6897
J. Phys. Chem. 1993,97, 6897-6901
Heat Capacities and Enthalpy of Fusion of Heavy Oxygen Water? Yatsuhisa Nagtino,. Yuji Miyazaki, Takasuke Matsuo, and Hiroshi Suga Microcalorimetry Research Center and Department of Chemistry, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Received: January 29, 1993; In Final Form: April 12, I993
The heat capacitiesof 180-enrichedwater under its saturatedvapor pressure have been measured in the temperature range 9-300 K by means of adiabatic calorimetry. The triple point temperature and the enthalpy of fusion of pure H2180 have been determined to be 273.46 f 0.01 K and 6.029 f 0.004 kJ mol-', respectively. The heat capacity difference between H2180 and H2160, Cp(H2180)- CP(H2l60), rises steeply in the temperature range 9-100 K and makes a shoulder peak of 0.70 J K-l mol-' a t 100 K. It increases from 0.67 J K-' mol-' at 160 K to 0.90 J K-l mol-' at 260 K. The difference is 0.83 f 0.12 J K-l mol-' for liquid water. It shows no drastic change from solid to liquid phase, while a discontinuous increase appears on melting in the case of C p ( D P O ) - C,(H2l60). The heavy oxygen isotope effect on the harmonic translational modes in the lattice vibrations dominantly contributes to Cp(H2180) - CP(H2l60) below 100 K. However, another contribution starts to appear above 100 K and becomes dominant above 200 K. Possibly, it is attributable to an isotope effect on the dipole reorientational energy for the "pseudorotation" of water molecules, which progresses with increasing orientational disorder above the glass transition at 100 K, and also to the heavy oxygen isotope shift of the librational frequencies by the anharmonic couplings with the translational motions at high temperatures. On the other hand, the heavy oxygen isotope effect in the liquid water is mainly explained by the energy level shifts of various hydrogen-bonded clusters.
Introduction
The heat capacities of water are known to exhibit several anomalous properties, which are attributable to the significant structures composed of hydrogen bonds called widely the "iceberg". First, the heat capacities have a remarkable increase from solid phase to liquid phase at the melting point.' Some hydrogen-bondedcompounds,such as HNO3, H202, H2S04, NH3, NzH4,and CH3COOH, also show discontinuous heat capacity increases at their melting points. The large heat capacities of liquid water have been interpreted in terms of successive breaking of the hydrogen bonds (or the melting of the "iceberg"). Second, the heat capacitiesof liquid water anomalously exhibit a minimum at 35 OC under atmospheric pressure. This phenomenon has been interpreted in relation to a stability limit of supercooled water at 4 5 "C, as well as to the density minimum of liquid water. However, the microscopic picture of this phenomenon is still controversial.2rs Ntmethy and Scheraga explained thermodynamic properties of liquid water on the basis of the flickering cluster model? which was originally proposed by Frank and Wen.lo Their calculation successfullyreproduced the thermodynamic quantities except for the heat capacities.ll Walrafen derived the mole fractions of 4-, 3-, and 2-hydrogen-bonded species by a deconvolutionof Raman spectra to explain the heat capacities.12 However, this cluster model could not account for the divergence of the heat capacities observed in supercooled water. Recently, it was indicated that a core-softened fluid model could explain density an0ma1ies.l~It has also been shown by a molecular dynamics simulation that the divergent nature of thermodynamic quantities in water is reproduced by using a suitable anisotropicintermolecular potential mode1.7~4 Oxygen atom motions intuitivelyseem to exclusively contribute to translational modes in the hydrogen-bonded network, while hydrogen atom motions are related to both the translational and librational modes. Therefore, the isotope effects of oxygen and hydrogen atoms would work differently on the heat capacities of water. Fluctuation properties such as heat capacity provide a t Contribution No. 69 from the Microcalorimetry Research Center.
0022-3654/93/2097-6897%04.00/0
rigorous test for the reliability of computer simulations.15 Calorimetric studies on several isotopic waters and their quantitative comparison will be valuable for testing the reliability of the computer simulations. Even for crystalline ice, the thermal properties have by no means been well established. In the crystalline state Ih, water molecules form a three-dimensional hydrogen bond network, in which the water molecules are orientationallydisordered.1.16 Very recently, the phonon density of states was determined by neutron scattering and reproduced computationally on the basis of an orientationallydisordered dipole model.17-19 However, the origin of the large anharmonic heat capacity of ice, which amounts to 10% of C, at the melting point,2O is not understood yet. The heat capacities of natural water and deuterated water have been measured by Haida et al. with great care paid to the glass transition in the hexagonal ice.21.22In the present study, the heat capacities of 180-enrichedwater have been determined by means of adiabatic calorimetry at temperatures between 9 and 300 K. Heavy oxygen isotope effects are briefly discussed on the basis of statistical models. The triple point temperature of pure H2I80 and the associated enthalpy change have been precisely determined. Experimental Section Materials. Commercial 180-enriched water (ICON, NY, (lsO)water at 97 atom %, 1 g) was degassed and distilled in vacuo. The purity of the sample was determined to be 99.9993% by a fractional melting method,23as will be described later. The isotope ratio was determined by means of mass spectrometry as follows. The relative peak heights of ion signals from natural water were measured for the ions of m / e = 18 (H2160+), 17 (H160+), and 16 (lag+). Those from the 180-enriched water were measured for the ions of mle = 21 (HD180+),20 (H2180+), 19 (H2170+ HISO+), and 18 (H2l6O++ H170+ lSO+)with the same ionizationvoltage as for the measurement of the natural water. On the basis of the reasonable assumption that the fragmentation did not depend on isotopic masses, we determined the abundance of the isotopes as follows:
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0 1993 American Chemical Society
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6898 The Journal of Physical Chemistry, Vol. 97, No. 26, I993
oxygen:
(96.2 i OS)% 0.1% 3.7% (99.4 i 0.1)% 0.6%
180 170
'60
hydrogen: 'H (D)
The average molar mass (the apparent molar mass) is 19.95 1 g mol-'. The standard deviations of the mean were derived from six experiments. Heat CapacityMeasurement. The heat capacity measurement was carried out by use of an adiabatic calorimeter developed at MicrocalorimetryResearch Center for samples as small as 1 cm3 by volume. Details of the calorimeter have been described elsewhere.24 The calorimeter cell (1.205 cm3) was loaded with 0.89413 g of the 180-enrichedwater together with helium gas of atmosphericpressure at 19 OC. Buoyancy correction was applied to the sample mass by using the density of 1.1072 g ~ m at- 19 ~ OC, which is the weighted average of the densities of liquid H2180, H2160,and D2180 given by Ke11.25 For the measurement of the crystalline phase, solidification was followed by annealing at 270 K for 24 h. The uncertainty in the heat capacities was 0.12 J K-' mol-' as calculated from the standard deviation of six experiments using liquid water. The contribution from the I7O species to the heat capacities was safely ignored on the basis of the mass spectrometric result, so the apparent heat capacities of the 180-enriched sample were treated as those of a mixture of 96.3% l8O species and 3.7% I6O species. This sample is mainly composed of H2180, H2l60, and DH180. In order to determine the heat capacities of pure H2I80, we need those of Hz160 and DH'8O. Because these are small correction terms, we used the heat capacities of the natural water for the former. The latter was assumed to be the average of the heat capacities of D2I80 and H2180, i.e., C,(DH180) = '/2C8(D2I80) + ' / Z C , ( H ~ ~ ~ OIn) . this equation, the symbol C, represents the heat capacity of condensed matter under saturated vapor pressure.26 In the present study, we actually measured the net heat capacity C,,,,which , includes the heat capacity of vapor and the vaporization enthalpy. However, these terms are negligibly small even at the highest temperature under our experimental condition, so the C,,,values are tabulated as those for C,without any correction. Thus, the molar heat capacity C, of the sample is described as
TABLE I: Triple Point Temperatures and Enthalpies of Fusion of Isotopic Water Tt/K AJllkJ mo1-l H2I80 H2l60
273.46 i 0.01' 273.16b 216.95d
6.029 i 0.0040 6.007 i 0.004C 6.315 0.006d
*
D2I60 a The present study. Defined in the temperature scale ITS-90. CGiauque, W. F.; Stout, J. W. J . Am. Ckem. SOC.1936, 58, 1032. Reference 21. solubility equilibrium inside the cell, etc. Because of these complications, the nature of the impurity will not be discussed further. For the determination of the triple point temperature, it was necessary to make a correction for the effect of the helium gas pressure. This was done by using the pressure dependence of the melting temperature of natural ice. A small correction for the effect of the thermometer leads (due to a finite input impedance of the thermometric bridge) was also applied. To check the validity of the corrections, the triple point temperature of natural water was determined by following the same procedure. The result (273.158 f 0.003 K) agrees satisfactorily with the defined triple point temperature of 273.16 K. Finally, the triple point temperature and the enthalpy of fusion of pure (I80)waterwere determined by application of corrections for the contributions from H2160 and D2I80 in the same way as was done for the heat capacities without assuming any excess quantities due to mixing. All the values for pure H2180 in the tables and the figures have been derived in this way.
Results
The triple point temperature and the enthalpy of fusion of pure H2'80 are shown in Table I with the literature values of H2160 and D2I60. Steckel and Szapird7determined the melting point of pure H2180 as 0.28 f 0.02 OC at atmospheric pressure, which agrees with the present result after pressure adjustment. The linear extrapolations of the melting temperature and the enthalpy of fusion of the actual mixed sample to pure H2180are equivalent to the assumption of the ideal solution model for both the liquid and solid solutions among H2I80, H P 0 , and D P 0 . The calculated liquidusline based on the model is convex upward, while the solidus line is convex downward. The calculation C,= 0.956228Cs(H2'80) 0.037772C,(H2'60) followed the method described by Oonk.28 The maximum 0.006Cs(D2180) temperature difference between the solidus and liquidus lines is 2X K. Recently, Kiyosawa reported the freezing point Because of their small contribution, the values of Cs(D2160)were variation of H2W-H2180 mixtures in the range 0 < x(H2'80) actually used instead of those of Cs(D2180). Using this equation < 0.05 and derived the relation AT = 0 . 3 2 2 ~ ( H 2 ~ ~ 0which ),2~ and the literature values of C,(HZ'~O)and C,(D2'60),21s22we alsojustifies the linear extrapolation of the melting temperatures. determined the heat capacitiesof pure H2180. The heat capacities of liquid natural water were also measured in the present study. The enthalpy of fusion was determined by subtracting the heat In order to determine the melting temperature of the 180capacity components from the total Joule energy supplied to the enriched ice and its chemical purity, a fractional melting sample until the last piece of solid phase disappeared. The experiment was carried o~t.23 The equilibrium melting tementhalpy involved in the excess heat capacity due to premelting was included in the enthalpy of fusion. Thenormal heat capacities perature ( Tm)plotted against the reciprocal fraction (1/j)of the sample already melted gave a straight line ( T , = 273.447 K at below the melting point wereevaluated by fitting the heat capacity f = 0.104, T , = 273.450 K at f = 0.561). The slope of the data of the ('80)ice to a combination of suitable Debye and straight line, least-squares fitted to five points, along with the Einstein functions. Above the melting point, those were detercryoscopicconstant gave rise to the fraction of 7 X 10-6for liquidmined by linear extrapolation of the heat capacities in the region soluble and solid-insoluble impurities. One possible impurity is of 277-284 K. The uncertainty in the enthalpy of fusion is due He gas used as a heat-exchange medium inside the calorimetric mainly to the ambiguity of the evaluation of the excess heat cell. The solubility data of He gas into water give 7 X 10-6,in capacities near the melting point. There have been severalindirect determinations of the enthalpy of fusion of H2180: A(Ar&) = good agreement with the amount of impurity determined experimentally. However, this result may besomewhat fortuitous 4 6 J mol-I,3O +33 J mol-'," and -42 J m0l-1,~~ where A(AfuH) because the helium exists both in the liquid and gaseous phases. = AfUsH(H2180) - AfJf(H2l60). Becauseof the large scattering This situation makes the simple application of Raoult's law of the values, it has been uncertain whether or not the enthalpy questionable. Rigorous treatment requires further consideration of fusion of HZ180 ice is significantly different from that of natural taking into account the Henry's law constant, dead space of the ice. Actually, the present result shows that the enthalpy of fusion cell, volume change of ice on melting, extent of attainment of of H2I80 is larger by 22 f 4 J mol-' than that of natural water.
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Heat Capacities of Heavy Oxygen Water
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6899
TABLE II: Molar Heat Capacities of H 2 W (Molar Mass = 20.015) C,/ J K-I C,/J K-I Tw/K mol-' AT/K T.,/K mol-' AT/K TaV/K Crystal (Series 1) 9.13 9.91 10.83 11.77 12.62 13.50 14.38 15.23 16.10 16.99 17.85 18.73 19.62 20.56 21.52 22.49 23.47 24.49 25.55 26.65 27.76 28.90 30.03 31.33
0.233 0.317 0.430 0.551 0.680 0.847 1.012 1.170 1.364 1.560 1.735 1.951 2.163 2.371 2.591 2.818 3.048 3.287 3.513 3.755 4.055 4.282 4.513 4.794
0.526 0.690 0.850 0.784 0.756 0.837 0.813 0.797 0.865 0.837 0.835 0.887 0.868 0.916 0.966 0.946 0.983 1.030 1.07 1 1.102 1.1 12 1.160 1.079 1.494
32.81 34.26 35.69 37.09 38.48 39.85 41.21 42.57 43.96 45.37 46.78 48.21 49.66 51.12 52.59 54.07 55.56 57.06 58.58 60.09 61.62 63.16 64.70
5.106 5.414 5.686 5.984 6.253 6.507 6.775 7.004 7.284 7.522 7.764 8.013 8.283 8.542 8.802 9.065 9.334 9.619 9.883 10.15 10.43 10.67 10.94
1.462 1.435 1.415 1.394 1.379 1.366 1.353 1.383 1.404 1.407 1.426 1.442 1.455 1.467 1.479 1.489 1.499 1SO7 1.517 1.526 1.533 1.544 1.552
66.26 67.82 69.34 70.82 72.30 73.79 75.28 76.77 78.27 79.78 81.29 82.80 84.31 85.83 87.35 90.39 91.93 93.48 95.03 96.58 98.14 99.71 101.50 103.51
C,/J K-1 mol-'
AT/K
T,,/K
CJ J K-I mol-'
AT/K
11.21 11.50 11.75 12.00 12.22 12.48 12.72 12.95 13.17 13.42 13.64 13.82 14.10 14.32 14.50 14.99 15.20 15.40 15.64 15.85 16.05 16.29 15.59 16.91
1.559 1.566 1.478 1.48 1 1.486 1.489 1.493 1.498 1S O 3 1.507 1.513 1.512 1.515 1.520 1.526 1.536 1.542 1.548 1.553 1.560 1.567 1.572 2.020 2.013
105.52 107.52 109.5 1 111.51 113.50 115.49 117.48 119.47 121.46 123.46 125.45 127.45 129.45 131.45 133.45 135.46 137.47 139.48 141.49 143.51 145.53 147.56 149.59
17.21 17.51 17.79 18.06 18.32 18.58 18.82 19.05 19.32 19.55 19.77 20.02 20.27 20.51 20.72 20.98 2 1.23 2 1.45 21.66 21.93 22.19 22.40 22.68
2.007 2.002 1.998 1.996 1.995 1.994 1.994 1.995 1.995 1.997 1.999 2.001 2.003 2.005 2.009 2.01 1 2.014 2.017 2.022 2.024 2.027 2.032 2.035
26.42 26.64 26.92 27.17 27.41 27.66 27.92 28.18
1.955 1.958 1.960 1.962 1.965 1.968 1.970 1.973
196.23 198.20 200.18 202.15 204.13 206.1 1 208.10
28.43 28.69 28.96 29.22 29.46 29.74 30.01
1.975 1.978 1.980 1.983 1.986 1.988 1.991
33.99 34.27 34.52 34.83 35.10 35.43 35.71 36.01
2.043 2.045 2.048 2.049 2.052 2.052 2.547 2.056
253.60 255.66 257.71 259.77 261.82 263.88 265.94
36.27 36.61 36.89 37.22 37.54 37.84 38.17
2.059 2.060 2.063 2.064 2.065 2.067 2.068
76.45 76.39 76.35
2.505 2.504 2.504
298.00 300.50
76.34 76.33
2.503 2.502
Crystal (Series 2) 151.55 153.47 155.39 157.3 1 159.24 161.16 163.09 165.02
22.88 23.11 23.28 23.58 23.81 24.05 24.29 24.51
1.920 1.922 1.926 1.926 1.928 1.930 1.932 1.935
166.95 168.89 170.83 172.77 174.71 176.65 178.60
24.75 25.00 25.25 25.46 25.72 25.94 26.18
206.94 208.87 210.89 212.90 214.92 216.94 218.96 220.98
29.83 30.09 30.37 30.65 30.89 31.17 31.48 3 1.76
1.860 2.012 2.014 2.017 2.020 2.022 2.023 2.025
223.01 225.03 227.06 229.09 231.13 233.16 235.20
32.02 32.30 32.58 32.85 33.15 33.45 33.69
2.628 2.030 2.032 2.034 2.036 2.038 2.041
275.45 277.96 280.47
76.84 76.71 76.58
2.508 2.509 2.510
282.98 285.48 287.99
76.55 76.49 76.44
2.51 1 2.508 2.507
1.937 1.939 1.941 1.944 1.946 1.950 1.952
180.55 182.50 184.46 186.41 188.37 190.33 192.30 194.26
Crystal (Series 3) . 237.23
239.27 241.32 243.36 245.41 247.45 249.50 251.55
Liquid (Series 4)
TABLE III: Molar Heat Capacities of Natural Water (Molar Mass = 18.015) TwI K CJJ K-1 mol-' TwIK C.lJ K-l mol-' 274.68 276.88 279.08 28 1.29 283.49 285.69 287.89
76.10 75.99 75.86 75.78 75.72 75.66 75.62
290.10 292.30 294.49 296.69 298.89 301.09
75.56 75.53 75.56 75.52 75.47 75.50
The present value agrees satisfactorily with 6034.5 f 20 J mol-' determined by using Tian-Calvet heat flow calorimeter.33 Tables I1 and I11 show the molar heat capacities of pure H2180 and liquid natural water, respectively. The former is drawn in Figure 1 as a function of temperature for the sake of visualization. The latter agrees with those measured by Haida et ~ 1 . 2 ' within its standard deviation, f0.12 J K-1 mol-', although the present mean values are larger than Touloukian's recommendati0n3~by 0.2 J K-1 mol-' even after a small correction for the evaporation effect. A weak anomaly in the heat capacities of H2180 ice due to a glass transition was found in the region of 90-150 K,in agreement with those of H2160 and D2160.2'922 Normal heat capacities in
290.50 293.00 295.50
this region were determined by interpolation with a seventhorder polynomial function in T fitted to the experimental data in the two temperature regions of 30-90 K and 150-250 K. The heat capacities of ice in the remaining temperature regions were fitted with three seventh-orderpolynomial functions,which cover the regions below 20 K, 13-50 K, and 230-270 K. The heat capacities of liquid (180)water were fitted with a fifth-order polynomial function. The same procedures were used for the literature values2lJzof H2'60 and D 2 W to determine their normal heat capacity values. Solid curves in Figures 2 and 3 show differences of the normal heat capacities among H2180,D2I60, and H2160determined in this way. Since C,is essentially equal to C, in the temperature range far below the critical temperature and since only the difference in heat capacities of three isotopic waters is the object of the present discussion,the difference C,(H2'80) - C,(H2160)is safelyreplacedby Cp(H2180)- C,(HZ'~O).
Discussion The difference in C, between H2180 and H2160 is less than 1 J K-1 mol-'. It makes a shoulder peak of 0.7 J K-l mol-' at 100 K (Figure 2). The negative slope observed between 100 and 160 K may or may not be genuine, because there is an anomaly due to the glass transition in this region, and the curvature depends
6900 The Journal of Physical Chemistry, Vol. 97, No. 26, 1993
Nagano et al.
1 l2
0
100
200
270 270
305
Figure 3. Heat capacity differences between D2160and H2160.The dashed curvewas calculated from the harmonic lattice-modedistributions in the ICice, taking isotopic mass difference into account.
from the average of those along the three principal axes, has been assumed for all the librational modes. Actually, the derived librational frequencies of the heavy oxgen ice are lower by only 0.3% than those of natural ice. This simplification for the T / K librational modes is good enough for the present purpose because Figure 1. Molar heat capacities of H2180 in the crystalline and liquid their contribution to C,(H218O) - C,(H2160) is very small. phases. The dashed curve in Figure 2 shows the Cu(H2lS0)- CU(H2l60) values calculated for the ICice. The values for CU(H2l80)I I C"(H2'60) aresimilar to thosefor C,,(H2180)- C,,(H2160),because the correction term is negligibly small for ice. It has a single peakat 80Kwithamagnitudeof0.65 JK-l mol-'. Theagreement between the calculated and the observed values below 100 K is excellent. However, the calculated difference decreases monotonically above 100 K, while the observed curve increases again above 160 K. The curve of CU(H2180)- C,(HZ'~O)values calculated for the Ih ice also exhibits a single peak with a similar shape to that for the ICice. The same calculation procedure has beenappliedtothecaseof C,(D2160)- C,(H2160). Thecalculated curve reproducesthe observed values very well, as shown in Figure " 3. This means that the present simple procedure is suitable for 0 100 200 270 270 305the evaluation of the heavy hydrogen isotope effect on the librational mode in ice. In the present calculation, the anharmonic coupling has not been taken into account. The anharmonic T / K component of C, increases up to 4 J K-I mol-' at the melting Figure 2. Heat capacity differences between H2180 arid H2160. The Therefore, the discrepancy between the observed and dashed curve was calculated from the harmonic lattice-mode distributions the calculated curves at high temperatures can be attributable in the ICice, taking isotopic mass difference into account. to such an anharmonic coupling. on the fitting polynomial functions to some extent. The curve Interestingly, the discrepancy increases above the glass tranroughly exhibits a plateau in this temperature region and gradually sition temperature, where the frozen-in orientational disorder of increases from 0.67 J K-1 mol-' at 160 K to 0.93 J K-l mol-' at water molecules is mobilized dynamically in the time scale of the heat capacity determination. Such a reorientational transition 210 K. involves an energy change of several kJ mol-I arising from the A lattice dynamics analysis df neutron inelastic scattering dipoldipole interactions between the neighboring molecules. showed that the frequency distribution of the lattice vibrations is well separated for the translationaland librational modes, which At the same time, the orientational disorder would significantly locate below 300 cm-1 and above 600 cm-I, r e ~ p e c t i v e l yThe . ~ ~ ~ ~ ~ deform the potential for the local translational motion. In fact, harmonic components of C, caq be calculated by a well-known it makes the frequencyof the optical phonons of the translational modes in ice shift.I9 Theoveralleffect induced by theorientational method using the Einstein functions.36 In fact, the densities of states for the ice Ih and ICmodels, which are respectively given disorder must bedestabilization(excitation) of the local potentials. in refs 18 and 35, have been used for this calculation. The This excitation energy for H2180 is larger than that for H2160, harmonic heat capacities of the isotopic ice can be evaluated by because the zero-point energies for H2180 at a stable ordered accounting for the isotopic frequency shift of each vibrational potential are lower than those for H2160. Therefore, a positive mode. In the present case, these frequency shifts have simply heavy oxygen isotope effect on the heat capacities is expected been evaluated by the following procedure. For the translational also from such orientational disordering processes. modes, the vibrationalfrequenciesof heavy oxygen water undergo There is no significant gap of Cp(H2180)- Cp(H2160)between a red shift by the ratio of ( 18/20)1/2. For the librational modes, ice and liquid water. At 0 OC,the C,, of water is very close to the frequency would shift by the square root of Zii(H2l6O)/ the C,.l The term &VT/K, of H2180 is very similar to that of Zii(H2180)depending on the rotational axis, where Zit is the moment H2160 at temperatures from 0 to 20 0C,25*37so the C,, difference of inertia along one principal axis ( i ) of a water molecule. of liquid water drawn in Figure 2 is essentially the same as the However, a singleZii(H2160)/Zii(H~180) value, which is determined C, difference.
4
Heat Capacities of Heavy Oxygen Water Recently, the vibrational density of states has been calculated for a rapidly quenched water as a function of vibrational f r e q u e n ~ i e s .The ~ ~ density exhibits a marked gap a t 300 cm-1 between the translational and librational modes. This feature resembles closely the frequency distribution of ice lattice vibration. The isotope effect on any harmonic translational mode does not dominantly contribute to the quantities CP(H2l8O) - CP(H2l60) at high temperature because of their low frequencies as discussed above. However, it possibly has a strong anharmonic coupling with the librational motions to some extent through the formation of the hydrogen bonds, as in the case of ordinary ice. This coupling would provide a heavy oxygen isotope effect on the librational motions. Compared with ice, the large heat capacities of liquid water have been interpreted in terms of the consecutive hydrogen bond rupture in liquid water. NCmethy and Scheraga proposed five kinds of hydrogen-bonded and nonbonded molecule^.^ These species have different energy levels due to the hydrogen-bonding stabilization. The transitions amoqg these energy levels, which correspond to the formation and the cleavage of hydrogen bonds, are induced by temperature variation. This model reproduces properly several thermodynamic quantities of liquid water? Such energy levels are anticipated to shift by isotope substitutions39 because of the difference of the zero-point vibrational energies. The isotope effect on the enthalpy of vaporization of water is interpreted in terms of such shifts of the energy levels.40 Actually, the difference in the enthalpies of vaporization between H2180 and H2I60 has been observed to be 77 J mol-' a t the melting point.30 If we suppose five energy levels separated by 2.76 kJ mol-' and the fraction of unbroken hydrogen bonds (XHB),0.528, as have been proposed by Nbmethy and Scheraga? the difference 77 J mol-' can be reproduced by a shift of the dissociation energy of the hydrogen bonds by 5%. Assuming the temperaturevariation of the fraction (dXHB/dn, -0.004K-l, the heat capacitydifference of 0.6 J K-I mol-I is derived from this isotopic modification of the energy levels. In this way, the consecutive rupture of hydrogen bonds in liquid water gives an additional positive component to Cp(HPO) Cp(H2I60) through the energy level shifts. At the same time, however, it effectively cuts the anharmonic coupling between the translational and librational modes in which the hydrogen bonds play an important role. Therefore, both of the effects on CP(H2l8O)- Cp(H2I60) compensate each other. This seems to be the reason why there is no significant jump of Cp(H2180) CP(H2l60)at the melting point.
Conclusions Heat capacities of 180-enriched water have been measured at temperatures from 9 to 300 K. The enthalpy of fusion and the triple point temperature of pure (180)waterhave been determined to be 6.029f 0.004 kJ mol-' and 273.46 f 0.01 K, respectively. The heat capacity difference between H2180 ice and H2160 ice has been analyzed on the basis of frequency distribution of the lattice vibrations in ice IC. Below 100 K, the difference is interpreted well by the heavy oxygen isotope effect on the translational vibrations. Above the glass transition temperature, it is necessary to take into account the anharmonic coupling between the translational and the librational modes through the hydrogen bonds and the excitation of the orientational disorder. In the liquid water, the anharmonic coupling would contribute
The Journal of Physical Chemistry, Vol. 97, No. 26, 1993 6901 to thequantities Cp(H2180)- CP(H2l60)tosomeextent. However, the consecutive disruption of the hydrogen bonds makes this coupling weak. An additional heavy oxygen isotope effect by this consecutive disruption of hydrogen bonds complements the decrease of the coupling term in CP(H2l80)- CP(H2l60). An analysis by computer simulation of the isotope effects would help further understanding.
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