -91.3 -152.5

-121.8 c -193.5 -136.5 -147.4 -214.3 -192.2 -302.8

-226 c -103 -239 -795 -1016 -1130 -3421

-125.2 -74.5 c -237.9 -171.2 -231.5 -260.4 -291.8

-252.9 -162.0 c -447.5 -331.2 -431.2 -477.3 -523.4

-1590 -268 c -8040 -2090 -2720 -3010 -3310

Con Cal Sol Sol Cal Sol Cal Sol Sol Con Cal Sol Sol Sol Sol

2, 3 d 4 5 d 5 d 4 5 2, 3 d 5 5 5 5

275 300

306 319 325 350 360 370

a Values from this study are valid at I = 0. Units: AH, kJ-mol'l; AS and ACp, j_K.l_mol.1, b Cal, calorimetry; Con, conductance; and Sol, solubility, c Values calculated by Ref. 4 from the values obtained by Ref. 2. d This study.

3. Results and Discussion LogK, AH, AS and ACp values for the nitric acid ionization reaction determined as a function of temperature and valid at I = 0 are given in Table II together with those determined by others. The method of logK determination is also indicated in Table II. Table I lists the calculated heats of dilution. In Figs. 1 and 2 the calculated heats of dilution are compared with those determined experimentally. The calculated heats of dilution at 300~ and mi = 0.4384m, and 319~ and mi = 0.3983m deviate appreciably from the experimental data. This could be due to the use of Lindsay's modified Meissner model which is only approximately valid at these conditions. LogK for reaction (1) measured by others together with those determined in this study are plotted v s . temperature in Fig. 3. The agreement of our values with those reported earlier at 250, 275, 300, and 325~ by Marshall and Slusher<4'~ and at 218~ by Young~2) is good. The value reported at 306~ by Young<2)is higher than those determined in this study or in Refs. 4 and 5. LogK values decrease as temperature

Oscarson et al.

796 i

,

i

,

i

,

-2

-~ -3 -4 @

I

E

I

J

I

'

.! -

13

-2

O•/•

319~

9 I 0.4

,

-

I

I

I

I

I

0.6

0.8

0.4

0.6

0.8

mr/

m i

mf/

m

1.0

i

Fig. 1. Heats of mixing Q as a function of the ratio between the final and initial molalities of the nitric acid (mf/mi) and tempera~tre. The initial molalities are, 250~ [] = 0.2744m, (~ = 0.5064m, hexagons = 1.025m; 275~ o = 0.5481m, 0 = 1.106m; 300~ 0 = 0.2195m, [] = 0.4348m and 319~ [] = 0.1917m, hexagons = 0.3983m. The solid lines represent heats of reaclSon calculated using the best set of thermodynamically consistent AH and l o g K values.

increases. The decrease in logK is more accelerated at temperatures above 250~ thus indicating that ion association becomes more prevalent as temperature rises. Nitric acid at 25~ is a very strong acid existing almost exclusively as H § and NO~ ions. However, nitric acid above 250~ is a weak acid in which the species HNO3(aq) dominates. The enthalpy of ionization for HNO3(aq) becomes increasingly exothermic as temperature increases. The AH values determined in this study are smaller than those reported previously. The differences can be explained by the method of AH determination. The AH values reported in earlier studies were calculated from the temperature variation of logK. This method generally provides enthalpy values of lower accuracy. It was assumed that In K values obtained in this study could be fitted to an equation of the form RInK = -a/T + bInT + cInp + d

(4)

where T is the temperature in Kelvins, a, b, and c are adjustable parameters, p is the density of water at the temperature and pressure at

Ionization of Nitric Acid in Aqueous Solution

797

-2

-4

-6

0

I 0.2

I 0.4

I I).6

mf/m

I 0.8

1.0

i

Fig. 2. Heats of reaction Q as a function of the ratio between the fmal and initial molalities of the nitric acid (mf/mi). The initial molalities are: r = 0.5071m, [] = 1.549m. The solid lines represent heats of reaction calculated using the best set of thermodynamicaUy consistent AH and logK values. 2

I

I

I

I

0 0 o

I 0 0 0

0

0 0

-I

iI

i -2

i -3

A A A

-4

1 0

I

I

I

100

200

300

400

Temperature ( ~

Fig. 3. Plot of logK for HNO3(aq) = H + + NO~ as a function of temperature. The solid squares are the results obtained in the present study; O, ReL 1; hexagons, Refs. 2, 3; o, Ref. 4; A, Ref. 5.

which the AH values were determined and d is the constant of integration determined by selecting a reference temperature. The term including the solvent density in Eq. (4) is intended to describe the pressure effect. Applying the Van't Hoff equation to Eq. (4) results in an expression for AH of the form AH = a + bT + cT2(~lnp/~T)p

(5)

798

Oscarson et al. 300 200

I

(al

_

[

I

I

i

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(b)

AH/

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100 .;g

AG

0

AG

-100

-T AS

,.1 m

-200

I

-300

250

300

I 350

250

I

I 300

I 350

Temperature (~ Fig. 4. Plots of AH, -T, AS and AG for the association as a function of temperature of (a) HNO3(aq) and (b) HCl(aq).

The parameters in Eqs. (4, 5) were determined by fitting AH values to Eq. (4). Values of p were taken from Ref. (21). The reference temperature of 250~ was chosen to determine d. Values of-715.690 kJ-mo1-1, and 1444.3,259.93 and -10,372.3 J-Kl-mo1-1 are obtained for a, b, c and d, respectively. Expressions giving AS and ACp as a function of temperature as derived from Eqs. (4, 5) are AS = b + d + c T ( ~ l n p / ~ T ) p + b l n T + clnp ACp

=

b + 2cT(~ln p/~T)p

+

cT2(021np/~T2)p

(6) (7)

The magnitudes of AH and AS increase substantially as temperature rises. These changes have important effects on the ion association. Figure 4a shows plots of AH, -TAS and the change in Gibbs energy (AG) for the association of nitric acid as a function of temperature. Figure 4b shows a similar plot for the association of hydrochloric acid taken from unpunished results from our laboratory. (22) The behavior of both acids is coincident. Both AH and AS are positive and large for the association and the balance is such that K increases with increasing temperature. The increased K value results from large TAS increases relative to those of AH and the association reaction is entropy-driven. HCl(aq) is somewhat less associated than HNOa(aq) at high temperatures. Values of logK for the ionization reaction are 0.49, 0.04, -0.63 and-1.31 at 250, 275, 300 and 325~ respectively. The large positive values of AH and AS for ion association reactions can be explained by considering solvation effects within the framework of the water model proposed by Frank and Wen. (2a) When

Ionization of Nitric Acid in Aqueous Solution 400 -8

-10

799

100

200

25

0~

L

I

~ o

0 0

_--- -12

0 0

-14 .1

o -16

-18

<>

I

,

2

I

I

3

4

103/T ( K 4)

Fig. 5. Plot of logK vs. 1/T for the isocoulombic reaction NOg + H20 = HNOa(aq) + OH-. The solid squares are the results obtained in the present study; 0, Ref. 1; hexagons, Refs. 2, 3; o, Ref. 4; A, Ref. 5. ion association o c c u r s , water molecules are released from the primary and secondary hydration spheres to the bulk phase. Considerable energy is required to restore the newly released water molecules to the rotational, vibrational, and translational freedom which exits in the bulk water. The absorption of the required energy from the sourroundings results in the large positive AH values for ion association reactions in water at high temperatures. Large positive AS values result from ion association because many water molecules are released from the ordered structure o f the primary and secondary hydration spheres to the highly disordered state of the bulk liquid. Similar values of AH and AS were found when the association of SO4z- with Na § and of C3H30~ with Na § and H § were studied from 150 to 320~ and from 275 to 320~ respectively. (24~s) The l o g K values determined in this study together with those determined by others were used to test the validity of the isocoulombic reaction principle; (17) logK values for reaction (1) were combined with data for the ionization of water (2~ to form the isocoulombic reaction NO~ + H20 = HNO3(aq) + O H -

(8)

The results are plotted in Fig. 5 as l o g K for the isocoulombic reaction vs. 1 / T . With the exception of the logK values obtained from the data reported for reaction (1) at 306~ by Young (z) and at 360 and 370~ by Marshall and Slusher, (s) this plot shows a linear relationship. The logK

800

Oscarson et al.

value reported at 306~ for reaction (1) by Young(2) deviates from values reported by others, as has been indicated. The logK values reported at 360 and 370~ for reaction (1) by Marshall and Slusher(s) were obtained from an equation for logK based on solubility data taken from 200 to 350~ We may conclude that the isocoulombic principle is valid for reaction (8) in the temperature range 0-350~ and that the principle may provide a technique for the extrapolation of logK values to temperatures above 350~

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