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Johnson Matthey Technol. Rev., 2018, 62, (1), 48

doi:10.1595/205651318x696648

A Re-assessment of the Thermodynamic Properties of Palladium

Improved values for the enthalpy of fusion

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Article Synopsis

The thermodynamic properties were reviewed by the author in 1995. A new assessment of the enthalpy of fusion has led to a revision of the thermodynamic properties of the liquid phase and although the enthalpy of sublimation at 298.15 K is retained as 377 ± 4 kJ mol–1 the normal boiling point is revised to 3272 K at one atmosphere pressure.

Introduction

The thermodynamic properties of palladium were reviewed by the author in 1995 (1). At that time the value for the enthalpy of fusion was considered to be tentative since it differed significantly from the only known experimental value. Newly considered enthalpy of fusion values now indicate that the original selected value was almost certainly incorrect and a more likely value has been suggested which leads to a major alteration to the selected values for the liquid phase. Additional measurements of the vapour pressure do not alter the selected enthalpy of sublimation value of 377 kJ mol–1 but the accuracy can now be refined to give a 95% confidence value of ±4 kJ mol–1.

Solid

Selected values in the low-temperature region as given in the previous review (1) were based mainly on the specific heat values of Boerstoel et al. (2), Clusius and Schachinger (3) and Mitacek and Aston (4) and continue to be considered satisfactory. However only limited information was given in the original review which above 50 K consisted of specific heat values at 10 K intervals from 50 to 100 K and at 20 K intervals from 100 to 280 K and with the value at 298.15 K also included. This is now considered to be far too little information and instead a comprehensive review of the low-temperature thermodynamic properties is given in Table I.

Table I

Low Temperature Thermodynamic Data

T, K p , J mol–1 K–1 T – H°0 K , J mol–1 T , J mol–1 K–1 –G°T – H°0 K , J mol–1 –(G°T – H°0 K)/T, J mol–1 K–1
5 0.0594 0.133 0.0512 0.123 0.0246
10 0.196 0.722 0.128 0.554 0.0554
15 0.490 2.355 0.256 1.485 0.0990
20 0.999 5.978 0.461 3.241 0.162
25 1.768 12.78 0.761 6.253 0.250
30 2.794 24.13 1.172 11.04 0.368
35 3.998 40.97 1.689 18.15 0.519
40 5.388 64.40 2.313 28.11 0.703
45 6.809 94.90 3.030 41.43 0.921
50 8.190 132.4 3.819 58.53 1.171
60 10.724 227.3 5.541 105.2 1.753
70 12.921 345.8 7.364 169.7 2.424
80 14.803 484.6 9.215 252.6 3.157
90 16.411 640.9 11.054 353.9 3.933
100 17.784 812.1 12.856 473.5 4.735
110 18.949 995.9 14.607 610.9 5.554
120 19.926 1190 16.299 765.5 6.379
130 20.746 1394 17.927 936.7 7.205
140 21.443 1605 19.491 1124 8.027
150 22.043 1822 20.991 1326 8.842
160 22.561 2046 22.431 1543 9.646
170 23.012 2273 23.813 1775 10.439
180 23.406 2506 25.139 2020 11.219
190 23.752 2741 26.414 2277 11.986
200 24.059 2980 27.641 2548 12.738
210 24.334 3222 28.821 2830 13.476
220 24.582 3467 29.959 3124 14.200
230 24.806 3714 31.057 3429 14.909
240 25.007 3963 32.117 3745 15.604
250 25.189 4214 33.141 4071 16.285
260 25.352 4467 34.133 4408 16.952
270 25.499 4721 35.092 4754 17.607
280 25.629 4977 36.022 5109 18.248
290 25.751 5234 36.923 5474 18.876
298.15 25.845 5444 37.638 5778 19.379

Notes to Table I

P is specific heat

T – H0 K is enthalpy

T is entropy

–G°T – H°0 K and –(G°T – H°0 K)/T are free energy functions

In the high-temperature solid region closely agreeing specific heat values derived from the enthalpy measurements of Cordfunke and Konings (5) (528 to 848 K) and the direct specific heat measurements of Miiller and Cezairliyan (6) (1400 to 1800 K) were selected since they were in excellent agreement with an extrapolation of the selected low-temperature values and allowed a single smooth specific heat curve to represent both the low- and high-temperature regions. More recent high-temperature specific heat values by Milošević and Babić (7) (248 to 1773 K) differ significantly from the selected values showing a trend from 1.3% lower at 323 K to 3.9% lower at 723 K to 2.3% lower at 1223 K to 5.9% lower at 1773 K. However, at the low-temperature change over point at 270 K the measurements of Milošević and Babić show a sharp change in the slope of the specific heat curve compared to the selected low-temperature values, indicating that these high-temperature measurements are incompatible with those obtained at low temperatures. On these grounds the original high-temperature values were retained and can be represented by Equation (i) to cover the range from 298.15 K to the accepted melting point at 1828.0 K:

(i)

Equivalent enthalpy and entropy equations are given in Table II and derived thermodynamic values are given in Table III.

Table II

Thermodynamic Equations Above 298.15 K

Solid: 298.15 to 1828.0 K
p (J mol–1 K–1) = 24.0658 + 9.55408 × 10–3 T – 5.31329 × 10–6 T 2 + 2.02516 × 10–9 T 3 – 57,835.6/T 2
T – H°298.15 K (J mol–1) = 24.0658 T + 4.77704 × 10–3 T 2 – 1.77109667 × 10–6 T 3 + 5.06290 × 10–10 T 4 + 57,835.6/T – 7750.91
T (J mol–1 K–1) = 24.0658 ln (T) + 9.55408 × 10–3 T – 2.656645 × 10–6 T 2 + 6.75053333 × 10–10 T 3 + 28,917.8/ T 2 – 102.4348
Liquid: 1828.0 to 3300 K
p (J mol–1 K–1) = 41.2000
T – H298.15 K (J mol–1) = 41.2000 – 10,903.0
T (J mol–1 K–1) = 41.2000 ln (T) – 208.9240

Notes to Table II

P is specific heat

T – H298.15 K is enthalpy

T is entropy

Table III

High Temperature Thermodynamic Data

T, K p , J mol–1 K–1 T – H°298.15 K , J mol–1 T , J mol–1 K–1 –(G°T – H°298.15 K)/T, J mol–1 K–1
298.15 25.845 0 37.638 37.638
300 25.866 48 37.798 37.639
400 26.805 2684 45.375 38.665
500 27.536 5402 51.438 40.633
600 28.162 8188 56.515 42.868
700 28.727 11,033 60.899 45.138
800 29.255 13,932 64.770 47.355
900 29.766 16,883 68.245 49.486
1000 30.274 19,885 71.407 51.522
1100 30.794 22,938 74.317 53.464
1200 31.339 26,045 77.019 55.316
1300 31.922 29,207 79.551 57.084
1400 32.555 32,431 81.939 58.774
1500 33.251 35,720 84.209 60.395
1600 34.023 39,083 86.379 61.952
1700 34.882 42,528 88.467 63.450
1800 35.841 46,063 90.487 64.896
1828 (s) 36.129 47,071 91.043 65.293
1828 (l) 41.200 64,411 100.528 65.293
1900 41.200 67,377 102.120 66.658
2000 41.200 71,497 104.232 68.485
2100 41.200 75,617 106.243 70.235
2200 41.200 79,737 108.160 71.916
2300 41.200 83,857 109.991 73.532
2400 41.200 87,977 111.745 75.088
2500 41.200 92,097 113.427 76.588
2600 41.200 96,217 115.043 78.036
2700 41.200 100,337 116.597 79.436
2800 41.200 104,457 118.096 80.790
2900 41.200 108,577 119.542 82.101
3000 41.200 112,697 120.938 83.373
3100 41.200 116,817 122.289 84.606
3200 41.200 120,937 123.597 85.805
3300 41.200 125,057 124.865 86.969

Notes to Table III

P is specific heat

T – H298.15 K is enthalpy

T is entropy

–(G°T – H°295.15 K)/T is the free energy function

In comparison with the selected equations the specific heat values of Vollmer and Kohlhaas (8) (300 to 1825 K) trend from 2.6% lower at 300 K to 5.3% lower at 800 K to an average of 1.5% higher above 1600 K (Figure 1). Enthalpy measurements of Holzmann (9) (575 to 1177 K) trend from 0.4% higher to 1.7% higher whilst those of Jaeger and Veenstra (10) (573 to 1772 K) scatter from 0.7% lower to 1.4% lower with an average of 1.1% lower (Figure 2). More recent enthalpy measurements of Cagran and Pottlacher (11) (1550 to 1828 K) determined using the rapid pulse heating technique trend from 1.4% to 3.7% lower in the solid range (Figure 3).

Fig. 1.

Percentage deviations of specific heat in the high-temperature region

Percentage deviations of specific heat in the high-temperature region

Fig. 2.

Percentage deviations of enthalpy in the high-temperature region

Percentage deviations of enthalpy in the high-temperature region

Fig. 3.

Percentage deviations of enthalpy in the high-temperature region

Percentage deviations of enthalpy in the high-temperature region

Liquid

Drop calorimetry enthalpy measurements by Treverton and Margrave (12) were initially determined over the range 1846 to 2334 K on the International Practical Temperature Scale of 1948 (IPTS-48) but a short note added in the proof indicated further corrections for radiation losses and a conversion to the temperature scale IPTS-68. However only the amended liquid specific heat value and the liquid enthalpy at the melting point (given as 1827 K) were given. After correction for atomic weight, to the melting point of 1828.0 K and to the International Temperature Scale of 1990 (ITS-90), the liquid enthalpy at the melting point is H°T – H°298.15 K = 63,151 J mol–1 which in combination with the enthalpy of the solid at the melting point leads to an enthalpy of fusion of 16.08 ± 0.74 kJ mol–1. This is notably lower than actual experimental values of 17.64 kJ mol–1 determined by Nedumov (13) using differential thermal analysis and rapid pulse heating values of 17.4 ± 2.0 kJ mol–1 determined by Seydel et al. (14, 15) and 16.98 kJ mol–1 determined by Cagran and Pottlacher (11). The reason why the indirect determination of the enthalpy of fusion was low is not known but may be due to either an overestimation of the enthalpy values for the solid or, more likely, to the fact that even the revised values of Treverton and Margrave had still not accounted for all of the systematic errors that may have been present in their measurements. Not including the measurement of Seydel et al. because of the large uncertainty, the two other enthalpy values were equivalent to entropy of fusion values of 9.65 J mol–1 K–1 and 9.29 J mol–1 K–1 respectively. Kats and Chekhovskoi (16) noted that for a particular structure type the entropies of fusion (ΔSM) could be linearly related to the melting points (Tm) by means of the equation ΔSM = a Tm + b where a and b are constants. For the face-centred cubic platinum group metals rhodium, iridium and platinum selected entropy of fusion values of 12.21 ± 0.38 J mol–1 K–1 at a melting point of 2236 K for rhodium (17), 15.20 ± 0.41 J mol–1 K–1 at a melting point of 2719 K for iridium (18) and 10.83 ± 0.46 J mol–1 K–1 at a melting point of 2041.3 K for platinum (19) when fitted to the above equation extrapolated to 9.52 J mol–1 K–1 for palladium, in excellent agreement with the above experimental entropy values. The two experimental entropy values for palladium were therefore combined with the values for rhodium, iridium and platinum and were fitted to the equation: ΔSM = 6.4574 × 10–3 Tm – 2.3211 with the derived value for palladium as 9.483 ± 0.40 J mol–1 K–1 where the error is assigned to match those obtained for the other elements. The derived enthalpy of fusion value is rounded to 17.34 ± 0.73 kJ mol–1 and leads to an enthalpy for the liquid at the melting point of 64,411 J mol–1, suggesting that even with corrections applied the enthalpy measurements of Treverton and Margrave were 2.0% too low. This confirms the suggestion that other liquid enthalpy measurements obtained by Treverton and Margrave also appear to be systematically low with, for example, the values obtained for vanadium (20) being on average 2.4% lower than the preferred values of Berezin et al. (21) and Lin and Frohberg (22).

The liquid specific heat determined by Treverton and Margrave (12) on IPTS-68 corrected to the value 41.20 ± 1.38 J mol–1 K–1 on ITS-90 which is notably higher than the value for the liquid of 37.3 J mol–1 K–1 determined by Cagran and Pottlacher (11) (1828 to 2900 K) using rapid pulse heating. However, it is noted that Cagran and Pottlacher obtained a specific heat value for the solid which is some 10% to 16% lower than the selected values. Therefore, the value of Treverton and Margrave was selected on the assumption that the apparently lower enthalpy values obtained are due to a constant systematic error. Over the range 1828 to 3300 K the actual enthalpy can be expressed as (Equation (ii)):

(ii)

Equivalent specific heat and entropy equations are also given in Table II whilst derived thermodynamic properties are given in Table III. The more recent liquid enthalpy measurements of Cagran and Pottlacher (11) trend from 3.3% lower at 1828 K to 5.8% lower at 2900 K.

Gas

Selected values are based on the 143 energy levels selected by Engleman et al. (23). The thermodynamic properties were calculated using the method of Kolsky et al. (24) and the 2014 Fundamental Constants selected by Mohr et al. (25, 26). Derived thermodynamic values based on a one bar standard state pressure are given in Table IV.

Table IV

Thermodynamic Properties of the Gaseous Phase

T, K C° p , J mol–1 K–1 H°T – H°298.15 K , J mol–1 S°T , J mol–1 K–1 –(G°T – H°298.15 K)/T , J mol–1 K–1
298.15 20.786 0 167.066 167.066
300 20.786 38 167.194 167.066
400 20.786 2117 173.174 167.881
500 20.786 4196 177.812 169.421
600 20.788 6274 181.602 171.145
700 20.802 8354 184.807 172.874
800 20.854 10,436 187.588 174.543
900 20.991 12,527 190.051 176.132
1000 21.273 14,639 192.276 177.637
1100 21.763 16,789 194.324 179.062
1200 22.508 19,000 196.248 180.414
1300 23.537 21,300 198.088 181.704
1400 24.850 23,717 199.878 182.938
1500 26.424 26,279 201.646 184.126
1600 28.213 29,009 203.407 185.276
1700 30.152 31,926 205.175 186.395
1800 32.167 35,042 206.955 187.488
1828 32.734 35,951 207.456 187.790
1900 34.179 38,360 208.749 188.559
2000 36.115 41,875 210.551 189.614
2100 37.908 45,578 212.358 190.654
2200 39.505 49,450 214.159 191.681
2300 40.869 53,471 215.946 192.698
2400 41.977 57,615 217.709 193.703
2500 42.823 61,858 219.441 194.698
2600 43.411 66,171 221.133 195.682
2700 43.757 70,532 222.779 196.656
2800 43.883 74,916 224.373 197.617
2900 43.815 79,302 225.912 198.567
3000 43.582 83,673 227.394 199.503
3100 43.213 88,014 228.817 200.426
3200 42.734 92,312 230.182 201.334
3300 42.172 96,558 231.489 202.229

Notes to Table IV

P is specific heat

T – H298.15 K is enthalpy

T is entropy

–(G°T – H°295.15 K)/T is the free energy function

298.15 K – H°0 K = 6197.4 J mol–1

Enthalpy of Sublimation at 298.15 K

Because of a general lack of detail as to what temperature scales were used and problems associated with the exact measurement of temperature, no attempt was made to correct vapour pressure measurements to ITS-90 from what would have been contemporary scales. For results given in the form of the Clausius-Clapeyron equation, log(p) = A + B/T (where p is pressure and T is temperature), the enthalpy of sublimation was calculated at the two temperature extremes and averaged. For the measurements of Walker et al. (27), Lindscheid and Lange (28) and Chegodaev et al. (29) no temperature ranges were given and therefore these measurements were not included. From Table V, in view of possible systematic errors in the earlier measurements, only the twelve determinations from Taberko et al. (42, 43) to Ferguson et al. (51) were considered. The unweighted average value of 377 kJ mol–1 is assigned an accuracy of ±4 kJ mol–1 which is equivalent to a 95% confidence level (two standard deviations).

Table V

Enthalpies of Sublimation at 298.15 K

Authors Ref. Method Temperature range, K ΔH°298.15 K (II), kJ mol–1 ΔH°298.15 K (III), kJ mol–1 Notes
Babeliowsky (30) MS 1250–1730 385 ± 4 (a)
Trulson and Schissel (31) MS 1370–1785 382 ± 5
Haefling and Daane (32) KE 1388–1675 332 ± 7 352.9 ± 0.5
Alcock and Hooper (33) Trans 1673–1773 459 376.1 ± 2.4
Zanitsanov (34) KE 1537–1841 368 ± 22 375.9 ± 1.2 (b)
Dreger and Margrave (35) L 1220–1640 362 ± 11 380.6 ± 1.0
Hampson and Walker (36) L 1294–1488 365 ± 4 373.4 ± 0.2
Norman et al. (37) KEMS 1485–1710 381 380.5 ± 0.1 (c)
Strassmair and Stark (38) L 1361–1603 372 ± 14 373.3 ± 0.6
Myles (39) TE 1515–1605 372 372.0 ± 0.1 (c)
Darby and Myles (40) TE 1517–1608 372 371.8 ± 0.1 (c)
Novosolov et al. (41) TE 1730–1938 363 370.0 ± 0.4 (c)
Taberko et al. (42, 43) Evap 1828–2023 381 ±10 376.9 ± 0.3
Zaitsev et al. (44) KE 1267–1598 377 ± 1 377.3 ± 0.1
Bodrov et al. (45) AA 1511–1678 (s) 389 ± 4 376.6 ± 0.2
1842–2046 (l) 394 ±12 373.1 ± 0.5
Naito et al. (46) KEMS 1567–1758 386 375.5 ± 0.5 (c)
Chandrasekharaiah et al. (47) KEMS 1439–1724 373 ± 5 377.9 ± 0.2 (d)
Stølen et al. (48) KEMS 1523–1743 389 375.5 ± 0.5 (c)
Bharadwaj et al. (49) KEMS 1627–1818 (s) 378 ± 7 377.7 ± 0.2 (d)
1833–2041 (l) 380 ± 8 376.7 ± 0.2 (d)
Kulkarni et al. (50) KEMS 1237–1826 375 ± 2 381.7 ± 0.3 (e)
Ferguson et al. (51) KE 1473–1825 (s) 373 ± 7 377.8 ± 0.4
1840–1973 (l) 385 ± 7 377.4 ± 0.2
Selected 377 ± 4

Notes to Table V

ΔH°298.15 K (II) and ΔH°298.15 K (III) are the Second Law and Third Law enthalpies of sublimation at 298.15 K

(a) Value given only at 298.15 K

(b) Two runs combined since individual Second Law values were 433 kJ mol–1 and 312 kJ mol–1 respectively

(c) Values given only in terms of the Clausius-Clapeyron equation

(d) Average of two runs

(e) Average of five runs

Methods

AA: atomic absorption

Evap: evaporation

KE: Knudsen effusion

KEMS: Knudsen effusion mass spectrometry

L: Langmuir free evaporation

MS: mass spectrometry

TE: torsion effusion

Trans: transpiration

Vapour Pressure Equations

The vapour pressure equations as given in Table VI were evaluated for the solid from free energy functions for the solid and the gas at 50 K intervals from 900 K to 1800 K and the melting point and for the liquid at the melting point and at 50 K intervals from 1850 to 3300 K and were fitted to the following equation (Equation (iii)):

Table VI

Vapour Pressure Equations

Phase Temperature range, K A B C D E
Solid 900–1828 14.71536 0.220029 –45,349.16 –1.26392 × 10–3 2.03201 × 10–7
Liquid 1828–3300 92.57304 –10.78530 –51,305.62 3.94374 × 10–3 –2.33142 × 10–7

Arblaster-62-1-Jan18-m3_NEW

(iii)
Table VII

Free Energy Equations Above 298.15 K

Solid: 298.15 to 1828.0 K
T – H°298.15 K (J mol–1) = 126.5006 T – 4.77704 × 10–3 T 2 + 8.85548333 × 10–7 T 3 – 1.68763333 × 10–10 T 4 + 28,917.8/ T – 24.0658 T ln (T) – 7750.91
Liquid: 1828.0 to 3300 K
T – H°298.15 K (J mol–1) = 250.1240 T – 41.2000 T ln (T) – 10,903.0

Note to Table VII

T – H°298.15 K is the free energy function

Table VIII

Transition Values Involved with the Free Energy Equations

Transition Temperature, K ΔHM , J mol–1 ΔSM , J mol–1 K–1
Fusion 1828.0 17,340.00 9.4858
Table IX

Vapour Pressure

T, K p, bar ΔG°T, J mol–1 ΔH°T, J mol–1 p, bar T, K
298.15 5.16 × 10–60 338,411 377,000 10–15 911
300 1.32 × 10–59 338,172 376,991 10–14 956
400 3.31 × 10–43 325,314 376,433 10–13 1005
500 2.20 × 10–33 312,606 375,794 1012 1060
600 7.59 × 10–27 300,034 375,087 10–11 1122
700 3.47 × 10–22 287,585 374,321 10–10 1191
800 1.07 × 10–18 275,250 373,504 10–9 1269
900 5.43 × 10–16 263,019 372,644 10–8 1359
1000 7.86 × 10–14 250,886 371,754 10–7 1462
1100 4.56 × 10–12 238,843 370,851 10–6 1582
1200 1.33 × 10–10 226,882 369,956 10–5 1725
1300 2.30 × 10–9 214,994 369,093 10–4 1899
1400 2.63 × 10–8 203,171 368,286 10–3 2121
1500 2.16 × 10–7 191,403 367,558 10–2 2403
1600 1.36 × 10–6 179,680 366,926 10–1 2770
1700 6.89 × 10–6 167,994 366,399 1 3268.52
1800 2.91 × 10–5 156,336 365,979 NBP 3271.88
1828 (s) 4.23 × 10–5 153,076 365,880
1828 (l) 4.23 × 10–5 153,076 348,540
1900 1.01 × 10–4 145,388 347,983
2000 3.03 × 10–4 134,742 347,378
2100 8.17 × 10–4 124,121 346,961
2200 2.02 × 10–3 113,516 346,713
2300 4.60 × 10–3 102,919 346,614
2400 9.79 × 10–3 92,323 346,638
2500 1.96 × 10–2 81,725 346,761
2600 3.73 × 10–2 71,120 346,954
2700 6.75 × 10–2 60,506 347,195
2800 0.117 49,883 347,459
2900 0.196 39,251 347,745
3000 0.318 28,609 347,976
3100 0.498 17,960 348,197
3200 0.760 7304 348,375
3268.52 1.000 0 348,467
3300 1.130 –3356 348,501

Notes to Table IX

ΔG°T is the free energy of formation at one bar standard state pressure and temperature T and ΔH°T is the enthalpy of sublimation at temperature T

Enthalpy of sublimation at 0 K: ΔH°0 = 376.247 ± 4.000 kJ mol–1

NBP is the normal boiling point at one atmosphere pressure (1.01325 bar)

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Acknowledgement

The author is indebted to Venkatarama Venugopal, Bhabha Atomic Research Centre, India, for supplying the vapour pressure data corresponding to the measurements of Kulkarni et al. (50).

The Author


John W. Arblaster is interested in the history of science and the evaluation of the thermodynamic and crystallographic properties of the elements. Now retired, he previously worked as a metallurgical chemist in a number of commercial laboratories and was involved in the analysis of a wide range of ferrous and non-ferrous alloys.

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