Modeling the Heat Capacities of Aqueous 1−1 Electrolyte Solutions with Pitzer's Equations

Abstract

The apparent molal heat capacities (φC p ) of 1−1 electrolytes at 25 °C have been fitted to the Pitzer equation φC p = C̄p ,2° + (AJ /1.2) ln(1 + 1.2I 1/2) − 2RT 2[mBJ MX + m 2 CJ MX], where C̄p ,2° is the partial molal heat capacity of at infinite dilution and B J MX and C J MX are empirical constants related to ion−ion interactions. The values of C̄p ,2° of the electrolytes have been used to determine partial molal heat capacities of ions. The coefficients BJ MX and CJ MX 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%.

Standard state heat capacities of aqueous electrolytes and some related undissociated species

“…After values of c,'"' have been calculated for an electrolyte system, these values are then subtracted from the experimental values of Cp,+ to obtain the Cp,+(species) values that are then combined with some version of the Debye-Hiickel theory (such as eq. [16]) to obtain the standard state partial molar heat capacities Can (26), and in other publications to be cited later that nearly all of the CpOvalues derived from results of measurements with the Picker calorimeter have smaller uncertainties than do CpO values derived from earlier measurements cited by Parker (2). Although we are not making use of the heat capacities for dilute solutions that have been cited by Parker (2), it is worth emphasizing that many of the results she has cited for more concentrated solution are still quite useful for other purposes.…”

“…We also mention that Abraham and Marcus (86) and Criss and Millero (26) have provided useful reviews of standard state partial molar heat capacities of aqueous electrolytes. The first of these reviews (86) that was published in 1986 was concerned with both inorganic and organic electrolytes.…”

Apparent molar heat capacities and apparent molar volumes ofY2(SO4)3(aq),La2(SO4)3(aq),Pr2(SO4)3(aq),Nd2(SO4)3(aq),Eu2(SO4)3(aq),Dy2(SO4)3(aq),Ho2(SO4)3(aq), andLu2(SO4)3(aq)atT= 298.15 K andp= 0.1 MPa

“…Given that this contribution for Sm 3+ (aq) is significantly less than the experimental uncertainty in the C p,φ values, and that for Eu 3+ (aq) it is comparable to the (17) but converted to the standard molar heat capacity values of Criss and Millero (64) experimental uncertainty at lower molalities, these electronic contributions to C p,φ do not alter the basic series trends and will be ignored in the following discussion.…”

“…Criss and Millero (63) (17) but adjust their reported average value to correspond to the C o p,φ of Criss and Millero (64) (65) whereas those of Cl − (aq) and ClO − 4 (aq) are Xiao and Tremaine's (17) recommended values. Although these two sources (17,65) 3 · mol −1 , with generally larger differences for the lighter rare earths than for the heavier ones.…”

The Speciation of Metals in Natural Waters

“…(1) Pitzer and Mayorga (1973), (2) Silvester and Pitzer (1978), (3) Criss and Millero (1996), (4) Pitzer and Mayorga (1973), (5) Kim and Frederick (1988), Pitzer et al (1978), (7) Criss and Millero (1999), (8) Millero and Byrne (1984), b determined from K* MX of Millero and Hawke (1992) Millero and Schreiber (1982), b Millero and Hawke (1992) except for HS complexes which were taken from Zhang and Millero (1994) and extrapolated to zero ionic strength, c Choppin (1989), d Sharma and Millero (1989), e Turner et al (1981) Aquat Geochem Table 5 Values for the association constants of ion pairs (logarithm of constants) for some trivalent metals in water at 25°C (K, mol kgH Millero (1992), b Byrne et al (1988) for hydrolysis data and Turner et al (1981) for the other ion pairs, c Millero and Pierrot (2007), d Millero et al (1995) Aquat Geochem are those from the Miami Pitzer Model (Millero and Pierrot 1998). References for some of the other Pitzer Parameters for the divalent and trivalent cations used are given in Table 2.…”