Mean Activity Coefficients and Osmotic Coefficients in Aqueous

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Mean Activity Coefficients and Osmotic Coefficients in Aqueous Solutions of Salts of Ammonium Ions with Univalent Anions at 25 °C Jaakko I. Partanen* Laboratory of Physical Chemistry, Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland ABSTRACT: The Hückel equation used in this study to describe the thermodynamic properties of dilute solutions of the ammonium salts of NH4Cl, NH4Br, NH4I, NH4NO3, NH4SCN, and NH4H2PO4 up to 1.5 mol·kg−1 is consisted of two electrolyte-dependent parameters B and b1. Parameter B is linearly related to the ionsize parameter a* in the Debye−Hückel equation, and parameter b1 is the coefficient of the linear correction term with respect to the molality. This coefficient is associated with the hydration numbers of the ions forming the electrolyte. For NH4ClO4 solutions, the estimated Hückel equation applies up to 2.1 mol·kg−1, and the equation was obtained from the isopiestic data measured by Esval and Tyree (J. Phys. Chem. 1962, 66, 940−942) against KCl solutions. For molalities above 1.5 mol·kg−1 (in the best case up to 10 mol·kg−1), an extended Hückel equation was used. For this equation, the Hückel equation is supplemented with a quadratic term in molality, and the coefficient of this term is parameter b2. All of the parameters for the Hückel equations of NH4Cl and NH4NO3 solutions were estimated from isopiestic data of Wishaw and Stokes (Trans. Faraday Soc. 1953, 49, 27−31). The former data were measured against KCl solutions and the latter against NaCl solutions. The Hü ckel parameters for NH4Br, NH4I, NH4SCN, and NH4H2PO4 solutions were estimated from the data measured by Covington and Irish (J. Chem. Eng. Data 1972, 17, 175−176), Bonner (J. Chem. Eng. Data 1976, 21, 498−499), Covington and Matheson (J. Solution Chem. 1977, 6, 263−267), and Filippov et al. (J. Appl. Chem., U.S.S.R., 1985, 58, 1807−1811), respectively, using the same experimental technique against NaCl solutions. In all of these estimations, the Hückel parameters of a recent KCl and NaCl study (J. Chem. Eng. Data 2009, 54, 208−219) were used for the solutions of the reference electrolyte. In the tests of the new parameter values, the cell potential difference, vapor pressure, and isopiestic data available in the literature were used. These data support well the tested Hückel parameters in most cases at least up to 3.5 mol·kg−1. Reliable thermodynamic activity quantities for ammonium salt solutions are, therefore, obtained using the new Hü ckel parameters. The activity coefficients, osmotic coefficients, and the vapor pressures obtained using these equations are tabulated here at rounded molalities. These values were compared to those suggested by Robinson and Stokes (Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959), to those obtained using Pitzer equations (Activity Coef f icients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, 1991; pp 100−101), and to those obtained using the extended Hü ckel equations presented by Hamer and Wu (J. Phys. Chem. Ref. Data 1972, 1, 1047−1099).

■

INTRODUCTION

KCl were applied as reference salts; and for NH4NO3, NH4I, and NH4H2PO4 solutions it was NaCl. It is shown here that reliable activity and osmotic coefficients for the tested ammonium salt solutions can also be determined using a simple Hückel equation up to about 1.5 mol·kg−1. The Hückel equation used in this study (see below and ref 10) to describe the thermodynamic properties of dilute solutions has two electrolyte-dependent parameters B and b1: parameter B is linearly related to the ion-size parameter a* in the Debye−Hückel equation and parameter b1 is the coefficient of the linear correction term with respect to the molality. This coefficient is associated with the hydration numbers of the ions forming the electrolyte. B and b1 were determined for the ammonium salts in the present study from the isopiestic data introduced above. For NH4SCN solutions, the isopiestic set of Covington and Matheson11

1

In the well-known tables of Robinson and Stokes, the values of the thermodynamic activity quantities for NH4Cl and NH4NO3 solutions (values are given up to 6.0 mol·kg−1) have been based on the isopiestic data of Wishaw and Stokes2 for these salt solutions against the solutions of KCl and NaCl as the reference electrolyte, respectively. All of the activity values in ref 1 for NH4Cl and NH4NO3 solutions have been taken without any changes from ref 2. Pitzer and Mayorga3,4 mainly used the values of ref 1 when they determined the parameters of the Pitzer equation for various electrolytes for the thermodynamic treatment of single electrolyte solutions. In these Pitzer tables (the revised values are given in ref 5) are also included the parameters for the following ammonium salts of NH4Br, NH4I, NH4ClO4, and NH4H2PO4 on the basis of the isopiestic data of Covington and Irish,6 Bonner,7 Esval and Tyree,8 and Filippov et al.,9 respectively. In the isopiestic measurements for NH4ClO4 solutions, the reference electrolyte was KCl; for NH4Cl and NH4Br solutions both NaCl and © XXXX American Chemical Society

Received: March 9, 2012 Accepted: August 29, 2012

A

dx.doi.org/10.1021/je300474k | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Values of the Parameters in the Equations of Hamer and Wu34 (See eqs 9 and 10) for the Electrolytes Considered in This Study at 25 °C NH4Cl NH4NO3 NH4ClO4 a

(B*)a

103β

103C

103D

106E

(mmax/mo)b

1.325 0.925 0.675

−4.5787 −34.748 −14.567

5.2712 1.1978

−0.70557 −0.019075

28.434

7.405 25.954 2.1

The unit is (mol·kg−1)−1/2. bThe maximum molality to which the equations apply (mo = 1 mol·kg−1).

Table 2. Values Recommended by Pitzer5 for the Parameters in the Pitzer Equations (see eqs 11 to 14) of the Electrolytes Considered in This Study at 25 °C

(measured against NaCl solutions) was used in the parameter estimation. Wishaw and Stokes2 measured isopiestically NH4Cl solutions against both KCl and NaCl solutions, but the NaCl points were measured at NH4Cl molalities higher than 5 mol·kg−1, and thus the KCl points alone were used in the parameter estimation. Also for the NH4Br solutions,6 only the points in the KCl set were used in the estimation. The Hückel parameters for the NaCl and KCl solutions for these estimations were taken from ref 12. The parameter values obtained were first tested with the isopiestic data used in the parameter determination. The NH4Cl parameters were also tested with the galvanic cell data measured by Verrall13 on concentration cells with transference. Additionally, it is shown in this study that the Hückel equation can be extended with an additional quadratic term in the molality, and the resulting equation applies well up to (5, 6, 8, 10, 3.5, and 8.2) mol·kg−1 for NH4Cl, NH4Br, NH4I, NH4NO3, NH4H2PO4, and NH4SCN solutions, respectively. The coefficient of this term is the parameter b2. It was also observed that for all of the ammonium salts considered, the same value of parameter B can be used in this extended equation as that obtained for dilute solutions. Then, the parameters b1 and b2 for this extended equation were estimated for solutions of all of these salts by using the same isopiestic data as those used above in the estimations for dilute solutions, but all points were taken in the estimation for each electrolyte (except for the NH4NO3/NaCl set,2 where only points up to 10 mol·kg−1 could be included from all of the points existing in this set up to 13.337 mol·kg−1). The resulting parameters were tested with the data in the isopiestic sets mentioned above and, additionally, the NH4Cl and NH4Br parameters with the data in the isopiestic sets of Wishaw and Stokes2 and Covington and Irish6 against NaCl solutions. The validity of the new NH4Cl parameters were also evaluated with the isopiestic data measured by Kirgintsev and Luk’yanov in 196314 and 196415 and by Shul’ts et al.16 for solutions of this salt and NaCl, with those measured by Shul’ts et al.16 for solutions of this salt and KCl, and with the vapor pressures measured directly by Pearce and Pumplin.17 The isopiestic data of Shul’ts and Simanova18 and those of Kirgintsev and Luk’yanov15 for solutions of NH4Br and NaCl were also predicted in the present tests using the new NH4Br parameters. The NH4SCN parameters were tested with the osmotic coefficients reported by Kálmán and Schwabe19 (based on isopiestic determinations against CaCl2 solutions). As found earlier,12,20−28 it was advantageous to perform all tests of this study on the raw experimental results of appropriate measurements. In these tests, it was observed that the Hückel equations are very reliable. The activity coefficients of the electrolyte and the osmotic coefficients and the vapor pressures of water were calculated using the Hückel equations and tabulated here at rounded molalities as the recommended values. These values have been compared with those of the previous studies in the literature, and the activity coefficient

NH4Cl NH4Br NH4I NH4H2PO4 NH4NO3 NH4ClO4 NH4SCNb

β0

β1

Cϕ

(mmax/mo)a

0.0522 0.0624 0.0570 −0.0704 −0.0154 −0.0103 0.02452

0.1918 0.1947 0.3157 −0.4156 0.1120 −0.0194 0.2615

−0.00301 −0.00436 −0.00308 0.00669 −0.00003

6.0 2.5 7.5 3.5 6.0 2.0 8.2

−0.00134

The maximum molality to which the equations apply (mo = 1 mol·kg−1). b Determined by Covington and Matheson11 from the isopiestic data against NaCl solutions. a

deviations between the new and the literature values are presented as the cell-potential deviations for galvanic cells (as in refs 10, 12, and 20−28) and the osmotic coefficient deviations as the vapor pressure deviations (refs 12 and 21−28).

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THEORY In the previous investigations,29,30 it was observed that the following Hückel equation predicts accurately the thermodynamic properties of NH4Cl solutions (as also of several other uniunivalent electrolytes) at 25 °C up to 0.1 mol·kg−1 ln γ = −

α m + 2M1(h − 1)m 1 + βDHa* m

(1) 31

The equation has the form presented by Pan. In it, m is the molality, γ is the mean activity coefficient on the molality scale, M1 is the molar mass of water (= 0.018015 kg·mol−1), and α and βDH are the Debye−Hückel parameters. Their values at t = 25 °C and at p = 101.325 kPa are 1.17444 (mol·kg−1)−1/2 and 3.2849 (mol·kg−1)−1/2·nm−1 (Archer and Wang32), respectively. The electrolyte parameters in eq 1 are the ion-size parameter a* and the hydration number h. Previously,30 the values of a* = 0.35 nm and h = 2.41 were determined for NH4Cl solutions. From this equation, the following equation can be derived for the osmotic coefficient of water based on the theoretical Gibbs− Duhem equation ϕ=1−

⎡ α ⎢(1 + βDHa* m ) 3 ⎢ (βDHa*) m ⎣

− 2 ln(1 + βDHa* m ) − + M1(h − 1)m

⎤ ⎥ 1 + βDHa* m ⎥⎦ 1

(2)

Generally for aqueous solutions of a uniunivalent electrolyte, the osmotic coefficient is related to the activity of the water (a1) as follows B



Article

Table 3. Results of the Parameter Estimation at 25 °C for the Hückel Equations (eqs 5 and 6) for Ammonium Salt Solutions by Least-Squares Fitting Using eq 15 NH4Cl NH4Br NH4I NH4NO3 NH4ClO4 NH4SCN NH4H2PO4

B/(mol·kg−1)−1/2

b1

s(b1)a

Nb

(mmax/mo)c

(s0/Pa)d

reference

1.3 1.32 1.53 0.97 0.86 1.33 0.08

0.0088 0.0250 0.0155 −0.0799 −0.0765 −0.0260 0.104

0.0005 0.0006 0.0012 0.0006 0.0010 0.0014 0.003

6 5 4 8 18e 9 8

1.407 1.509 1.650 1.514 2.1 1.3547 1.949

0.05 0.05 0.12 0.08 0.3 0.12 0.6

2 6 7 2 8 11 9

a

The standard deviation of parameter b1. bNumber of points included in the estimation. cThe maximum molality included in the estimation (mo = 1 mol·kg−1). dStandard error between the vapor pressures of water over the tested and reference solutions, see eq 17. eThe point (mx = 1.106 mol·kg−1 and my = 1.495 mol·kg−1) was omitted as an outlier.

Figure 2. Plot of eE (eq 23), the deviation between the observed and predicted cell potential difference (cpd) from the concentration cell data measured by Verrall 13 in dilute NH4Cl solutions on cell 19 (m1 = 0.201940 mol·kg−1) as a function of molality m2. The predicted cpd was calculated by using eq 20 where eq 5 with the parameter values of B = 1.3 (mol·kg −1)−1/2 and b1 = 0.0088 were used for the activity coefficients (for details see text).

Figure 1. Plot of eip (eq 18), the difference between the vapor pressure of water over the reference solution (x) and that over the tested solution (y), as a function of the molality of the tested solution (my) in the isotonic solutions of NaCl or KCl (x) and the tested ammonium salts (y) (see Table 3). The vapor pressures were calculated with eqs 3 and 4 using eq 6 with BNaCl = 1.4 (mol·kg−1)−1/2, b1,NaCl = 0.0716, BKCl = 1.3 (mol·kg−1)−1/2, and b1,KCl = 0.011 and with the recommended parameter values shown in Table 3 for the tested electrolytes. Symbols: ●, NH4Cl; ○, NH4Br; ▼, NH4I; ▽, NH4NO3; ■, NH4SCN; □, NH4ClO4; ⧫, NH4H2PO4. The errors for the points (mx = 1.155mo, my = 1.659mo) and (1.299, 1.949) obtained by Filippov et al.9 lay outside the scale of the figure. These errors are −0.77 and 0.95 Pa, respectively.

ln γ = −

α m + b1(m /mo) 1+B m

α ⎡ ⎢(1 + B m ) − 2 ln(1 + B m ) B3 m ⎣ ⎤ 1 1 o − ⎥ + b1(m /m ) 1+B m⎦ 2

(5)

ϕ=1−

ln a1 = −2mM1ϕ

(3)

The activity of water depends on the vapor pressure of water over the solution (p1) and that of pure solvent at the temperature under consideration (p*1 ) by a1 =

p1 p* 1

(6)

In more concentrated solutions, as earlier, the following extended Hückel equations were now used

(4)

α m + b1(m /mo) + b2(m /mo)2 1+B m

(7)

α ⎡ ⎢(1 + B m ) − 2 ln(1 + B m ) B3 m ⎣ ⎤ 1 1 2 o o 2 − ⎥ + b1(m /m ) + b2(m /m ) 1+B m⎦ 2 3

(8)

ln γ = −

For water at 25 °C, p1* = 3.1686 kPa (i.e., 23.766 mmHg; see Kell33). In the present study, it is not used the Hückel equation in the exactly same form as that of eq 1, but the new parameters B and b1 are defined by equations B = βDHa* and b1 = 2M1(h − 1)mo where mo = 1 mol·kg−1. The thermodynamic treatment of dilute solutions is here the same as that in the previous studies12,21−28 where it was found that this treatment applies very well to the thermodynamic properties of solutions of many uniunivalent salts at least up to about 1 mol·kg−1. With the parameter definitions, eqs 1 and 2 simplify to the forms

ϕ=1−

Hamer and Wu34 also used the extended Hückel equations to describe the thermodynamic properties of aqueous solutions of uniunivalent electrolytes at 25 °C. Their equations for ammonium salts have the general forms C



Article

Table 4. Results of the Parameter Estimation at 25 °C for the Extended Hückel Equations (eqs 7 and 8) for the Ammonium Salt Solutions by Least-Squares Fitting Using eq 16 from the Same Data Sets as Those Used for Table 3 [B/(mo)−1/2]a

b2

b1

s(b1)b

Nc

(mmax/mo)d

(s0/Pa)e

1.3 1.32 1.53 0.97 1.33 0.08

0.0011 −0.0013 −0.00004 0.00242 0.00123 −0.0036

0.0164 0.0373 0.0237 −0.08305 −0.02441 0.1139

0.0002 0.0003 0.0002 0.00006 0.00014 0.0007

14 12 14 29 20 15

4.647 4.7955 7.748 9.985 8.201 3.405

0.18 0.3 0.7 0.5 0.6 0.5

NH4Cl NH4Br NH4I NH4NO3 NH4SCN NH4H2PO4

Taken from Table 3 and mo = 1 mol·kg−1. bThe standard deviation of parameter b1. cNumber of points included in the estimation. dMaximum molality included in the estimation (mo = 1 mol·kg−1). eStandard error between the vapor pressures of water over the tested and reference solutions, see eq 17. a

log(γ ) = −

A m + β(m /mo) + C(m /mo)2 1 + B* m

+ D(m /mo)3 + E(m /mo)4

f1 = ln a1,x + 2M1m y − (9)

⎧ A ⎡ ϕ = 1 − ln(10)⎨ ⎢(1 + B* m ) ⎩ (B*)3 m ⎣ ⎤ 1 1 o − 2 ln(1 + B* m ) − ⎥ − β (m / m ) 1 + B* m ⎦ 2 ⎫ 2 3 4 − C(m/mo)2 − D(m/mo)3 − E(m /mo)4 ⎬ 3 4 5 ⎭

− 2 ln(1 + By m y ) −

= f0 + k1m y2

m α + (β 0 + β1e−2 3 1 + 1.2 m /mo

(11) m / mo

)

× (m /mo) + C ϕ(m /mo)2

(12)

In the former equation ⎤ α⎡ m 2 mo o ⎥ + + m m f =− ⎢ ln(1 1.2 / ) 3 ⎣ 1 + 1.2 m/mo 1.2 ⎦

f2 = ln a1,x + 2M1m y −

γ

(13)

Bγ = 2β 0 +

β1mo ⎡ −2 ⎢1 − e 2m ⎣

⎛ m / mo ⎜ ⎝

1 + 2 m / mo − 2

(15)

where k1 = −b1,yM1/mo. In these determinations, NaCl or KCl was the reference electrolyte (x) because the activities in solutions of this salt are known. The ammonium salt was the tested electrolyte (y). The details of the estimations are described, for example, in ref 25 (see eq 13 and the text associated with this equation in that study). The parameter values suggested in ref 12 for the extended Hückel equations of NaCl solutions [i.e., those of B = 1.4 (mol·kg−1)−1/2, b1 = 0.0699, and b2 = 0.0062] and of KCl solutions [B = 1.3 (mol·kg−1)−1/2, b1 = 0.01324, and b2 = 0.0036] apply well up to the molalities of the saturated solutions (i.e., up to 6.14 and 4.80 mol·kg−1, respectively). These values were used in the following equation for the determination of the Hückel parameters for more concentrated solutions of the ammonium salts

where the Debye−Hü ckel parameter A [= α/ln(10)] has a value of 0.5108 (mol·kg−1) −1/2. The values of parameters of eqs 9 and 10 for the ammonium salts are shown in Table 1. For activity and osmotic coefficients of a uniunivalent electrolyte, the Pitzer equations3−5 have the forms

ϕ=1−

⎤ 1 ⎥ 1 + By m y ⎥⎦

= f0 − b1,y M1(m y2 /mo)

(10)

ln γ = f γ + Bγ (m /mo) + (3/2)C ϕ(m /mo)2

⎡ 2αM1 ⎢ (1 + By m y ) By3 ⎢⎣

⎡ 2αM1 ⎢ (1 + By m y ) 3 By ⎢⎣

− 2 ln(1 + By m y ) −

m ⎟⎞⎤ ⎥ m o ⎠⎦

⎤ 4M1b2,y m3 1 ⎥+ 1 + By m y ⎥⎦ 3(mo)2

= f0 − b1,y M1(m y2 /mo)

(14)

= f0 + k 2m y2

In eqs 11, 12, and 14, β0, β1, and Cϕ are the electrolyte parameters, and their values at 25 °C are shown in Table 2 for the ammonium salts. All of the parameter estimations were here based on the isopiestic data where ammonium salt solutions were measured against KCl or NaCl solutions. The parameter values suggested in ref 12 for the Hückel equations of NaCl solutions [i.e., those of B = 1.4 (mol·kg−1)−1/2 and b1 = 0.072] and of KCl solutions [B = 1.3 (mol·kg−1)−1/2 and b1 = 0.011] apply well up to about 1.5 mol·kg−1. These values were used in the following equation for the determination of the Hückel parameters for dilute solutions of the ammonium salts

(16)

where k2 = −b1,yM1/mo. The details of the estimations are also presented in ref 25 (see eq 25 in that study).

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RESULTS AND DISCUSSION

Determination of Hü ckel Parameters B and b1 for Dilute Solutions. The results from the estimation of the Hückel parameters for the present electrolytes using eq 15 are shown in Table 3. The standard error s0 in this table is obtained by D



Article

Figure 4. Plot of ep (eq 24), the difference between the reported and predicted vapor pressures of water over NH4Cl and NH4SCN solutions as a function of molality m. The reported vapor pressures were obtained from the data measured by Pearce and Pumplin17 for NH4Cl (symbol ●) solutions and from the osmotic coefficients reported by Kálmán and Schwabe 19 for NaSCN solutions (symbol ○). The vapor pressures were predicted using eqs 3 and 4 with eq 8 with the recommended parameter values shown in Table 4. The error for the point of the saturated solution where m = 7.3800 mol·kg−1 and p = 18.281 mmHg in the set of Pearce and Pumplin 17 lies outside the scale of the figure (its value is 14.5 Pa).

Figure 3. Plot of eip (eq 18), the difference between the vapor pressure of water over the reference solution (x) and that over the tested solution (y), as a function of the molality of the tested solution (my) in the isotonic solutions of NaCl or KCl (x) and the tested ammonium salts (y). The vapor pressures were calculated with eqs 3 and 4 using eq 8 with BNaCl = 1.4 (mol·kg−1)−1/2, b1,NaCl = 0.0699, b2,NaCl = 0.0062, BKCl = 1.3 (mol·kg−1)−1/2, b1,KCl = 0.01324, and b2,KCl = 0.0036 and with the recommended parameter shown in Table 4 for the tested electrolytes. Symbols: ●, NH4Cl with reference electrolyte KCl2 (graph A), NH 4Cl with NaCl2 (B); ○, NH 4Br with KCl 6 (A), NH 4Br with NaCl 6 (B); ▼, NH 4I 7 (A), NH4Cl with NaCl measured by Shul’ts et al.16 (B); ▽, NH4NO32 (A), NH4Cl with KCl measured by Shul’ts et al.16 (B); ■, NH4SCN 11 (A), NH4Cl measured by Kirgintsev and Luk’yanov in 196314 (B); □, NH4H2PO49 (A), NH4Cl measured by Kirgintsev and Luk’yanov in 196415 (B); ⧫, NH4Br measured by Shul’ts and Simonova 18 (B); ◇ , NH 4 Br measured by Kirgintsev and Luk’yanov15 (B). The errors for the points (mx = 4.860mo, my = 5.799mo) and (5.812, 7.210) of Bonner 7 and those for the points (4.878, 6.642) and (5.694, 8.201) of Covington and Matheson11 lie outside the scale of graph A. These errors are (+1.70, −1.58, −1.57, and 1.42) Pa, respectively. The errors of the six NH4Cl/ NaCl points above my = 6 mol·kg−1 from the data of Wishaw and Stokes, 2 those from the two NH 4Cl/NaCl points of Shul’ts et al.16 where my = (7.0981 and 7.418) mol·kg−1, and those from the two NH4Cl/NaCl points of Kirgintsev and Luk’yanov14 where my = (6.2279 and 6.8293) mol·kg−1 lay outside the scale of graph B. The errors from ref 2 increase gradually from (11.8 to 20.0) Pa as a function of the molality, and the remaining errors are (15.6, 18.2, 9.4, and 14.9) Pa, respectively.

P is the number of estimated parameters. The new parameter values for the Hückel equations presented in Table 3 were first tested using the values of px and py. The results are shown in Figure 1 where the isopiestic vapor pressure error (eip) is defined as e ip = px − py (18) and presented as a function of the molality my. The largest absolute error in this figure at molalities smaller than 1.5 mol·kg −1 is less than 0.7 Pa (= 0.005 mmHg). For all sets, the errors form a random pattern. The results support, therefore, well the new parameters for all tested electrolytes. The most reliable technique to determine activity coefficients of alkali metal and ammonium halides in very dilute aqueous solutions is to measure appropriate concentration cells with transference (see, e.g., ref 12). For the present purposes is available in literature only one study that consists of data measured on cells of this kind in dilute ammonium halide solutions, that is, that of Verrall13 for NH4Cl solutions at 25 °C on cells Ag(s)|AgCl(s)|NH4Cl(aq, m1)|NH4Cl(aq, m2)|AgCl(s)|Ag(s) (19)

These data were used here to test the validity of the new Hückel parameters in Table 3 for NH4Cl solutions [i.e., those of B = 1.3 (mol·kg−1)−1/2 and b1 = 0.0088]. In the data sets measured with similar concentration cells as cell 19, the molality of solution 1 is often kept constant within the set, and the molality m2 is varied. In the study of Verrall, the molality of solution 1 was in a constant value of 0.201940 mol·kg−1, and the molalities m2 were always less than this value, and they start at a value of 0.000626 mol·kg−1. Theoretically, the cell potential difference (= cpd) of this cell (E) can be calculated from equation (see refs 12 and 35)

N

s0 =

∑ (px,i i=1

− py, i )2 /(N − P)

(17)

where px is the vapor pressure over the reference solution and py that over the tested solution, N is the number of points, and E



Article

Table 5. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Chloride Solutions at 25 °C as Functions of the Molality (m)a m/mol·kg−1

γ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0.770 0.720 0.690 0.669 0.654 0.642 0.632 0.624 0.617 0.611 0.601 0.593 0.587 0.582 0.578 0.571 0.568 0.566 0.566 0.567 0.570

(−0.21b) (−0.25b) (−0.30b) (−0.35b) (−0.40b) (−0.45b) (−0.55b)

ϕ

Table 6. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Bromide Solutions at 25 °C as Functions of the Molality (m)a m/mol·kg−1

p/Pa

0.928 0.915 0.909 0.905 0.903 0.902 0.902 0.902 0.902 0.902 0.904 0.906 0.908 0.910 0.913 0.919 0.927 0.935 0.943 0.951 0.960

3158.0 3147.8 3137.6 3127.5 3117.4 3107.4 3097.3 3087.3 3077.3 3067.2 3047.2 3027.1 3007.1 2987.0 2966.9 2916.8 2866.6 2816.3 2766.0 2715.6 2665.2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

(−0.1c) (−0.1c) (−0.2c) (−0.2c) (−0.3c) (−0.3c) (−0.4c) (−0.5c) (−0.7c)

a

The activity values were calculated using the extended Hückel equation with B = 1.3 (mol·kg−1)−1/2, b1 = 0.0164, and b2 = 0.0011. b Galvanic cell deviation in mV calculated using the equation

eE,GC = −

2RT γ(eq 7) ln F γ(eq 5)

eE,GC = −

F 2RT − F

m2

∫m

1

2RTt+,1 F

ln γ2

∫ln γ

where co = 1 mol·dm−3. The following equation can be estimated for t+ from these moving boundary data

Δt+d ln(γ )

1

t+ = 0.49077 − 0.00244 m /mo + 0.00702(m /mo)

(20)

(22)

This equation was given in ref 10. The concentrations from (0.01 to 0.2) mol·dm−3 were used by Longsworth when he measured the experimental t+ values, and the resulting values were given with four digits. Equation 22 predicts the measured values within ± 0.0003, and it shows that the t+ value of ammonium ions is almost constant in the used concentration range. This equation can be directly used in the evaluation of integral in the third term on the right-hand side of eq 20, but the values of the integral in the fourth term must be evaluated numerically. The latter values are very small. The cpd errors, defined by equation

where t+ is the transference number of NH4+ ions. In eq 20, it is divided into the following two parts: t+ = t+,1 + Δt+ where t+,1 is the transference number of NH4+ ions at the molality m1. The relationship t+ = t+(m) for eq 20 was estimated from the moving boundary data of Longsworth36 at 25 °C. These transference number data have been reported on the concentration (molarity, c) scale. For the conversion of these data on the molality (m) scale, the following equation (estimated from the pycnometric data of Jones and Talley37) was used ⎛ c ⎞2 m c ⎜ ⎟ = + 1.00288 0.037231 ⎝ co ⎠ mo co

2RT γ(eq 7) ln γ(eq 5) F

where the ϕ(eq 6) values were calculated using the recommended Hückel equation and the ϕ(eq 8) values using the extended Hückel equation (see footnotes a and b).

ln(γ2/γ1)

2RT Δt+(dm /m) − F

(−0.1c) (−0.1c) (−0.2c) (−0.3c) (−0.3c) (−0.4c) (−0.5c) (−0.6c)

ep,VPW = p(ϕ from eq 8) − p(ϕ from eq 6)

where the ϕ(eq 6) values were calculated using the recommended Hückel equation and the ϕ(eq 8) values using the extended Hückel equation (see footnotes a and b).

ln(m2 /m1) −

p/Pa 3158.0 3147.7 3137.5 3127.3 3117.1 3106.9 3096.7 3086.5 3076.3 3066.1 3045.6 3025.1 3004.6 2984.0 2963.5 2912.1 2860.7 2809.6 2758.8 2708.4 2658.4 2609.0 2560.3

where the γ(eq 5) values were calculated using the Hückel equation with B = 1.32 (mol·kg−1)−1/2 and b1 = 0.0250, and the γ(eq 7) values using the recommended parameter values (see footnote a). cVapor pressure deviation in Pa calculated using the equation

ep,VPW = p(ϕ from eq 8) − p(ϕ from eq 6)

2RTt+,1

(−0.24b) (−0.30b) (−0.36b) (−0.41b) (−0.46b) (−0.51b) (−0.57b)

ϕ 0.929 0.918 0.913 0.910 0.909 0.909 0.910 0.910 0.911 0.913 0.915 0.919 0.922 0.925 0.929 0.937 0.946 0.954 0.961 0.968 0.975 0.981 0.986

a The activity values were calculated using the extended Hückel equation with B = 1.32 (mol·kg−1)−1/2, b1 = 0.0373, and b2 = −0.0013. b Galvanic cell deviation in mV calculated using the equation

where the γ(eq 5) values were calculated using the Hü c kel equation with B = 1.3 (mol·kg−1)−1/2 and b1 = 0.0088, and the γ(eq 7) values using the recommended parameter values (see footnote a). cVapor pressure deviation in Pa calculated using the equation

E=−

γ 0.772 0.724 0.696 0.677 0.663 0.652 0.643 0.636 0.630 0.625 0.617 0.611 0.606 0.603 0.601 0.597 0.595 0.595 0.596 0.598 0.600 0.603 0.605

eE = E(observed) − E(predicted)

(21) F

(23)



Article

Table 7. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Iodide Solutions at 25 °C as Functions of the Molality (m)a m/mol·kg−1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

γ 0.780 0.736 0.710 0.692 0.679 0.669 0.661 0.654 0.648 0.644 0.636 0.630 0.626 0.623 0.620 0.616 0.615 0.615 0.616 0.618 0.621 0.624 0.628 0.632 0.637 0.641 0.646

(−0.21b) (−0.25b) (−0.29b) (−0.34b) (−0.38b) (−0.42b) (−0.50b)

ϕ 0.933 0.924 0.920 0.918 0.917 0.917 0.918 0.919 0.919 0.921 0.923 0.926 0.929 0.931 0.934 0.942 0.949 0.957 0.964 0.971 0.978 0.985 0.992 0.999 1.006 1.013 1.020

Table 8. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Nitrate Solutions at 25 °C as Functions of the Molality (m)a

p/Pa 3158.0 3147.6 3137.3 3127.0 3116.7 3106.4 3096.1 3085.8 3075.5 3065.2 3044.6 3024.0 3003.5 2982.9 2962.3 2910.9 2859.6 2808.5 2757.6 2706.9 2656.5 2606.5 2556.8 2507.4 2458.5 2409.9 2361.8

(−0.1c) (−0.1c) (−0.2c) (−0.3c) (−0.4c) (−0.5c) (−0.7c)

a The activity values were calculated using the extended Hückel equation with B = 1.53 (mol·kg−1)−1/2, b1 = 0.0237, and b2 = −0.00004. b Galvanic cell deviation in mV calculated using the equation

eE,GC = −


m/mol·kg−1

γ

ϕ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

0.746 0.682 0.641 0.611 0.587 0.566 0.549 0.534 0.520 0.508 0.487 0.468 0.452 0.438 0.425 0.396 (−0.37b) 0.373 0.353 0.335 0.320 0.306 0.294 0.283 0.273 0.263 0.255 0.247 0.240 0.234 0.228 0.223

0.913 0.891 0.876 0.865 0.856 0.848 0.841 0.835 0.829 0.823 0.813 0.804 0.796 0.788 0.780 0.762 0.746 0.731 0.717 0.704 0.692 0.681 0.670 0.661 0.652 0.644 0.637 0.630 0.624 0.620 0.615

p/Pa 3158.2 3148.3 3138.7 3129.3 3120.1 3111.1 3102.1 3093.3 3084.6 3076.0 3059.1 3042.6 3026.6 3010.8 2995.4 2958.3 2923.1 2889.5 2857.4 2826.7 2797.2 2768.7 2741.2 2714.4 2688.3 2662.7 2637.5 2612.6 2587.8 2563.2 2538.5

(0.1c)

(−0.1c) (−0.2c) (−0.2c) (−0.5c) (−0.7c) (−1.7c)

a The activity values were calculated using the extended Hückel equation with B = 0.97 (mol·kg−1)−1/2, b1 = −0.08305, and b2 = 0.00242. b Galvanic cell deviation in mV calculated using the equation


eE,GC = −


where the γ(eq 5) values were calculated using the Hückel equation with B = 0.97 (mol·kg−1)−1/2 and b1 = −0.0799, and the γ(eq 7) values using the recommended parameter values (see footnote a). cVapor pressure deviation in Pa calculated using the equation

ep,VPW = p(ϕ from eq 8) − p(ϕ from eq 6) where the ϕ(eq 6) values were calculated using the recommended Hückel equation and the ϕ(eq 8) values using the extended Hückel equation (see footnotes a and b).


and are shown in Figure 2 as a function of the molality m2. These errors are small, and they thus support quite well the suggested Hückel parameters. It seems, however, that the concentration cell set of Verrall is not as reliable as the corresponding sets considered in ref 12 for NaCl and KCl solutions. According to the parameter values of a* and h presented here in connection with eq 1, the following Hückel parameters can be calculated for dilute NH4Cl solutions: B = 1.15 (mol·kg−1)−1/2 and b1 = 0.051. These values were estimated in ref 30 from the cpd data of Verrall.13 In ref 10, the following values were also estimated from the same data for these parameters: B = 1.1 (mol·kg−1)−1/2 and b1 = 0.078. The former values were recommended up to 0.1 mol·kg−1 and the latter up to

0.5 mol·kg−1. The parameter values from both of these sets will be considered below together with the values B = 1.3 (mol·kg−1)−1/2 and b1 = 0.0088 recommended here up to 1.5 mol·kg−1. Determination of the Parameters b1 and b2 for More Concentrated Solutions. The extended Hückel equations for NaCl and KCl solutions and eq 16 were used in the determination of Hückel parameters b1 and b2 for more concentrated solutions of NH4Cl, NH4Br, NH4I, NH4NO3, NH4SCN, and NH4H2PO4. In these estimations, NaCl or KCl was again the G



Article

Table 9. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Perchlorate Solutions at 25 °C as Functions of the Molality (m)a

Table 10. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Thiocyanate Solutions at 25 °C as Functions of the Molality (m)a

m/mol·kg−1

γ

ϕ

p/Pa

m/mol·kg−1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0

0.741 0.674 0.631 0.599 0.574 0.553 0.535 0.519 0.505 0.493 0.470 0.451 0.434 0.419 0.406

0.910 0.886 0.870 0.857 0.847 0.839 0.831 0.824 0.818 0.812 0.801 0.791 0.781 0.772 0.763

3158.2 3148.4 3139.0 3129.7 3120.6 3111.7 3102.9 3094.2 3085.7 3077.3 3060.8 3044.7 3029.1 3013.8 2999.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0

a The activity values were calculated using the Hückel equation with B = 0.86 (mol·kg−1)−1/2 and b1 = −0.0765.

reference electrolyte (x), ammonium salt was the tested electrolyte (y), and the values of parameter By were taken from Table 3. For each ammonium salt, the same isopiestic set as that used for eq 15 was accepted for the new parameter estimations, but all of the data points were included in the calculations, except for the NH4NO3 data where only the data up to my = 9.985 mol·kg−1 could be included. The results from these estimations are shown in Table 4. The new parameters in this table were then first tested in the same way as the Hückel equation parameters in Table 3 above. The vapor pressures at each isotonic point of these salt solutions were predicted using eqs 3, 4, and 8 with the recommended activity parameters. The results are shown in graph A of Figure 3 where the isopiestic vapor pressure error (eq 18) is presented as a function of the molality my. Nearly all of the absolute vapor pressure errors in this graph are smaller than 1.5 Pa (= 0.011 mmHg), and the experimental data thus support well the recommended activity parameters. The NH4Cl parameters in Table 4 were further tested by using the isopiestic data reported by Wishaw and Stokes2 and those measured by Kirgintsev and Luk’yanov in 196314 and in 196415 and by Shul’ts et al.16 for the solutions of this salt and NaCl. Shul’ts et al.16 measured also NH4Cl solutions against KCl solutions, and the resulting data were included in the present tests. Additionally, the NH4Br parameters in this table were further tested with the data measured by Covington and Irish,6 Shul’ts and Simanova,18 and Kirgintsev and Luk’yanov15 by this technique for the solutions of this salt and NaCl. The results of the tests from these data are shown as eip plots (eq 18) in graph B of Figure 3. The NH4Cl results in these plots are consistent with each other and support the suggested Hückel parameters up to 5 mol·kg−1. For NH4Br solutions, the Hückel parameters apply to stronger solutions, and they are supported by the experimental data quite well up to 8 mol·kg−1. The recommended NH4SCN parameter values in Table 4 were tested, in addition, with the osmotic coefficients reported by Kálmán and Schwabe.19 The osmotic coefficients were first changed into the vapor pressures using eqs 3 and 4, and then these reported values were predicted using eqs 3, 4, and 8 with

γ 0.768 0.716 0.684 0.662 0.644 0.630 0.618 0.607 0.598 0.590 0.576 0.565 0.554 0.546 0.538 0.521 0.508 0.496 0.487 0.479 0.471 0.465 0.459 0.454 0.450 0.446 0.443 0.440 0.438 0.436 0.434

(−0.24b) (−0.29b) (−0.35b) (−0.42b)

ϕ 0.926 0.912 0.904 0.899 0.895 0.892 0.890 0.888 0.886 0.884 0.882 0.880 0.878 0.876 0.875 0.872 0.869 0.867 0.865 0.864 0.863 0.863 0.863 0.863 0.863 0.864 0.866 0.867 0.869 0.872 0.874

p/Pa 3158.0 3147.8 3137.8 3127.8 3117.9 3108.1 3098.3 3088.6 3078.9 3069.2 3050.1 3031.1 3012.3 2993.6 2975.1 2929.4 2884.5 2840.4 2797.0 2754.3 2712.2 2670.6 2629.5 2588.9 2548.6 2508.6 2469.0 2429.5 2390.3 2351.2 2312.3

(−0.1c) (−0.1c) (−0.1c) (−0.2c) (−0.2c) (−0.2c) (−0.4c) (−0.6c) (−0.8c) (−1.0c)

a The activity values were calculated using the extended Hückel equation with B = 1.33 (mol·kg−1)−1/2, b1 = −0.02441, and b2 = 0.00123. bGalvanic cell deviation in mV calculated using the equation

eE,GC = −


where the γ(eq 5) values were calculated using the Hückel equation with B = 1.33 (mol·kg−1)−1/2 and b1 = −0.0260, and the γ(eq 7) values using the recommended parameter values (see footnote a). cVapor pressure deviation in Pa calculated using the equation


the recommended parameters. The results are presented in Figure 4 where the vapor pressure error (ep), defined as ep = p(reported) − p(predicted)

(24)

are shown versus the molality m. The reported osmotic coefficients of Kálmán and Schwabe support satisfactorily the new parameters for the extended Hückel equation for NH4SCN solutions up to 10 mol·kg−1. Finally, the NH4Cl parameters were tested with the vapor pressure data of Pearce and H



Article

The values of activity quantities in Tables 5 to 11 were calculated using the parameter values recommended here for the extended Hückel equations, except for NH4ClO4 solutions (for those only Hückel equation parameters were determined). In dilute solutions for the activity and osmotic coefficients obtained with the two-parameter Hückel equations are given in the tables the galvanic cell and vapor pressure deviations, respectively, in case the values are different from those recommended in the tables. The definitions of these quantities are given in the tables (see also below). The absolute galvanic cell deviation for γ is always smaller than 0.5 mV, and the absolute vapor pressure deviation for ϕ is smaller than 2 Pa. According to Tables 8 to 11, the simple two-parameter Hückel equations for NH4NO3, NH4ClO4, NH4SCN, and NH4H2PO4 solutions seem to apply quite well at least up to 2 mol·kg−1. Comparison of the New Activity Values to Those Presented in the Literature. The activity and osmotic coefficients in Tables 5 to 11 were compared to those presented by Robinson and Stokes,1 Hamer and Wu,34 and Pitzer.5 The comparison with these literature values are shown in Figure 5 for

Table 11. Recommended Activity Coefficient (γ), Osmotic Coefficient (ϕ), and Vapor Pressure of Water (p) in Aqueous Ammonium Dihydrogen Phosphate Solutions at 25 °C as Functions of the Molality (m)a m/mol·kg−1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5

γ 0.704 0.616 0.559 0.516 0.482 0.454 0.430 0.410 0.392 0.376 0.349 0.327 0.309 0.292 0.278 0.250 0.228 0.211

(−0.21b) (−0.24b) (−0.27b) (−0.29b) (−0.31b) (−0.32b) (−0.34b) (−0.35b) (−0.34b) (−0.32b) (−0.28b) (−0.12b) (+0.14b)

ϕ 0.886 0.845 0.816 0.793 0.773 0.756 0.742 0.728 0.717 0.706 0.687 0.671 0.657 0.644 0.633 0.610 0.592 0.577

p/Pa 3158.5 3149.4 3140.8 3132.6 3124.8 3117.2 3109.9 3102.8 3095.8 3089.0 3075.9 3063.2 3050.9 3038.9 3027.3 2999.1 2972.3 2946.4

(−0.1c) (−0.1c) (−0.2c) (−0.2c) (−0.2c) (−0.3c) (−0.3c) (−0.3c) (−0.3c) (−0.3c) (−0.2c) (0.7c) (2.2c)

a

The activity values were calculated using the extended Hückel equation with B = 0.08 (mol·kg−1)−1/2, b1 = 0.1139, and b2 = −0.0036. b Galvanic cell deviation in mV calculated using the equation

eE,GC = −




Pumplin.17 These vapor pressures were predicted using eqs 3, 4, and 8. The older value of 23.752 mmHg was used in this case for the vapor pressure of pure water at 25 °C (i.e., the same value as that in the original paper and also in the other papers of this group for different electrolytes, see for example refs 25 and 27). The results are given in Figure 4 where the vapor pressure error (ep in eq 24) is presented as a function of the molality. These data support quite well the suggested Hückel parameters up to 5 mol·kg−1 in the same way as the existing isopiestic data for NH4Cl solutions in Figure 3B. Recommended Activity and Osmotic Coefficients. On the basis of the experimental evidence provided by the tests in the present study (Figures 1 to 4), the Hückel and extended Hückel equations apply well to the experimental data available for ammonium salt solutions. New tables for the thermodynamic activity quantities in solutions of these salts at 25 °C were calculated using these equations. The new values are given in Tables 5 to 11 as follows: NH4Cl, Table 5; NH4Br, Table 6; NH4I, Table 7; NH4NO3, Table 8; NH4ClO4, Table 9; NH4SCN, Table 10; and NH4H2PO4, Table 11. The activity coefficients of the electrolyte and the osmotic coefficients and vapor pressures of water are included in these tables.

Figure 5. (A) Deviation, expressed as galvanic cell error eE,GC (eq 25), between the literature activity coefficients and those recommended in this study (eq 7) and (B) deviation, expressed as vapor pressure error ep,VPW (eq 26), between the literature osmotic coefficients and those recommended in this study (eq 8) for NH4Cl solutions (see Table 5). Symbols: ●, Robinson and Stokes;1 ○, Hamer and Wu;34 ▼, Pitzer and Mayorga.4 The deviations for the literature osmotic coefficients at m = (5.5 and 6.0) mol·kg−1 lay outside the scale of graph B. Their values are (3.4 and 5.6) Pa,1 (2.1 and 5.0) Pa,34 and (2.4 and 5.1) Pa.4

NH4Cl, Figure 6 for NH4Br, NH4I and NH4SCN, Figure 7 for NH4NO3, and Figure 8 for NH4ClO4 and NH4H2PO4. In each figure, the activity coefficient results of the comparison are shown in graph A and the osmotic coefficient results in graph B. The quantity presented on the y-axis in these graphs is the I



Article

Figure 6. (A) Deviation, expressed as galvanic cell error eE,GC (eq 25), between the literature activity coefficients from Pitzer equation (eq 11) and those recommended in this study (eq 7) and (B) deviation, expressed as vapor pressure error ep,VPW (eq 26), between the literature osmotic coefficients from Pitzer equation (eq 12) and those recommended in this study (eq 8) for NH4Br (symbol ●), NH4I (○), and NH4SCN (▼) solutions (see Tables 6, 7, and 10, respectively). The deviations for the literature osmotic coefficients at m = (9, 9.5, and 10.0) mol·kg−1 for the NH4SCN solutions lay outside the scale of graph B. Their values are (5.1, 9.0, and 13.9) Pa, respectively.

Figure 7. (A) Deviation, expressed as galvanic cell error eE,GC (eq 25), between the literature activity coefficients and those recommended in this study (eq 7) and (B) deviation, expressed as vapor pressure error ep,VPW (eq 26), between the literature osmotic coefficients and those recommended in this study (eq 8) for NH4NO3 solutions (see Table 8). Symbols: ●, Robinson and Stokes;1 ○, Hamer and Wu;34 ▼, Pitzer and Mayorga.4 The deviations for the activity coefficients of the Pitzer equation at m = (9, 9.5, and 10.0) mol·kg−1 lay outside the scale of graph A. Their values are (1.12, 1.43, and 1.78) mV, respectively. The deviation for the osmotic coefficients of Hamer and Wu at m = 10.0 mol·kg−1 lay outside the scale of graph B. This value is 3.2 Pa. Also all deviations for osmotic coefficients of Pitzer equation above 6.5 mol·kg−1 lay outside are in the range (3.5 to 26) Pa and are thus outside the scale of graph B.

cell-potential deviation eE,GC (A) or the vapor pressure deviation ep,VPW (B). Details of these quantities are given, for example, in eqs 22 and 23 and in the text associated with these equations in ref 27. They are defined by equations eE,GC = −

2RT γ(literature) ln F γ(recd)

ep,VPW = p(literature) − p(recd)

and the recommended values were obtained using the new two-parameter Hückel equation. To show that the ammonium ions in dilute aqueous solutions behave thermodynamically like potassium ions, the activity coefficients for dilute KCl solutions [obtained using the Hückel equation with B = 1.3 (mol·kg−1)−1/2 and b1 = 0.011] were also included in this figure. Both previous Hückel equations for NH4Cl were obtained from the electrochemical cell data of Verrall,13 and they give activity coefficients that agree quite well with the values recommended here on the basis of isopiestic data at least up to about 0.7 mol·kg−1. The deviation plot for KCl parameters shows that the new activity coefficients for NH4Cl solutions are practically the same as those for KCl solutions up to 1.0 mol·kg−1. For NH4Br, NH4I, and NH4SCN solutions, neither Robinson and Stokes1 nor Hamer and Wu34 have presented activity parameters. Therefore, here only the Pitzer parameters (Table 2) are considered in Figure 6 for these salt solutions. The activity coefficients obtained using the Pitzer equations for NH4I and NH4SCN solutions agree well in graph A of this figure with those recommended up to 9 mol·kg−1, but for NH4Br solutions the agreement is not as well even in less concentrated solutions. In graph B of this figure, the agreement for

(25) (26)

For the recommended values, those obtained from eqs 7 and 8 were used, except for NH4ClO4 solutions because for those only the Hückel equation (eq 5 or 6) was determined. The activity and osmotic coefficients suggested in the literature for NH4Cl solutions agree satisfactorily in Figure 5 with those recommended in Table 5 up to 5.0 mol·kg−1. However, the literature activity coefficients are slightly smaller than those obtained with the extended Hückel equation above 1 mol·kg−1 (leading to a galvanic cell errors of about 0.7 mV). The activity coefficients obtained with the two previous Hückel equations mentioned above for NH4Cl solutions [where B = 1.15 (mol·kg−1)−1/2 and b1 = 0.051 or B = 1.1 (mol·kg−1)−1/2 and b1 = 0.078] were compared with the values obtained by the Hückel equation with B = 1.3 (mol·kg−1)−1/2 and b1 = 0.0088 (i.e., the recommended one). The results are illustrated as deviation plots in Figure 9 where the activity coefficient errors were calculated for these dilute solutions from eq 25, J



Article

in Figure 7 with those recommended in Table 8 at least up to 6 mol·kg−1. In Figure 8, the activity and osmotic coefficients from the Pitzer equations for NH4ClO4 solutions agree quite well with those recommended in Table 9 as well as the osmotic coefficients (graph B) from the Hamer equation, but the activity coefficients from the latter equation (graph A) are quite different from those recommended. For NH4H2PO4 solutions in this figure, the osmotic coefficients (graph B) from the Pitzer equation agree well with those in Table 11, but the activity coefficients (graph A) are very different. The aqueous solutions of NH4H2PO4 can equivalently be regarded as solutions of phosphoric acid in solvent mixtures of ammonia and water. Therefore, the data from these salt solutions are probably associated with the first dissociation of phosphoric acid in these mixtures. This can be seen, for example, in the value of parameter B of the Hückel equation in Table 3 which is very different from those of the other strong electrolytes. It seems that the activity coefficients suggested in Table 11 or those calculated from the Pitzer equations have in this case only a very limited significance and use. Comparison of the Activity Values of the Potassium and Ammonium Salts. In Figure 9, it was observed that the activity coefficients of NH4Cl and KCl in dilute aqueous solutions are very close to each other. The thermodynamic similarity between K+ and NH4+ ions was also tested here in the following way. In Figure 10, the following differences are presented as a function of the molality

Figure 8. (A) Deviation, expressed as galvanic cell error eE,GC (eq 25), between the literature activity coefficients and those recommended in this study (eq 5 or 7) and (B) deviation, expressed as vapor pressure error ep,VPW (eq 26), between the literature osmotic coefficients and those recommended in this study (eq 6 or 8) for NH4ClO4 and NH4H2PO4 solutions (see Tables 9 and 11, respectively). Symbols: ●, NH4ClO4, Hamer and Wu;34 ○, NH4ClO4, Pitzer and Mayorga;4 ▼, NH4H2PO4, Pitzer.5

Figure 10. Deviation, expressed as vapor pressure error ep,VPW (eq 27), between the osmotic coefficients of ammonium and potassium salt solutions as a function of the molality m. The osmotic coefficients were calculated using the extended Hückel equation (eq 8) with the recommended parameter values (except for NH4H2PO4 solutions, see citations in the text and Tables 3 and 4). Symbols: ●, X = Cl−; ○, Br−; ▼, I−; ▽, NO3−; □, SCN−; ■, H2PO4−. Deviations for the nitrate solutions at (2.0, 2.5, 3.0, and 3.5) mol·kg−1 are outside the scale of the figure. These deviations are (−23, −34, −45, and −56) Pa, respectively.

Figure 9. Deviation, expressed as galvanic cell error eE,GC (eq 25), between the literature activity coefficients and those recommended in this study (eq 5) for dilute NH4Cl solutions as a function of the molality m (see Table 5). Symbols: ●, the Hückel equation with B = 1.15 (mol·kg−1)−1/2 and b1 = 0.051; ○, the Hückel equation with B = 1.1 (mol·kg−1)−1/2 and b1 = 0.078; ▼, the Hückel equation for KCl solutions with B = 1.3 (mol·kg−1)−1/2 and b1 = 0.011.

ep,VPW = pNH X − pKX 4

(27)

where X represents one of the anions considered here. The vapor pressure of the solution of an ammonium salt is thus compared at the same molality to that of the potassium salt solution. The osmotic coefficients were taken for KCl, KBr, KI, KNO3, KSCN, and KH2PO4 solutions from refs 12, 25, 26, 27, 23, and 23, respectively. KClO4 is only slightly soluble in aqueous solutions, but three isopiestic points measured by Bonner7 are available for solutions of this salt and NaCl. The vapor pressures of these three points were predicted here with

the osmotic coefficients is good for NH4Br and NH4SCN solutions, but the Pitzer values for NH4I solutions in the range (3.5 to 7) mol·kg−1 are somewhat higher than those recommended [leading to the highest absolute vapor pressure error of about of 5 Pa (= 0.04 mmHg) at 5.5 mol·kg−1]. The activity quantities given by Robinson and Stokes, Hamer and Wu, and Pitzer and Mayorga for NH4NO3 solutions agree quite well K



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(8) Esval, O. E.; Tyree, S. Y. The activity coefficients of ammonium perchlorate in water at 25°. J. Phys. Chem. 1962, 66, 940−942. (9) Filippov, V. K.; Charykova, M. V.; Trofimov, Y. M. Thermodynamics of system NH4H2PO4−(NH4)2SO4−H2O at 25 °C. J. Appl. Chem., U.S.S.R. 1985, 58, 1807−1811. (10) Partanen, J. I. Prediction of activity coefficients of uni-univalent electrolytes in pure aqueous solutions at 298.15 K by means of equations containing no adjustable parameters. Trends Phys. Chem. 2006, 11, 31−60. (11) Covington, A. K.; Matheson, R. A. Osmotic and activity coefficients of ammonium thiocyanate in aqueous solution at 25 °C. J. Solution Chem. 1977, 6, 263−267. (12) Partanen, J. I.; Covington, A. K. Re-evaluation of the thermodynamic activity quantities in aqueous sodium and potassium chloride solutions at 25 °C. J. Chem. Eng. Data 2009, 54, 208−219. (13) Verrall, R. E. Determination of activity coefficients of ammonium chloride at 25 °C. J. Solution Chem. 1975, 4, 319−329. (14) Kirgintsev, A. N.; Luk’yanov, A. V. Isopiestic investigation of ternary solutions. I. Russ. J. Phys. Chem. (Engl. Transl.) 1963, 37, 1501−1502. (15) Kirgintsev, A. N.; Luk’yanov, A. V. Isopiestic investigation of ternary solutions. III. Sodium chloride−sodium nitrate−water, sodium chloride−sodium bromide−water, and ammonium chloride−ammonium bromide−water. Russ. J. Phys. Chem. (Engl. Transl.) 1964, 38, 867−869. (16) Shul’ts, M. M.; Makarov, L. L.; Yu-jêng, S. Activity coefficients of NiCl2 and NH4Cl in binary and ternary solutions at 25°. Russ. J. Phys. Chem. (Engl. Transl.) 1962, 36, 1181−1183. (17) Pearce, J. N.; Pumplin, G. G. The vapor pressures and activity coefficients of aqueous solutions of ammonium chloride. J. Am. Chem. Soc. 1937, 59, 1219−1220. (18) Shul’ts, M. M.; Simanova, S. A. Activity coefficients of ammonium bromide at 25°. Russ. J. Phys. Chem. (Engl. Transl.) 1966, 40, 247−248. (19) Kálmán, E.; Schwabe, K. Osmotic and activity coefficients of ammonium thiocyanate in aqueous solution at 25 °C. J. Solution Chem. 1979, 8, 1−4. (20) Partanen, J. I.; Juusola, P. M.; Vahteristo, K. P.; de Mendonça, A. J. G. Re-evaluation of the activity coefficients of aqueous hydrochloric acid solutions up to a molality of 16.0 mol·kg−1 using the Hückel and Pitzer equations at temperatures from 0 to 50 °C. J. Solution Chem. 2007, 36, 39−59. (21) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous lithium chloride solutions at 25 °C up to a molality of 6.0 mol·kg−1. J. Chem. Eng. Data 2009, 54, 882−889. (22) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous rubidium and cesium chloride solutions at 25 °C. J. Chem. Eng. Data 2010, 55, 249−257. (23) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous solutions of silver nitrate, alkali metal fluorides and nitrites, and dihydrogen phosphate, dihydrogen arsenate, and thiocyanate salts with sodium and potassium ions at 25 °C. J. Chem. Eng. Data 2011, 56, 2044−2062. (24) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in pure aqueous solutions of chlorate, perchlorate, and bromate salts with lithium, sodium or potassium ions at 298.15 K. J. Solution Chem. 2012, 41, 271−293. (25) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous alkali metal bromide solutions at 25 °C. J. Chem. Eng. Data 2010, 55, 2202−2213. (26) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous alkali metal iodide solutions at 25 °C. J. Chem. Eng. Data 2010, 55, 3708−3719. (27) Partanen, J. I. Re-evaluation of the thermodynamic activity quantities in aqueous alkali metal nitrate solutions at T = 298.15 K. J. Chem. Thermodyn. 2010, 42, 1485−1493. (28) Partanen, J. I.; Covington, A. K. Re-evaluation of the thermodynamic activity quantities in aqueous solutions of uniunivalent alkali metal salts of aliphatic carboxylic acids and thallium acetate at 25 °C. J. Chem. Eng. Data 2011, 43, 4524−4543.

Table 12. Isopiestic Vapor Pressure Errors (eip in eq 18) Obtained from the Data Measured by Bonner7 for NaCl (= x) and KClO4 (= y) Solutions at 25 °C Using the Hückel Equation Recommended in the Present Study for NH4ClO4 Solutions (See Table 3) for the Tested KClO4 Solutions mx/mol·kg−1

my/mol·kg−1

eip/Pa

0.0527 0.1075 0.1326

0.0539 0.1103 0.1373

0.042 −0.014 0.038

the recommended parameter values of NH4ClO4 (see Table 3), and the results are presented in Table 12. The isopiestic errors in this table are small, and so the ammonium perchlorate parameters apply well to these potassium perchlorate data (despite the fact that this test is not very selective because the solutions in Table 12 are quite dilute). The deviation plots of Figure 10 are interesting: The vapor pressures of potassium and ammonium bromide solutions are very similar to each other. At 3.5 mol·kg−1, the difference is only about 3 Pa. Also the vapor pressures of chlorides of these two cations are very close to each other. At 3.5 mol·kg−1, the difference is about 5 Pa. Vapor pressures between potassium and ammonium iodides and between potassium and ammonium thiocyanates differ more, but the differences for these anions are very close to each other at all molalities in this figure. Also for these salts, however, the vapor pressure difference between potassium and ammonium ions is less than 5 Pa at molalities smaller than 2 mol·kg−1. Larger absolute differences even at dilute solutions are observed in this figure for nitrate and dihydrogen phosphate solutions. The latter data extend only up to 1.8 mol·kg−1 because of the low solubility of KH2PO4. The theoretical problems associated with the solutions of NH4H2PO4 were discussed above in connection with Figure 8.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +358 5 621 2350. E-mail: jpartane@lut.fi. Funding

The author is indebted to the Research Foundation of Lappeenranta University of Technology for financial support. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959; Appendix 8.10. (2) Wishaw, B. F.; Stokes, R. H. The osmotic and activity coefficients of aqueous solutions of ammonium chloride and ammonium nitrate at 25°. Trans. Faraday Soc. 1953, 49, 27−31. (3) Pitzer, K. S. Thermodynamics of electrolytes. I. Theoretical basis and general equations. J. Phys. Chem. 1973, 77, 268−277. (4) Pitzer, K. S.; Mayorga, G. Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 1973, 77, 2300−2308. (5) Pitzer, K. S., Ed. Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, FL, 1991; pp 100−101. (6) Covington, A. K.; Irish, D. E. Osmotic and activity coefficients of aqueous ammonium bromide solutions at 25 °C. J. Chem. Eng. Data 1972, 17, 175−176. (7) Bonner, O. D. The osmotic and activity coefficients of some salts having relatively large molar volumes. J. Chem. Eng. Data 1976, 21, 498−499. L



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(29) Partanen, J. I. Mean activity coefficients of several uni-univalent electrolytes in dilute aqueous solutions at 298.15 K. Acta Polytech. Scand., Chem. Technol. Metall. Ser. 1989, 188, 1−89. (30) Partanen, J. I. Recalculation of activity and osmotic coefficients of hydrohalic acids and some alkali metal halides in dilute aqueous solutions at 298.15 K. Acta Chem. Scand. 1991, 45, 993−997. (31) Pan, C. F. Activity and osmotic coefficients in dilute aqueous solutions of uni-univalent electrolytes at 25 °C. J. Chem. Eng. Data 1981, 26, 183−184. (32) Archer, D. G.; Wang, P. The dielectric constant of water and Debye−Hückel limiting law slopes. J. Phys. Chem. Ref. Data 1990, 19, 371−411. (33) Kell, G. S. Density, thermal expansivity, and compressibility of liquid water from 0° to 150 °C: correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Eng. Data 1975, 20, 97−105. (34) Hamer, W. J.; Wu, Y. C. Osmotic coefficients and mean activity coefficients of uni-univalent electrolytes in water at 25 °C. J. Phys. Chem. Ref. Data 1972, 1, 1047−1099. (35) Longsworth, L. G. Transference numbers of aqueous solutions of potassium chloride, sodium chloride, lithium chloride and hydrochloric acid at 25° by the moving boundary method. J. Am. Chem. Soc. 1932, 54, 2741−2758. (36) Longsworth, L. G. Transference numbers of aqueous solutions of some electrolytes at 25° by the moving boundary method. J. Am. Chem. Soc. 1935, 57, 1185−1191. (37) Jones, G.; Talley, S. K. The viscosity of aqueous solutions as a function of the concentration. J. Am. Chem. Soc. 1933, 55, 624−642.

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Mean Activity Coefficients and Osmotic Coefficients in Aqueous

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