1288
J. Phys. Chem. 1996, 100, 1288-1294
Modeling the Heat Capacities of Aqueous 1-1 Electrolyte Solutions with Pitzer’s Equations C. M. Criss Department of Chemistry, UniVersity of Miami, Coral Gables, Florida 33124
F. J. Millero* Rosenstiel School of Marine and Atmospheric Science, UniVersity of Miami, Miami, Florida 33149-1098 ReceiVed: May 16, 1995; In Final Form: July 7, 1995X
The apparent molal heat capacities (φCp) of 1-1 electrolytes at 25 °C have been fitted to the Pitzer equation φCp ) C h p,2° + (AJ/1.2) ln(1 + 1.2I1/2) - 2RT2[mBJMX + m2CJMX], where C h p,2° is the partial molal heat capacity of at infinite dilution and BJMX and CJMX are empirical constants related to ion-ion interactions. The values of C h p,2° of the electrolytes have been used to determine partial molal heat capacities of ions. The coefficients BJMX and CJMX have been combined with Pitzer coefficients for enthalpies and osmotic coefficients to develop equations that can be used to determine activity coefficients of these electrolytes from 10 to 70 °C and from 0.1 to 2 m to within 1%.
Introduction Ionic interactions in natural waters have major effects on the rates of ionic reactions,1 equilibrium processes,2 and biochemical activity.3 A quantitative treatment of these effects requires a self-consistent model that can be used to describe the variation of activity coefficients of ions and non-electrolytes as a function of ionic strength, composition, temperature, and pressure. In 1973 Pitzer4 developed a set of equations that can accurately represent the activity coefficients of electrolytes as well as other thermodynamic properties as a function of composition, temperature, and pressure.5 The equations have an appropriate form that makes them useful for estimating the properties of mixed electrolytes and can adequately fit the thermodynamic properties over a wide range of concentration and temperature. The Pitzer model has been shown to be useful in estimating activity coefficients in a wide variety of natural waters2,6-9 as a function of temperature10-14 and pressure.15-18 In this paper we have examined the heat capacity of a number of 1-1 electrolytes using the Pitzer equations at 25 °C. The Pitzer parameters for heat capacities can be combined with enthalpy data19,20 to estimate the effect of temperature (10-70 °C) and concentration (0-2 m) on the activity coefficient of electrolytes.21 The general from the equations used by Pitzer5 are given for the total excess Gibbs free energy by
3/2
GX
m [2(νMνX) ]C
MX
(1)
By appropriate differentiation this equation gives the following equations for the osmotic (φ) and activity (γ) coefficients
φ - 1 ) |ZMZX|fφ + m(2νMνX/ν)BφMX + m2[2(νMνX)3/2/ν]CφMX (2) ln γ( ) |ZMZX|fγ + m(2νMνX/ν)BγMX + m2[2(νMνX)3/2/ν]CγMX (3) where the limiting slopes for eqs 1-3 are given by X
(4)
fφ ) -AφI1/2/(1 + 1.2I1/2)
(5)
fγ ) -Aφ[I1/2/(1 + 1.2I1/2) + (2/1.2)ln(1 + 1.2I1/2)] (6) and the B and C coefficients for 1-1, 1-2, 2-1, and 3-1 electrolytes are given by
BGXMX ) β(0)MX + (2β(1)MX/4I)[1 - exp(-2I1/2)(1 + 2I1/2)] (7) BφMX ) β(0)MX + β(1)MX exp(-2I1/2)
Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-1288$12.00/0
(8)
BγMX ) 2β(0)MX + (2β(1)MX/4I)[1 - exp(-2I1/2)(1 + 2I1/2 - 2I)] (9) CGXMX ) CφMX/2
(10)
CγMX ) (3/2)CφMX
(11)
The limiting slope Aφ is given by
Aφ ) (1/3)(2πN0d0/1000)1/2(e2/DkT)3/2
GEX/(nWRT) ) fGX + m2(2νMνX)BGXMX + 3
fGX ) -Aφ(4I/1.2) ln(1 + 1.2I1/2)
(12)
where N0 is the Avogadro number, d0 is the density of the solvent, e is the electronic charge, and D is the dielectric constant. At 25 °C the value of Aφ is 0.3915.5 Short range interactions of unlike ions are the principle contribution to the β(1)MX term. The interaction of like and unlike charged ions will contribute to β(0)MX. For multicharged ions the interactions of like-charged ions would be less and may be negligible for β(0)MX. The values of BφMX also include the differences due to corrections in f due to the ion size parameter. The limiting equation of Pitzer’s gives an implied ion size parameter of 3.6 Å (this contribution will be negative). Effect of Temperature on the Pitzer Equations Differentiation of the Pitzer free energy, activity, and osmotic coefficient equations with respect to temperature and pressure © 1996 American Chemical Society
Heat Capacities of 1-1 Electrolyte Solutions
J. Phys. Chem., Vol. 100, No. 4, 1996 1289
can be used to derive the equations needed to represent the apparent and partial molal properties of solutions. The equations needed to derive the equations for the enthalpy and heat capacity are given by5
L ) H - H° ) -T [∂G /T)/∂T]P,m
(13)
Cp ) (∂H/∂T)P,m ) Cp° + (∂L/∂T)P,m
(14)
2
EX
The relative enthalpy of a solution, φL, is defined by
φL ) L/m
(15)
The derivative of the excess free energy (eq 1) according to eq 13 gives
φL ) ν|ZMZX|(AL/2.4) ln(1 + 1.2I1/2) 2νMνXRT2[mBLMX + m2(νMZM)CLMX] (16) where BLMX ) (∂BMX/∂T)P,I and CLMX ) (∂CMX/∂T)P,I
BLMX ) β(0)LMX + 2β(1)LMX[1 - (1 + 2I1/2) exp(-2I1/2)]/(4I) (17) The coefficients β(i)LMX ) (∂β(i)MX/∂T)P, where i ) 0 or 1. The CLMX term is given by
CLMX ) (∂CφMX/∂T)P/(2|ZMZX|1/2)
(18)
TABLE 1: Infinite Dilute Partial Molal Heat Capacity of Electrolytes at 25 °C C h p,2° (J mol-1 K-1)
electrolyte
C h p,2° (J mol-1 K-1)
HCl HBr HClO4 HNO3
-126.32 -131.09 -27.52 -72.48
LiCl LiBr LiOH
-63.25 -68.09 -75.72
NaF NaCl NaBr NaI NaOH NaClO3 NaClO4 NaNO3 NaHCO3 NaBrO3 NaC2H2O2 NaIO3 NaReO4 NaTcO4 NH4Cl NH4Br NH4ClO4 NH4NO3
-74.70 -82.85 -88.72 -79.74 -99.60 -16.68 17.35 30.60 -10.32 -50.74 67.23 -32.29 30.24 25.04 -55.59 -58.62 -46.74 -1.21
KF KCl KBr KI KOH KNO3 KBrO3 KC2H3O2 KClO3 KIO3 KMnO4
-105.45 -114.32 -118.35 -106.88 -128.53 -63.54 -77.71 5.08 -42.94 -59.12 1.02
RbCl RbBr RbI
-135.18 -136.91 -134.13
CsF CsCl CsBr CsI
-139.48 -149.20 -155.69 -146.01
electrolyte
capacity of electrolytes (C h p,2) can be obtained from the differentiation of eq 22 with respect to molality (C h p,2 ) φCp + m(∂φCp/∂m).
The Debye-Huckel slope AL can be calculated from
AL/RT ) 4T(∂Aφ/∂T)P ) -6Aφ[1 + T(∂ ln D/∂T)P + TR0/3] (19) where R0 ) (∂ ln V0/∂T)P is the expansivity of water. At 25 °C the limiting slope AL/RT ) 0.801 at 25 °C.5 The apparent molal heat capacity, φCp is defined by
φCp ) (Cp - n1Cp1°)/n2
(20)
where n1 and n2 are the number of moles of solvent and solute, respectively. The value of φCp can be related using eqs 14 and 15
h p,2° + (∂φL/∂T)P,m φ Cp ) C
Heat Capacities of Electrolytes The heat capacities of aqueous electrolyte solutions have been determined by a number of workers.21,22 All of the data tabulated by Parker22 was measured before the invention of flow calorimeters. The more recent measurements have been made with high precision with a flowing heat capacity system.23 While most of the data in Parker’s tabulation22 appear to be reliable at higher molalities, serious descrepancies appear for many electrolytes at molalities less than 1 m, especially for the infinitely dilute values. Many recent measurements have been fitted to an equation of the form
φCp ) C h p,2° + SCpI0.5 + BCpI
(26)
(21)
Differentiation of eq 16 upon substitution into eq 21 gives
h p,2° + ν|ZMZX|(AJ/2.4) ln(1 + 1.2I1/2) φ Cp ) C 2νMνXRT2[mBJMX + m2(νMνX)1/2CMX] (22) where
BJMX ) (∂2BMX/∂T2)P,I + (2/T)(∂BMX/∂T) ) β(0)JMX + 2β(1)JMX[1 - (1 + 2I1/2) exp(-2I1/2)]/(4I) (23) CJMX ) (∂2CGXMX/∂T2)P,I + (2/T)(∂CGXMX/∂T)
(24)
AJ ) (∂AL/∂T)P
(25)
The value of AJ/R ) 3.94 at 25 °C.5 The partial molal heat
where SCp is the traditional Debye-Hu¨ckel limiting law slope and BCp is an empirical constant.21 Although this equation can adequately fit the experimental data over a wide range of concentrations, it does not have the proper form for use with the tabulated osmotic coefficient and enthalpy data of Pitzer and co-workers.5 In this paper we have examined the experimental heat capacity for 1-1 electrolytes at 25 °C using the Pitzer equation described above (eq 22). Sources of data used in the calculations were limited primarily to newer measurements24-42 obtained from flow heat capacity calorimeters and the comprehensive tabulation of uni-univalent electrolytes of Parker22 for the higher molality data. The details of the data used and concentration ranges covered are given in the Appendix. The calculations were divided into several parts. The first step was to obtain reliable standard state heat capacities for as many electrolytes as possible from φCp data below 1 m obtained from flow calorimeters. These data were fitted to eq 22, from which C h p,2° was evaluated. The values for the various electrolytes are given in Table 1. In most cases these data could be fitted with one Pitzer parameter, β(0)J. None of the data from
1290 J. Phys. Chem., Vol. 100, No. 4, 1996
Criss and Millero
TABLE 2: Infinite Dilute Partial Molal Heat Capacity of Cations and Anions at 25 °C cation +
H Li Na+ K+ Rb+ Cs+ NH4+
C h p,2° (J mol-1 K-1) 0.00 63.12 43.01 12.47 -7.25 -23.65 71.93
anion FCl BrIOHNO3HCO3ClO3BrO3IO3ClO4MnO4ReO4TcO4C2H3O2-
C h p,2° (J mol-1 K-1) -117.75 -126.32 -131.27 -122.84 -140.80 -73.51 -53.33 -57.55 -91.97 -73.44 -26.82 -11.45 -12.77 -17.97 24.22
Parker’s tabulation22 were used in these initial calculations. The additivities of the ionic Cp,2° values were examined from the results obtained from the different electrolytes. Obvious failures in additivity indicated which data were unreliable, and these were not used in evaluating a “best” set of ionic heat capacities. The electrolyte data indicated that the alkali metal chlorides and bromides were most likely to give the best ionic values. All the ionic values are ultimately derived from C h p,2°(Cl-), + h p,2°(H ) set equal which is itself derived from C h p,2°(HCl), with C to zero, following the conventional scale of ionic values. h p,2° C h p,2°(Cl-) was used to obtain a preliminary estimate of C for the alkali metal cations. The average differences in the C h p,2° for NaBr and NaCl and C h p,2° for KBr and KCl were added to h p,2°(Br-). This was then combined with C h p,2°(Cl-) to obtain C C h p,2° for the alkali metal bromides to obtain a second set of C h p,2° values for the alkali metal cations. The final values of C h p,2° for the cations are an average obtained from the chloride and bromide salts. The averaged C h p,2° values for the alkali metals were then used to obtain C h p,2° for F-, I-, and other anions. Whenever possible the C h p,2° for several electrolytes with the same common anion were used to obtain C h p,2° for that anion. Thus, C h p,2° for F- and I- are the averages obtained from four alkali metal fluorides and iodides. Other data were treated similarly to obtain average values of C h p,2° for each ion. For only five ions, MnO4-, ReO4-, TcO4-, C2H3O2-, and HCO3-, was it not possible to obtain average values. The ionic values determined in this manner are given in Table 2. The value of C h p,2°(Na+), 43.0 J K-1 mol-1, is in good agreement with the most recently accepted value suggested by others.43 From the best ionic C h p,2° values, new values of C h p,2° were generated for every electrolyte for which data exist. We used these ionic values to determine the Pitzer heat capacity parameters from the equation
φCp - C h p,2° - (AJ/1.2) ln(1 + 1.2I1/2) ) -2RT2[mβ(0)JMX + β(1)JMX f1 + m2CJMX] (27) where
f1 ) (1/4I)[1 - (1 + 2I1/2) exp(-2I1/2)]
(28)
In these calculations, the data from Parker’s tabulation22 at molalities less than 1 m were frequently omitted (see Appendix). The fit of the apparent molal heat capacities for NaCl solutions to eq 22 is shown in Figure 1. The Pitzer coefficients for various 1-1 electrolytes fitted to eq 27 are given in Table 3 along with the standard error of the
Figure 1. Apparent molal heat capacity of NaCl as a function of I1/2. The solid line is calculated from the Pitzer equation (22).
Figure 2. Value of β(1)J plotted versus β(0)J for various electrolytes at 25 °C.
fit and the C h p,2° of each electrolyte determined by additivity. The number of parameters (β(0)J, β(1)J, and CJ) needed to fit the apparent molal heat capacities for each electrolyte was decided by examining the standard errors using an F-test. For dilute solutions the CJ parameter was generally not needed to give an adequate fit of the measurements. The full equation with three parameters gave a satisfactory fit to high concentrations (22 m) with standard errors below 4 J mol-1 K-1. As found for the activity5 and enthalpies44 specific interaction coefficients, the heat capacity coefficients β(0)JMX, β(1)JMX, and CJ correlate with one another (see Figures 2 and 3). Since the values of β(0)JMX are of the same order of magnitude, they do not show a strong correlation with the osmotic and enthalpy parameters. Effect of Temperature on Activity Coefficients The Pitzer osmotic and activity coefficient parameters are known5,10-14 for a number of electrolytes (HCl, NaCl, KCl, RbCl, CsCl, NaOH, MgCl2, CaCl2, Na2SO4, MgSO4) over a wide range of temperatures (0-250 °C) and are frequently fitted to equations of the form
Heat Capacities of 1-1 Electrolyte Solutions
J. Phys. Chem., Vol. 100, No. 4, 1996 1291
TABLE 3: Pitzer Parameters for the Heat Capacity (J mol-1 K-1) of 1-1 Electrolytes
a
electrolyte
C h p,2°
β(0)J
β(1)J
HCl HBr HI HClO4 HNO3 LiCl LiBr LiI LiOH NaF NaCl NaBr NaI NaOH NaHCO3 NaClO3 NaClO4 NaNO3 NaBrO3 NaIO3 NaC2H3O2 NaReO4 NaTcO4 KF KCl KBr KI KOH KNO3 KBrO3 KC2H3O2 KClO3 KIO3 KMnO4 RbF RbCl RbBr RbI CsF CsCl CsBr CsI NH4Cl NH4Br NH4ClO4 NH4NO3
-126.32 -131.27 -122.84 -26.82 -73.51 -63.20 -68.15 -59.71 -77.67 -74.74 -83.31 -88.26 -79.83 -97.79 -10.32 -14.54 16.19 -30.50 -48.96 -30.43 67.23 30.24 25.04 -105.28 -113.86 -118.81 -110.37 -128.33 -61.04 -79.50 36.69 -45.08 -60.97 1.02 -124.99 -133.57 -138.52 -130.08 -141.40 -149.97 -154.92 -146.49 -54.40 -59.35 45.11 -1.58
-3.04 × 10-6 -3.57 × 10-6 -1.15 × 10-6 -1.42 × 10-5 -8.13 × 10-6 -3.10 × 10-6 -2.92 × 10-6 -2.15 × 10-5 -1.06 × 10-5 -2.37 × 10-5 -1.53 × 10-5 -1.30 × 10-5 -1.01 × 10-5 -1.41 × 10-5 -1.76 × 10-5 -1.56 × 10-5 -6.11 × 10-6 -2.24 × 10-5 -6.50 × 10-5 -5.44 × 10-5 -1.39 × 10-5 -4.55 × 10-5 -6.41 × 10-5 -1.39 × 10-5 -1.24 × 10-5 -1.43 × 10-5 -7.48 × 10-6 -9.46 × 10-6 -7.85 × 10-6 9.17 × 10-5 -4.31 × 10-6 1.51 × 10-4 -4.68 × 10-5 -5.23 × 10-5 -1.06 × 10-5 -1.93 × 10-5 -1.76 × 10-5 -1.02 × 10-5 1.09 × 10-5 -1.54 × 10-5 -1.75 × 10-5 -1.75 × 10-5 -5.97 × 10-6 -5.97 × 10-6 1.11 × 10-4 -4.13 × 10-6
6.78 × 10-6 -9.13 × 10-6
1.86 × 10-8 6.36 × 10-8
-2.47 × 10-5 1.36 × 10-5 1.17 × 10-5 6.85 × 10-5 -2.18 × 10-5
2.32 × 10-7 6.28 × 10-8 4.65 × 10-8 3.37 × 10-6 4.35 × 10-7
-3.65 × 10-7 -1.06 × 10-5 -2.54 × 10-5 -3.76 × 10-5 -3.99 × 10-5 -2.69 × 10-5 -6.35 × 10-5 -2.96 × 10-5 5.45 × 10-5 -7.00 × 10-5 -6.88 × 10-7
9.12 × 10-7 5.80 × 10-7
2.92 × 10-6 7.62 × 10-6 -1.80 × 10-5 -2.59 × 10-5 -8.26 × 10-5 -2.02 × 10-4 -2.23 × 10-5 -2.70 × 10-4 -7.06 × 10-5
9.17 × 10-7 1.08 × 10-6
CJMX
6.70 × 10-7 1.11 × 10-6 2.81 × 10-7 2.97 × 10-6 1.25 × 10-5 1.11 × 10-6
3.19 × 10-7 -1.33 × 10-4 2.05 × 10-7 -1.91 × 10-4
3.08 × 10-5 1.57 × 10-5
-1.87 × 10-5 4.44 × 10-6
3.83 × 10-6 2.89 × 10-7
-2.07 × 10-4 -4.16 × 10-5
-1.36 × 10-4 1.21 × 10-7
σ(φCp)
max m
1.19 2.38 a 0.60 3.80 0.70 0.88 0.85 0.74 0.50 2.22 1.52 1.25 2.59 2.04 3.22 3.69 1.64 2.51 2.21 1.65 3.79 6.80 0.65 0.79 1.23 1.03 2.33 3.35 0.17 1.60 0.20 0.41 0.39 2.25 1.30 1.03 4.66 1.35 0.97 1.48 1.70 1.59 2.24 0.34 3.33
15.85 22.20 7.60 0.37 22.20 18.50 18.50 2.78 4.63 0.72 6.17 9.25 3.70 12.33 0.77 9.25 17.08 2.22 2.22 0.40 7.40 0.65 0.25 1.00 5.55 5.84 2.78 15.51 3.70 0.24 11.10 0.22 0.23 0.18 0.90 0.99 0.96 0.72 1.12 0.80 0.94 2.22 7.40 1.00 0.29 22.43
Statistically inapplicable. See Appendix.
BMX(T) ) q1 + q2(1/T - 1/TR) + q3 ln(T/TR) +
T gives
q4(T - TR) + q5(T - TR ) (29) 2
2
where TR is some reference temperature (298.15 °C) and qi are adjustable parameters. There is a need, however, to make reasonable estimates of activity coefficients over smaller ranges of temperature (0-75 °C). Heat capacity and enthalpy data at 25 °C have been shown21 to provide reasonable estimates of activity coefficients from 0 to 75 °C and from 0 to 2 m. The Pitzer coefficients derived from the heat capacities and enthalpies of electrolytes can be used to estimate the effect of temperature on the osmotic and activity coefficients. From the definition of the effect of temperature on the coefficients used to fit the enthalpies and heat capacities, the temperature dependencies of the necessary Pitzer coefficients may be obtained.
β(0)L ) ∂β(0)/∂T
(30)
β(0)J ) ∂2β(0)/∂T2 + (2/T)(∂β(0)/∂T)
(31)
The integration of these equations between TR (298.15 °C) and
β(0) ) β(0)R + a(1/T - 1/TR) + b(T2 - TR2)
(32)
a ) (β(0)J/3)TR3 - TR2β(0)LR
(33)
b ) β(0)J/6
(34)
where
similar equations can be derived for β(1) and Cφ. We have combined the values of β(0)J determined in this study with literature values of β(0)R and β(0)LR to derive equations that can be used to estimate osmotic and activity coefficients of the electrolytes examined in this study (eqs 2 and 3). As found in our earlier work,21 the 25 °C enthalpy and heat capacity data can yield reasonable estimates for the activity coefficients. This is demonstrated in Figure 4, where the measured activity coefficients of NaCl are compared to those calculated using eq 2, 3, and 32-34 by means of a contour map. The maximum differences between the measured and calculated values of the mean activity coefficient ∆γ(, at various temperatures relative
1292 J. Phys. Chem., Vol. 100, No. 4, 1996
Criss and Millero Office of Naval Research, the National Oceanographic and Atmospheric Administration, and the Department of Energy for their support of the Marine Physical Chemistry studies of F.J.M. This work is dedicated to Dr. Harold Friedman, who is a valued friend and inspired our studies of electrolyte mixtures.
Figure 3. Value of CJ plotted versus β(0)J for various electrolytes at 25 °C.
Figure 4. Contour map of differences between measured and calculated γ( for various temperatures and molalities for sodium chloride.
to 25 °C and zero molality are given by the contours; the area between contours having the same numerical value represents values of ∆γ( less than or equal to the numerical value of the contour line. The calculated mean activity coefficients are in reasonable agreement (0.005) from 10 to 70 °C and from 0 to 2 m with the equations valid over a wider range of temperatures.11,12 To expand the calculations to higher concentrations and temperatures, it is necessary to have measurements for the effect of temperature on the heat capacity of electrolytes or enthalpy data over a wide range of temperatures. Since most natural waters are between 0 and 40 °C, the Pitzer coefficients for electrolytes given in this paper should provide reasonable estimates for osmotic and activity coefficients for binary and multicomponent electrolyte solutions. In future studies we will examine the use of the Pitzer equations in fitting the apparent molal heat capacities of 2-1, 1-2, 3-1, and 2-2 electrolytes at 25 °C. Acknowledgment. We acknowledge the support of the Oceanographic Section of the National Science Foundation, the
Appendix Data for several of the alkali metal halides listed below were taken from Fortier et al.24 An unequal heat leak in the earliest version of their flow calorimeter, which was not known at the time the measurements were made, caused these data to be in error by a small amount. Desnoyers et al.25 corrected the standard state values for this error. In the calculations reported here, all the data from Fortier et al.24 at all molalities were recalculated, taking into account the heat leak factor, and the newly recalculated data treated by eq 22. The only reliable data available for several of the electrolytes are reported by the above authors. These are considered as a group in one section below. All of the data reported below are at 25 °C and 1 atm. The parameters (β(0)J, β(1)J, and CJ) needed to fit the apparent molal heat capacities for each electrolyte was decided by examining the standard errors using an F-test. HCl. Allred and Woolley26 report φCp data from 0.02 to 0.34 m. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.04 to 1.02 m. Singh et al.27 have reported φCp data from 0.07 to 0.57 m. Parker22 tabulates φCp data from infinite dilution to 15.85 m. The Parker22 data for m < 1.85 m were omitted from the calculations. HBr. Singh et al.27 have reported φCp data from 0.05 to 0.35 m. Parker22 tabulates φCp data from infinite dilution to 22.20 m. Parker’s tabulation22 is inconsistent with recent values and the value for C h p,2° obtained from additives of the values for the ions. We have reexamined the original literature to which Parker22 refers. Richards and Rowe28 reported specific heat measurements on water and HBr solutions at 0.555 m and over a range of 16-20.2 °C, from which we have evaluated φCp at 18 °C and corrected to 25 °C, to obtain a value for φCp of -97.48 J K-1 mol-1. Johnson et al.29 report specific heats of water and HBr solutions at 11.102 m and over the range of 25-27 °C. We have calculated φCp at 26 °C and corrected the value to 25 °C, to obtain a value for φCp of -33.27 J K-1 mol-1. These two values, along with the recent low concentration data,27 and the standard state value obtained from addivity were used in the calculations. HI. Parker22 has tabulated φCp data for HI from infinite dilution to 20 m. However, the infinite dilution value was widely different from that given by addition of the ionic values. Parker22 cited only two sources for the data, which we have reexamined. Richards and Rowe28 reported specific heat measurements on water and HI solutions at 0.555 m and over a range of 16-20.2 °C, from which we have evaluated φCp at 18 °C and corrected to 25 °C, to obtain -89.62 J K-1 mol-1. Johnson et al.29 report specific heats of water and HI solutions at 7.604 m and over the range of 25-27 °C. We have calculated φCp at 26 °C and corrected the value to 25 °C, to obtain -71.17 J K-1 mol-1. These two values, along with the standard state value, C h p,2°, obtained from additivities were used to estimate the single Pitzer parameter β(0)J. HClO4. Singh et al.30 report φCp data from 0.05 to 0.37 m. HNO3. Enea et al.31 report φCp from 0.04 to 0.15 m. Parker22 tabulates φCp data from infinite dilution to 55 m. The Parker22 data for m < 3.7 m and m g 22.20 m were omitted from the calculations. LiCl. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.05 to 0.96 m Parker22 tabulates φCp data from infinite dilution to 18.50 m. Parker’s data 22 with m < 1.11 m were omitted.
Heat Capacities of 1-1 Electrolyte Solutions LiBr. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.02 to 1.08 m. Parker22 tabulates φCp data from infinite dilution to 18.50 m. Parker’s data22 with m < 1.11 m were omitted. LiOH. Roux et al.41 have reported φCp data from m ) 0.053.79 m. Parker22 tabulates φCp data from infinite dilution to 4.63 m. Parker’s data22 with m < 0.55 m were omitted. LiI. Parker22 tabulates φCp data from infinite dilution to 2.78 m. Parker’s data22 with m < 0.55 m were omitted. The infinitely dilute value was obtained from additivity of the ions. NaF. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.08 to 0.72 m. NaCl. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.01 to 3.02 m. Singh et al.27 have reported φCp data from 0.09 to 0.50 m. Allred and Woolley26 report φCp data from 0.04 to 0.26 m. Olofsson32 reports φCp data from 0.06 to 0.18 m. Parker22 tabulates φCp data from infinite dilution to 6.17 m. Parker’s data22 with m < 1.11 m were omitted. NaBr. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.03 to 1.01 m. Singh et al.27 have reported φCp data from 0.04 to 0.46 m. Parker22 tabulates φCp data from infinite dilution to 9.25 m. Parker’s data22 with m < 1.11 m were omitted. NaI. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.06 to 0.98 m. Parker22 tabulates φCp data from infinite dilution to 3.70 m. Parker’s data22 with m < 1.11 m were omitted. NaOH. Allred and Woolley26 report φCp data from 0.05 to 0.37 m. Simonson et al.33 report φCp from 0.01 to 6.00 m. Singh et al.27 have reported φCp data from 0.10 to 0.73 m. Perron et al.34 have reported φCp from 0.04 to 1.00 m. Roux et al.41 have reevaluated these data, making a correction for a heat leak in an earlier version of the calorimeter, and have made additional φCp measurements to m ) 10.88 m. Parker22 tabulates φCp data from infinite dilution to 27.75 m. Parker’s data22 with m < 6.00 m and m > 12.33 m were omitted. NaNO3. Roux et al.35 have reported φCp from 0.03 to 2.12 m. Enea et al.31 have reported φCp from 0.05 to 0.41 m. Parker22 tabulates φCp data from infinite dilution to 2.22 m. Parker’s data22 with m < 0.74 m were omitted. NaBrO3. Roux et al.35 have reported φCp from 0.02 to 1.98 m. Parker22 tabulates φCp data from infinite dilution to 2.22 m. Parker’s data22 with m < 1.11 m were omitted. NaClO3. Roux et al.35 have reported φCp from 0.05 to 7.79 m. Parker22 tabulates φCp data from infinite dilution to 9.25 m. Parker’s data22 with m < 0.55 m and m > 4.63 m were omitted. NaClO4. Roux et al.35 have reported φCp from 0.05 to 16.68 m. Singh et al.27 report φCp data from 0.08 to 0.37 m. h p,2°, obtained by Mastroianni and Criss36 report a value for C the integral heat method, which agrees satisfactorily with the value obtained from the higher concentration data. Parker22 tabulates φCp data from infinite dilution to 17.08 m. Parker’s data22 with m < 0.55 m and m > 4.63 m were omitted. NaHCO3. Perron et al.34 have reported φCp from 0.008 to 0.77 m. These data were corrected for the heat leak in the calorimeter in accordance with Desnoyers et al.25 NaIO3. Spitzer et al.37 have reported φCp from 0.03 to 0.15 m. Roux et al.35 have reported φCp from 0.02 to 0.40 m. Three values of φCp from Roux et al.,35 at 0.048, 0.103, and 0.159 m, were outside the standard deviation of the fit of the data and were omitted from the calculation. NaC2H3O2. Allred and Woolley38 have reported φCp data from 0.03 to .40 m. Leduc and Desnoyers40 report φCp data from 0.02 to 2.97 m. The latter data were corrected for the heat leak in the flow calorimeter reported for the early model calorimeter.24 Parker22 tabulates φCp data from infinite dilution to 7.40 m. Parker’s data with m < 1.1 m were omitted.
J. Phys. Chem., Vol. 100, No. 4, 1996 1293 NaReO4. Lemire et al.42 have reported φCp data from m ) 0.05 m to m ) 0.65 m. NaTcO4. Lemire et al.42 have reported φCp data from m ) 0.01 m to m ) 0.25 m. KF. Fortier et al.24 and Desnoyers et al.25 report φCp for KF from approximately 0.02 to 1 m. KCl. Singh et al.27 have reported φCp data from 0.06 to 0.72 m. Stakhanova et al.39 have reported φCp from 2 to 4.5 m. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.02 to 1.00 m. Olofsson32 has reported φCp from 0.05 to 2.01 m. Parker22 tabulates φCp data from infinite dilution to 5.55 m. Parker’s22 data for m < 1.11 m were omitted. KBr. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.06 to 0.98 m. Singh et al.27 have reported φCp data from 0.05 to 0.60 m. Parker22 tabulates φCp data from infinite dilution to 5.84 m. The Parker22 data for m e 1.11 m were omitted from the calculations. KI. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.06 to 1.00 m. Parker22 tabulates φCp data from infinite dilution to 2.78 m. Parker’s data22 for m < 1.11 m were omitted. KOH. Singh et al.27 have reported φCp data from 0.06 to 0.44 m. Roux et al.41 have reported φCp data from m ) 0.05 m to m ) 15.51 m. Parker22 tabulates φCp data from infinite dilution to 2.22 m. Parker’s data22 with m < 0.55 m were omitted. KNO3. Enea et al.31 have reported φCp from 0.07 to 0.67 m. Parker22 tabulates φCp data from infinite dilution to 3.70 m. Parker’s data22 with m < 0.55 m were omitted. Olofsson32 reports φCp from 0.06 to 2.92 m. KClO3. Roux et al.35 have reported φCp from 0.05 to 0.22 m. KBrO3. Roux et al.35 have reported φCp from 0.05 to 0.24 m. KIO3. Roux et al.35 have reported φCp from 0.04 to 0.23 m. Parker22 tabulates φCp data from infinite dilution to 0.37 m. There is a large discrepancy between Parker’s tabulation22 and the newer data; consequently, all of Parker’s data22 have been omitted from the calculations. KMnO4. Spitzer et al.27 have reported φCp from 0.05 to 18 m. Parker22 tabulates φCp data from infinite dilution to 0.56 m. There is a large discrepancy between Parker’s tabulation22 and the newer data; consequently, all of Parker’s data22 have been omitted from the calculations. KC2H3O2. Parker22 tabulates φCp data from infinite dilution to 11.10 m. The infinitely dilute value was obtained via additivity of the ions and combined with data from the Parker22 compilation for m g 0.74 m. RbF, RbCl, RbBr, RbI, CsF, CsCl, and CsBr. Fortier et al.24 and Desnoyers et al.25 report φCp for all of these electrolytes from approximately 0.02 to 1 m. CsI. Fortier et al.24 and Desnoyers et al.25 report φCp from 0.02 to 0.72 m. Parker22 tabulates φCp data from infinite dilution to 2.22 m. The Parker22 data for m e 1.11 m were omitted from the calculations. NH4Cl. Leduc and Desnoyers40 report φCp data from 0.05 to 3.08 m. Roux et al.35 have reported φCp from 0.04 to 0.22 m. Allred and Woolley38 have reported φCp data from 0.05 to 0.40 m. Parker22 tabulates φCp data from infinite dilution to 7.40 m. The Parker22 data for m e 1.11 m were omitted from the calculations. NH4Br. Leduc and Desnoyers40 report φCp data from 0.01 to 1.00 m. NH4ClO4. Roux et al.35 have reported φCp from 0.05 to 0.29 m.
1294 J. Phys. Chem., Vol. 100, No. 4, 1996 NH4NO3. Roux et al.35 have reported φCp from 0.04 to 22.29 m. Parker22 tabulates φCp data from infinite dilution to 22.20 m. The Parker22 data for m e 1.11 m were omitted from the calculations. References and Notes (1) Millero, F. J. Mar. Chem. 1990, 30, 205. (2) Clegg, S. L.; Whitfield, M. In ActiVity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; Chapter 4, pp 279-434. (3) Anderson, M. A.; Morel, F. M. Limnol. Oceanogr. 1982, 27, 789. (4) Pitzer, K. S. J. Phys. Chem. 1973, 77, 268. (5) Pitzer, K. S. In ActiVity Coefficients in Electrolyte Solutions, 2nd ed.; Pitzer, K. S., Ed.; CRC Press: Boca Raton, FL, 1991; Chapter 3, p 775. (6) Harvie, C. E.; Weare, J. H. Geochim. Cosmochim. Acta 1980, 44, 981. (7) Harvie, C. E.; Møller, N.; Weare, J. H. Geochim. Cosmochim. Acta 1984, 48, 723. (8) Krumgalz, B. S.; Millero, F. J. Mar. Chem. 1982, 11, 209. (9) Felmy, A. R.; Weare, J. H. Geochim. Cosmochim. Acta 1986, 50, 2771. (10) Pabalan, R. T.; Pitzer, K. Geochim. Cosmochim. Acta 1987, 51, 2429. (11) Møller, N. Geochim. Cosmochim. Acta 1988, 52, 821. (12) Greenberg, J. P.; Møller, N. Geochim. Cosmochim. Acta 1989, 53, 2503. (13) Spencer, R. J.; Møller, N.; Weare, J. H. Geochim. Cosmochim. Acta 1990, 54, 575. (14) Campbell, D. M.; Millero, F. J.; Roy, R. N.; Roy, L.; Lawson, M.; Vogel, K.; Moore, C. P. Mar. Chem. 1993, 44, 221. (15) Connaughton, L. M.; Hershey, J. P.; Millero, F. J. J. Solution Chem. 1986, 15, 989. (16) Monnin, C. Geochim. Cosmochim. Acta 1989, 53, 1177. (17) Connaughton, L. M.; Millero, F. J.; Pitzer, K. S. J. Solution, Chem. 1989, 18, 1007. (18) Monnin, C. Geochim. Cosmochim. Acta 1990, 54, 3265. (19) Silvester, L. F.; Pitzer, K. S. J. Phys. Chem. 1977, 81, 1977. (20) Silvester, L. F.; Pitzer, K. S. J. Solution Chem. 1978, 7, 325. (21) Millero, F. J. In ActiVity Coefficients in Electrolyte Solutions, 1st ed.; Pytkowicz, R. M., Ed.; CRC Press: Boca Raton, FL; 1979; Chapter 2, p 63.
Criss and Millero (22) Parker, V. B. Thermal properties of aqueous uni-univalent electrolytes from 0 to 100 °C, NSRDS-NBS 2, Superintendent of Documents, U. S. Government Printing Office: Washington, D.C., 1968. (23) Picker, P. Can. Res. DeV. 1974, 7, 11. (24) Fortier, J.-L., Leduc, P.-A.; Desnoyers, J. E. J. Solution Chem. 1974, 3, 323. (25) Desnoyers, J. E.; de Visser, C.; Perron, G.; Picker, P. J. Solution Chem. 1976, 5, 605. (26) Allred, G. C.; Woolley, E. M. J. Chem. Thermodyn. 1981, 13, 147. (27) Singh, P. P.; Woolley, E. M.; McCurdy, K. G.; Hepler, L. G. Can. J. Chm. 1976, 54, 3315. (28) Richards, T. W.; Rowe, A. W. Proc. Am. Acad. 1913, 49, 173. (29) Johnson, W. H.; Gilliland, A. A.; Prosen, E. J. J. Res. Natl. Bur. Stand. 1959, 63A, 161. (30) Singh, P. P.; McCurdy, K. G.; Woolley, E. M.; Hepler, L. G. J. Solution Chem. 1977, 6, 327. (31) Enea, O.; Singh, P. P.; Woolley, E. W.; McCurdy, K. G.; Hepler, L. G. J. Chem. Thermodyn. 1977, 9, 731. (32) Olofsson, I. J. Chem. Thermodyn. 1979, 11, 1005. (33) Simonson, J. M.; Mesmer, R. E.; Rogers, P. S. Z. J. Chem. Thermodyn. 1989, 21, 561. (34) Perron, G.; Desnoyers, J. E.; Millero, F. J. Can. J. Chem. 1975, 53, 1134. (35) Roux, A.; Musbally, G. M.; Perron, G.; Desnoyers, J. E.; Singh, P. P.; Woolley, E. M.; Hepler, L. G. Can. J. Chem. 1978, 56, 24. (36) Mastroianni, M.; Criss, C. M. J. Chem. Eng. Data 1972, 17, 222. (37) Spitzer, J. J.; Olofsson, I. V.; Singh, P. P.; Hepler, L. G. Thermochim. Acta 1979, 28, 155. (38) Allred, G. C.; Woolley, E. M. J. Chem. Thermodyn. 1981, 13, 155. (39) Stakhanova, M. S.; Karapet’yants, M. Kh.; Vasil’ev, V. A.; Epikhin, Yu. A. Russ. J. Phys. Chem. 1964, 38, 1306. (40) Leduc, P.-A.; Desnoyers, J. E. Can. J. Chem. 1973, 51, 2993. (41) Roux, A. H.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1984, 62, 878. (42) Lemire, R. J.; Saluja, P. P. S.; Campbell, A. B. J. Solution Chem. 1992, 21, 507. (43) Hovey, J.; Hepler, L. G.; Tremaine, P. Can. J. Chem. 1988, 66, 881. (44) Millero, F. J.; Leung, W. H. J. Chem. Thermodyn. 1975, 7, 1067.
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