thermodynamic properties of the coexisting phases - and ... · the partial molal volume of nacl in...

Thermodynamic Properties of the Coexisting Phaseso

- and Thermochemical Properties oi the NaCl Component in Boiling XuCl Solulions

(. I. O I. O (. 1 C A L S t : K V I. \ l'» I 1 I I I I N ! 1 L' ! - It

Thermodynamic Properties of the Coexisting Phases and Thermochemical Properties of the NaCl Component in Boiling NaCl Solutions

By JOHN L. HAAS, JR.

PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS

GEOLOGICAL SURVEY BULLETIN 1421-B

Tables giving the temperature-vapor pressure- density-molal volume-molal enthalpy-molal entropy relations for the coexisting liquid and gas and the partial molal volume, enthalpy, and entropy of the NaCl component in the coexisting phases between 80° and 325° C up to saturation in halite

This revised reprint of Bulletin 14&1-B supersedes the first printing, in December 1976

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1976

UNITED STATES DEPARTMENT OF THE INTERIOR

CECIL D. ANDRUS, Secretary

GEOLOGICAL SURVEY

V. E. McKelvey, Director

First printing 1976 Revised 1977

j;

Library of Congress Cataloging in Publication Data

Haas, John LThermodynamic properties of the coexisting phases and thermochemical properties

of the NaCl component in boiling Nad solutions. (Preliminary steam tables for NaCl solutions) (Geological Survey bulletin ; 1421-

B)Bibliography: p. Supt. of Docs, no.: I 19.3:1421-B1. Thermochemistry Tables, etc. 2. Solution (Chemistry) Tables. 3. Salt Tables.

Title: Thermodynamic properties of the coexisting phases .... II. Series. III. Series: United States. Geological Survey Bulletin ; 1421-B.

QE75.B8 no. 1421-B [QD511.8] 557.3'08s [546.'382'24] 76-608097

For sale by the Superintendent of Documents, U.S. Government Printing OfficeWashington, D.C. 20402

Stock Number 024-001-03022-5

CONTENTS

Abstract ___ ____ __-- --Introduction _____________________ ___ _ _ - __ ______ __Units, symbols, and constants ________ -__ - --

Units and symbols used in tables and text _____ _ Fundamental constants used in calculations __ -Empirical constants used in the text and calculations _

Vapor pressure and density of the vapor-saturated liquid phase ____Thermochemical data for NaCl in the vapor-saturated liquid phase__

Synopsis of the theoretical approach _ _ Partial molal volume of NaCl in the liquid _._ __ The partial molal free energy of NaCl in the liquid ________ The partial molal entropy of NaCl in the liquid ____ _______ The partial molal enthalpy of NaCl in the liquid ____________

Partial molal thermochemical properties of NaCl in the gas phase _ Thermodynamic data for the phases in the H^O-Nad system ___ Recommendations for research _______________________________Tables for NaCl solutions _____________________References cited _________________________________________

ILLUSTRATIONS

PageFIGURE 1. The partial molal volume of NaCl in the liquid phase

for vapor-saturated NaCl solutions from 0 wt per cent to halite saturation between 80° and 325° C_ B7

2. Temperature-pressure-concentration diagram for the .vapor-liquid coexistence surface of the H^O-NaCl system between 80° and 325° C ___________ 8

3. The partial molal free energy of NaCl in the liquid phase of vapor-saturated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C__ 11

4. The partial molal entropy of NaCl in the liquid for vapor-saturated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C ___ 12

5. The partial molal enthalpy of NaCl in the liquid for vapor-saturated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C_____ 13

6. The molal volume of liquid solutions in the H20-NaCl system from 0 wt percent NaCl to halite saturation between 80° and 325° C ________________ 14

Hi

IV CONTENTS

PageFIGURE 7. The molal entropy of the gas and the liquid phases in

the HaO-NaCl system from 0 wt percent NaCl to halite saturation in the liquid phase between 80° and 325° C ________________________ B15

8. The molal enthalpy of the gas and the liquid phases in the HaO-NaCl system from 0 wt percent to halite saturation in the liquid phase between 80° and 325° C ______________________________ 16

TABLES

Page TABLES 1-28. NaCl concentration:

1. 0.0000 mol/kg H20, 0.00 wt percent, 0.000 molpercent ______________________ B22

2. 0.5000 mol/kg H20, 2.84 wt percent, 0.893 molpercent ______ _ _________________ 24

3. 0.9006 mol/kg H20, 5.00 wt percent, 1.597 molpercent ____________________ 26

4. 1.0000 mol/kg H20, 5.52 wt percent, 1.770 molpercent __ ____ 28

5. 1.5000 mol/kg H20, 8.06 wt percent, 2.631 molpercent _____ _ _ _____ ____ 30

6. 1.9012 mol/kg H20, 10.00 wt percent, 3.312 molpercent ______________________ 32

7. 2.0000 mol/kg H20, 10.47 wt percent, 3.478 molpercent ______________________ 34

8. 2.5000 mol/kg H20, 12.75 wt percent, 4.310 molpercent ___________ __________ 36

9. 3.0000 mol/kg H20,14.92 wt percent, 5.127 molpercent __________________ 38



12. 4.0000 mol/kg H20, 18.95 wt percent, 6.722 molpercent _____ _____________ 44

13. 4.2777 mol/kg H2O, 20.00 wt percent, 7.155 molpercent _____ ___________ 46


15. 5.0000 mol/kg H20, 22.61 wt percent, 8.263 molpercent ___________________._ 50

16. 5.5000 mol/kg H20, 24.32 wt percent, 9.015 molpercent _____________________ 52

17. 5.7036 mol/kg H20, 25.00 wt percent, 9.318 molpercent ______________:______ 54

18. 6.0000 mol/kg H20, 25.96 wt percent, 9.755 molpercent _____________________ 56

CONTENTS V

Page TABLES 1-28. NaCl concentration Continued

19. 6.5000 mol/kg H20, 27.53 wt percent, 10.482mol percent _ _ B58

20. 7.0000 mol/kg H20 29.03 wt percent, 11.198mol percent __ ___ ____ __ 60

21. 7.3332 mol/kg H20, 30.00 wt percent, 11.670mol percent ____________ _ - 61

22. 7.5000 mol/kg H20, 30.47 wt percent, 11.903mol percent'.. 62

23. 8.0000 mol/kg H20, 31.86 wt percent, 12.597mol percent ______ . _ 63

24. 8.5000 mol/kg H20, 33.19 wt percent, 13.279mol percent __ 64

25. 9.0000 mol/kg H20, 34.47 wt percent, 13.952mol percent ____________________ 65

26. 9.2135 mol/kg H20, 35.00 wt percent, 14.235mol percent ________: ______ __ 66

27. 9.5000 mol/kg H20, 35.70 wt percent, 14.613mol percent __________________ _ 67

28. 10.0000 mol/kg H20, 36.89 wt percent, 15.265mol percent ________________ 67

29. Halite-saturated NaCl solutions, concentrations inwt percent ________________________ 68

30. Halite-saturated NaCl solutions, concentrations in molNaCl/kg H20 (molal) _________________ __ 70

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PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS

THERMODYNAMIC PROPERTIESOF THE COEXISTING PHASES AND

THERMOCHEMICAL PROPERTIESOF THE NaCl COMPONENT IN

BOILING NaCl SOLUTIONS

By JOHN L. HAAS., JR.

ABSTRACT

Preliminary steam tables that give the thermodynamic data for the co existing liquid and gas and that give the thermochemical data for the NaCl component in the liquid for the system H«0-NaCl are given for liquid con centrations between 0 mol NaCl/kg H20 and halite saturation at temperatures between 80° and 325° C. The tables were calculated from parametric equa tion of state.

INTRODUCTION

The tables assembled present the thermochemical properties of aqueous NaCl in the vapor-saturated liquid phase and the thermo dynamic properties of the coexisting liquid and gas phases for the H20-NaCl system as follows :

partial molal volume of NaCl in the liquid,partial molal entropy of NaCl in the liquid,partial molal enthalpy of NaCl in the liquid,molal volume of the liquid,molal entropy of the liquid,difference between the molal entropy of the liquid and the

molal entropy of the gas, molal entropy of the gas, molal enthalpy of the liquid, difference between the molal enthalpy of the liquid and the

molal enthalpy of the gas, molal enthalpy of the gas.

Bl

B2 PRELIMINARY STEAM TABLES FOR NaCl SOLUTIONS

The data are tabulated for liquid compositions from 0 mol NaCl/kg H20 to halite saturation at temperatures from 80° to 325° C. As an aid in using the tables, the vapor pressure and the density of the liquid are also given. These tables complement the steam tables prepared by Haas (1976) in which the physical properties of the solutions and the thermochemical data for H20 are tabulated.

The tables presented here are preliminary. The functions upon which they are based represent a reasonably complete analysis of the available data through 1971. Improvement can be made when measurements and analysis are completed on the volumetric prop erties of vapor-saturated and vapor-absent liquid at high tempera tures and at concentrations of more than 30 wt percent NaCl. Be cause there is an immediate need for the contained data, they have been made available in this preliminary form.

The tables are given as an aid in geochemical and engineering studies related to the geothermal energy program of the United States. Support for this work has come exclusively from the U.S. Geological Survey's geothermal research program.

UNITS, SYMBOLS, AND CONSTANTS

UNITS AND SYMBOLS IN TABLES AND TEXT

The chosen units in the tables for temperature, pressure, and density are °C, bars, and g cm- 3 , respectively. These are the same as those used in several widely referenced steam tables (Bain, 1964; Keenan and others, 1969). The partial molal and the molal entropy, enthalpy, and volume are given as J mol~ 1K~ 1 , J mol" 1 , and cm3 mol" 1 , respectively, because these units are most used in thermodynamic calculations. Both weight percent and molal (mol NaCl/kg H20) scales for units of sodium chloride concentration are widely used in engineering and geochemical research. Both scales are used here to achieve the maximum use of the tables.

The quantities, their symbols, and the associated units used in this text and in the tables are as follows:

Quantity Symbol Units

activity afitted parameter in the activity B kg H20/mol NaCl

coefficient function (eq 12) fitted parameter in the activity C (kg H20/mol NaCl) 2

coefficient function (eq 12)heat capacity at constant pressure Cf J mol^K"1 density d g cm"a dielectric constant for pure H20 D molal free energy G J mol"1

NaCl COMPONENT IN BOILING NaCl SOLUTIONS B3

Quantity Symbol

molal enthalpy H equilibrium constant K mole fraction of NaCl N pressure p generalized thermodynamic quantity Q molar gas constant R temperature t

Tmolal volume V molecular weight W concentration of NaCl in the liquid x Debye-Hiickel limiting slope a fitted parameter in activity coeffi- ft

cient function (eq 12) activity coefficient 7 number of moles of ions per mole v

of NaCl in solution

Units

J mol'

J mol-'K"1

degrees Celsius, °Ckelvins, Kcm" 8 mol"1g mol"1

mol NaCl/kg H20 (molal)(kg H.O/mol NaCl)*(kg H.O/mol NaCl) 1'4

kg H.O/mol NaCl moles Na+ + moles Cl" per

mole dissolved NaCl

In the text and the tables, the following superscripts are used:

SUSolrt Connotation

G The superscripted quantity is an attribute of the gaseous phase.

L The superscripted quantity is an attribute of the liquidphase.

- (bar) The overscored quantity is a partial molal quantity of the component indicated by the subscript, in the solution.

0 The superscripted quantity is an attribute of the chemical species in the standard state.

* The symbol is a generalized symbol representing the super scripts G and L above.

In the text and the tables, the following subscripts are used:Subscript

symbol Connotation

The subscripted quantity is a partial quantity for the component H20.

The subscripted quantity is a partial quantity for the component NaCl.

The subscripted quantity is an attribute of the pure sub stance HsO.

The subscripted quantity is a measure of the difference in the thermochemical property between the compound in its standard state and its component elements in their standard states.

FUNDAMENTAL CONSTANTS USED IN CALCULATIONS

The Committee on Data for Science and Technology (1973b) of the International Council of Scientific Unions gives the molar gas constant^ as (8.31441 ±0.00026) J

The Commission on Atomic Weights (1972) gives the follow ing atomic weights:

H (1.0079±0.0001) gmol- 10 (15.9994±0.0003) gmol- 1Na (22.98977±0.00001) gmol- 1Cl (35.453±0.001) gmol- 1

From these atomic weights the molecular weights of the com ponents are:

H2O W1 =(18.0152±0.0005) gmol- 1 Nad W2 = (58.4428±0.0010) gmol- 1

EMPIRICAL CONSTANTS USED IN THE TEXT AND CALCULATIONS

The following list gives the constants for the equations pre sented in the text. The equation numbers and constants are as follows:

Equation 9:go = 1.895555 XlO3 g!=-1.944135 g2 =-7.343150 XlO7 g3 =-9.938067 XlO3

Equation 16:Bo = 4.43570 XlO- 2 #! = 2.14240 XlO- 4 £2 =-1.21582xlO- 6

Equation 17:C0 = 4.86989 XlO- 3 Ci=- 6.65184 XlO- 5 C2 = 1.69534 XlO- 7

Equation 18:For temperatures at and below 100°C the constants are the

following:0o = 0.98007501 = 0.707654 XlO- 202 =-2.97433 XlO- 5

For temperatures above 100°C the constants are the following:00 = 1.64801ft =-2.83246 XlO- 3


VAPOR PRESSURE AND DENSITY OF THE VAPOR- SATURATED LIQUID PHASE

The functions for the vapor pressure and density were given in Haas, 1976. They are not repeated here because there has been no change.

THERMOCHEMICAL DATA FOR NaCl IN THE VAPOR- SATURATED LIQUID PHASE

SYNOPSIS OF THE THEORETICAL APPROACH

An attribute of steam tables is that differences in the energy content between two states of matter can be calculated by simple subtraction of the data in the tables. The ease in calculation re sults from all values in the tables being given as the energy difference between the state of the compound at temperature and pressure and the reference temperature and reference pressure. For H20 in the NaCl-H2 0 system such values were comparatively easy to derive because the thermodynamics for the pure component H20 had been established (Bain, 1964; Keenan and others, 1969). It only remained to determine the appropriate departure that dis solved NaCl would cause relative to the pure H20 system.

For the NaCl component, no approach has been established. First, a reference state must be chosen. In this set of tables, the chosen reference state is the hypothetical ideal NaCl solution of unit molality at the ice liquid vapor triple point for pure H2 0.

With the reference state established, calculation of energy differences between any arbitrary temperature, pressure, and com position and the chosen reference state can be made. The approach used here is as follows:

1. The partial molal volume of NaCl was obtained from a den sity temperature composition function for the vapor- saturated NaCl liquid phase.

2. The partial molal free energy of NaCl in the hypothetical ideal 1-molal liquid as a function of temperature and pressure was obtained.

3. The dependence of the partial molal free energy of NaCl with composition at constant temperature and pressure was obtained.

4. The dependence of the partial molal free energy of NaCl with pressure at constant temperature and composition was ob tained.


5. Then, using the relation

82= 1+Fj ?- (1)

the partial molal entropy at temperature, pressure, and com position was calculated.

6. The partial molal enthalpy of NaCl at temperature, pressure, and composition was obtained from

(2)Each of these steps is described in further detail in the follow

ing sections.

PARTIAL MOLAL VOLUME OF NaCl IN THE LIQUID

The partial molal volume of NaCl in the binary liquid system is given by equation 3.

(cm'mol- 1 ) (3)

where VL is the volume of the liquid containing a total of one mole of molecules. The term NL is the mole fraction of NaCl in the liquid phase and is given by equation 4 in terms of x, the molality of the solution, c

W = - (4) 1000/17! + x

Wl is the molecular weight of H20. The molal volume VL of an x molal liquid of density d is given by equation 5.

d 1000/Wi + a;

The partial molal volume of NaCl, Ff , was obtained by using equations 3 through 5, given here, the equations for density of the liquid phase in the preceding report (Haas, 1976, equations 7 through 10) , and standard analytical techniques.

Figure 1 shows the partial molal volume of NaCl in the liquid at constant composition. The contour interval is 5 wt percent NaCl.

THE PARTIAL MOLAL FREE ENERGY OF NaCl IN THE LIQUID

Figure 2 shows graphically the route which was taken through temperature-pressure-composition space to obtain the partial molal free energy at an arbitrary temperature, pressure, and com position (point D) from the reference state at 0.01° C (point A).

NaCl COMPONENT IN BOILING Nad SOLUTIONS B7

uj 75.00 i oS

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75.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00 TEMPERATURE, IN DEGREES CELSIUS

FIGURE 1. The partial molal volume of NaCl in the liquid phase for vapof- saturated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C. The contour interval is 5 wt percent NaCl. The stippled zone was calculated by the extrapolation of the functions given in the text.

Steps 2, 3, and 4 in the synopsis above correspond to the segments AB, BC, and CD on the figure.

Step 2 of the approach, given in the section entitled "Synopsis of the theoretical approach," involved the derivation of a partial

molal free energy function for aqueous NaCl, AG 2 (AB), in the hypothetical ideal liquid solution of unit molality, that is, in the solute standard state, relative to the reference-state partial molal

free energy at the triple point where G2 is defined to be 0.0 J mol" 1 . 1 To accomplish this, consider here the interrelations be tween free energy, temperature, pressure, entropy, enthalpy, heat capacity, and partial molal volume. By using equations 1 and 2 and the relation between enthalpy and heat capacity, equations 6 through 8 were derived.

1 As used in this report, the reference state for a chemical species is an arbitrarily chosen single point on the temperature, pressure, and composition scales which is taken as the zero point for the energy scale. That is. the thermochemical parametei's of free energy, enthalpy, and entropy are defined to be zero at this point. In contrast, as used here (and also as in many applications in aqueous chemistry), the standard state for a dissolved com pound in H^O is taken as the hypothetical ideal liquid solution of unit molality at the temperature and pressure of the vapor-saturated pure H^O liquid. In this standard state, the partial molal free energy, enthalpy, and heat capacity of the dissolved compound is the same as that for the infinitely dilute real solution. The advantage of a standard state .in aqueous chemistry is that it allows correlations of properties as a function of composition at constant temperature and pressure, whereas a reference state is necessary when correla tions or calculations in temperature-pressure-composition space are being made.


. /-. / ' , <o / / // / '/S'30^ / / 7 3

1 i i I I T~ J -' / i /J ! ''.' ' ic/ -?-?7

350

0 2 4 6 8 10 12 CONCENTRATION, IN MOLES

FIGURE 2. Temperature pressure concentration diagram for the vapor- liquid coexistence surface of the H20 NaCl system between 80° and 325° C. The surface is contoured both in temperature (50° intervals) and con centration (1-molal intervals). The concentration contours are truncated by the focus of the three-phase coexistence liquid vapor halite at high con centrations. The blank vertical plane between 250° and 300° C represents an arbitrary isotherm upon which lie the points B, C, and D and the heavy solid lines connecting them. Steps 2, 3, and 4 of the chosen approach repre sent the temperature pressure composition paths AB, BC, and CD, re spectively, along which partial molal free energy functions were sought. The combination of these functions then gives the partial molal free energy of NaCl at the arbitrary point D relative to the reference state at A, the triple point of pure H20.

(6)

(7)

.= -T- (8)

Internal consistency demands that any free-energy function must satisfy the above relations and the available data for the hypothetical ideal 1-molal solution. The available data were

Nad COMPONENT IN BOILING NaCl SOLUTIONS B9

evaluated, subject to the.above constraints, by use of a com puterized algorithm described by Haas and Fisher (1976).

The data used in the evaluation are as follows. For the partial molal volume of dissolved NaCl, the function given in the previous section was used. Data for the relations between halite and dis solved NaCl and for dissolved NaCl, all in their standard states, were taken from the following references:

Reference

Committee on Data for Science and Technology (1973a).

Likke and Bromley (1973) __ Criss and Cobble (1961) __ Gardner and others (1969) __ Liu and Lindsay (1972) ____

Data type

Si (298.15K)

AG». i (298.15K) o

Op, 2

A//°[halite=:NaCl(aq)] AH°[halite=NaCl(aq)] log K°[halite=NaCl(aq)]

Number Tempera-of ture

observa- rangetions (°C)

1

1

7133

10

25

25

80-2000-95

114-20075-300

Stull and Prophet (1971) _ CP, S, (Hr-H ) [halite] Tabulated data,100° intervals,

25-727.

The partial molal free energy of the hypothetical ideal 1-molal solution as a function of temperature is given by equation 9; the constants are tabulated in the section entitled "Empirical con stants used in the text and the calculations."

&G 2L (AB)=g0 (T-T In T-273.16 + 273.16 In 273.16)-5r 1 (2l2 -273.162 )-flf 2 (l/2r-l/2x273.16)-03 (r-273.16) (Jmol- 1 ) (9)

The procedure of Haas and Fisher (1976) uses 25° C (298.15K) as the reference temperature. Therefore, the free-energy function has been corrected to reflect the shift in the reference temperature to 0.01° C (273.16K) for use here.

Step 3 of the chosen approach for deriving the thermochemical functions requires the description of the change in the free energy

with concentration, AG 2J (5C), at constant temperature and pres sure. This dependence is given by equations 10 and 11.

(10)(11)

where R is the molar gas constant and a2 and y are the activity and activity coefficient, respectively, for the dissolved NaCl at point C relative to the standard state, the hypothetical ideal 1-

BIO PRELIMINARY STEAM TABLES FOR Nad SOLUTIONS

molal solution, point B. Liu arid Lindsay (1972) gave the follow ing equations for the temperature and concentration dependence of In y at the vapor-saturation pressure for pure H20.

ln y = ~ aXA + 2Bx + -Cx2 (12)2

B, C, and £ are second-order polynomials in temperature and « is the Debye-Hiickel limiting slope :

113/2

^ (13)|~2.33752-104 T lA L DT J

The term d0 is the density of pure H20 and, for use in this calcula tion, d0 is described by :

do = 1.00157 - 1.56096 W~*t - 2.69491 10-°i2 (g cm- 3 )(14)

The term D is the dielectric constant for pure H20 as given by the Akerlof equation :

5321 '+233.76-0.9297 T + 1.417 10- 3 7T2 -8.292-10-T3

T(15)

The functions for B, C, and /J are, respectively,

(16)(17)(18)

The constants Bit Cit and fa are given in the section entitled "Em pirical constants used in the text and calculations."

Step 4 of the chosen approach for deriving the thermochemical functions requires the description of the change in the partial

molal free energy with pressure, AG 2 (CD), at constant tempera ture and composition. Basic thermodynamic principles state that the pressure dependence of free energy is :

-dG = V-dp (19) Therefore,

V2 dp (20)Po

where p0 and p are the vapor pressures of H20 and of the liquid solution, respectively. The dependence of the partial molal volume of dissolved NaCl with pressure in the vapor-absent liquid is un

available, but the change in V2 with pressure is small relative to

NaCl COMPONENT IN BOILING NaCl SOLUTIONS Bll

the total magnitude of this correction. Therefore, by neglecting

the pressure dependence of V2 , equation 20 can be approximated by

&G% (CD) = V2 (Po~p) (21)

In summary, the partial molal free energy of aqueous NaCl at an arbitrary temperature, pressure, and composition relative to the reference state at 0.01 °C is given by summing equations 9, 11, and 21.

G2 =*G2 (AB)+*G2 (BC)+*G2 (CD) (Jmol- 1 ) (22) Figure 3 shows the partial molal free energy of NaCl in the

liquid at constant composition. The contour interval is 5 wt per cent NaCl.

THE PARTIAL MOLAL ENTROPY OF NaCl IN THE LIQUID

The partial molal entropy at an arbitrary temperature, pres sure, and composition was calculated using equation 1:

+v>- (i)10.00

0.00i

_ 10.00

^ »

si- 20.00

: -30.00

-40.0075.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00

TEMPERATURE, IN DEGREES CELSIUS

FIGURE 3. The partial molal free energy of NaCl in the liquid phase of vapor-saturated NaCl solutions from 0 wt percent to halite saturation be tween 80° and 325° C. The contour interval is 5 wt percent NaCl. All con tours between 5 wt percent and halite saturation are systematic. Below the 5 wt percent contour, there is a reversal in the free-energy function so that the partial molal free energy of aqueous NaCl at infinite dilution lies above the partial molal free energies of NaCl at greater concentrations. For de tails, one is referred to the tables. The shaded zone at concentrations greater than 30 wt percent and at temperatures greater than 300° C contains data .that were calculated by the extrapolation of the functions given in the text.

The term was obtained, analytically, from equation 22

above; the term V2 was obtained from equation 3; and the term 'dp/'dT was calculated in the manner described in the section en titled "Enthalpy difference between the gas and the liquid at con stant liquid composition," of the preceding report (Haas, 1976).

Figure 4 shows the partial molal entropy of NaCl in the liquid phase at constant composition. The contour interval is 5 wt per cent NaCl.

The surface depicted on figure 4 is complicated as can be seen by the crossover of the concentration contours as temperature de creases. For details, the reader is referred to the appropriate tables. The erratic behavior of the contours near 110° C is due to the use of two sets of constants to fit the empirical term ft in the activity coefficient equation (eq 12). This will be discussed fur ther in the section "Recommendations for research."

THE PARTIAL MOLAL ENTHALPY OF NaCl IN THE LIQUID

The partial molal enthalpy of NaCl was calculated from equa tion 2 using the previously computed entropy and free energy :

| 100.00LLJ^

g 50.00^ oz.

^ 0.00GOLLJ

O

I -50.00

i-100.00

j-150.00

i-200.0075.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00


FIGURE 4. The partial molal entropy of NaCl in the liquid for vapor-saturated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C. The contour interval is 5 wt percent NaCl. The inflection near 110° C is due to the use of two sets of constants to describe the fitted con stant /? in the activity coefficient equation. The surface is complex. Most of the change in the partial molal entropy with change in composition oc curs between 0 and 5 wt percent. For details, the reader is referred to the tables.

B13

Figure 5 shows the partial molal enthalpy of NaCl in the liquid phase at constant composition. The contour interval is 5 wt per cent NaCl. The erratic behavior in the contours near 110°C are due to the use of two sets of constants to fit the empirical term ft in the activity coefficient equation (eq 12). This will be dis cussed further in the section "Recommendations for research."

'jr

PARTIAL MOLAL THERMOCHEMICAL PROPERTIES OF NaCl IN THE GAS PHASE

The available experimental data for the concentration of NaCl in the gas phase do not permit the estimation of the partial molal quantities of NaCl in the gas phase.

-20 -

-40 -

-60 -

-so -

75 100 125 150 175 200 225 250TEMPERATURE, IN DEGREES CELSIUS

275 300 325

FIGURE 5. The partial molal enthalpy of NaCl in the liquid for vapor-satu rated NaCl solutions from 0 wt percent to halite saturation between 80° and 325° C. The contour interval is 5 wt percent NaCl. The inflection near 110° C is due to the use of two sets of constants to describe the fitted con stant /? in the activity coefficient equation. The shaded area contains data that were calculated by the extrapolation of the functions given in the text.


THERMODYNAMIC DATA FOR THE PHASES IN THE H2O-NaCl SYSTEM

The molal properties of the liquid and gas phases in the H 20- NaCl system can be calculated readily from the thermochemical data for NaCl that were formulated here, and for H20 that were given in the preceding report (Haas, 1976). The formulation is identical for all molal quantities:

'Q= (l N*)Qi+N*Q* (23)

where Q is the quantity of interest (volume, entropy, enthalpy) and N* is the mole fraction of NaCl in phase $. In the liquid phase, the mole fraction of NaCl was calculated from the con centration by using equation 4. In the gas phase, the available data

28.00

18.0075.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00


FIGURE 6. The molal volume of liquid solutions in the HoO-NaCl system from 0 wt percent NaCl to halite saturation between 80° and 325° C. The con tour interval is 5 wt percent NaCl. As is obvious from the crossing of contours, the surface is complex. For details, the reader is referred to the tables.


do not permit the estimation of the mole fraction of NaCl with any precision. However, the mole fraction of NaCl in the gas is small, being less than or equal to 10-° in most of the tempera ture pressure composition space covered in this report. There-

ci f1fore, the quantity N Q 2 was neglected, and the thermodynamic properties of the gas were assumed to be the same as the thermochemical properties of pure H^O at the temperature and pres sure of the solution.

Figure 6 shows the molal volume of the liquid phase. The con tour interval is 5 wt percent NaCl.

Figures 7 and 8 show the molar entropy and the gas at com position of NaCl in the liquid. The contour interval is 5 wt per cent NaCl contained in the liquid phase.

RECOMMENDATIONS FOR RESEARCH

In the preparation of these preliminary steam tables, several areas where one can improve the precision and accuracy were

Liquid + Gas

140.00

1120.00LU:*:

§100.00scc.LU

£ 80.00LU

=>

oJ 60.00

o.

I 40.00UJ

o 20.00

0.0075.00 100.00 125.00 150.00 175.00 200.00 225.00 250.00 275.00 300.00 325.00


FIGURE 7. The molal entropy of the gas and the liquid phases in the H-0- NaCl system from 0 wt percent NaCl to halite saturation in the liquid phase between 80° and 325° C. The contour interval is 5 wt percent NaCl in the liquid. The shaded area contains data that were calculated by the extrapolation of functions given in the text. The bunching of the contours between 300° and 325° C is most probably due to an artifact in the equa tions which is exaggerated when the partial molal entropy of aqueous NaCl is calculated.

Liquid

B1660

LU

150ce LUQ_

GO Af\LU 40

o o S 30z

| 20z i

5 10

PRELIMINARY STEAM TABLES FOR Nad SOLUTIONS

i i i i i i i i I

Liquid + Gas

Liquid

75 100 125 150 175 200 225 250 275 300 325


FIGURE 8. The molal enthalpy of the gas and the liquid phases in the H^O- NaCl system from 0 wt percent to halite saturation in the liquid phase be tween 80° and 325° C. The contour interval is 5 wt percent NaCl in the liquid phase. The shaded area contains data that were calculated by the extrapolation of functions given in the text. The bunching of the contours between 300° .and 325° C is most probably due to an artifact in the equa tions which is exaggerated when the partial molal enthalpy of aqueous NaCl is calculated.

noted. The most obvious place for improvement is the description of In y, the activity coefficient for aqueous NaCl. Use of several equations to describe ft in the activity coefficient function (eq 12) is acceptable as long as the derivative is not needed. However, this was not the situation in these steam tables where entropy is cal culated from equation 1:

-r

T K > (1)

The term was obtained from equation 22 as follows :

2 (AB) ^ (CD) (24)

The taking of the partial derivative for the first term is ther-

modynamically sound, because AG,' (AB) was evaluated using equilibrium constants, entropies, heats of solution, heat capacities, and partial molal volumes. Whereas the function is empirical, the function and its partial derivatives are consistent with thermodynamic theory.

NaCl COMPONENT IN BOILING Nad SOLUTIONS B17

Not so for the second term 3AG (BC) foT. When Liu and Lind- say (1972) evaluated the osmotic coefficient and activity coeffi cient data, no constraints were imposed except that the Debye- Hiickel limiting slope be obeyed. An improved evaluation of In y using the available heats of solution of halite and the heat capaci ties of aqueous NaCl would eliminate the obvious discordance in the data at about 110°C as shown on figures 4 and 5.

The other problem is the density and therefore the partial molal volumes of H 20 and NaCl. The available experimental data for the H20 NaCl system at temperatures above 100°C are poor. Apart from imprecise experimental methods, most experimental techniques involved the use of equipment that was corroded by the brine. The reported densities included the effects of dissolved H2 and metal ions. Improvement in this area entails the remeasure- ment of densities in the H20 NaCl system with an experimental design that is both highly accurate and free from corrosion.

TABLES FOR NaCl SOLUTIONS

Tables 1 through 28 give the temperature, pressure, and the density of the liquid at constant composition and 5° intervals be tween 80° C (or at the 5° interval just above halite saturation) and 325° C. The partial molal quantities of volume, entropy, and enthalpy for NaCl in the liquid are given. The third part of the tables gives the molar volume of the liquid and the molar entropy and molar enthalpy of the liquid and the gas that coexists with the liquid.

Tables 3, 6, 10, 13, 17, 21, and 26 give data at 5, 10, 15, 20, 25, 30, and 35 wt percent NaCl, respectively. The other tables give the data at intervals of 0.5 mol NaCl/kg H20 (molal) .

Tables 29 and 30 give the same data but at the given concentra tion on the halite saturation equilibrium between 80° and 325° C. Table 29 is in concentration units of wt percent NaCl and table 30 is mol NaCl/kg H2 0.

The tables were calculated by using the functions that are given in the preceding section. The data contained in parentheses were calculated by extrapolation of the functions beyond their range.

A detailed analysis of the accuracy and precision of the tabu lated data is not possible in this preliminary report. Haas (1976) discussed the accuracy of the vapor pressure, density, and volume data for the liquid and[ the gas and of the partial molal quantities for Ha O (#!,<$!, and Vi) in the liquid and the gas. In preparing this report, the following additional equations have been used:


Equation Property Source

(9) AG2 (A£) This report.(12) In 7 Liu and Lindsay (1972)

Assuming that the JANAF data for halite (NaCl[c]) are with

out error (?), the maximum error in AG 2° (AB) is 200 J mol- 1 . For the activity coefficient equation, Liu and Lindsay (1972) gave no estimate of either the accuracy or precision. However, an anal ysis of the graphical data which they supplied indicates that the maximum error in the activity coefficients is less than 0.003.

Even having this information, an estimate of the error in the

partial molal quantities for NaCl in the liquid ( V2 , H2 , and S2 ) cannot be made because these properties were calculated in part by the partial differentiation of equations 9 and 12, above, as well as other equations cited by Haas (1976).

In the tables, data are given that have as many as six digits. This is particularly true for data for entropy and enthalpy where most of the value represents the relative difference in the property between T and 0.01 °C and only a minor part of the value is due to change in concentration. The number of digits reported in the tables is governed by the need to have a reasonable resolution in the property when small changes in concentration or temperature are considered.

REFERENCES CITED

Bain, R. W., 1964, Steam tables 1964: Edinburgh, H. M. Stationery Office, 147 p.

Comm. on Atomic Weights, 1972, Atomic weights for 1971: Pure and Appl. Chemistry, v. 30, p. 637-649.

Committee on Data for Science and Technology, 1973a, CODATA recom mended key values, for thermodynamics, 1973, Report of the CODATA Task Group on key values for thermodynamics, November, 1973: CODATA Bull. 10, p. 1-11.

1973b, Recommended consistent values of the fundamental physical constants, 1973: CODATA Bull. 11, p. 1-8.

Criss, C. M., and Cobble, J. W., 1961, The thermodynamic properties of high temperature aqueous solutions. I. Standard partial molal heat capacities of sodium chloride and barium chloride from 0 to 100°. Am. Chem. Soc. Jour., v. 83, p. 3223-3228.

Gardner, W. L., Mitchell, R. E., and Cobble, J. W., 1969, The thermodynamic properties of high-temperature aqueous solutions. XI. Calorimetric deter mination of the standard partial molal heat capacity and entropy of sodium chloride solutions from 100 to 200°: Jour. Phys. Chemistry, v, 73, p. 2025-2032.


Haas, J. L., Jr., 1976, Physical properties of the coexisting phases and ther-mochemical properties of the H20 component in boiling NaCl solutions:U.S. Geol. Survey Bulletin 1421-A, 73 p.

Haas, J. L., Jr., and Fisher, J. R., 1976, Simultaneous evaluation and cor relation of thermodynamic data: Am. Jour. Sci., v. 276, (In press).

Keenan, J. H., Keyes, F. G., Hill, P. G., and Moore, J. G., 1969, Steam tables;Thermodynamic properties of water, including vapor, liquid, and solidphases: New York, John Wiley and Sons, 162 p.

Likke, Senay, and Bromley, L. A., 1973, Heat capacities of aqueous NaCl, KC1,MgCl2 , MgSO<, and Na-SO., solutions between 80° and 200°C: Jour. Chem.and Eng. Data, v. 18, p. 189-195.

Liu, Chia-tsun, and Lindsay, W. T., Jr., 1972, Thermodynamics of sodiumchloride solutions at high temperatures: Jour. Solution Chemistry, v. 1,p. 45-69.

Stull, D. R., and Prophet, H., 1971, JANAF thermodynamic tables: U.S. Natl.Bur. Standards, NSRDS-NBS 37, 1141 p.

TABLES 1-30

w to

to

Tab

le

1.N

aC

l co

nce

ntr

atio

n:

0.00

00 m

ol/

kg H

O0.

00

wt

per

cent

0.00

0 m

ol

per

cent

t(°

C)

80

.85.

.9

9.

95

.

100.

105.

110.

115.

120.

125.

130.

1.35

.li

*0.

1U5.

150.

155.

ICO

.1C

S.

170.

175.

130.

185.

1'JO

.1U

5.

' P

(bar

s)

0.1*

71*

0.5

78

0.7

01

0.8U

5

1.0

13

1.2

08

1.1*

331.0

91

1.1

85

2.3

21

2.7

01

3.1

31

3.61

1*it

. 15

5

it.

760

5.U

336.1

80

7.0

08

7.9

20

8.9

25

10.0

27

11.2

31*

12.5

52

13

.'J8

9

dL

(g c

m"

3)

0.9

72

0.9

69

0.9

65

0.9

62

0.9

58

0.9

55

0.9

51

0.9U

70.

91*3

0.9

39

0.9

35

0.9

31

0.9

26

0.9

22

0.9

17

0.9

12

0.3

07

0.9

02

0.8

97

0.8

92

0.8

87

0.8

82

0.8

76

0.8

70

'a

(cm

m

ol

17.9

117.6

117.2

916

.91*

1C.

5816.1

915.7

815

.31*

11*.

87

11*.

38

13.8

IJ13.3

112.7

212.1

1

11.1

*510.7

610.0

39.2

58.

1*3

7.5

66.

6U5.6

6U

. 62

3.5

2

saLH

Jmol^

-K"1

)

-21

.80

6-2

2.75

1*-2

3.7

37

-2U

. 76

2

-25

.83

6-2

6.9

66

-28.1

57

-29.U

16

-30.7

U5

-32

.15

1-3

3 .

i.3L

-35.

201*

-36

.85

9-3

8.6

02

-1*0

.1*3

8-1

*2.3

67-1

*1*.

392

-1*6

.516

-1*8

.739

-51

.06

1*

-53

.1*

92

-56

.02

1*

-58

.66

2-6

1.U

08

"a

(J m

ol"

1)

-6650.

.-6

98

7.

-73U

2.

-77

16

.

-811

1*.

-85

3S

.-8

99

1.

-9U

76.

-99

95

.-1

0551.

- 1

1 1

'. 5

.-1

1781.

-121

*60.

-131

81*.

-13955.

-11*

776.

-156

1*7.

-16572.

-17550;

-18586.

-19679.

-20832.

-220

1*7.

-23325.

VL

(cm

. m

ol

)

18.5

1*18.6

018.6

618.7

3

18.8

018.8

718

.9U

19.0

219.

1019.1

91:1

.27

19.3

619

.U5

19

.55

19.6

519.7

519.8

519.9

620.0

820.1

920.3

120

.1*1

*20.5

620.7

0

SL

19.2

96

20.3

56

21.U

0522

.1*1

*3

23.1

*69

21*.

U80

25.1

*79

26.1

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27.1

*1*1

*28

.U09

29.3

65

30.3

11

31.2

U8

32.1

77

33.0

97

31*.

009

31*.

911

.35.8

11

36.7

03

37.5

87

38.1

*66

39.3

1*0

U0.2

08

U1.0

72

i S

(J m

ol"

1 K

"1

117.

811*

11

5.5

3U

11

3.3

07

11

1.1

31

10

9.0

06

10

6.9

31

10U

. 901

10

2.9

15

10

0.9

71

99.0

65

97.1

96

95.3

62

J3.5

61

91

.73

1

90.0

1*9

88.3

36

86.6

1*8

8>*.

981

*83.3

U2

81.7

22

80.1

22

78.5

39

76.9

71*

75.U

2U

sc

13

7.1

10

13

5.8

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131*

. 712

13

3.5

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132.

1*75

131.

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13

0.3

81

12

9.3

82

128.

1*11

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7.U

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12

6.5

61

12

5.6

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121*

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r!23.9

67

123.

11*6

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2.3

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12

1.5

61

12

0.7

95

120.

01*5

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10

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11

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96

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60

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67

73

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96

97

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1*1*

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35

65

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31

0.

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U76

2U.

1*77

73.

1*79

21.

1*80

66.

1*82

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1*83

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1*81

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1*86

22.

U87

51*.

U88

83.

1*90

09.

1*91

31.

U92

U9.

1*93

61*.

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1*95

80.

1*96

82.

1*97

79.

1*98

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58.

500U

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50

11

6.

50

18

6.

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25

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M I I 3 Cd O w

O O

2 CO


FHiHiH«HiHrHiHi-4r-tr-4 OOOOOOOOOO O O O O ffl Cl

cowoooooocococowoo r* r* ^ ^ ^ ^ ^ ^ ^ ^ ^ °. . I

OOOOOOOOOO OOOOOOOOOO OOOOOO 0

I

Q

bd

to

NaC

l co

nce

ntr

atio

n:

0.50

00 m

ol/

kg

H O

2.84

w

t per

cent

0.89

3 m

ol

per

cent

t(°

C)

80.

85

.0

0.

95

.

100.

105.

110.

115.

120.

125.

130.

135.

1UO

.Id

5.

150.

155.

100.

165.

170.

175.

180.

185.

iao.

195.

P

(bar

B)

O.d

GS

0.5

68

0.6

89

0.8

31

0.9

96

1.1

87

l.d

OS

1.0

62

1.51

512.2

81

2.6

55

3.0

77

3.5

52

d.O

Sd

'4.0

79

5.3

dl

6.

076

6.8

89

7.7

86

8.7

73

9.8

57

12!3

dO

13.7

52

dL

(g c

m"

)0.9

91

0.9

88

0.9

85

0.9

81

0.9

78

0.9

7d

0.9

71

0.9

67

0.9

63

0.9

59

0.9

55

0.9

51

0.9

d7

0.9

d2

0.9

38

0.1

33

0.9

28

0.9

2d

0.9

19

0.9

1U

0.0

09

0.90

1*

0.8

98

0.8

93

VL

(cm

m

ol

19.6

019.d

l19.2

118.9

9

18.7

618.5

118

.21*

1

7.9

51

7.6

51

7.3

2lf

i.97

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.1*9

3

.979

.1*6

5).9

51)

.1*3

5).9

17

).3

97

)

11 .

198

mol

per

cent

HL

8861.

9190.

9518.

981*

3.10166.

101*

88.

10

80

8.

11

12

6.

111*

1*3.

11

75

8.

12

07

3.

12

38

8.

12

70

2.

13017.

13332.

13

65

0.

13

97

0.

11*2

93.

11*6

21.

1U95

I*.

1529

1*.

156i

»U.

16

00

3.

16

37

6.

1676

1*.

17170.

17599.

1805

1*.

185U

1.19065.

19635.

20258.

209U

7.

21713.

( 2257U

.)(

23550.)

( 21.6

68.)

( 25959.)

( 2

7U

67

.)

AH

(J m

ol"

1)

1*01

*17.

1*02

21.

1*00

25.

39

82

8.

39

63

0.

391*

31.

39

23

1.

39

02

9.

38

82

5.

38

61

8.

381*

08.

38

19

6.

37

97

9.

37

75

8.

37

53

2.

37

29

9.

37

06

0.

36

81

3.

30

55

6.

30

28

9.

30

01

0.

35

71

7.

351*

08.

35

08

1.

31*7

32.

31*3

59.

33

95

8.

3352

1*.

33

05

1.

3253

1*.

31

96

5.

31

33

5.

30

63

3.

2981

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( 28

95U

. )

( 27939.)

( 26775.)

( 2

5U

29

.)(

23856.)

HG

U92

73.

1*91

*12.

1*95

1*3.

1*90

71.

U97

97.

U99

19.

50

03

9.

50

15

5.

50

26

7.

50

37

6.

50U

82.

50

58

3.

50

08

1.

50

77

5.

5086

1*.

5091

*9.

51030.

51100.

51

17

7.

512U

3.5

13

05

.5

13

61

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U12

.

51U

57.

51U

9G.

51

53

0.

51

55

7.

51

57

8.

51

59

2.

51

00

0.

51

00

0.

5159

1*.

51

58

0.

51

55

8.

( 5

15

28

.)(

51

U9

0.)

( 51

UU

3.)

( 5

13

87

.)(

51

32

3.)

td o K s O

CO o r c: H I < o 2 172

Tab

le

t

21.

NaC

l

P

(°C

) (b

ars)

160.

1C5.

170.

175.

180.

185.

190.

195.

200.

205.

210.

215.

220.

225.

230.

235.

21*0

.2i

»5.

250.

255.

260.

265.

270.

275.

280.

285.

290.

2'J5

.

300.

305.

310.

315.

320.

325.

I*'

5 5 6 7 8 9 10 11 12 11*

15 17 1'J

20 22 25 27 20 32 35 38 1*1

1*1*

1*8

52 50 60 c;<i

( ('.9

( 7U

( 79

( 85

( 91

.523

.138

.818

.568

.392

.295

.283

.361

.535

.810

.192

.687

.302

.01*

2.9

11*

.925

.080

.388

.855

.1*8

7.2

93

.280

.1*5

5.8

26

.1*0

1.1

88

.195

.U31

.905

.625)

.601)

.81*

2).3

50

).1

61)

conce

ntr

atio

n:

dL

'

(g c

m"

)

1.1

37

1.1

33

1.1

28

1.12

1*1.1

20

1.1

15

1.1

11

1.1

07

1.1

02

1.0

98

1.0

93

1.0

89

1.0

85

1.0

80

1.0

76

1.0

72

1.0

67

1.0

03

1.0

59

1.0

55

1.0

51

1.01

*71.

01*3

1.0

39

1.0

35

1.0

32

1.0

28

1.0

25

1.0

21

1.0

18

1.0

15

1.0

12

1.0

00

1.0

07

a(c

m m

ol

26

.60

26.7

226

.81*

26.9

52

7.0

627.1

527

.2U

27

.33

27.U

O27

.1*6

27.

SI

27.5

1*2

7.5

72

7.5

72

7.5

727

.51*

27.5

027

.M3

27

.35

27.2

1*2

7.1

126

.91*

26.7

620

.5U

26

.29

26

.01

25.7

02

5.3

7

25

.00

21*.

03

21*.

25

23

.88

23

.58

23.3

8

7.3

33

2m

ol/

kgH

30

'

s: a_

_ a_

..V

L

30.0

0 w

t p

erce

nt

SL

AS

SG

11.6

70 m

ol p

erce

nt

HL

) (J

mo

l K

)

(J m

ol

) (c

m

mol

) (J

mol

K

)

-23

-21*

-21*

-21*

-2U

-21*

-21*

-25

-25

-25

-25

-26

-26

-26

-26

-26

-25

-25

-21*

-23

-22

-21

-10

-16

-13 -9 -50 7

( 15

( 25

( 37

( 51

( 69

.H21

.02

0.1

56

.326

.526

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8.9

88

.237

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5.7

21*

.91*

0.1

21

.25

1.3

11

.28

3.1

1*2

.861

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0

.751

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50

.65

1.1

01

.13

3.6

71

.871

*.2

98

.268

.01

9.1

01*)

(

.. U

4 3

) (

.089)

(.0

59)

(.1

*17)

(

1*75

0.1*

680.

1*59

2.1*

1*87

.1*

367.

1*23

1* .

U09

2!39

1*3.

3791

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1*2.

3502

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76.

3273

.32

02.

3175

.32

02.

3300

.3U

85.

3778

.1(

202.

1*78

5.55

60.

6566

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1*9.

91*6

5.11

1*80

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975.

1705

0.

2082

1*.

25i*

i»7.

)3

11

07

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0UO

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r,5i*

6. )

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7. )

20

.00

20.0

72

0.1

520.2

32

0.3

020.3

820

.U6

20.5

1*

20

.63

20

.71

20.7

92

0.8

720.9

621

.01*

21.'

132

1.2

121.3

021.3

8

21.1

*721.5

52

1.6

321.7

22

1.8

021.8

82

1.9

622

.0U

22

.11

22

.19

22. 2

G2

2.3

32

2.3

922

. U6

22

.52

22.5

8

28.2

73

29.0

08

29.7

30

30.1

*1*0

31.1

i*0

31.8

31

32.5

12

33.1

86

33.8

53

31*.

515

35.1

71*

35.8

31

36.U

8837

.1U

837.8

12

38.U

8U39.1

68

39.8

65

1*0.

582

1*1.

322

1*2.

092

U2.

898

U3.

7U7

1*1*

. 6U

81*

5.61

1*1*

6.65

51*

7.78

81*

9.03

0

50.1

*06

( 51

.91*

2)(

53.6

73)

( 5

5.6

U2

)(

57.9

01.)

( 60.5

31)

96.3

1*6

9U. 8

6893

.U20

92.0

01

90.6

10

89.2

1*1*

. 87.9

02

86.5

82

85.2

81

83.9

97

82.7

29

81.U

7380.2

27

78.9

89

77.7

51*

76.5

20

75.2

82

7fc.

036

72.7

78

71.5

02

70.2

01

68.8

69

67.1

*98

66.0

77

6U. 5

9563.0

39

61.3

91*

59.6

39

57.7

53

( 5

5.7

05

)(

53.U

62)

( 5

0.9

80

)(

U8.2

03)

( 1*

5.06

0)

12U

.620

123.8

75

123.1

50

122.

1*1*

2121.7

50

121.0

75

120.

U1U

119.7

67

119.

131*

118.5

12

117.9

03

117.

SOU

116.7

15

116.1

36

115.5

66

115.

001*

111*

. UU9

113.9

02

113.3

60

112.

82U

112.2

93

111.7

67

111.

21*1

*110.7

25

110.2

09

109.

691*

109.1

82

108.6

70

108.1

58

(107

.61*

7)(1

07.1

35)

(106.6

22)

(10

6.1

08

)(1

05

.59

1)

101*

31*.

1075

2.11

068.

1138

3.11

6-96

.12

008.

1232

0.12

632.

1291

*1*.

1325

7.13

572.

1388

9.11

*210

.11

*535

.11

*866

.15

205.

1555

2.15

911.

1628

2.16

670.

1707

8.17

508.

1796

7.18

1*58

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989.

1956

7.20

201.

2090

1*.

2168

8.(

22

57

2.)

( 2

35

76

.)(

21*7

29.)

( 26

065.

)(

27

62

8.)

AH

(J m

ol"

1)

391*

97.

39

29

9.

3910

0.38

899.

3869

6.38

U90

.38

281.

3806

8.

3785

1.37

628.

371*

00.

3716

5.36

922.

3666

9.36

1*06

.36

131.

3581

*1.

3553

5.

3521

0.3U

86I*

.31

*1*9

2.3U

091.

3365

6.33

181.

3266

0.32

086.

311(

1(7.

3073

3.

2993

0.(

29

01

9.)

( 27980.)

( 26

78U

.)(

25397.)

( 23772.)

HG

U99

31.

50

05

1.

5016

8.50

282.

5039

2.50

1*98

.50

601.

5070

0.

5079

5.50

885.

5097

2.51

05U

.51

131.

5120

U.

5127

2.51

335.

5139

3.51

1*1*

6.

511*

93.

5153

1*.

5157

0.51

599.

5162

2.51

639.

516U

9.51

652.

5161

*8.

5163

7.

5161

8.(

51

59

1.)

( 5

15

56

.)(

51

51

3.)

( 51

1*61

.)(

51U

OO

.)

SB

O O

O "d

O M S3

O 25

O a; O r1 d

NO

TE

. D

ata

con

tain

ed

in par

enth

eses

w

ere

calc

ulat

ed

by e

xtr

apo

lati

on

of

th

e fu

nct

ion

s be

yond

th

eir

ran

ge.

bd Oi

Tab

le

t(°

C)

170.

175.

180.

185.

190.

1'J

S.

200.

205.

210.

215.

220.

225.

230.

235.

2UO

.2U

5.

250.

255.

260.

2G5.

270.

275.

280.

285.

290.

295.

.30

0.

305.

310.

315.

320.

325.

22.

NaC

l co

nce

ntr

atio

n:

P

(bars

)

5.7U

86.5

12

7.3

50

8.2

27

0.2

09

10

.28

0

11.1

*1*6

12.7

13

11*.

087

15

.57

31

7.1

78

18.9

08

20

.77

0

.2

2.7

69

21*.

913

27

.20

9

20.6

62

32.2

82

35.0

71*

38.0

1*6

U1.2

05

.1*

1*. 5

601*

8.11

95

1.8

89

55.8

78

60

.09

6

6U.5

5U(

69.2

50)

( 71

*. 2

06)

( 7

9.U

26

)(

81*.

92

0)

( 90.6

99)

dL

(g c

m"

)

(1.1

32)

(1.1

28)

(1.1

23)

(1.1

19)

(1.1

15)

(1.1

10)

(1.1

06)

(1.1

01

)(1

.097)

(1.0

93)

(1.0

88)

(1.0

81*)

(1.0

80)

(1.0

75)

(1.0

71)

(1.0

67)

(1.0

63)

(1.0

58)

(1.0

51*)

(1.0

50)

(1.0

U6

)(1

.01*3)

(1.0

39

)(1

.035)

(1.0

32)

(1.0

28)

(1.0

25)

(1.0

22)

(1.0

19)

(1.0

16)

(1.0

13)

(1.0

11)

VL

7.5

00

0m

ol/

kg

H O

'

**a

(cm

m

ol

) (J

mol

K

) (J

mo

l" )

( 27.0

5M

( 27.1

7M

( 2

7.2

9H

( 27

.UO

M(

27

.50

M(

27.5

9M

( 27.6

8M

( 2

7.7

6M

( 27.E

2H

( 27.8

7M

( 2

7 . 9

1 )

((

27

.9U

M(

27.9

5M

( 27.9

5M

( 27.9

3H

( 27.8

8M

( 27.8

2H

( 27.7

UH

( 27.6

i*)(

( 27.5

1M

( 27.3

5H

( 27.1

7M

( 26.9

6M

( 20.7

2M

( 26.1

*6)(

( 26.1

8)(

( 2S

.88M

( 2

5.5

6M

( 25.2

5.H

( 2i*

.98)(

( 2!*

.76)(

( 2i*

.68)(

-23

.83

9)

(-2

1*. 0

06

) (

-2i»

. 202)

(-2

1*. 1

*21)

(

-21*

. 65

8)

(-2

1*. 9

01.)

(

-25.1

51)

(-2

5.3

87)

(-2

5.6

01)

(-2

5.7

80)

(-2

5.9

08)

(-2

5.9

66)

(-2

5.9

35)

(-2

5.7

92)

(-2

5.5

08)

(-2

5.0

51

*)

(

-21*

. 391

*)

(-2

3.1

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5)

(-2

2.2

81)

(-2

0.7

23)

(-1

8.7

1*

7)

(-1

6.2

75)

(-1

3.2

13)

(-9

.1.5

1)

(-U

.85

6)

(0

.73

3)

(

7.5

11

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15

.72

1)

(2

5.6

61

) (

37

.70

8)

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3U2)

(

70

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0)

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U9I

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727.

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596.

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7. )

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86

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371.

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361*

2.)

3572.)

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3571

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3671

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38

61

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1*15

5. )

1.58

2. )

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59

1.6

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95

7.

)8

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5.)

98

68

.)11891.)

1U

39

7.)

17

U8

5.)

21275.)

25918.

)31602.)

38565.)

1*71

09.

)57629.)

VL

30.4

7 w

t per

cent

SL

asSG

11 .

903

mol

per

cent

HL

(cm

m

ol

)

(J m

ol"

K

" )

(20.1

7)

(20.2

U)

(20.3

2)

(20.1

.0)

(20.U

8)

(20.5

6)

(20.6

1*)

(20.7

3)

(20.8

1)

(20.8

9)

(20

.98

)(2

1.0

6)

(21.1

1*)

(21.2

3)

(21

.31

)(2

1.U

O)

(21.1

*8)

(21.5

7)

(21.6

5)

(21.7

3)

(21.8

1)

(21.8

9)

(21.9

7)

(22.0

5)

(22

.12

)(2

2.2

0)

(22.2

7)

(22.3

3)

(22

. U

O)

(22.1

*6)

(22

.52

)(2

2.5

9)

( 29.5

61)

( 30.2

C9)

( 30.9

67)

( 3

1.G

55

)(

32.3

33)

( 3

3.0

0U

)

( 33.6

69)

( 31

*. 3

28)

( 3l

*.98

i»)

( 35.6

30)

( 3

6.2

0U

)(

36.9

51)

( 37.6

13)

( 38

.281

*)(

38.9

66)

( 39.6

62)

( 1*

0.37

9)(

1*1.

119)

( 1*

1.89

0)(

1*2.

697)

( 1*

3.51

*9)

( U

l*. 1

*56)

( U

5.U

27)

( 1*

6.1*

76)

( 1*

7.61

9)(

i*8.

87l»

)

( 50.2

66)

( 51.8

22)

( 53.5

78)

( 55.5

78)

( 57.8

78)

( 60.5

51)

( 93.6

72)

( 9

2.2

56

)(

90.8

66)

( 89.5

02)

( 88.1

63)

( 86

.81*

1*)

( 85

.51*

6)(

8U. 2

65)

( 82.9

99)

( 81

.71*

6)(

80.5

02)

( 79.2

66)

( 78.0

33)

( 76.8

00)

( 75

.561

*)(

71*.

32

0)

( 73.0

62)

( 71.7

86)

( 7

0.U

85

)(

69.1

52)

( 67.7

78)

( 66.3

53)

( 6U

. 866)

( 63.3

03)

( 6

1.6

U8

)(

59.8

82)

( 57.9

80)

( 5

5.9

1U

)(

53.6

1.7

)(

51

.13

6)

( 1.

8. 3

22)

( 1.

5.13

1.)

123.

231.

12

2.5

25

12

1.8

33

12

1.1

57

12

0.U

96

119.

81.9

119.2

15

118.5

93

11

7.9

83

117.

38U

11

6.7

96

116.2

17

115.

61*6

115.

081*

111*

. 530

11

3.9

82

113.

1*1*

1112.9

05

11

2.3

75

111.

81*9

11

1.3

27

110.8

08

11

0.2

93

10

9.7

79

10

9.2

67

10

8.7

56

108.

21*6

(107.7

36)

(10

7.2

25

)(1

06

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3)

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6.2

00

)(1

05

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5)

( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (

11038.)

11352.)

1166

U.

)11975.)

12286.)

12596.)

12907.)

13218.)

13532.)

1381

*8.)

11.1

67.)

i

li*

82

l!)

15158.)

15505.)

15863.)

1623

1*.)

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16622.)

i

17030.)

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17

U6

1.)

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17921.)

. i

18l»

ll».)

1

18948.)

i

19530.)

i

20170.)

i

20880.)

i

21673.)

1

22568.)

1

23587.)

1

21*7

57.)

1

26115.)

1

27706.)

1

AH

(J m

ol"

1)

( 39135.)

( 38937.)

( 38735.)

( 38531.)

( 38

321*

.)(

38113.)

( 37898.)

( 37678.)

( 37

1*51

.)(

37218.)

( 36977.)

( 36727.)

( 36

1*66

.)(

36192.)

( 35

901*

.)(

35600.)

( 35276.)

( 3

U9

31

.)(

31*5

59.)

( 3

U1

58

.)(

33723.)

( 33

21*7

.)(

32725.)

t 3

21

U7

.)[

3150

1*.

)(

30785.)

t 29

97U

. )

[ 29

051*

.)

([

28002.)

(

[ 26790.)

(

[ 25382.)

(

[ 23732.)

(

HG

50

17

5.

50

28

9.

50

39

9.

50

50

6.

50

61

0.

50

70

3.

50

80

5.

50

89

6.

50

98

3.

51

06

6.

511U

I*.

51

21

8.

51

28

6.

51

35

0.

51U

09.

511*

62.

51

51

0.

51

55

3.

51

58

9.

51

62

0.

5161

*1*.

51

66

2.

51

67

3.

51

67

7.

51

67

5.

51

66

5.

516U

7.51622.)

51588.)

51

5U

7.)

511*

96.)

51

U3

8.)

bd Oi

to w HH

S H

>

g H

>

W r1

w CO .*J

o

» S5

»

O GO

O

f O si-

NO

TE

. Dat

a co

ntai

ned

in p

aren

thes

es w

ere

calc

ulat

ed b

y ex

trap

olat

ion

of t

he f

unct

ions

bey

ond

thei

r ra

nge.

Tab

le

t(°

C)

200.

205.

210.

215.

220.

225.

230.

235.

21*0

.21

*5.

250.

255.

260.

265.

270.

275.

280.

285.

290.

295.

300.

305.

310.

315.

320.

325.

23.

NaC

l co

nce

ntr

atio

n:

P

(bar

e)

11.1

78

12.U

21

13

.76

915.2

29

16.8

06

18

.50

62

0.3

37

22.3

0U

21*.

1*1

32

6.6

73

29

.09

03

1.6

70

3U. 1

*21

37.3

51

U0.

i*67

U3.7

77

U7.2

89

51.0

10

51*.

91*

959

.111

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63.5

15

( 68.1

60

)(

73

.05

8)

( 7

6.2

19

)(

83.6

53

)(

89

.36

9)

8.0

000

mo

l/k

g H

aO

'

dL

V

L

<£

' H

aL

(g c

m"

)

(1.1

16

)(1

.112)

(1.1

07)

(1.1

03)

(1.0

99)

(1.0

9U

)(1

.090)

(1.0

86)

(1.0

81)

(1.0

77)

(1.0

73)

(1.0

69)

(1.0

65)

(1.0

61)

(1.0

57)

(1.0

53)

(1.0

U9"

)(1

.0U

6)

(1.0

U2

)(1

.039)

(1.0

36)

(1.0

33)

(1.0

30)

(1.0

27

)(1

.025)

(1.0

22)

(cm

m

ol

) (J

mol

( 28

( 28

( 28

( 28

( 28

( 29

( 29

( 29

( 29

( 29

( 2'

J(

29(

29(

29(

29(

29(

28(

28(

28(

28

( 28

( 28

( 28

( 28

( 28

( 28

.SIM

.63

)(. 7

1* )

(.S

UM

.93M

.01 )

(.0

8M

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) (

. 18

)(.2

1M

.22

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1)

(. 1

9)

(. 1

5)

(.1

0X

.02

)(.9

3M

.82M

.69M

.56

M

.U3

M. 3

1 ) (

. 21

) (. 1

8 ) (

.25M

.50M

-2U

-2U

-21.

-21.

-2U

-2U

-21.

-21.

-21.

-21.

-23

-22

-21

-19

-17

-15

-12 -8 -31 8

17 27 39 5U 72

^K

"1)

(J m

ol"

1)

.112

) (

.350)

(.5

66

) (

.7U

6)

(.8

76

) (

.937

) (

.009

) (

.767)

(.1

.85)

(.0

31)

(

.369

) (

.1.5

7)

(.2

1.6

) (

.680)

(.6

90

) (

.109)

(.1

12

) (

.318)

(.6

81)

(.9

61

) (

.806)

v.1

01)

(.1

1*8)

(

.331

) (

.137)

(.1

91.)

(

52U

3.)

5091

.. )

1*95

3.)

U82

7. )

U72

U.

)1

.65

3.)

1.62

1..

)1.

652.

)1*

751.

)1*

937.

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52

33

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66

1.)

62

50

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70

33

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05

1.)

931*

0. )

10985.

)13027.)

15557.

)18

671*

. )

22

50

3.)

27

19

6.)

329U

3. )

39985.

)1*

8632

. )

59283.

)

VL

(cm

m

ol"

i

(20.7

0)

- (2

0.7

9)

(20

.87

)(2

0.9

5)

(21.0

1*)

(21.1

2)

(21.2

0)

(21.2

9)

(21.3

7)

(21

.1.5

)

(21.5

1*)

(21.6

2)

(21.7

0)

(21.7

8)

(21.8

6)

(21

.91

.)(2

2.0

2)

(22.0

3)

(22.1

7)

(22

.21

.)

(22.3

1)

(22.3

7)

(22

.1.3

)(2

2.1

.9)

(22.5

0)

(22.6

2)

31.8

6 w

t p

erc

en

t

SL

ass°

12.5

97 m

ol

perc

en

t

HL

) (J

mor'

K"

1)

( 33

( 33

( 31

.(

35(

35(

36(

37(

37(

38(

39

( 39

( (.0

( U

l(

U2

( 1.

2(

1.3

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( 45

( 1.

7(

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( 51

( 53

( 55

( 57

( 60

.108)

.75

9)

.1.0

6)

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2)

.69

9)

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).0

05)

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39

)

.75

3)

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It )

J26

7)

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9)

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58)

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6).9

18

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90

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81.)

.822)

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8).2

67

).3

58

).7

71)

.581

*)

( 86

( 85

( 83

( 82

( 81

( 80

( 78

( 77

( 76

( 75

( 73

( 72

( 71

( 70

( 68

( 67

( 65

( 6U

( 62

( 60

( 58

( 56

( 5U

( 51

(. US

( 1*

5

.355)

.08

1)

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.57

7)

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O)

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1)

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U)

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6).1

85

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0)

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33)

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7)

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10)

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6)

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6)

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9)

.69

6)

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119.

118.

118.

117.

117.

116.

115.

115.

111*

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1*.

113.

113.

112.

112.

111.

. 111.

110.

110.

100.

109.

108.

(10

7.

(10

7.

(10

6.

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(105.1*

6381

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901

*01*

6088

932

777

222

5

681*

1>*8

619

093

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51*1

028

518

009

501

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7)

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)955)

( 12790.)

( 13097.)

( 1

3U

06

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13718.)

( 11

*035

.)(

11*3

53.)

( 1U

679.)

( 15013.)

T

15356.)

( 15712.)

( 16082.)

( 1

6U

69

.)(

16877.)

( 17311.)

( 17

771*

.)(

1827

U.

)(

18816.)

( 19

1*10

.)(

20

06

6.)

( 20796.)

( 21616.)

( 22

5UU

. )

( 23

601*

.)(

21*8

27.)

( 26250.)

( 27923.)

AH

(J m

ol"

1)

( 38

01*5

.)(

37831.)

( 37611.)

( 37

38U

. )

( 371U

9.)

( 36905.)

( 36650.)

( 36382.)

( 36100.)

( 35800.)

( 35

1*81

.)(

35139.)

( 31

*770

.)(

31*3

70.)

( 33933.)

( 33

1*55

.)(

32927.)

( 32

3UO

.)(

31685.)

( 30

91*9

.)

( 30116.)

( 29166.)

( 28077.)

( 26817.)

( 25

31*8

.)(

23620.)

HG

50835.

50928.

51

01

7.

51102.

51182.

51

25

8.

51329.

51395.

511.

56.

51

51

2.

515G

3.5

16

08

.51

0U7.

51080.

51708.

51

72

3.

517U

3.5

17

51

.5

17

52

.51

7U5.

51

73

2.

( 51710.)

( 51681.)

( 51

61*1

*.)

( 51538.)

( 5

15

U3

.)

o

o W

O a; o O CQ O H

i

O as CO

NO

TE

. Dat

a co

ntai

ned

in p

aren

thes

es w

ere

calc

ulat

ed b

y ex

trap

olat

ion

of t

he f

unct

ions

bey

ond

thei

r ra

nge.

w o» CO


O OOOlAlAO r»»K>CniAf-tlO«~*lAOOfH C-INtfH

CT» f1*. IA H> O

^H O 01 <

O oo r- i

6 S O O O O OOOOCOOOOO O O O O O O

Tab

le

t

25.

NaC

l co

nce

ntr

atio

n:

P

(°C

) (b

ars

)

250.

255.

260.

265.

270.

275.

280.

285.

290.

295.

500.

505.

510.

515.

520.

525.

27 30 33 35 38 U2

U5

U9

53 57 61(

60(

70(

75(

81(

86

.925

.U31

.105

.955

.989

.215

.639

.271

.119

.191

.U97

.OU

U)

.8U

2)

.902)

.233)

.8U

U)

9.00

00 m

ol/

kg

H30

'

a a

a(g

cm

'3)

(1.0

91)

(1.0

87)

(1.0

83)

(1.0

79)

(1.0

75)

(1.0

71)

(1.0

68)

(1.0

6U

)(1

.061)

(1.0

57)

(1.0

5U

)(1

.051)

(1.0

U8)

(1.0

U5)

(1.0

U2)

(1.0

59)

(cm

m

ol

) (J

mol

K

) (J

mo

l" )

( 51

( 32

( 32

( 32

( 32

( 32

( 52

( 32

( 32

( 33

( 33

( 35

( 33

( 3U

( 5U

( 55

.88

)(.0

5)(

. 17

) (.3

0)(

.U3)(

,55

)(.6

8)(

.81H

.95

)(.!

!)(

,30

)(,5

U)(

.86

)(.5

0)(

.91 )

(.7

9)(

-21.5

70)

(-2

0.6

98)

(-1

9.5

2U

) (

-17.9

89)

(-1

6.0

2U

) (

-15.5

50)

(-1

0.U

70

) (

-6.6

69

) (

-2.0

09

) (

3.6

76

) (

10.5

90)

(18.9

85)

(29.1

7U

) (

U1.5

50)

(5

6.6

15

) (

75

.02

1)

(

715U

.)7561.

)8

13

1.

)8

89

7.)

9901.

)11190.

)12823.

)1U

860.

)17U

11.)

20

55

3.)

2UU

22.)

29

17

3.)

55

00

3.)

U2160.

)50962.

)61823.

)

VL

(cm

m

ol

(21

.68

)(2

1.7

6)

(21.

8U)

(21

.92

)(2

2.0

0)

(22

.08

)(2

2.1

6)

(22

.25

)(2

2.5

0)

(22

.57

)

(22

. U

U)

(22.5

0)

(22

.57

)(2

2.6

5)

(22.7

0)

(22

.77

)

34.4

7 w

t p

erc

en

t

SL

AS

SG

13.9

52

mol

perc

en

t

HL

) (J

mo

l"1

K"

1)

( 58.

( 59.

( 59.

( U

O.

( U

l.(

U2.

( U

5.(

UU

.(

us.

( U

7.

( U

S.(

50.

( 52.

( 5U

.(

57.

( 60.

U15

)150)

923)

7UO

)612)

550)

56

7)

67

9)

90

5)

267)

79

5)

52

2)

U92

)7

58

)3

90

)U

77)

( 75

( 7U

( 73

( 71

( 70

( 69

( 67

( 65

( 6U

( 62

( 60

( 57

( 55

( 52

( U

9(

US

.76

9)

.U9

7)

.195)

.85

0)

.U5

6)

.00

0)

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9)

.8U

5)

.lin

).2

UO

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.20

6)

.97

2)

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7)

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U)

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U)

.98

8)

11U

115

115

112

112

111

111

lin

110

109

109

(108

(10

7(1

07

(106

(106

. 18

U.6

U7

.116

.590

.068

.551

.056

.52U

.015

.507

.000

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).9

88)

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2)

.97

U)

.U6

5)

( 15727.)

( 16110.)

( 16517.)

( 16952.)

( 1

7U

21

.)(

17930.)

( 1

8U

87

.)(

19102.)

( 19780.)

( 2055U

.)

( 21U

23.)

( 22

U1U

.)(

2555U

.)(

2U

878.)

( 26U

28.)

( 28265.)

AH

(J m

ol"

1)

( 359U

1.)

( 35607.)

( 55

2UU

.)(

3U

8U

8.)

( 3U

U12

.)(

53929.)

( 33392.)

( 32791.)

( 5211U

.)(

513U

6.)

( 30U

70.)

( 29U

65.)

( 28502.)

( 269U

8.)

( 25558.)

( 2

5U

77

.)

HG

51

66

7.

51

71

7.

51

76

1.

51

80

0.

51

83

5.

51

85

9.

51

88

0.

51

39

3.

51

30

0.

51

90

0.

51

89

5.

( 51878.)

( 51856.)

( 51825.)

( 51787.)

( 51

7UO

.)

O

O O 52!

H W

O O So CO

O O as

c/2

NO

TE

. Dat

a co

nta

ined

in

par

enth

eses

wer

e ca

lcu

late

d

by e

xtra

pol

atio

n

of t

he

fun

ctio

ns

beyo

nd t

hei

r ra

nge

.w o

or

w CTJ

M

I I §

Tab

le

t

26.

NaC

l co

nce

ntr

atio

n:

P

(°C

) (b

are)

260.

265.

270.

275.

280.

285.

290.

295.

300.

305.

310.

315.

320.

325.

32 35 38 1*1

1*5

1*3

52 56 61(

65(

70(

75(

80(

86

.813

.01*

6.6

63

.870

.277

.891

.720

.772

.058

.58

6)

.36

5)

.1*0

1*)

.71

5)

.30

6)

dL

'

-3(g

cm

)

(1.0

87)

(1.0

83)

(1.0

79)

(1.0

75)

(1.0

71)

(1.0

68)

(1.0

61*)

(1.0

61)

(1.0

58)

(1.0

51*)

(1.0

51)

(1.0

1*8)

(1.0

1*5)

(1.0

U2)

j »

9.21

35 m

ol/

kg H

aO

'

§*-.

a

(cm

m

ol

) (J

mol

K

) (J

mol"

)

( 32

( 32

( 33

( 33

( 33

( 33

( 33

( 31

*

' (

31*

( 31

*(

35(

35(

36'

( 37

.78

)(.9

5)(

. 11

) (

,28)(

. 1*5

) (

.63

)(.8

3)(

.05H

.31

)(! 6

2 )

(.0

3)(

.56

)(.2

8)(

.29

)(

-10.2

17)

(-1

7.6

97)

(-1

5.7

1*

6)

(-1

3.2

85)

(-1

0.2

15)

(-6

.U22

) (

-1.7

68)

(3

.91

5)

(

10

.83

3)

(1

9.2

38

) (

29.1

*1*5

) (

U1.8

U9)

(56.9

57

) (

75

.1*

23

) (

81*8

5.)

921*

3.)

10239.)

11522.)

131U

8.)

15189.)

17729.)

20871.

)

21*7

1*1.

)29

U99

. )

35339.

)1*

2513

.)51

31*0

.)62237.

)

VL

(cm

m

ol

(21

.88

)(2

1.9

0)

(22.0

U)

(22

.12

)(2

2.1

9)

(22.2

7)

(22

. 3U

)(2

2.1

*1)

(22.1

*8)

(22.5

1*)

(22.6

1)

(22.6

7)

(22.7

1*)

(22.8

1)

35.0

0 w

t per

cent

SL

AS

sc14

.235

mol

per

cent

HL

) (J

mo

r'K

"1)

( 39.

( 1*

0.(

111.

( 1*

2.(

1*3.

( 1*

1*.

( 1*

5.(

U7.

( U

S.(

50.

( 52.

( 51

*.(

57.

( 60.6

16

)1*

33)

30

7)

2U8)

27

0)

38

9)

621*

)001)

5U6)

295)

29i»

)596)

27<»

)1*

18)

( 73.6

12)

( 72.2

67)

( 7

0.8

72

)(

69.1

*13)

( 67.8

76)

( 66

.21*

5)(

61*.

U99

)(

62.6

15)

( 60.5

63)

( 58.3

07)

( 55.8

03)

( 52

.991

*)(

1*9.

809)

( 1*

6.15

6)

11

3.2

27

11

2.7

01

11

2.1

79

111.6

60

111.

11*6

110.

631*

110.

121*

10

9.6

16

10

9.1

09

(10

8.6

03

)(1

08

.09

7)

(10

7.5

90

)(1

07

.08

3)

(106.5

71*)

( 16

1*28

.)(

16863.)

( 1

73

32

.)(

1781

*3.)

( 18

1*02

.)(

19

02

1.)

( 19710.)

( 20

1*85

.)

( 21

36U

. )

( 22367.)

( 23

521*

.)(

21*8

68.)

( 26

1*1*

6.)

( 28

311*

.)

AH

(J m

ol"

1)

( 35358.)

( 3fc

963.)

( 31

*528

.)(

3I*O

U5.

)(

33507.)

( 3

29

03

.)(

32222.)

( 31

1*1*

8.)

( 30

561*

.)(

2951

*6.)

( 28369.)

( 26995.)

( 25381.)

( 23

1*67

.)

H°

51

78

6.

51

82

6.

51860.

51888.

51909.

5192

1*.

51

93

2.

51933.

51927.

( 51

91U

. )

( 5

18

93

.)(

51

86

U.)

( 51826.)

( 5

17

81

.)

M VI

.0 r

a H i i

O

NO

TE

. Dat

a co

ntai

ned

in p

aren

thes

es w

ere

calc

ulat

ed b

y ex

trap

olat

ion

of t

he f

unct

ions

bey

ond

thei

r ra

nge.

Tab

le

t

27.

NaC

l co

ncen

trati

on

:

P

(°C

) (b

ars

)

27

0.

275.

28

0.

285.

290.

29

5.

300.

305.

310.

315.

320.

525.

38 1*1

'.I*

US

52 56 60(

6U(

69(

7U(

80(

85

.21

3.3

96

.778

.36

6.1

70

.19

7

.1*5

6.9

57)

.710

).7

22

).0

06)

.570

)

9.5

000 m

ol /

kg

HaO

'

dL

V

aL

S£

HaL

(g c

m"

)

(1.0

83)

(1.0

79

)(1

.07

5)

(1.0

72)

(1.0

68)

(1.0

65)

(1.0

62)

(i.o

sn)

(1.0

56)

(1.0

52

)(1

.01

*9

)(l

.OU

G)

(cm

3m

ol~

1)(J

mo

l"i

K"1

) (J

mo

l"1)

( 31

*(

3U(

31*

( 31

*(

31*

( 35

( 35

( 36

( 36

( 37

( 38

( 39

.02

)(.2

5)(

. 1*8

) (

.72

)(.9

9)(

. 2-9

) {

.6U

)(.0

5)(

.57H

.23

)(.

10 )

(.2

8)(

-15.U

16)

(-1

2.9

77

) (

-9.9

27)

(-6

.150)

(-1

.509)

(I*

. 167)

(

11.0

81*)

(1

9.1

*3

7)

(29.7

21)

(1

*2

.15

6)

(.57.3

13)

(75.8

52)

(

10662.)

11933.)

13

5U

9.)

15580.)

18113.)

21

25

1.)

25121.)

29883.)

3573U

. )

1*

29

26

.)51783.)

6272

1*.

)

VL

(cm

m

ol"

(22.0

9)

(22.1

7)

(22

.2U

)(2

2.3

2)

(22.3

9)

(22.1

*6)

(22.5

3)

(22.0

0)

(22.6

7)

(22.7

3)

(22.8

0)

(22.8

8)

35.7

0 w

t perc

ent

SL

)

( 1*

0(

1*1

( U

2(

1*3

( U

5(

U6

( 1*

8(

1*9

( 52

( 5U

( 57

( 60

(.

.88

3)

.827)

.85

5)

.98

3)

.23

1)

.625)

.19

3)

.972)

.008)

.358)

.09

5)

.315)

AS

Fm

or

( 7

1.

( 6

9.

( 6

8.

( 6

6.

( 6

5.

( 6

3.

( 6

1.

( 5

8.

( 5

6.

( 5

3.

( 5

0.

( 1*

6.

V1'

1*1*

9)986)

U U

2)802)

01*3

)11.1

)

066)

780)

237)

381)

135)

1.07

)

SG

112.3

31

11

1.8

12

111.2

97

11

0.7

81

*1

10

.27

1*

109.7

65

10

9.2

58

(108.7

52)

(10

8.

2U

5)

(107.7

38)

(10

7.2

31

)(1

06

.72

2)

14.6

13

mo

l perc

en

t

HL

A

H

(J m

ol"

1)

( 17201*.)

31

*691

*.)

( 17716.)

( 18278.)

( 18901.)

( 19598.)

( 20382.)

( 21273.)

( 22293.)

( 231*71.)

( 2

1*

81

.3.)

( 2

61

*5

5.)

31

*2

11

.)3

36

72

.)3

30

65

.)3

23

78

.)31596.)

30701.)

29669.)

28U

72.

)2

70

73

.)251.2

5.)

( 28368.)

(

23

U6

9.)

H°

51897.

51

92

7.

51950.

51

96

6.

51

97

6.

51

97

9.

51971..

( 51962.)

( 5

19

U3

.)(

5191G

.)(

51880.)

( 51836.)

P

O O

O S

NO

TE

. Dat

a co

ntai

ned

in p

aren

thes

es w

ere

calc

ulat

ed b

y ex

trap

olat

ion

of t

he f

unct

ions

bey

ond

thei

r ra

nge.

ta

o

Tab

le

28.

NaC

l co

ncen

trati

on

:1

0.0

00

0 m

ol/

kg H

O3

6.8

9

wt

perc

ent

15.2

65 m

ol

perc

ent

t

(C)

29

0.

29

5.

300.

30

5.

310.

315.

32

0.

32

5.

P

(bars

)

51.1

56

55.1

36

59.3

U8

( 6

3.8

01

)(

68

.50

5)

( 73.U

69

)(

78.7

01.)

( 8U

.220

)

dL

(g c

m"

)

(1.0

75)

(1.0

72)

(1.0

68)

(1.0

65

)(1

.062)

(1.0

58)

(1.0

55)

(1.0

51

)

vsL

saL

(cm

m

ol

) (J

mo

l K

)

( 3

6.9

8M

( 3

7.l

)2)(

( 3

7.9

1M

( 3

8.5

0M

( 39.2

1H

( U

O. 0

9M

( il

l .2

1)

((

U2

.G9

M

-1.2

30)

U.U

18)

11.3

17)

19.7

25)

29.9

63)

1*2

.1.3

5 )

57.6

58)

76.3

05)

HL

(J m

ol"

1)

( 18669.)

( 21791.)

( 25651.)

( 3

01

*1

1.)

( 36270.)

( U

31

.85

.)(

52382.)

( 63388.)

VL

3

-1(c

m

mo

l )

(22.5

0)

((2

2.5

7)

(

(22.6

1.)

(

(22.7

1)

((2

2.7

8)

((2

2.8

5)

((2

2.9

3)

((2

3.0

2)

(

SL

(J

i»i*

.i*9l

»)1*5.9

15)

1*

7.5

20

)1*

9.31

*8)

51.1

*1*7

)5

3.8

78

)56.7

17)

60

.06

6)

AS

mo

l"1

K"

1)

( 66.0

58)

( 61

*. 1

27)

( 62.0

13)

( 59.6

78)

( 57.0

72)

( 5U

. 131.)

( 50.7

86)

( U

G.9

28

)

SG

11

0.5

52

110.0

1*2.

109.5

33

(10

9.0

26

)(1

08.5

19)

(10

8.0

11

)(1

07

.50

3)

(106.9

93)

HL

( 19368.)

( 20167.)

( 21079.)

( 22126.)

( 2

33

UO

.)(

2U

75

8.)

( 2

GU

29

.)(

28

1*

18

.)

AH

(J m

ol"

1)

( 32687.)

( 31

891*

.)

( 30981.)

( 29925.)

( 28695.)

( 27253.)

( 255U

9.)

( 23520.)

HG

52

05

5.

52

06

1.

52060.

( 52051.)

( 52035.)

( 52010.)

( 51978.)

( 51937.)

o 63 o o tr1 a

NO

TE

. Dat

a co

ntai

ned

in p

aren

thes

es w

ere

calc

ulat

ed b

y ex

trap

olat

ion

of t

he f

unct

ions

bey

ond

thei

r ra

nge.

bd

w OS oo

Table

29.

Hali

te

- sa

tura

ted

NaC

l so

luti

ons,

co

ncen

trati

ons

in

wt

perc

ent

M

f

w wt

perc

en

t

27.1

*72

27

.59

62

7.7

25

27

.85

9

27

.99

828.1

U3

28.2

93

28.1

*1*8

28

.60

828.7

7U

2^.

91

*5

29

.12

22

9.3

01

.29.1

*91

29.6

83

29.8

81

30

.08

U3

0.2

92

30.5

05

30.7

21*

30

.9U

831.1

78

31.1

*13

31.6

53

t to 80

.85.

90.

95.

100.

105.

110.

11

5.

120.

12

5.

130.

13

5.

11*0

.11

*5.

150.

155.

160.

165.

17

0.

175.

180.

18

5.

190.

195.

P

(bars

)

0.3

53

0.1

*31

0.5

22

0.6

29

0.7

5U

0.8

97

1.0

63

1.2

53

1.1*

701

.71

61.9

91*

2.3

08

2.6

59

3.0

53

3.1

*91

3.9

78

U.5

16

5.1

11

5.7

65

6.1

*83

7.2

68

8.1

25

9.0

58

10

.07

2

dL

VL

. -3

3

-1(g

cm

)

(cm

mo

l )

1.1

77

1.1

75

1.1

73

1.1

71

1.1

68

1.1

66

1.1

63

1.1

61

1.1

58

1.1

56

1.1

53

1.1

51

1.11

*8l.

liiS

1.1

1*3

1.11

*01

.13

7(1

.13

5)

((1

.132)

((1

.130)

((1

.127)

((1

.12U

) (

(1.1

22

) (

(1.1

19)

(

23.9

821

*. 1

021

*. 2

1*21

*. 3

8

2U.

5221

*. 6

7 .

21*.

83

2U

.98

25.1

52

5.3

12

5.U

925.6

725.8

526

.01*

26

.23

26.U

326.6

32B

.8U

)2

7.0

6)

27

.29

)27.5

2)

27.7

6)

28

.01

)2

8.2

7)

saL

H^

(J

mol"

1!?"

1)

(J m

ol"

1)

-38

-37

-36

-35

-31*

-33

-32

-25

-25

-25

-2U

-21*

-21*

-2U

-2U

-23

-23

(-23

(-23

(-23

(-23

(-23

(-23

(-2

1..0

68

.25

2.1

*08

.539

.6U

6.7

26

.779

.676

.31*

6.0

1*6

.777

.51*

1.3

39

.172

.038

.93

7.8

69

.830)

(.8

18)

(.8

31

) (

.863)

(.9

11

) (

.967)

(.0

27)

(

-15

13

.-1

178.

-82

6.

-U5

9.

-77

.3

22

.738.

3502.

3690.

38

G9

.U

039.

1*19

8.U

3U5.

1*1*

80.

U603.

U71

1*.

1*81

2.1*

898.

)1*

973.

)5037.)

5093.)

511*2.)

51

87

.)5229.

)

VL

S

L

AS

/ 3

.-1

(cm

mo

l

18.8

918.9

519.0

119.0

6

19.1

319.1

919.2

519.3

219.3

919

.1*6

19.5

319.6

119.6

819.7

6

19.8

U19.9

220.0

0(

20.0

8)

( 20.1

7)

( 20.2

5)

( 2

0.3

1*

)(

20.1

*3)

( 2

0.5

2)

( 2

0.6

1)

)

11*.

292

15.2

59

16

.21

51

7.1

61

18.0

96

19

.02

219

.931

*21.5

03

22

.32

1*

23

.12

623.9

11

2U.

67

725.U

26

26.1

57

26

.87

02

7.5

66

28.2

UI*

( 28.9

06)

( 29.5

50)

( 3

0.1

78

)(

30.7

90)

( 31.3

87)

( 31.9

68)

( 32.5

36)

SG

HL

(J m

ol"

lK

"')

125

12

3121

118

116

115

113

110

108

107

10

510

310

2100 99 97 96

( 95

( 93

( 9

2(

91(

89(

88(

87

.33

9.1

68

.05

3.9

91

.97

9.0

15

.10

0.5

62

.80

6.0

99

.1*3

8,8

2U

.25

U.7

27

.2U

1.7

96

.39

0.0

21

).6

89

).3

92)

.128)

.89

6)

.69

5)

.52

3)

139.6

31

13

8.1

*2

71

37

.26

91

36

.15

2

13

5.0

75

13U

.036

13

3.0

31

*132.0

66

13

1.1

30

13

0.2

25

129.3

1*9

12

8.5

01

12

7.6

80

126.8

81*

126.1

12

125.3

62

121*

. 631

*1

23

.92

71

23

.23

9122.5

70

12

1.9

18

12

1.2

83

12

0.6

61

*1

20

.06

0

1*81

6.5167.

5518.

5871.

6225.

6581.

6937.

75U

9.

7879.

8208.

853U

.8857.

9177.

91*9

5.

9809.

10121.

10

U2

9.

( 1

07

3U

.)(

11036.)

( 11335.)

( 11631.)

( 11921*.)

( 1221U

.)(

12501.)

AH

(J m

ol"

1)

1*28

1*1*

.1*

261*

9.1*

21*5

1.1*

2251

.

U20

U7.

i*18

<*0.

1*16

32.

1*11

66.

U0

98

0.

1*07

93.

1*06

07.

1*01

*22.

1*02

37.

1*00

52.

39

86

8.

39

68

5.

39

50

2.

( 3

93

20

.)(

39

13

9.)

( 3

89

57

.)(

38776.)

( 38595.)

( 38

1*11

*. )

( 3

82

32

.)

HG

1*76

60.

1*78

15.

1*79

69.

1*81

21.

1*82

72.

1*81

*22.

1*85

69.

U8

71

5.

1*88

59.

1*90

01.

1*91

1*1.

U9

27

8.

U9i

*li«

.U

95U

7.

1*96

78.

1*98

06.

U9

93

2.

50055.

50

i75

.5

02

93

.5

0U

07

.50519.

50628.

50

73

3.

t-1

w 03 o OT O t-1

a H h

I O cc

31.8

98

32. U

932

.1*0

532.6

66

32.9

32

33.2

01*

33.1

*81

33,7

61*

3U

.05

231

*. 3

i»5

31*.

01*

33U

.9U

735.2

56

35.5

70

35

.88

936

.211

*30

.5U

I*30.8

80

37.2

21

37.5

67

37

.91

83

8.2

75

38

.63

733.0

0U

39.3

76

39.7

51*

200.

205.

210.

215.

220.

225,

230.

235.

2<*0

.21

*5.

250.

255.

260.

2C5.

270.

275.

280.

285.

290.

295.

300.

305.

310.

315.

320.

325.

11.1

70

12.3

57

13.6

39

15

.01

91

6.5

02

18.0

93

19.7

97

21

.61

923.5

6U

25

.63

6

27.8

1*1

30

.18

33

2.6

68

35

.30

138.0

86

1*1.

029

<»l»

.133

1*7.

1*01

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