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Apparent molar volumes and apparent molar heat capacities of aqueous silver nitrate at molalities from 0.015mol·kg−1 to 0.5mol·kg−1 , at temperatures from 278.15 K to 393.15 K, and at the pressure 0.35 MPa
J. Chem. Thermodynamics 2002, 34, 1531–1543 doi:10.1016/S0021-9614(02)00168-4 Available online at http://www.idealibrary.com on
Apparent molar volumes and apparent molar heat capacities of aqueous silver nitrate at molalities from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures from 278.15 K to 393.15 K, and at the pressure 0.35 MPa W. B. Clayton, B. A. Patterson, J. J. Jardine, and E. M. Woolleya Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA
Densities of aqueous silver nitrate solutions were determined at molalities m from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures T from 278.15 K to 368.15 K, and at the pressure 0.35 MPa, using a vibrating tube densimeter (DMA 512P, Anton Paar, Austria). A fixed cell, power-compensation, differential-output, temperature-scanning calorimeter (NanoDSC 6100, Calorimetry Sciences Corporation, American Fork, UT, USA) was used to measure the heat capacities of the same solutions at the same pressure and at 278:15 6 T=K 6 393:15. Apparent molar heat capacities Cp;/ and apparent molar volumes V/ were calculated for these solutions and fitted by regression to empirical equations describing the surfaces (Cp;/ ; T; m) and (V/ ; T; m). Ó 2002 Elsevier Science Ltd. All rights reserved.
KEYWORDS: apparent molar volume; apparent molar heat capacity; silver nitrate
1. Introduction Silver nitrate has several uses in industry including the manufacturing of mirrors and dyes. It is an important reagent used extensively in analytical chemistry. However, not much information is available regarding the thermodynamic properties of its aqueous solutions as a function of temperature. In this paper we present the apparent molar heat capacities Cp;/ and apparent molar volumes V/ for silver nitrate aqueous solutions at molalities m from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures T from 278.15 K to
a
To whom correspondence should be addressed (E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Elsevier Science Ltd. All rights reserved.
W. B. Clayton et al.
1532
393.15 K, and at the pressure 0.35 MPa. The results are fitted to empirical regression equations for the surfaces (Cp;/ ; T; m) and (V/ ; T; m).
2. Experimental An aqueous stock solution of silver nitrate m ¼ 0:49983 mol kg1 was prepared using carefully dried reagent grade silver nitrate (Sargent-Welch Scientific Company, Skokie, IL, USA). The reagent purity was found to be greater than 0.994 mass fraction pure by the Mohr method. We have used 1.000 mass fraction purity in our calculations. The water used was distilled, deionized, autoclaved, and degassed. All other solutions were prepared by mass dilution using this stock solution. All weighings were corrected for buoyancy. Precautions were taken so that all solutions were stored away from direct light. TABLE 1. Apparent molar volumes V/ for aqueous silver nitrate at p ¼ 0:35 MPa. The uncertainties are standard deviations from a minimum of thirty measurementsa m
V/ 1
mol kg
3
V/ 1
cm mol
V/ 1
V/
cm mol
1
cm mol
cm3 mol1
3
3
T ¼ 278:15 K
T ¼ 283:15 K
T ¼ 288:15 K
T ¼ 298:15 K
0.49983
28:079 0:008
28:617 0:007
29:277 0:005
30:516 0:006
0.24986
27:297 0:007
27:829 0:008
28:53 0:01
29:81 0:01
0.12499
26:20 0:02
27:08 0:02
28:01 0:02
29:33 0:02
0.05000
24:97 0:04
25:96 0:04
26:91 0:05
28:36 0:05
0.02500
29:12 0:08
28:93 0:08
29:00 0:09
29:3 0:1
0.01484
26:7 0:1
26:5 0:1
27:7 0:1
28:1 0:1
T ¼ 308:15 K
T ¼ 318:15 K
T ¼ 328:15 K
T ¼ 338:15 K
0.49983
31:402 0:005
32:027 0:006
32:451 0:005
32:723 0:006
0.24986
30:665 0:008
31:35 0:01
31:87 0:01
32:135 0:009
0.12499
30:27 0:02
30:99 0:02
31:58 0:02
31:78 0:02
0.05000
29:50 0:05
30:24 0:05
30:59 0:05
30:68 0:05
0.02500
29:3 0:1
29:0 0:1
29:0 0:1
29:35 0:06
0.01484
28:0 0:1
27:5 0:1
28:3 0:1
25:5 0:2
T ¼ 348:15 K
T ¼ 358:15 K
T ¼ 368:15 K
0.49983
32:823 0:007
32:907 0:006
32:715 0:006
0.24986
32:21 0:01
32:228 0:009
32:02 0:01
0.12499
31:85 0:03
31:96 0:02
31:85 0:02 30:23 0:07
0.05000
30:51 0:05
30:52 0:05
0.02500
28:8 0:1
28:6 0:1
29:0 0:1
0.01484
24:5 0:2
24:9 0:1
25:2 0:2
a
Average values of qs can be obtained with equation (3) using qw given in reference 2.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1533
The densities of the aqueous silver nitrate solutions were determined from a vibrating tube densimeter (DMA 512P, Anton Paar, Austria) at 278:15 6 T=K 6 368:15 and at the pressure 0.35 MPa. A temperature circulator (PolyScience 9510, Niles, IL) controlled the temperature of the densimeter. As reported previously,ð1;2Þ the temperature was controlled within an average standard deviation of 0:0020 K and a maximum deviation of 0:0029 K for all solutions and temperatures recorded, and the pressure was maintained constant at ð0:350 0:001Þ MPa. The periods of oscillation s 4 ms had an average standard deviation Ds ¼ 0:68 ns and a maximum deviation of 1:0 ns. Densities were calculated with HookeÕs Law by equation (1), qs ¼ qw þ kq ðs2s s2w Þ;
ð1Þ
FIGURE 1. Apparent molar volumes V/ for aqueous silver nitrate AgNO3 (aq) plotted against molality m and temperature T. s, Experimental values at p ¼ 0:35 MPa from table 1; surface at p ¼ 0:35 MPa generated from regression parameters in table 2 with equation (5); O from reference 6 at T ¼ 298:15 K and p ¼ 0:10 MPa.
W. B. Clayton et al.
1534
where qs and qw are the densities of the silver nitrate solution and water, respectively, and ss and sw are the periods of oscillation of the tube when it contains the solution and water, respectively. Values of kq , the calibration constant for the densimeter, were determined, as described previouslyð1;2Þ from experiments with water and 1:0 mol kg1 NaCl(aq), both of which have well known densities.ð3;4Þ The calorimeter used to measure the heat capacities was calibrated as described in earlier work.ð5Þ Results used were the average of eight temperature scans between 273.15 K and 398.15 K at the rate r ¼ 16:6667 mK s1 and at the pressure ð0:35 0:015Þ MPa. The heat capacity of a solution was determined from the difference in the calorimetric power output from two experiments performed under the same conditions: one with the reference and sample cells filled with water, and the other with the sample cell filled with the solution of interest and the reference cell again filled with water. The massic heat capacity is determined by equation (2), cp;s ¼ kc ðDPs DPw Þ=ðr qs Þ þ cp;w qw =qs ;
ð2Þ
where cp;s and cp;w are the massic heat capacities of the solution of interest and of water, respectively; DPs and DPw are the differences in power required to maintain the two calorimetric cells at the same temperature during the two experiments; and kc is the calibration constant for this calorimeter, obtained as reported previouslyð5Þ from measurements on 1:0 mol kg1 NaCl(aq) and water.ð3;4Þ Experiments were performed with water in both cells every few days to determine and compensate for any small changes in the calorimetric baseline signal.
TABLE 2. Regression parameters of equation (5) for the apparent molar volume V/ of aqueous silver nitrate. The values are chosen so that equation (5) reproduces the generated V/ values to within 0:01 cm3 mol1 at m 6 0:5 mol kg1 , at 278:15 6 T=K 6 393:15, and at p ¼ 0:35 MPa v0;0 =ðcm3 mol1 Þ
1603:68 0:01
v1;0 =ðcm3 mol1 K1 Þ
4:43798 0:00003
103 v2;0 =ðcm3 mol1 K2 Þ
4:1629 0:0001
v3;0 =ðcm3 mol1 KÞ
185610 1
v0;1 =ðcm3 kg mol2 Þ
9253:99 0:002
v1;1 =ðcm3 kg mol2 K1 Þ 2
2
3
10 v2;1 =ðcm kg mol
28:06966 0:00006 2
K Þ
2:8286 0:0001
v3;1 =ðcm3 kg mol2 KÞ
1014850 6
v0;2 =ðcm3 kg2 mol3 Þ
12916:78 0:03
v1;2 =ðcm3 kg2 mol3 K1 Þ 2
3
2
3
10 v2;2 =ðcm kg mol
39:2211 0:0001 2
K Þ
v3;2 =ðcm3 kg2 mol3 KÞ Da /ðcm3 mol1 Þ a
Standard deviation of the regression.
3:95252 0:00002 1413430 7 0.15
Apparent molar volumes and heat capacities of aqueous silver nitrate
1535
Apparent molar volumes V/ and apparent molar heat capacities Cp;/ were calculated by equations (3) and (4), respectively, V/ ¼ M2 =qs 1000 ðqs qw Þ=ðqs qw mÞ;
ð3Þ
Cp;/ ¼ M2 cp;s þ 1000 ðcp;s cp;w Þ=m:
ð4Þ
In equations (3) and (4), M2 ¼ 169:8717 g mol1 is the molar mass of silver nitrate.
TABLE 3. Standard partial molar volumes V02 and standard partial molar heat capacities C0p;2 for aqueous silver nitrate at infinite dilution and at p ¼ 0:35 MPa from equations (5) and (6) and the parameters in tables 2 and 5 T
V20
0 Cp;2
K
cm3 mol1
278.15
24.0
)106.8
283.15
25.3
)89.4
288.15
26.4
)74.5
293.15
27.3
)61.8
298.15
28.0
)51.1
303.15
28.6
)42.4
308.15
29.1
)35.3
313.15
29.5
)29.8
318.15
29.7
)25.7
323.15
29.9
)22.8
328.15
30.0
)21.0
333.15
30.1
)20.2
338.15
30.1
)20.2
343.15
30.1
)21.1
348.15
30.1
)22.6
353.15
30.0
)24.6
358.15
30.0
)27.1
363.15
29.9
)30.0
368.15
29.9
)33.1
373.15
29.9
)36.5
378.15
29.9
)40.0
383.15
30.0
)43.6
388.15
30.1
)47.1
393.15
30.2
)50.6
J K1 mol1
W. B. Clayton et al.
1536
TABLE 4. Apparent molar heat capacities Cp;/ for aqueous silver nitrate at p ¼ 0:35 MPa. The uncertainties are standard deviations for the averages from a total of at least four scans each at both increasing and decreasing temperaturea m
Cp;/ 1
1
Cp;/ 1
JK
Cp;/ 1
mol
JK
1
Cp;/ 1
mol
JK
1
Cp;/ 1
mol
1
JK
mol1
mol kg
JK
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 278:15 K 40:1 0:1 67:0 0:7 86:2 1:9 101:1 4:1 105:9 4:6 108:6 4:9
T ¼ 283:15 K 24:4 0:2 47:8 1:1 64:4 1:9 77:8 3:8 82:4 4:0 85:2 3:8
T ¼ 288:15K 12:4 0:1 32:9 0:9 47:8 1:6 60:0 3:4 64:6 3:4 67:7 3:6
T ¼ 293:15 K 3:0 0:1 21:5 0:8 35:1 1:5 46:5 3:2 51:1 2:5 53:9 2:9
T ¼ 298:15 K 4:1 0:2 12:7 0:5 25:4 1:1 36:0 2:7 41:0 2:1 43:6 2:8
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 303:15 K 9:6 0:2 5:8 0:4 17:7 0:9 27:7 2:2 33:0 1:8 35:6 2:4
T ¼ 308:15 K 13:8 0:2 0:6 0:4 11:9 0:8 21:5 1:6 27:3 1:3 29:5 2:2
T ¼ 313:15 K 17:0 0:2 3:4 0:2 7:4 0:6 16:6 1:2 22:4 1:0 24:5 2:0
T ¼ 318:15 K 19:2 0:2 6:2 0:2 4:2 0:5 13:3 0:8 19:4 0:8 20:9 1:9
T ¼ 323:15 K 20:8 0:2 8:3 0:1 1:8 0:4 10:8 0:6 17:1 0:9 18:2 2:1
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 328:15 K 21:7 0:2 9:7 0:1 0:3 0:3 9:3 0:4 15:7 1:0 16:6 2:2
T ¼ 333:15 K 22:2 0:3 10:5 0:1 0:6 0:2 8:4 0:4 14:6 1:1 15:1 2:4
T ¼ 338:15 K 22:3 0:3 10:8 0:2 1:0 0:1 7:9 0:3 14:4 1:2 14:6 2:5
T ¼ 343:15 K 21:9 0:3 10:6 0:2 0:7 0:1 8:4 0:4 14:9 1:2 15:1 2:9
T ¼ 348:15 K 21:2 0:2 9:9 0:2 0:0 0:1 9:4 0:4 15:6 1:1 15:4 2:9
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 353:15 K 20:2 0:2 9:0 0:2 1:0 0:2 10:6 0:4 17:1 1:2 17:3 2:9
T ¼ 358:15 K 19:0 0:2 7:7 0:1 2:4 0:1 12:0 0:4 18:4 1:3 18:7 2:8
T ¼ 363:15 K 17:4 0:3 6:0 0:2 4:2 0:2 14:1 0:5 20:5 1:2 21:4 2:9
T ¼ 368:15 K 15:6 0:3 4:2 0:2 6:3 0:2 16:6 0:5 23:3 1:1 24:3 3:5
T ¼ 373:15 K 13:7 0:2 2:0 0:2 8:6 0:3 19:4 0:5 25:9 0:9 26:8 3:6
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 378:15 K 11:3 0:2 0:5 0:2 11:5 0:2 22:4 0:5 29:4 1:1 30:7 3:2
T ¼ 383:15 K 9:0 0:2 3:1 0:2 14:4 0:2 25:6 0:7 32:4 1:0 34:0 2:6
T ¼ 388:15 K 6:4 0:2 6:0 0:1 17:5 0:2 29:1 1:0 36:1 0:7 37:9 2:9
T ¼ 393:15 K 3:6 0:1 8:9 0:2 20:9 0:9 32:9 0:7 40:8 0:7 43:1 2:4
a
mol
1
Average experimental values of cp;s can be obtained with equation (4) and with cp;w given in reference 2.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1537
3. Results and discussion Values for the apparent molar volumes V/ for aqueous silver nitrate are given in table 1. Figure 1 shows (V/ ; T; m) for aqueous silver nitrate along with the results of Singh et al.ð6Þ The regression surface in figure 1 corresponds to equation (5), V/ ¼ AV m1=2 þ
2 X
mn ðv0;n þ v1;n T þ v2;n T 2 þ v3;n =T Þ;
ð5Þ
n¼0
where AV is the Debye–H€ uckel coefficient for volumes. We have used values for AV based on the equations of Bradley and Pitzerð7Þ that are tabulated by Ford et al.ð2Þ The parameters for equation (5) given in table 2 are based on a regression with weighting factors inversely proportional to the uncertainties in table 1. Values calculated from this
FIGURE 2. Apparent molar heat capacities Cp;/ for aqueous silver nitrate AgNO3 (aq) plotted against molality m and temperature T. s, Experimental values at p ¼ 0:35 MPa from table 4; surface at p ¼ 0:35 MPa generated from regression parameters in table 5 with equation (6). O From reference 6 at T ¼ 298:15 K and p ¼ 0:10 MPa. From reference 8 at T ¼ 298:15 K and m ¼ 0:068 mol kg1 .
W. B. Clayton et al.
1538
equation agree with the values of Singh et al.ð6Þ to within 0:8 cm3 mol1 . From this equation, V/ ¼ V02 at infinite dilution has been estimated and values are given in table 3. Our results for the apparent molar heat capacities for aqueous silver nitrate are given in table 4. Figure 2 shows (Cp;/ ; T; m) for aqueous silver nitrate, along with results of Singh et al.ð6Þ and Sergeeva et al.ð8Þ The regression surface in figure 2 corresponds to equation (6), Cp;/ ¼ AC m1=2 þ
2 X
mn ðc0;n þ c1;n T þ c2;n T 2 þ c3;n =T Þ;
ð6Þ
n¼0
where AC is the Debye–H€ uckel coefficient for heat capacities based on the equations of Bradley and Pitzerð7Þ that are tabulated by Ford et al.ð2Þ The regression used weighting factors equal to the inverse of the uncertainties in Cp;/ from table 4. The regression parameters for equation (6) are given in table 5. Values calculated from this equation agree with the values of Singh et al.ð6Þ and Sergeeva et al.ð8Þ to within 11 J K1 mol1 . Extrapolated values for Cp;/ ¼ C0p;2 at infinite dilution are given in table 3. Figures 3 and 4 show (V/ ; T; m) and (Cp;/ T; m), respectively, for aqueous silver ion with comparable surfaces for the aqueous potassium and sodium ions obtained from results by Patterson and Woolleyð9Þ and with other literature values.ð8;10;11Þ Single ion apparent molar volumes V/;i and heat capacities Cp;/;i for aqueous silver ion were
TABLE 5. Regression parameters of equation (6) for the apparent molar heat capacity Cp;/ of aqueous silver nitrate. The values are chosen so that equation (6) reproduces the generated Cp;/ values to within 0:1 J K1 mol1 at m 6 0:5 mol kg1 , 278:15 6 T=K 6 393:15, and p ¼ 0:35 MPa c0;0 =ðJ K1 mol1 Þ
14904:6 0:1
c1;0 =ðJ K2 mol1 Þ
39:0184 0:0001
102 c2;0 =ðJ K3 mol1 Þ
3:33263 0:00006
101 c3;0 =ðJ mol1 Þ
187378 1
c0;1 =ðJ kg K1 mol2 Þ
12817:6 0:2
c1;1 =ðJ kg K2 mol2 Þ 2
10 c2;1 =ðJ kg K
3
33:8676 0:0005 2
mol Þ
2:9689 0:0001
101 c3;1 =ðJ kg mol2 Þ
162628 5
c0;2 =ðJ kg2 K1 mol3 Þ
13950:6 0:4
c1;2 =ðJ kg2 K2 mol3 Þ 2
2
3
10 c2;2 =ðJ kg K
38:491 0:001 3
mol Þ
3:4775 0:0002
102 c3;2 =ðJ kg2 mol3 Þ
16786 1
Da /ðJ K1 mol1 Þ
1.5
a
Standard deviation of the regression.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1539
FIGURE 3. Apparent molar volumes V/;i for aqueous potassium ion Kþ (aq), sodium ion Naþ (aq), and silver ion Agþ (aq) at p ¼ 0:35 MPa plotted against molality m and temperature T. The error bar represents our estimate of the total experimental uncertainties for each surface: DV 6 1:0 cm3 mol1 . s, , M, for Kþ (aq), Naþ (aq), and Agþ (aq), respectively, from reference 10 at p ¼ 0:10 MPa. d, j, N, for Kþ (aq), Naþ (aq), and Agþ (aq), respectively, from reference 11 at T ¼ 298:15 K.
estimated by subtracting V/ and Cp;/ values for HNO3 (aq)ð9Þ from those for AgNO3 (aq) at the same m, T, and p. The surfaces are described by the empirical equations (7) and (8) V/;i ¼
2 X
mn ðv0;n þ v1;n T þ v2;n T 2 þ v3;n =T Þ;
ð7Þ
n¼0
Cp;/;i ¼
2 X n¼0
mn ðc0;n þ c1;n T þ c2;n T 2 þ c3;n =T Þ;
ð8Þ
1540
W. B. Clayton et al.
FIGURE 4. Apparent molar heat capacities Cp;/;i for aqueous potassium ion Kþ (aq), silver ion Agþ (aq), and sodium ion Naþ (aq) at p ¼ 0:35 MPa plotted against molality m and temperature T. The error bar represents our estimate of the total experimental uncertainties for each surface: DC 6 10 J K1 mol1 . From reference 8 at T ¼ 298:15 K and m ¼ 0:068 mol kg1 .
with the parameters in table 6. Estimated values for V2;i and Cp;2;i at infinite dilution are given in table 7. We estimate the total experimental uncertainties in these single ion quantities as DV/;i 6 1:0 cm3 mol1 and DCp;/;i 6 10 J K1 mol1 , respectively, over the entire ranges of m and T. We have calculated V/;i ¼ V02 ¼ 1:4 cm3 mol1 at m ¼ 0 mol kg1 for Agþ (aq) from results reported by Kapustinky et al.ð11Þ using the conventional V/;i ¼ V02 ¼ 0:0 cm3 mol1 at m ¼ 0 mol kg1 for Hþ (aq). We have also calculated Cp;/;i C0p;2 ¼ 28:0 J K1 mol1 at m ¼ 0:068 mol kg1 for Agþ (aq) from results reported by SergeevaÕs et al.ð8Þ using the recently reported Cp;/;i C0p;2 ¼ 62:2 J K1 mol1 at m ¼ 0:068 mol kg1 for NO 3 (aq) from Patterson and Woolley.ð9Þ
Apparent molar volumes and heat capacities of aqueous silver nitrate
1541
TABLE 6. Parameters of equations (7) and (8) for the apparent molar volume V/;i and apparent molar heat capacity Cp;/;i , of aqueous silver ion Agþ , potassium ion Kþ , and sodium ion Naþ at m 6 0:5 mol kg1 , at 278:15 6 T=K 6 393:15, and at p ¼ 0:35 MPa. Values are given to the precision needed to reproduce V/;i to 0:01 cm3 mol1 and Cp;/;i to 0:1 J K1 mol1 Agþ (aq) 1
v0;0 =ðcm3 mol Þ
1521.21
Kþ (aq) 220.96
Naþ (aq) 1032.73
)4.63162
)0.66693
)3.08436
103 v2;0 =ðcm3 mol1 K2 Þ
4.6889
0.7497
3.0978
v3;0 =ðcm3 mol1 KÞ
)166512
)24047
)116146
v0;1 =ðcm3 kg mol2 Þ
)12795.836
)776.627
)5164.744
v1;1 =ðcm3 kg mol2 K1 Þ
39.29881
3.19980
16.06586
1
3
v1;0 =ðcm mol
1
K Þ
102 v2;1 =ðcm3 kg mol2 K2 Þ
)4.0115
)0.4254
)1.6641
v3;1 =ðcm3 kg mol2 KÞ
1386748
61176
553479
v0;2 =ðcm3 kg2 mol3 Þ
17987.58
431.08
6162.03
v1;2 =ðcm3 kg2 mol3 K1 Þ
)55.2299
)2.6607
)19.3464
2
3
3
2
10 v2;2 =ðcm kg mol
2
K Þ
5.63427
0.42721
2.01966
v3;2 =ðcm3 kg2 mol3 KÞ
)1948234
)6293
)653180
c0;0 =ðJ K1 mol1 Þ
389.3
3649.3
6704.6
c1;0 =ðJ K2 mol1 Þ
)0.0057
)9.8098
)17.6417
103 c2;0 =ðJ K3 mol1 Þ
)0.9574
8.8878
15.4992
101 c3;0 =ðJ mol1 Þ
)8426
)45092
)83068
1
c0;1 =ðJ kg K
2
mol Þ
c1;1 =ðJ kg K2 mol2 Þ
)3050.3
)4137.8
)8767.9
8.2074
10.3403
25.0065
102 c2;1 =ðJ kg K3 mol2 Þ
)0.7924
)0.9134
)2.4724
101 c3;1 =ðJ kg mol2 Þ
42028
58142
106487
c0;2 =ðJ kg2 K1 mol3 Þ
)427.8
)4889.9
)2630.3
c1;2 =ðJ kg2 K2 mol3 Þ
2.876
17.307
8.756
102 c2;2 =ðJ kg2 K3 mol3 Þ
)0.4283
)1.9740
)0.9091
102 c3;2 =ðJ kg2 mol3 Þ
)260
4240
2350
It is interesting to note from figure 3 that the single ion apparent molar volume for Kþ (aq) is larger by about 10 cm3 mol1 than those for Naþ (aq) and Agþ (aq) at all m and T. On the other hand, we see from figure 4 that the single ion apparent molar heat capacities of all three ions show quite different patterns compared with those in figure 3. Figure 4 shows that, at low temperature, the single ion apparent molar heat capacities for all three ions increase significantly and with nearly the same dependence on m, whereas this dependence on m nearly disappears or becomes slightly negative for all three ions at high temperature.
1542
W. B. Clayton et al.
TABLE 7. Standard partial volumes V02;i and standard partial molar heat capacities C0p;2;i for aqueous silver ion Agþ (aq) at infinite dilution and at p ¼ 3:5 MPa from equations (7) and (8) and the parameters in table 6 T
V2;i0
K
cm3 mol1
0 Cp;2;i
J K1 mol1
278.15
)2.9
10.7
283.15
)2.4
13.4
288.15
)1.9
15.8
293.15
)1.6
18.0
298.15
)1.4
19.9
303.15
)1.2
21.7
308.15
)1.1
23.2
313.15
)1.1
24.6
318.15
)1.1
25.8
323.15
)1.1
26.8
328.15
)1.2
27.6
333.15
)1.2
28.3
338.15
)1.2
28.7
343.15
)1.2
29.1
348.15
)1.2
29.3
353.15
)1.2
29.3
358.15
)1.1
29.2
363.15
)0.9
29.0
368.15
)0.7
28.6
373.15
)0.4
28.1
378.15
)0.1
27.4
383.15
0.4
26.7
388.15
0.9
25.8
393.15
1.5
24.8
REFERENCES 1. Ballerat-Busserolles, K.; Ford, T. D.; Call, T. G.; Woolley, E. M. J. Chem. Thermodyn. 1999, 31, 741–762. 2. Ford, T. D.; Call, T. G.; Origlia, M. L.; Stark, M. A.; Woolley, E. M. J. Chem. Thermodyn. 2000, 32, 499–516. 3. Hill, P. G. J. Phys. Chem. Ref. Data 1990, 19, 1233–1274. 4. Archer, D. G. J. Phys. Ref. Data 1992, 21, 793–829. 5. Woolley, E. M. J. Chem. Thermodyn. 1997, 29, 1377–1385. 6. Singh, P. P.; Spitzer, J.; McKay, R. M.; McCurdy, K. G.; Hepler, L. G. Thermochim. Acta 1978, 24, 111–115.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1543
7. Bradley, D. J.; Pitzer, K. S. J. Phys. Chem. 1979, 83, 1599–1603. 8. Sergeeva, R. I.; Drakin, S. I.; KarapetÕyants, M. Kh. Russ. J. Phys. Chem. 1970, 44, 1665–1666. 9. Patterson, B. A.; Woolley, E. M. J. Chem. Thermodyn. 2002, 34, 535–556. 10. Millero, F. J. Structure and Transport Processes in Water and Aqueous Solutions. Horne, R. A.: editor. Wiley-Interscience: New York. 1971. Chap. 15. 11. Kapustinky, A. F.; Yakushevskii, B. M.; Drakin, S. I. Zh. Fiz. Khim. 1953, 27, 433–442. (Received 25 September 2001; in final form 23 April 2002)
WE-326
Apparent molar volumes and apparent molar heat capacities of aqueous silver nitrate at molalities from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures from 278.15 K to 393.15 K, and at the pressure 0.35 MPa W. B. Clayton, B. A. Patterson, J. J. Jardine, and E. M. Woolleya Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA
Densities of aqueous silver nitrate solutions were determined at molalities m from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures T from 278.15 K to 368.15 K, and at the pressure 0.35 MPa, using a vibrating tube densimeter (DMA 512P, Anton Paar, Austria). A fixed cell, power-compensation, differential-output, temperature-scanning calorimeter (NanoDSC 6100, Calorimetry Sciences Corporation, American Fork, UT, USA) was used to measure the heat capacities of the same solutions at the same pressure and at 278:15 6 T=K 6 393:15. Apparent molar heat capacities Cp;/ and apparent molar volumes V/ were calculated for these solutions and fitted by regression to empirical equations describing the surfaces (Cp;/ ; T; m) and (V/ ; T; m). Ó 2002 Elsevier Science Ltd. All rights reserved.
KEYWORDS: apparent molar volume; apparent molar heat capacity; silver nitrate
1. Introduction Silver nitrate has several uses in industry including the manufacturing of mirrors and dyes. It is an important reagent used extensively in analytical chemistry. However, not much information is available regarding the thermodynamic properties of its aqueous solutions as a function of temperature. In this paper we present the apparent molar heat capacities Cp;/ and apparent molar volumes V/ for silver nitrate aqueous solutions at molalities m from 0:015 mol kg1 to 0:5 mol kg1 , at temperatures T from 278.15 K to
a
To whom correspondence should be addressed (E-mail: [email protected]).
0021-9614/02/$ - see front matter
Ó 2002 Elsevier Science Ltd. All rights reserved.
W. B. Clayton et al.
1532
393.15 K, and at the pressure 0.35 MPa. The results are fitted to empirical regression equations for the surfaces (Cp;/ ; T; m) and (V/ ; T; m).
2. Experimental An aqueous stock solution of silver nitrate m ¼ 0:49983 mol kg1 was prepared using carefully dried reagent grade silver nitrate (Sargent-Welch Scientific Company, Skokie, IL, USA). The reagent purity was found to be greater than 0.994 mass fraction pure by the Mohr method. We have used 1.000 mass fraction purity in our calculations. The water used was distilled, deionized, autoclaved, and degassed. All other solutions were prepared by mass dilution using this stock solution. All weighings were corrected for buoyancy. Precautions were taken so that all solutions were stored away from direct light. TABLE 1. Apparent molar volumes V/ for aqueous silver nitrate at p ¼ 0:35 MPa. The uncertainties are standard deviations from a minimum of thirty measurementsa m
V/ 1
mol kg
3
V/ 1
cm mol
V/ 1
V/
cm mol
1
cm mol
cm3 mol1
3
3
T ¼ 278:15 K
T ¼ 283:15 K
T ¼ 288:15 K
T ¼ 298:15 K
0.49983
28:079 0:008
28:617 0:007
29:277 0:005
30:516 0:006
0.24986
27:297 0:007
27:829 0:008
28:53 0:01
29:81 0:01
0.12499
26:20 0:02
27:08 0:02
28:01 0:02
29:33 0:02
0.05000
24:97 0:04
25:96 0:04
26:91 0:05
28:36 0:05
0.02500
29:12 0:08
28:93 0:08
29:00 0:09
29:3 0:1
0.01484
26:7 0:1
26:5 0:1
27:7 0:1
28:1 0:1
T ¼ 308:15 K
T ¼ 318:15 K
T ¼ 328:15 K
T ¼ 338:15 K
0.49983
31:402 0:005
32:027 0:006
32:451 0:005
32:723 0:006
0.24986
30:665 0:008
31:35 0:01
31:87 0:01
32:135 0:009
0.12499
30:27 0:02
30:99 0:02
31:58 0:02
31:78 0:02
0.05000
29:50 0:05
30:24 0:05
30:59 0:05
30:68 0:05
0.02500
29:3 0:1
29:0 0:1
29:0 0:1
29:35 0:06
0.01484
28:0 0:1
27:5 0:1
28:3 0:1
25:5 0:2
T ¼ 348:15 K
T ¼ 358:15 K
T ¼ 368:15 K
0.49983
32:823 0:007
32:907 0:006
32:715 0:006
0.24986
32:21 0:01
32:228 0:009
32:02 0:01
0.12499
31:85 0:03
31:96 0:02
31:85 0:02 30:23 0:07
0.05000
30:51 0:05
30:52 0:05
0.02500
28:8 0:1
28:6 0:1
29:0 0:1
0.01484
24:5 0:2
24:9 0:1
25:2 0:2
a
Average values of qs can be obtained with equation (3) using qw given in reference 2.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1533
The densities of the aqueous silver nitrate solutions were determined from a vibrating tube densimeter (DMA 512P, Anton Paar, Austria) at 278:15 6 T=K 6 368:15 and at the pressure 0.35 MPa. A temperature circulator (PolyScience 9510, Niles, IL) controlled the temperature of the densimeter. As reported previously,ð1;2Þ the temperature was controlled within an average standard deviation of 0:0020 K and a maximum deviation of 0:0029 K for all solutions and temperatures recorded, and the pressure was maintained constant at ð0:350 0:001Þ MPa. The periods of oscillation s 4 ms had an average standard deviation Ds ¼ 0:68 ns and a maximum deviation of 1:0 ns. Densities were calculated with HookeÕs Law by equation (1), qs ¼ qw þ kq ðs2s s2w Þ;
ð1Þ
FIGURE 1. Apparent molar volumes V/ for aqueous silver nitrate AgNO3 (aq) plotted against molality m and temperature T. s, Experimental values at p ¼ 0:35 MPa from table 1; surface at p ¼ 0:35 MPa generated from regression parameters in table 2 with equation (5); O from reference 6 at T ¼ 298:15 K and p ¼ 0:10 MPa.
W. B. Clayton et al.
1534
where qs and qw are the densities of the silver nitrate solution and water, respectively, and ss and sw are the periods of oscillation of the tube when it contains the solution and water, respectively. Values of kq , the calibration constant for the densimeter, were determined, as described previouslyð1;2Þ from experiments with water and 1:0 mol kg1 NaCl(aq), both of which have well known densities.ð3;4Þ The calorimeter used to measure the heat capacities was calibrated as described in earlier work.ð5Þ Results used were the average of eight temperature scans between 273.15 K and 398.15 K at the rate r ¼ 16:6667 mK s1 and at the pressure ð0:35 0:015Þ MPa. The heat capacity of a solution was determined from the difference in the calorimetric power output from two experiments performed under the same conditions: one with the reference and sample cells filled with water, and the other with the sample cell filled with the solution of interest and the reference cell again filled with water. The massic heat capacity is determined by equation (2), cp;s ¼ kc ðDPs DPw Þ=ðr qs Þ þ cp;w qw =qs ;
ð2Þ
where cp;s and cp;w are the massic heat capacities of the solution of interest and of water, respectively; DPs and DPw are the differences in power required to maintain the two calorimetric cells at the same temperature during the two experiments; and kc is the calibration constant for this calorimeter, obtained as reported previouslyð5Þ from measurements on 1:0 mol kg1 NaCl(aq) and water.ð3;4Þ Experiments were performed with water in both cells every few days to determine and compensate for any small changes in the calorimetric baseline signal.
TABLE 2. Regression parameters of equation (5) for the apparent molar volume V/ of aqueous silver nitrate. The values are chosen so that equation (5) reproduces the generated V/ values to within 0:01 cm3 mol1 at m 6 0:5 mol kg1 , at 278:15 6 T=K 6 393:15, and at p ¼ 0:35 MPa v0;0 =ðcm3 mol1 Þ
1603:68 0:01
v1;0 =ðcm3 mol1 K1 Þ
4:43798 0:00003
103 v2;0 =ðcm3 mol1 K2 Þ
4:1629 0:0001
v3;0 =ðcm3 mol1 KÞ
185610 1
v0;1 =ðcm3 kg mol2 Þ
9253:99 0:002
v1;1 =ðcm3 kg mol2 K1 Þ 2
2
3
10 v2;1 =ðcm kg mol
28:06966 0:00006 2
K Þ
2:8286 0:0001
v3;1 =ðcm3 kg mol2 KÞ
1014850 6
v0;2 =ðcm3 kg2 mol3 Þ
12916:78 0:03
v1;2 =ðcm3 kg2 mol3 K1 Þ 2
3
2
3
10 v2;2 =ðcm kg mol
39:2211 0:0001 2
K Þ
v3;2 =ðcm3 kg2 mol3 KÞ Da /ðcm3 mol1 Þ a
Standard deviation of the regression.
3:95252 0:00002 1413430 7 0.15
Apparent molar volumes and heat capacities of aqueous silver nitrate
1535
Apparent molar volumes V/ and apparent molar heat capacities Cp;/ were calculated by equations (3) and (4), respectively, V/ ¼ M2 =qs 1000 ðqs qw Þ=ðqs qw mÞ;
ð3Þ
Cp;/ ¼ M2 cp;s þ 1000 ðcp;s cp;w Þ=m:
ð4Þ
In equations (3) and (4), M2 ¼ 169:8717 g mol1 is the molar mass of silver nitrate.
TABLE 3. Standard partial molar volumes V02 and standard partial molar heat capacities C0p;2 for aqueous silver nitrate at infinite dilution and at p ¼ 0:35 MPa from equations (5) and (6) and the parameters in tables 2 and 5 T
V20
0 Cp;2
K
cm3 mol1
278.15
24.0
)106.8
283.15
25.3
)89.4
288.15
26.4
)74.5
293.15
27.3
)61.8
298.15
28.0
)51.1
303.15
28.6
)42.4
308.15
29.1
)35.3
313.15
29.5
)29.8
318.15
29.7
)25.7
323.15
29.9
)22.8
328.15
30.0
)21.0
333.15
30.1
)20.2
338.15
30.1
)20.2
343.15
30.1
)21.1
348.15
30.1
)22.6
353.15
30.0
)24.6
358.15
30.0
)27.1
363.15
29.9
)30.0
368.15
29.9
)33.1
373.15
29.9
)36.5
378.15
29.9
)40.0
383.15
30.0
)43.6
388.15
30.1
)47.1
393.15
30.2
)50.6
J K1 mol1
W. B. Clayton et al.
1536
TABLE 4. Apparent molar heat capacities Cp;/ for aqueous silver nitrate at p ¼ 0:35 MPa. The uncertainties are standard deviations for the averages from a total of at least four scans each at both increasing and decreasing temperaturea m
Cp;/ 1
1
Cp;/ 1
JK
Cp;/ 1
mol
JK
1
Cp;/ 1
mol
JK
1
Cp;/ 1
mol
1
JK
mol1
mol kg
JK
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 278:15 K 40:1 0:1 67:0 0:7 86:2 1:9 101:1 4:1 105:9 4:6 108:6 4:9
T ¼ 283:15 K 24:4 0:2 47:8 1:1 64:4 1:9 77:8 3:8 82:4 4:0 85:2 3:8
T ¼ 288:15K 12:4 0:1 32:9 0:9 47:8 1:6 60:0 3:4 64:6 3:4 67:7 3:6
T ¼ 293:15 K 3:0 0:1 21:5 0:8 35:1 1:5 46:5 3:2 51:1 2:5 53:9 2:9
T ¼ 298:15 K 4:1 0:2 12:7 0:5 25:4 1:1 36:0 2:7 41:0 2:1 43:6 2:8
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 303:15 K 9:6 0:2 5:8 0:4 17:7 0:9 27:7 2:2 33:0 1:8 35:6 2:4
T ¼ 308:15 K 13:8 0:2 0:6 0:4 11:9 0:8 21:5 1:6 27:3 1:3 29:5 2:2
T ¼ 313:15 K 17:0 0:2 3:4 0:2 7:4 0:6 16:6 1:2 22:4 1:0 24:5 2:0
T ¼ 318:15 K 19:2 0:2 6:2 0:2 4:2 0:5 13:3 0:8 19:4 0:8 20:9 1:9
T ¼ 323:15 K 20:8 0:2 8:3 0:1 1:8 0:4 10:8 0:6 17:1 0:9 18:2 2:1
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 328:15 K 21:7 0:2 9:7 0:1 0:3 0:3 9:3 0:4 15:7 1:0 16:6 2:2
T ¼ 333:15 K 22:2 0:3 10:5 0:1 0:6 0:2 8:4 0:4 14:6 1:1 15:1 2:4
T ¼ 338:15 K 22:3 0:3 10:8 0:2 1:0 0:1 7:9 0:3 14:4 1:2 14:6 2:5
T ¼ 343:15 K 21:9 0:3 10:6 0:2 0:7 0:1 8:4 0:4 14:9 1:2 15:1 2:9
T ¼ 348:15 K 21:2 0:2 9:9 0:2 0:0 0:1 9:4 0:4 15:6 1:1 15:4 2:9
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 353:15 K 20:2 0:2 9:0 0:2 1:0 0:2 10:6 0:4 17:1 1:2 17:3 2:9
T ¼ 358:15 K 19:0 0:2 7:7 0:1 2:4 0:1 12:0 0:4 18:4 1:3 18:7 2:8
T ¼ 363:15 K 17:4 0:3 6:0 0:2 4:2 0:2 14:1 0:5 20:5 1:2 21:4 2:9
T ¼ 368:15 K 15:6 0:3 4:2 0:2 6:3 0:2 16:6 0:5 23:3 1:1 24:3 3:5
T ¼ 373:15 K 13:7 0:2 2:0 0:2 8:6 0:3 19:4 0:5 25:9 0:9 26:8 3:6
0.49983 0.24986 0.12499 0.05000 0.02500 0.01484
T ¼ 378:15 K 11:3 0:2 0:5 0:2 11:5 0:2 22:4 0:5 29:4 1:1 30:7 3:2
T ¼ 383:15 K 9:0 0:2 3:1 0:2 14:4 0:2 25:6 0:7 32:4 1:0 34:0 2:6
T ¼ 388:15 K 6:4 0:2 6:0 0:1 17:5 0:2 29:1 1:0 36:1 0:7 37:9 2:9
T ¼ 393:15 K 3:6 0:1 8:9 0:2 20:9 0:9 32:9 0:7 40:8 0:7 43:1 2:4
a
mol
1
Average experimental values of cp;s can be obtained with equation (4) and with cp;w given in reference 2.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1537
3. Results and discussion Values for the apparent molar volumes V/ for aqueous silver nitrate are given in table 1. Figure 1 shows (V/ ; T; m) for aqueous silver nitrate along with the results of Singh et al.ð6Þ The regression surface in figure 1 corresponds to equation (5), V/ ¼ AV m1=2 þ
2 X
mn ðv0;n þ v1;n T þ v2;n T 2 þ v3;n =T Þ;
ð5Þ
n¼0
where AV is the Debye–H€ uckel coefficient for volumes. We have used values for AV based on the equations of Bradley and Pitzerð7Þ that are tabulated by Ford et al.ð2Þ The parameters for equation (5) given in table 2 are based on a regression with weighting factors inversely proportional to the uncertainties in table 1. Values calculated from this
FIGURE 2. Apparent molar heat capacities Cp;/ for aqueous silver nitrate AgNO3 (aq) plotted against molality m and temperature T. s, Experimental values at p ¼ 0:35 MPa from table 4; surface at p ¼ 0:35 MPa generated from regression parameters in table 5 with equation (6). O From reference 6 at T ¼ 298:15 K and p ¼ 0:10 MPa. From reference 8 at T ¼ 298:15 K and m ¼ 0:068 mol kg1 .
W. B. Clayton et al.
1538
equation agree with the values of Singh et al.ð6Þ to within 0:8 cm3 mol1 . From this equation, V/ ¼ V02 at infinite dilution has been estimated and values are given in table 3. Our results for the apparent molar heat capacities for aqueous silver nitrate are given in table 4. Figure 2 shows (Cp;/ ; T; m) for aqueous silver nitrate, along with results of Singh et al.ð6Þ and Sergeeva et al.ð8Þ The regression surface in figure 2 corresponds to equation (6), Cp;/ ¼ AC m1=2 þ
2 X
mn ðc0;n þ c1;n T þ c2;n T 2 þ c3;n =T Þ;
ð6Þ
n¼0
where AC is the Debye–H€ uckel coefficient for heat capacities based on the equations of Bradley and Pitzerð7Þ that are tabulated by Ford et al.ð2Þ The regression used weighting factors equal to the inverse of the uncertainties in Cp;/ from table 4. The regression parameters for equation (6) are given in table 5. Values calculated from this equation agree with the values of Singh et al.ð6Þ and Sergeeva et al.ð8Þ to within 11 J K1 mol1 . Extrapolated values for Cp;/ ¼ C0p;2 at infinite dilution are given in table 3. Figures 3 and 4 show (V/ ; T; m) and (Cp;/ T; m), respectively, for aqueous silver ion with comparable surfaces for the aqueous potassium and sodium ions obtained from results by Patterson and Woolleyð9Þ and with other literature values.ð8;10;11Þ Single ion apparent molar volumes V/;i and heat capacities Cp;/;i for aqueous silver ion were
TABLE 5. Regression parameters of equation (6) for the apparent molar heat capacity Cp;/ of aqueous silver nitrate. The values are chosen so that equation (6) reproduces the generated Cp;/ values to within 0:1 J K1 mol1 at m 6 0:5 mol kg1 , 278:15 6 T=K 6 393:15, and p ¼ 0:35 MPa c0;0 =ðJ K1 mol1 Þ
14904:6 0:1
c1;0 =ðJ K2 mol1 Þ
39:0184 0:0001
102 c2;0 =ðJ K3 mol1 Þ
3:33263 0:00006
101 c3;0 =ðJ mol1 Þ
187378 1
c0;1 =ðJ kg K1 mol2 Þ
12817:6 0:2
c1;1 =ðJ kg K2 mol2 Þ 2
10 c2;1 =ðJ kg K
3
33:8676 0:0005 2
mol Þ
2:9689 0:0001
101 c3;1 =ðJ kg mol2 Þ
162628 5
c0;2 =ðJ kg2 K1 mol3 Þ
13950:6 0:4
c1;2 =ðJ kg2 K2 mol3 Þ 2
2
3
10 c2;2 =ðJ kg K
38:491 0:001 3
mol Þ
3:4775 0:0002
102 c3;2 =ðJ kg2 mol3 Þ
16786 1
Da /ðJ K1 mol1 Þ
1.5
a
Standard deviation of the regression.
Apparent molar volumes and heat capacities of aqueous silver nitrate
1539
FIGURE 3. Apparent molar volumes V/;i for aqueous potassium ion Kþ (aq), sodium ion Naþ (aq), and silver ion Agþ (aq) at p ¼ 0:35 MPa plotted against molality m and temperature T. The error bar represents our estimate of the total experimental uncertainties for each surface: DV 6 1:0 cm3 mol1 . s, , M, for Kþ (aq), Naþ (aq), and Agþ (aq), respectively, from reference 10 at p ¼ 0:10 MPa. d, j, N, for Kþ (aq), Naþ (aq), and Agþ (aq), respectively, from reference 11 at T ¼ 298:15 K.
estimated by subtracting V/ and Cp;/ values for HNO3 (aq)ð9Þ from those for AgNO3 (aq) at the same m, T, and p. The surfaces are described by the empirical equations (7) and (8) V/;i ¼
2 X
mn ðv0;n þ v1;n T þ v2;n T 2 þ v3;n =T Þ;
ð7Þ
n¼0
Cp;/;i ¼
2 X n¼0
mn ðc0;n þ c1;n T þ c2;n T 2 þ c3;n =T Þ;
ð8Þ
1540
W. B. Clayton et al.
FIGURE 4. Apparent molar heat capacities Cp;/;i for aqueous potassium ion Kþ (aq), silver ion Agþ (aq), and sodium ion Naþ (aq) at p ¼ 0:35 MPa plotted against molality m and temperature T. The error bar represents our estimate of the total experimental uncertainties for each surface: DC 6 10 J K1 mol1 . From reference 8 at T ¼ 298:15 K and m ¼ 0:068 mol kg1 .
with the parameters in table 6. Estimated values for V2;i and Cp;2;i at infinite dilution are given in table 7. We estimate the total experimental uncertainties in these single ion quantities as DV/;i 6 1:0 cm3 mol1 and DCp;/;i 6 10 J K1 mol1 , respectively, over the entire ranges of m and T. We have calculated V/;i ¼ V02 ¼ 1:4 cm3 mol1 at m ¼ 0 mol kg1 for Agþ (aq) from results reported by Kapustinky et al.ð11Þ using the conventional V/;i ¼ V02 ¼ 0:0 cm3 mol1 at m ¼ 0 mol kg1 for Hþ (aq). We have also calculated Cp;/;i C0p;2 ¼ 28:0 J K1 mol1 at m ¼ 0:068 mol kg1 for Agþ (aq) from results reported by SergeevaÕs et al.ð8Þ using the recently reported Cp;/;i C0p;2 ¼ 62:2 J K1 mol1 at m ¼ 0:068 mol kg1 for NO 3 (aq) from Patterson and Woolley.ð9Þ
Apparent molar volumes and heat capacities of aqueous silver nitrate
1541
TABLE 6. Parameters of equations (7) and (8) for the apparent molar volume V/;i and apparent molar heat capacity Cp;/;i , of aqueous silver ion Agþ , potassium ion Kþ , and sodium ion Naþ at m 6 0:5 mol kg1 , at 278:15 6 T=K 6 393:15, and at p ¼ 0:35 MPa. Values are given to the precision needed to reproduce V/;i to 0:01 cm3 mol1 and Cp;/;i to 0:1 J K1 mol1 Agþ (aq) 1
v0;0 =ðcm3 mol Þ
1521.21
Kþ (aq) 220.96
Naþ (aq) 1032.73
)4.63162
)0.66693
)3.08436
103 v2;0 =ðcm3 mol1 K2 Þ
4.6889
0.7497
3.0978
v3;0 =ðcm3 mol1 KÞ
)166512
)24047
)116146
v0;1 =ðcm3 kg mol2 Þ
)12795.836
)776.627
)5164.744
v1;1 =ðcm3 kg mol2 K1 Þ
39.29881
3.19980
16.06586
1
3
v1;0 =ðcm mol
1
K Þ
102 v2;1 =ðcm3 kg mol2 K2 Þ
)4.0115
)0.4254
)1.6641
v3;1 =ðcm3 kg mol2 KÞ
1386748
61176
553479
v0;2 =ðcm3 kg2 mol3 Þ
17987.58
431.08
6162.03
v1;2 =ðcm3 kg2 mol3 K1 Þ
)55.2299
)2.6607
)19.3464
2
3
3
2
10 v2;2 =ðcm kg mol
2
K Þ
5.63427
0.42721
2.01966
v3;2 =ðcm3 kg2 mol3 KÞ
)1948234
)6293
)653180
c0;0 =ðJ K1 mol1 Þ
389.3
3649.3
6704.6
c1;0 =ðJ K2 mol1 Þ
)0.0057
)9.8098
)17.6417
103 c2;0 =ðJ K3 mol1 Þ
)0.9574
8.8878
15.4992
101 c3;0 =ðJ mol1 Þ
)8426
)45092
)83068
1
c0;1 =ðJ kg K
2
mol Þ
c1;1 =ðJ kg K2 mol2 Þ
)3050.3
)4137.8
)8767.9
8.2074
10.3403
25.0065
102 c2;1 =ðJ kg K3 mol2 Þ
)0.7924
)0.9134
)2.4724
101 c3;1 =ðJ kg mol2 Þ
42028
58142
106487
c0;2 =ðJ kg2 K1 mol3 Þ
)427.8
)4889.9
)2630.3
c1;2 =ðJ kg2 K2 mol3 Þ
2.876
17.307
8.756
102 c2;2 =ðJ kg2 K3 mol3 Þ
)0.4283
)1.9740
)0.9091
102 c3;2 =ðJ kg2 mol3 Þ
)260
4240
2350
It is interesting to note from figure 3 that the single ion apparent molar volume for Kþ (aq) is larger by about 10 cm3 mol1 than those for Naþ (aq) and Agþ (aq) at all m and T. On the other hand, we see from figure 4 that the single ion apparent molar heat capacities of all three ions show quite different patterns compared with those in figure 3. Figure 4 shows that, at low temperature, the single ion apparent molar heat capacities for all three ions increase significantly and with nearly the same dependence on m, whereas this dependence on m nearly disappears or becomes slightly negative for all three ions at high temperature.
1542
W. B. Clayton et al.
TABLE 7. Standard partial volumes V02;i and standard partial molar heat capacities C0p;2;i for aqueous silver ion Agþ (aq) at infinite dilution and at p ¼ 3:5 MPa from equations (7) and (8) and the parameters in table 6 T
V2;i0
K
cm3 mol1
0 Cp;2;i
J K1 mol1
278.15
)2.9
10.7
283.15
)2.4
13.4
288.15
)1.9
15.8
293.15
)1.6
18.0
298.15
)1.4
19.9
303.15
)1.2
21.7
308.15
)1.1
23.2
313.15
)1.1
24.6
318.15
)1.1
25.8
323.15
)1.1
26.8
328.15
)1.2
27.6
333.15
)1.2
28.3
338.15
)1.2
28.7
343.15
)1.2
29.1
348.15
)1.2
29.3
353.15
)1.2
29.3
358.15
)1.1
29.2
363.15
)0.9
29.0
368.15
)0.7
28.6
373.15
)0.4
28.1
378.15
)0.1
27.4
383.15
0.4
26.7
388.15
0.9
25.8
393.15
1.5
24.8
REFERENCES 1. Ballerat-Busserolles, K.; Ford, T. D.; Call, T. G.; Woolley, E. M. J. Chem. Thermodyn. 1999, 31, 741–762. 2. Ford, T. D.; Call, T. G.; Origlia, M. L.; Stark, M. A.; Woolley, E. M. J. Chem. Thermodyn. 2000, 32, 499–516. 3. Hill, P. G. J. Phys. Chem. Ref. Data 1990, 19, 1233–1274. 4. Archer, D. G. J. Phys. Ref. Data 1992, 21, 793–829. 5. Woolley, E. M. J. Chem. Thermodyn. 1997, 29, 1377–1385. 6. Singh, P. P.; Spitzer, J.; McKay, R. M.; McCurdy, K. G.; Hepler, L. G. Thermochim. Acta 1978, 24, 111–115.
Apparent molar volumes and heat capacities of aqueous silver nitrate
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7. Bradley, D. J.; Pitzer, K. S. J. Phys. Chem. 1979, 83, 1599–1603. 8. Sergeeva, R. I.; Drakin, S. I.; KarapetÕyants, M. Kh. Russ. J. Phys. Chem. 1970, 44, 1665–1666. 9. Patterson, B. A.; Woolley, E. M. J. Chem. Thermodyn. 2002, 34, 535–556. 10. Millero, F. J. Structure and Transport Processes in Water and Aqueous Solutions. Horne, R. A.: editor. Wiley-Interscience: New York. 1971. Chap. 15. 11. Kapustinky, A. F.; Yakushevskii, B. M.; Drakin, S. I. Zh. Fiz. Khim. 1953, 27, 433–442. (Received 25 September 2001; in final form 23 April 2002)
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