The Thermodynamic Properties of Platinum
The Thermodynamic Properties of Platinum
REVISED DATA FOR THE LIQUID STATE AND VAPOUR PRESSURE
The thermodynamic properties of platinum were reviewed here by the author in 1994. However, the use of superior values for the enthalpy of liquid platinum have resulted in a major revision of the thermodynamic values for the liquid phase. One consequence of the revision is that the boiling point at one atmosphere pressure is altered from 4125 K, as calculated in the 1994 paper, to 4149 K. Previously accepted values for solid platinum are not altered, and there are only very minor changes to the gaseous phase values as a result of using a new atomic weight for platinum and the CODATA 2002 recommended values of the fundamental constants.
Platinum has a face centred cubic structure with a lattice parameter at 20ºC of 0.39236 nm and a density of 21.45 × 103 kg m–3 (1). In the present paper the variation of the thermodynamic values of the specific heat at constant pressure, enthalpy, entropy and Gibbs free energy with temperature have been revised in the condensed phases and gaseous phase at a 1 bar standard state pressure. The vapour pressure data was calculated from the selected heat of sublimation of 565 kJ mol–1 as shown in Table I and from the nett Gibbs free energy between the condensed and gaseous phases. Values for these properties are reassessed in the light of revised data.
|Reference||Temperature range, K||ΔH°298.15, kJ mol–1||Notes|
|Koch, Calvert, Thomas and Beall (13)||2032–2445||559.4 ± 1.1||a|
|Jones, Langmuir and Mackay (14)||1697–2034||564.8 ± 1.7||b|
|Dreger and Margrave (15)||1573–1785||566.5 ± 1.4||c|
|Hampson and Walker (16)||1918–2049||565.7 ± 0.5||d|
|Plante, Sessoms and Fitch (17)||1675–1977||564.4 ± 0.2||e|
|Selected value for the heat of sublimation of platinum at 298.15 K:||
565 ± 2*
[i] a Weighted average of two data sets
b Temperatures corrected to ITS-90 from a laboratory temperature scale
c Two data points rejected by the authors
d Eight data points rejected by the authors
e Weighted average of eight data sets
* Following the practice of the National Institute of Standards and Technology (the former National Bureau of Standards), the accuracy quoted for the individual heats of sublimation are standard errors not standard deviations. Therefore the value quoted for the "accuracy" of the selected value tries to take into account not only the variations in the quoted values but also individual internal variations in the vapour pressure data sets. This practice is commonly used and represents a "real" accuracy rather than a mathematically derived accuracy which would tend to be lower and not realistic
The thermodynamic properties of platinum were reviewed in this Journal in 1994 (2). The current revision leaves all values for the solid phase unaltered, with equations representing the variation with temperature of enthalpy and specific heat at constant pressure given in the box below. These equations have an overall accuracy of 0.3 per cent, equivalent to a standard deviation of ± 0.09 J mol–1 K–1 for the specific heat values. These equations were used to generate the thermodynamic properties of the solid phase shown in Table IIA.
[i] s is solid, l is liquid
The values of enthalpy and entropy at 298.15 K are shown below.
|Platinum at 298.15 K||Solid||Gas|
|Enthalpy: H°298.15 – H°0, J mol-1||5694||6576.6|
|Entropy: S°298.15, J mol-1 K-1||41.53||192.409|
Recent measurements of the enthalpy of platinum by Wilthan and colleagues (3, 4) using differential scanning calorimetry (at 473–1573 K) lead to values 3.6% higher falling to 1.7% higher than the selected values, while rapid pulse heating measurements by the same authors (at 1700–2040 K) lead to values of 1.1 to 1.4% lower.
For the gaseous phase the introduction of a new atomic weight for platinum of 195.078 (5) and of the CODATA 2002 fundamental constants (6) have caused only two values (the free energy at 2800 K and the entropy at 3400 K) to be altered, but only by one digit in the last decimal place. Thermodynamic properties of the gaseous phase are shown in Table IIB and the values of enthalpy and entropy at 298.15 K are on the previous page.
However, selected values used in that paper, in the liquid region, were based on the enthalpy values of Chaudhuri et al. (8) which were supposedly the measurements made by David Bonnell who was working on his Ph.D. thesis at Rice University. Bonnell's Ph.D. thesis was published two years later (9) and it was assumed that this was because he was completing work on other metals and that, as is the usual practice, the values in the earlier paper were definitive. However, private communication with Bonnell has indicated that this was not the case. In fact, the thesis contains the fully corrected values. The values given in the paper published two years earlier were only preliminary and should not have been given the attention they received.
Therefore, in now selecting the values given in Bonnell's thesis, his temperature values in the range 2205 to 2650 K are accepted for this review; while his enthalpy values have been adjusted by 195.08/195.09 to ensure that the atomic weight is the same as that used previously for the solid phase (2). These measurements can then be represented by the following equation which has an overall accuracy of 1.2%, equivalent to a standard deviation of ± 1190 J mol–1:
H°T – H°298.15 = 38.9928 T – 3805.63 J mol–1
Thus, derived values are:
Specific heat (Cp): 39.0 ± 2.2 J mol–1 K–1
Heat of fusion: 22.11 ± 0.94 kJ mol–1 and
Entropy of fusion: 10.83 ± 0.46 J mol-1 K-1.
The difference between the above three values and those tabulated for the liquid phase in Table IIA is due to the values in the Table being taken beyond their true accuracy for interpolation purposes.
Other measurements made on platinum in the liquid region used the rapid pulse heating technique, but the different values obtained show marked differences, and currently this method does not appear to be as accurate as the levitation calorimetry method used by Bonnell.
For instance, Gather, Shaner and Hodgson (10) (at 2041–8000 K) obtained a value for the specific heat of 49 J mol–1 K–1 and for the heat of fusion of 27 ± 6 kJ mol–1, while Lebedev, Savvatimskii and Smirnov (11) obtained a heat of fusion of 25 kJ mol–1.
The two most recent sets of measurements: by Hixson and Winkler (12) (at 2041–5100 K) lead to a specific heat of 41.35 J mol–1 K–1 and a heat of fusion of 24.2 kJ mol–1, and the measurements of Wilthan and colleagues (5, 6) (at 2045–2830 K) lead to a specific heat of 36.5 J mol–1 K–1 and a heat of fusion of 21.8 kJ mol–1. On average these latter two sets of results show satisfactory agreement with values selected here.
Only the measurements of Koch et al. (13) on liquid platinum are affected by the revision, and even in this case the derived heat of sublimation is only lowered by 0.1 kJ mol–1, see Table I. However, these measurements of Koch et al. are still discrepant when compared to the other four values obtained on solid platinum as shown in Table I and have again been rejected. In selecting the heat of sublimation most weight is given to the measurements of Hampson and Walker (16) and those of Plante, Sessoms and Fitch (17).
[i] s is solid, l is liquid
|Vapour Pressure Equations|
|Solid: 1200–2041.3 K:||ln(P, bar) = 28.3308 – 1.29944 ln(T) – 69207.9/T|
|Liquid: 2041.3–4200 K:||ln(P, bar) = 32.1390 – 1.89944 ln(T) – 67647.6/T|
Previous accepted values for the vapour pressure of the solid phase and revised values for the liquid phase are given in Table III.
Vapour pressure equations for both the liquid and the gas are given above. For the solid the values are given over a practical range from 1200 K to the melting point of platinum, while although the values for the liquid are given over a much larger temperature range from the melting point to 4200 K the derived normal boiling point is only 0.2 K higher than that obtained from a proper thermodynamic treatment.
The free energy equations, see below, are derived from those given above for the solid and liquid phases. It is a requirement that the two equations given must be equal at the melting point.
The thermodynamic properties of platinum have been revised by introducing superior values for the enthalpy of the liquid. The vapour pressure curve for the liquid is also reassessed as shown in Table III. Sets of revised values for specific heat at constant pressure, enthalpy, entropy, Gibbs' free energy and vapour pressure are presented.
Calculation of the Thermodynamic Properties of an Ideal Monatomic Gas
The thermodynamic properties of platinum gas given in Table IIB were calculated using the method of Kolsky, Gilmer and Gilles (18) outlined below. All values given correspond to the 2002 CODATA fundamental constants (6) and to a standard state pressure of one bar.
Velocity of light, c = 299792458 m s–1 exactly
Avogadro constant, NA = (6.0221415 ± 0.0000010) × 1023 mol–1
Planck constant, h = (6.6260693 ± 0.0000011) × 10–34 J s
Gas constant, R = 8.314472 ± 0.000015 J mol–1 K–1
Second radiation constant, c2 = 0.014387752 ± 0.000000025 m K (metre Kelvin)
Atomic weight, Ar
Energy level = νi cm–1; Quantum number of energy level, Ji
α = c2 = 1.4387752 cm K
K1 = Rα = 11.962656 J cm mol–1
K2 = 2.5R = 20.786180 J mol–1 K–1
K3 = Rα2 = 17.211573 J cm2 K mol–1
K4 = 1.5R = 12.471708 J mol–1 K–1
K5 = S0 = – 9.5758165 J mol–1 K–1
K6 = K5 – 2.5R = – 30.3619965 J mol–1 K–1
S0, the Sackur-Tetrode constant, is derived from: S0 = R[2.5 + ln 4.980463969 x 10–9 R5/2/h3 NA 4)], where the numerical value in the equation is equal to (2π/1000)3/2/105
Q = ∑(2Ji + 1)e–ανi/T
Q1 = ∑(2Ji + 1)νi e–ανi/T
Q2 = ∑(2Ji + 1)νi2 e–ανi/T
Values are initially referred to 0 K:
Cop = (K3/T2)(Q2/Q1 – (Q1/Q)2) + K2 J mol–1 K–1
Hop – Ho0 = K1(Q1/Q) + K2 T J mol–1
So = (K1/T)(Q1/Q) + R ln(Q) + K4 ln(Ar) + K2 ln(T) + K5 J mol–1 –1
– (GoT – Ho0)/T = R ln(Q) + K4 ln(Ar) 2 ln(T) + K6 J mol–1 K–1 = So – (HoT o0)/T J mol–1 K–1
HoT – Ho298.15 = (HoT o0) – (Ho298.15– Ho0) J mol–1
– (GoT – Ho298.15)/T = – (GoT – Ho0)/T + (Ho298.15 – Ho0)/T J mol–1 K–1
ΔHo = ΔHo298.15 + δ(HoT – Ho298.15)
ΔGo = ΔHo298.15 – Tδ – (GoT – Ho298.15)/T
ln(P) = – ΔGo/RT
δ(HoT – Ho298.15) = (HoT – Ho298.15) (gas) – (HoT – Ho298.15) (solid, liquid)
δ – (GoT – Ho298.15)/T = – (GoT – Ho298.15)/T (gas) – – (GoT – Ho298.15)/T (solid, liquid)
Calculation of the Heat of Sublimation from Vapour Pressure Data (as relating to Table I )
Calculated values are the Second Law heat of sublimation, ΔH o 298.15 (II), and the Third Law heat of sublimation, ΔH o 298.15 (III). Significant differences between these two evaluations may indicate that the vapour pressure measurements are erroneous. The selected heat of sublimation is calculated from the Third Law values.
Third Law Heat of Sublimation
Each data point is evaluated separately and the selected value is based on averaging the derived heats of sublimation:
ΔH o 298.15 (III) = T[δ – (G o T – H o 298.15 )/T – R ln(P, bar)]
Revised Second Law Heat of Sublimation
All data points are fitted to the following equation:
δ – (G o T – H o 298.15 )/T – R ln(P, bar) = B + A/T where A = ΔH o 298.15 (II) and B = entropy drift = δS o 298.15 (III) – δS o 298.15 (II)
Ideally B should be zero but if it is an unacceptably large number then this may again indicate that the vapour pressure measurements are erroneous.
Traditional Second Law Heat of Sublimation
All data points are fitted to the Clausius-Clapeyron equation:
ln(P, bar) = B + A/T
ΔH o 298.15 (II) = – δ(H o T – H o 298.15 )) – R A
Temperature is either the average experimental value or the average value obtained from reciprocal temperatures, but there is no formal definition.
"Pseudo" Third Law Heat of Sublimation
For vapour pressure measurements given only in the form of an equation, usually the Clausius-Clapeyron equation, Third Law values are calculated at the extreme ends of the temperature range and averaged. Where possible the assigned accuracy is that given by the authors who generally carried out a proper Third Law evaluation using previously selected thermodynamic values but reported the results only in the form of the above equation.
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John W. Arblaster is Chief Chemist working in metallurgical analysis on a wide range of ferrous and non-ferrous alloys for standards in chemical analysis at Coleshill Laboratories, in the West Midlands of England. He is interested in the history of science and in the evaluation of the thermodynamic and crystallographic properties of the elements.