- Email: [email protected]
Heat capacity and phase transitions of scandium ethanoate
M-2791
J. Chem. Thermodynamics 1992, 24, 1189-1196
H e a t c a p a c i t y and p h a s e t r a n s i t i o n s o f scandium ethanoate a Y O U S U K E OHTA, T A K A S U K E MATSUO, and HIROSHI SUGA b
Department of Chemistry and Microcalorimetry Research Center, Faeulty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received 30 March 1992) The heat capacity of scandium ethanoate, 8 c ( C H 3 C 0 2 ) 3 , has been measured with an adiabatic calorimeter at temperatures between 11 K and 300 K. Two phase transitions were found: a firstorder transition at T = 59.0 K with A t r s H m = 213 J'mo1-1 and Atr~Sm = 3.70J'K 1.mol-1, and a higher-order transition at T = 167.0K with A t r s n m = 536J'mol 1 and AtrsSm = 3.81 J-K 1.mol 1. A mechanism for the phase transitions is proposed in which rotational disorder of methyl groups and their interaction play the main role. Standard thermodynamic functions have been calculated from the heat capacities and tabulated for selected temperatures between 5 K and 300 K.
1. Introduction S c a n d i u m e t h a n o a t e , Sc(CH3C02)3, crystallizes in a structure of h e x a g o n a l s y m m e t r y in which p o l y m e r i c c o l u m n s of the ionic c o o r d i n a t i o n - b o n d e d linear m a c r o m o l e c u l e s {Sc(CH3CO2)3}~ are a r r a n g e d in closest packing, m As s h o w n in figure 1, three e t h a n o a t e ions form an e q u i l a t e r a l triangle b r i d g i n g two a d j a c e n t s c a n d i u m ions. T h e linear chain thus f o r m e d b y cations a n d a n i o n s is c h a r a c t e r i z e d by the ionic central core of ScO6 o c t a h e d r a a n d a n electrically neutral sheath of m e t h y l groups. T h e p r i m a r y chemical b o n d s of trivalent s c a n d i u m ion a n d three b i d e n t a t e e t h a n o a t e ions are b o t h satisfied within the linear chain. Therefore the m a i n i n t e r a c t i o n which the c o l u m n s have with each o t h e r is weak van d e r W a a l s i n t e r a c t i o n s a m o n g the i n t e r c o l u m n a r m e t h y l groups. This results in the closest p a c k i n g of the p o l y m e r i c columns. (2) I n view of the possibility o f interesting collective b e h a v i o u r of w e a k l y interacting m e t h y l groups, we s t u d i e d the c o m p o u n d by lowtemperature calorimetry.
2. Experimental C o m m e r c i a l l y a v a i l a b l e s c a n d i u m e t h a n o a t e was purified b y recrystallization from 2.9 m o l ' d m -3 C H 3 C O 2 H ( a q ) . A s a m p l e crystallizing as a colourless p o w d e r was dried in vacuo to a c o n s t a n t mass. C h e m i c a l analysis gave the following mass fractions: C, 0.325 (0.3245); H, 0.042 (0.0408). T h e values in parentheses were c a l c u l a t e d for the s t o i c h i o m e t r y of Sc(CH3CO2) 3. Contribution No. 53 from the Microcalorimetry Research Center. 0021 9614/92/111189 + 08 $08.00/0
© 1992 Academic Press Limited
1190
Y. OHTA, T. MATSUO, AND H. SUGA
FIGURE 1. A part of the structure of Se(CH3CO2) 3 (from reference 1). The dosed ellipsoids denote the carbons in the methyl groups which we focus on.
The heat-capacity measurements were performed in the temperature region 11 K to 300 K by the use of an adiabatic calorimeter33) The mass of the calorimetric sample was 2.0616 g. It was sealed in a gold-plated copper sample cell of the calorimeter in a helium atmosphere. The heat capacity of the sample was 0.557 of the gross heat capacity at T = 20 K, 0.248 at T = 100 K, and 0.265 at T = 300 K. The heat capacity of the empty cell was measured in a separate experiment and expressed as a polynomial in temperature. The heat capacity of the helium gas sealed in the cell for better thermal conduction was also corrected for by taking the molar heat capacity of He as 1.5R. The temperature increment of a heat-capacity determination was ~ 2 K in the normal region and ~ 0.2 K near the transition temperature.
3. Results and discussion The heat capacities are plotted in figure 2 and the numerical values are given in table 1. Two peaks due to phase transitions occurred at T = 59.0 K and 167.0 K. The former was a first-order phase transition, as the peak shape shows. The time required for the calorimeter to reach thermal equilibrium after heating was 10 min to 15 min at the peak of the phase transition, compared with a normal equilibration time < 5 min. The long endothermic drift is a characteristic of some of first-order p h a s e transitions. The latter (the T = 167 K transition) was a higher-order transition. The heat capacity was measured by small steps of A T ~ 0.2 K near the peak as shown in figure 3. No infinite heat capacity was observed even with this small step. For determination of the transition enthalpies and entropies, the normal heat capacity was calculated by interpolation using a polynomial in temperature that reproduced the experimental points to 0 . 0 0 1 . C o , m in the temperature interval 13 K to 52 K and to _0.01 "Cp, m in the interval 178 K to 300 K. The enthalpy of the first-order
1191
HEAT CAPACITY AND PHASE TRANSITIONS O F S c ( C H a C O 2 ) 3 I
I
I
I
I
I 200
I 250
200
oOOO°° ooo°
I
-6 150
ooOO°°
T ~d ~100
50
0
I 100
50
I 150 T/K
300
F I G U R E 2. Molar heat capacity of Sc(CH3CO2) 3. Two series of measurement are distinguished at the lower transition point by the open and closed circles.
190
185
i
o
O
o
o
~
180
o o
175 160
I
165
170
175
T/K
F I G U R E 3. Molar heat capacity of S c ( C H a C O 2 ) 3 n e a r the higher-order transition.
T A B L E 1. Experimental molar heat capacities of Sc(CH3CO2) 3. R = 8.31441J.K -l.mol 1
T/K 11.49 12.76 13.89 14.93 15.87 16.73 17.57 18.40 19.17 19.91 13.07 14.01 14.91 15.78 16.60 17.53 18.60 19.63 20.58 21.47 22.35 23.21 24.04 24.92 25.88 27.15 28.63 29.84 31.00 32.29 33.62 34.99 36.58 38.44 40.23 41.91 43.48 44.96 46.44 47.90 49.32 50.70 52.09 53.48 54.82 56.21 57.67
Cp,~/R AT/K
T/K
Cp.m/R AT/K
series 1 0.630 0.824 1.029 1.227 1.415 1.588 1.765 1.951 2.118 2.300 series 2 0.879 1.049 1.222 1.398 1.559 1.758 2.005 2.232 2.458 2.658 2.861 3.062 3.259 3.469 3.701 4.013 4.371 4.663 4.952 5.274 5.610 5.953 6.352 6.822 7.271 7.690 8.088 8.463 8.844 9.218 9.591 9.972 10.349 10.720 11.147 11.750 14.504
58.98 60.31 61.79 63.30 64.83
22.96 12.252 11.808 11.881 12.04,7 series 3 9.266 9.738 10.207 10.675 11.184 11.924 16.420 20.86 12.109 11.813 11.877 12.024 12.167 12.362 12.647 12.854 13.140 13.397 13.664 13.892 14.146 14.395 14.587 14.804 15.005 15.232 15.507 15.823 16.137 16.424 16.713 16.963 17.212 17.459 17.689 17.915 18.155 18.398 18.644 18.871 19.095 19.331 19.557
1.3646 1.1302 1.0925 0.9715 0.8859 0.8252 0.8399 0.7889 0.7492 0.7129 0.9699 0.8811 0.9083 0.8392 0.7900 1.0662 1.0666 0.9832 0.9174 0.8675 0.8840 0.8402 0.8021 0.9567 0.9680 1.5566 1.4168 0.9871 1.3339 1.2485 1.4112 1.3267 1.8441 1.8615 1.7289 1.6243 1.5150 1.4463 1.4979 1.4380 1.3894 1.3640 1.4179 1.3599 1.3125 1.4745 1.4407
48.05 49.89 51.63 53.30 54.91 56.46 57.89 59.16 60.45 61.82 63.17 64.51 65.84 67.14 68.73 70.73 72.83 74.88 76.88 78.84 80.76 82.65 84.52 86.37 88.21 90.15 92.71 95.75 98.72 101.64 104.51 107.34 110.13 112.90 115.63 118.34 121.18 124.17 127.13 130.06 132.98 135.87 138.74
1.1709 1.4853 1.4762 1.5390 1.5138 1.8939 1.7765 1.6958 1.6426 1.5699 1.5265 1.3331 1.2050 1.3703 1.3558 1.3467 1.3329 1.3145 1.2925 1.8680 2.127 2.071 2.022 1.9794 1.9368 1.9033 1.8742 1.8587 1.8420 1.8321 2.045 3.066 3.001 2.943 2.893 2.845 2.808 2.776 2.745 2.718 2.692 2.999 2.970 2.946 2.921 2.901 2.883 2.864
T/K 141.60 144.44 147.27 150.23 153.32 156.40 159.46 162.49 165.51 168.52 171.55 174.58 177.61 180.78 184.07 187.36 190.65 193.92 197.18 200.44 203.69 206.93 210.16 213.52 217.00 220.48 223.95 227.41 230.87 237.76 241.21 244.64 248.18 251.85 255.51 259.17 262.82 266.46 270.10 273.73 277.37 281.00 284.75 288.59 292.42 296.24 300.07
C~,m/R AT/K 19.767 20.02 20.22 20.47 20.75 21.03 21.37 21.79 22.39 21.75 21.24 21.15 21.18 21.30 21.47 21.60 21.76 21.91 22.09 22.26 22.44 22.61 22.77 22.95 23.12 23.33 23.51 23.72 23.97 24.29 24.48 24.66 24.81 25.03 25.24 25.41 25.66 25.79 26.05 26.23 26.48 26.68 26.82 27.12 27.31 27.55 27.72
2.848 2.834 2.819 3.101 3.082 3.065 3.046 3.028 3.001 3.020 3.032 3.036 3.028 3.300 3.293 3.285 3.278 3.267 3.263 3.255 3.240 3.236 3.231 3.489 3.481 3.472 3.470 3.461 3.455 3.447 3.440 3.429 3.674 3.668 3.660 3.658 3.654 3.641 3.641 3.639 3.63t 3.650 3.857 3.838 3.828 3.832 3.831 4
21.07 21.06 21.03 21.06 21.17 21.18
0.1992 0.1989 0.1987 0.1988 0.1986 0.1981
Experimental values around the higher-order phase transition
154.44 154.64 154.84 155.05 155.25
series 4 20.84 20.81 20.92 20.90 20.89
0.2003 0.2000 0.2004 0.2005 0.1998
155.45 155.65 155.85 156.05 156.25 156.45
20.93 20.97 20.90 20.95 20.99 21.04
0.1995 0.1996 0.1998 0.1993 0.1994 0.1992
156.65 156.85 157.05 157.25 157.45 157.65
TABLE
1--continued
T/K
Cp,m/R
AT/K
T/K
C.p,~/R AT/K
T/K
157.85 158.05 158.24 158.44 158.64 158.84 159.04 159.24 159.44 159.64 159.83 160.03 160,23 160.43 160.63 160.82 161.02
21.14 21.25 21.22 21.29 21.26 21.32 21.33 21.30 21.36 21.37 21.39 21.40 21.44 21.48 21.49 21.51 21.48 series 5 21.39 21.43 21.46 21.48 21.52 21.54 21.54 21.54 21.55 21.62 21.68 21.67 21.69 21.74 21.77 21.79 21.85 21.89 21.92 21.96 21.95 22.02 22.03 22.09 22.11 22.15 22.23 22.31 22.31 22.32 22.40 22.44 22.47 22.56 22.60 22.74 22,89 22.63 22.23 22.03 21.93
0.1984 0.1983 0.1979 0.1980 0.198l 0.1980 0.1979 0.1975 0.1972 0.1971 0.1970 0.1971 0.1969 0.1968 0.1968 0.1966 0.1962
167.94 168.14 168.33 168.53 168.72 168.92 169.11 169.31 169.51 169.70 169.90 170.09 170.29 170.48 170.68 170.88 171.07 171.27 171.47 171.67 171.86 172.06 172.26 172.45 172.65 172.85 173.04 173.24 173.44 173.64 173.83 174.03 174.23 174.42 174.62 174,81 175.01 175.20 175.40 175.59 175.79 175.98 176.18 176.37 176.57 176.76 176.96 177.15 177.35 177.54 177.73 177.93 178.12 178.31 178.70 178.90 179.09 179.28 179.48
21.81 21.73 21.68 21.61 21.56 21.51 21.48 21.44 21.41 21.40 21.35 21.35 21.32 21.29 21.26 21.30 21.25 21.29 21.28 21.24 21.16 21.14 21.20 21.20 21.20 21.19 21.22 21.21 21.19 21.~7 21.20 21.17 21.17 21.20 21.16 21.20 21.18 21.17 21.16 21.19 21.16 21.16 21.17 21.16 21.19 21,20 21.18 21.21 21.21 21.20 21.19 21.16 21.15 21.21 21.23 21.23 21.20 21.31 21.24
179.67 179.86 180.06 180.46 180.65 180.84 181.03 181.23
159.90 160.10 160.30 160.50 160.70 160.89 161.09 161.29 161.49 161.68 161.88 162.08 162.27 162.47 162.67 162.86 163.06 163.25 163.45 163.65 163.84 164.04 164.23 164.43 164.62 164.82 165.01 165.21 165.40 165.60 165.79 165.99 166.18 166.38 166.57 166.77 166.96 167.16 167.35 167.55 167.74
0.1973 0.1972 0.1971 0.1969 0,1968 0.1965 0.1964 0.1963 0.1963 0.1962 0.1960 0.1958 0.1956 0.1953 0.1954 0.1953 0.1951 0.1950 0.1949 0.1947 0.1946 0.1944 0.1944 0.1942 0.1941 0.1940 0.1937 0.1935 0.1933 0.1930 0.1927 0.1934 0.1942 0.1947 0.1940 0.1937 0.1936 0.1943 0.1952 0.1945 0.1945
0.1945 0.1947 0.1941 0.1939 0.1942 0.1946 0.1948 0.1957 0.1950 0.1949 0.1940 0,1939 0.1942 0.1942 0.1949 0.1962 0.1961 0.1960 0.1961 0.1960 0.1963 0.1959 0.1958 0.1958 0.1956 0.1957 0.1955 0.1956 0.1957 0.1960 0.1958 0.1958 0.1955 0.1951 0.1945 0.1943 0.1944 0.1943 0.1942 0.1942 0.1944 0.1942 0.1941 0.1938 ~ 0.1936 0.1935 0.1935 0.1933 0.1933 0.1932 0.1930 0.1930 0.1931 0.1930 0.1929 0.1927 0.1932 0.1927 0.1925
165.06 165.15 165.23 165.31 165.40 165.48 165.56 165.65 165.73 165.81 165.89 165.98 166.06 166.14 166.23 166.31 166.39 166.47 166.56 166.64 166.72 166.80 166.89 166.97 167.05 167.13 167.21 167.30 167.38 167.46 167.55 167.63 167.71 167.79 167.88 167.96 168.04 168.12 168.21 168.29 168.38 168.46 168.54 168.63 168.71 168.80 168.88 168.96 169.05
G,m/R AT/K 21.30 21.31 21.27 21.29 21.35 21.34 21.31 21.27 series 6 22.19 22.21 22.22 22.29 22.27 22.29 22.30 22.25 22.22 22.36 22.40 22.45 22.38 22.46 22.50 22.48 22.40 22.60 22.55 22.61 22.60 22.77 22.87 22.82 22.71 22.52 22.32 22.20 22.12 22.08 21.92 21.86 21.80 21.77 21.79 21.77 21.72 21.71 21.70 21.59 21.64 21.62 21.63 21.63 21.60 21.46 21.42 21.47 21.41
0.1924 0.1923 0.1926 0.1915 0.1914 0.1913 0.1913 0.1914 0.0824 0.0825 0.0828 0.0825 0.0825 0.0824 0.0822 0.0824 0.0824 0.0820 0.0821 0.0822 0.0824 0.0820 0.0817 0.0820 0.0816 0.0814 0.0815 0.0814 0.0817 0.0816 0.0819 0.0816 0.0817 0.0817 0.0817 0.0819 0.0823 0.0818 0.0824 0.0822 0.0822 0.0819 0.0818 0.0822 0.0817 0.0822 0.0830 0.0830 0.0826 0.0846 0.0830 0.0831 0.0825 0.0834 0.0827 0.0824 0.0821
Y. OHTA, T. MATSUO, AND H. SUGA
1194 I
I
50
100
I
I
I 0
'7 E
.el
150
200
T/K
FIGURE 4. Excess molar entropy associated with the transitions in Sc(CH3CO2) 3.
transition was calculated by summing the Joule energies supplied to the sample and cell in a series of measurement covering the transition, and subtracting the enthalpy increment of the empty cell and base-line contribution. The entropy change was similarly calculated by summing the Joule energies divided by T. For the higherorder transition, integration of ACp, m and ACp, m/T gave the transition enthalpy and entropy, respectively, where ACp, m is the excess molar heat capacity. Transition enthalpies and entropies thus determined are tabulated in table 2. Two determinations made on the phase transition at T = 59 K gave 3.696 and 3.701 for AtrsSm/(J-K-l'mol-1), and 213.0 and 213.3 for AtrsHm/(J.mo1 1). The difference between the two measurements was insignificant and only the mean values are given in table 2. Figure 4 shows the temperature dependence of the excess molar entropies associated with the transitions. In this figure one confirms that a discontinuous increase of the entropy occurs at the first-order transition, with a small gradual part below the transition temperature which amounts to about 1/4 of the total entropy change of this phase transition. For the phase transition at T -- 167 K, the entropy increases without discontinuity. The excess heat capacity above the transition temperature (figure 3) is due to local ordering and a characteristic of a critical phase TABLE 2. Thermodynamicquantities for the phase transitions in Sc(CH3CO2) 3
First-order transition Higher-order transition
Ttrs/K
AtrsHm/(J'mo1-1)
AtrsSm/(J'K1.mo1-1)
59.0 167.0
2.13.102 5.36.102
3.70 3.81
H E A T C A P A C I T Y A N D P H A S E T R A N S I T I O N S O F Sc(CH3CO2) 3
1195
)
I
k O
F I G U R E 5. Two types of equivalent orientations of the methyl groups in vertical and horizontal mirror planes.
S c ( C H 3 C O 2 )
3.
-
-
-
, The
T A B L E 3. Molar thermodynamic functions of Sc(CH3CO2) 3. R = 8 . 3 1 4 4 1 J . K - l . m o l 1, ~mo = AoSm T o AoHm/T r o
T/K 5 10 15 20 25
C~,m/RATH~,/RT ATS~,/R ~m/R 0.0607 0.437 1.236 2.310 3.485
0.015 0.115 0.344 0.699 1.137
0.0205 0.154 0.469 0.969 1.609
0.0052 0.0397 0.125 0.270 0.472
T/K 30 35 40 45 50
C~,m/RA~H~,/RT A~S~/R 4.713 5.959 7.209 8.471 9.775
1.630 2.160 2.713 3.282 3.866
2.352 3.173 4.050 4.972 5.931
~P~/R 0.722 1.013 1.337 1.689 2.065
first-order phase transition at 59.0 K 70 80 90 100 110 120 130 140 150 160 170 180 190
12.768 14.042 15.207 16.260 17.205 18.063 18.864 19.647 20.47 21.40 21.34 21.29 21.74
6.336 7.221 8.045 8.814 9.535 10.210 10.846 11.446 12.020 12.575 13.124 13.573 13.991
10.121 11.910 13.633 15.290 16.885 18.419 19.897 21.32 22.71 24.06 25.38 26.60 27.76
3.785 4.689 5.588 6.476 7.350 8.209 9.052 9.877 10.687 11.481 12.260 13.023 13.768
200 210 220 230 240 250 260 270 273.15 280 290 298.15 300
22.24 22.76 23.30 23.85 2&40 24.94 25.49 26.04 26.21 26.59 27.17 27.65 27.77
14.391 14.777 15.152 15.518 15.877 16.228 16.574 16.914 17.021 17.250 17.582 17.851 17.912
28.89 29.98 31.06 32.10 33.13 34.14 35.13 36.10 36.40 37.05 38.00 38.76 38.93
14.496 15.207 15.903 16.585 17.253 17.908 18.551 19.183 19.380 19,805 20.42 20.91 21.02
1196
Y. OHTA, T. MATSUO, AND H. SUGA
transition. The entropy associated with this fluctuation effect is 0.42 J. K - 1 . tool-1 which is 0.11 of the entropy change of this phase transition. The molar transition entropy AtrsSm is related to the ratio Wn/W0 of the number of the allowed equiprobable orientations of a molecule in the high- and lowtemperature phases by the equation: AtrsSm = R" ln(Wh/W3. This supposes that the phase transition is an order-disorder type which is reasonable for the present case in view of large value (7.51 J. K -1. mo1-1) of the total transition entropy. As can be seen in figure 1, all methyl groups are located at the intersection of the two mirror planes. Because of this site symmetry and the threefold rotational symmetry of methyl groups, each methyl group should be allowed to have at least two equivalent orientations. There are two possibilities for this disorder depending on which of the mirror planes (vertical and horizontal) relates the alternative orientations of a methyl group as shown in figure 5. Both pairs satisfy the symmetry, but their energies are in general different and if one of them is realized, the other will not correspond to the actual structure. There are three ethanoate groups, i.e. three methyl groups in Sc(CH3CO2) 3. Assuming that the methyl groups are ordered in the low-temperature phase and disordered in the high-temperature phase, we may put W1 = 1 and Wh = 23. Consequently Atrs Sm(calc) = R ' ln(23) ~ 17.3 J" K - 1. mol 1. This value, however, is 2.3 times as large as the sum of the molar transition entropies. The difference, 9.8 J. K 1. mol 1, cannot be explained by a change of the base-line heat capacity within a reasonable range. A possible explanation for this discrepancy is that the methyl groups are either disordered to some extent in the low-temperature phase or ordered to some extent in the high-temperature phase. These should be amenable to experimental tests by neutron-diffraction and scattering experiments. Standard molar thermodynamic functions of Sc(CH3CO2)3(cr) were calculated from the heat capacities and are presented in table 3. For the calculation the heat capacities were extrapolated below 15 K by the use of a polynomial in temperature of the form: Cp, m = a T 3 + b T S + c T 7.
Parameters a, b, and c were determined so as to reproduce the experimental points up to T = 20 K. For T > 15 K, polynomial interpolation functions were employed to represent the heat capacities, except in the first-order phase-transition regions where direct numerical integration was performed. We wish to thank Mr M. Okumiya and Mrs K. Hayashi for the chemical ana,lysis of the sample. This work was financed partly by the Japanese Ministry of Education. REFERENCES 1. Fuchs, R.; Strfihle,J. Z. Naturforsch. B 1984, 39, 1662. 2. O'Keeffe, M.; Andersson, S. Acta Crystallogr. 1977, A33, 914. 3. Matsuo, T.; Suga, H. Thermochim. Acta 1985, 88, 149.
J. Chem. Thermodynamics 1992, 24, 1189-1196
H e a t c a p a c i t y and p h a s e t r a n s i t i o n s o f scandium ethanoate a Y O U S U K E OHTA, T A K A S U K E MATSUO, and HIROSHI SUGA b
Department of Chemistry and Microcalorimetry Research Center, Faeulty of Science, Osaka University, Toyonaka, Osaka 560, Japan (Received 30 March 1992) The heat capacity of scandium ethanoate, 8 c ( C H 3 C 0 2 ) 3 , has been measured with an adiabatic calorimeter at temperatures between 11 K and 300 K. Two phase transitions were found: a firstorder transition at T = 59.0 K with A t r s H m = 213 J'mo1-1 and Atr~Sm = 3.70J'K 1.mol-1, and a higher-order transition at T = 167.0K with A t r s n m = 536J'mol 1 and AtrsSm = 3.81 J-K 1.mol 1. A mechanism for the phase transitions is proposed in which rotational disorder of methyl groups and their interaction play the main role. Standard thermodynamic functions have been calculated from the heat capacities and tabulated for selected temperatures between 5 K and 300 K.
1. Introduction S c a n d i u m e t h a n o a t e , Sc(CH3C02)3, crystallizes in a structure of h e x a g o n a l s y m m e t r y in which p o l y m e r i c c o l u m n s of the ionic c o o r d i n a t i o n - b o n d e d linear m a c r o m o l e c u l e s {Sc(CH3CO2)3}~ are a r r a n g e d in closest packing, m As s h o w n in figure 1, three e t h a n o a t e ions form an e q u i l a t e r a l triangle b r i d g i n g two a d j a c e n t s c a n d i u m ions. T h e linear chain thus f o r m e d b y cations a n d a n i o n s is c h a r a c t e r i z e d by the ionic central core of ScO6 o c t a h e d r a a n d a n electrically neutral sheath of m e t h y l groups. T h e p r i m a r y chemical b o n d s of trivalent s c a n d i u m ion a n d three b i d e n t a t e e t h a n o a t e ions are b o t h satisfied within the linear chain. Therefore the m a i n i n t e r a c t i o n which the c o l u m n s have with each o t h e r is weak van d e r W a a l s i n t e r a c t i o n s a m o n g the i n t e r c o l u m n a r m e t h y l groups. This results in the closest p a c k i n g of the p o l y m e r i c columns. (2) I n view of the possibility o f interesting collective b e h a v i o u r of w e a k l y interacting m e t h y l groups, we s t u d i e d the c o m p o u n d by lowtemperature calorimetry.
2. Experimental C o m m e r c i a l l y a v a i l a b l e s c a n d i u m e t h a n o a t e was purified b y recrystallization from 2.9 m o l ' d m -3 C H 3 C O 2 H ( a q ) . A s a m p l e crystallizing as a colourless p o w d e r was dried in vacuo to a c o n s t a n t mass. C h e m i c a l analysis gave the following mass fractions: C, 0.325 (0.3245); H, 0.042 (0.0408). T h e values in parentheses were c a l c u l a t e d for the s t o i c h i o m e t r y of Sc(CH3CO2) 3. Contribution No. 53 from the Microcalorimetry Research Center. 0021 9614/92/111189 + 08 $08.00/0
© 1992 Academic Press Limited
1190
Y. OHTA, T. MATSUO, AND H. SUGA
FIGURE 1. A part of the structure of Se(CH3CO2) 3 (from reference 1). The dosed ellipsoids denote the carbons in the methyl groups which we focus on.
The heat-capacity measurements were performed in the temperature region 11 K to 300 K by the use of an adiabatic calorimeter33) The mass of the calorimetric sample was 2.0616 g. It was sealed in a gold-plated copper sample cell of the calorimeter in a helium atmosphere. The heat capacity of the sample was 0.557 of the gross heat capacity at T = 20 K, 0.248 at T = 100 K, and 0.265 at T = 300 K. The heat capacity of the empty cell was measured in a separate experiment and expressed as a polynomial in temperature. The heat capacity of the helium gas sealed in the cell for better thermal conduction was also corrected for by taking the molar heat capacity of He as 1.5R. The temperature increment of a heat-capacity determination was ~ 2 K in the normal region and ~ 0.2 K near the transition temperature.
3. Results and discussion The heat capacities are plotted in figure 2 and the numerical values are given in table 1. Two peaks due to phase transitions occurred at T = 59.0 K and 167.0 K. The former was a first-order phase transition, as the peak shape shows. The time required for the calorimeter to reach thermal equilibrium after heating was 10 min to 15 min at the peak of the phase transition, compared with a normal equilibration time < 5 min. The long endothermic drift is a characteristic of some of first-order p h a s e transitions. The latter (the T = 167 K transition) was a higher-order transition. The heat capacity was measured by small steps of A T ~ 0.2 K near the peak as shown in figure 3. No infinite heat capacity was observed even with this small step. For determination of the transition enthalpies and entropies, the normal heat capacity was calculated by interpolation using a polynomial in temperature that reproduced the experimental points to 0 . 0 0 1 . C o , m in the temperature interval 13 K to 52 K and to _0.01 "Cp, m in the interval 178 K to 300 K. The enthalpy of the first-order
1191
HEAT CAPACITY AND PHASE TRANSITIONS O F S c ( C H a C O 2 ) 3 I
I
I
I
I
I 200
I 250
200
oOOO°° ooo°
I
-6 150
ooOO°°
T ~d ~100
50
0
I 100
50
I 150 T/K
300
F I G U R E 2. Molar heat capacity of Sc(CH3CO2) 3. Two series of measurement are distinguished at the lower transition point by the open and closed circles.
190
185
i
o
O
o
o
~
180
o o
175 160
I
165
170
175
T/K
F I G U R E 3. Molar heat capacity of S c ( C H a C O 2 ) 3 n e a r the higher-order transition.
T A B L E 1. Experimental molar heat capacities of Sc(CH3CO2) 3. R = 8.31441J.K -l.mol 1
T/K 11.49 12.76 13.89 14.93 15.87 16.73 17.57 18.40 19.17 19.91 13.07 14.01 14.91 15.78 16.60 17.53 18.60 19.63 20.58 21.47 22.35 23.21 24.04 24.92 25.88 27.15 28.63 29.84 31.00 32.29 33.62 34.99 36.58 38.44 40.23 41.91 43.48 44.96 46.44 47.90 49.32 50.70 52.09 53.48 54.82 56.21 57.67
Cp,~/R AT/K
T/K
Cp.m/R AT/K
series 1 0.630 0.824 1.029 1.227 1.415 1.588 1.765 1.951 2.118 2.300 series 2 0.879 1.049 1.222 1.398 1.559 1.758 2.005 2.232 2.458 2.658 2.861 3.062 3.259 3.469 3.701 4.013 4.371 4.663 4.952 5.274 5.610 5.953 6.352 6.822 7.271 7.690 8.088 8.463 8.844 9.218 9.591 9.972 10.349 10.720 11.147 11.750 14.504
58.98 60.31 61.79 63.30 64.83
22.96 12.252 11.808 11.881 12.04,7 series 3 9.266 9.738 10.207 10.675 11.184 11.924 16.420 20.86 12.109 11.813 11.877 12.024 12.167 12.362 12.647 12.854 13.140 13.397 13.664 13.892 14.146 14.395 14.587 14.804 15.005 15.232 15.507 15.823 16.137 16.424 16.713 16.963 17.212 17.459 17.689 17.915 18.155 18.398 18.644 18.871 19.095 19.331 19.557
1.3646 1.1302 1.0925 0.9715 0.8859 0.8252 0.8399 0.7889 0.7492 0.7129 0.9699 0.8811 0.9083 0.8392 0.7900 1.0662 1.0666 0.9832 0.9174 0.8675 0.8840 0.8402 0.8021 0.9567 0.9680 1.5566 1.4168 0.9871 1.3339 1.2485 1.4112 1.3267 1.8441 1.8615 1.7289 1.6243 1.5150 1.4463 1.4979 1.4380 1.3894 1.3640 1.4179 1.3599 1.3125 1.4745 1.4407
48.05 49.89 51.63 53.30 54.91 56.46 57.89 59.16 60.45 61.82 63.17 64.51 65.84 67.14 68.73 70.73 72.83 74.88 76.88 78.84 80.76 82.65 84.52 86.37 88.21 90.15 92.71 95.75 98.72 101.64 104.51 107.34 110.13 112.90 115.63 118.34 121.18 124.17 127.13 130.06 132.98 135.87 138.74
1.1709 1.4853 1.4762 1.5390 1.5138 1.8939 1.7765 1.6958 1.6426 1.5699 1.5265 1.3331 1.2050 1.3703 1.3558 1.3467 1.3329 1.3145 1.2925 1.8680 2.127 2.071 2.022 1.9794 1.9368 1.9033 1.8742 1.8587 1.8420 1.8321 2.045 3.066 3.001 2.943 2.893 2.845 2.808 2.776 2.745 2.718 2.692 2.999 2.970 2.946 2.921 2.901 2.883 2.864
T/K 141.60 144.44 147.27 150.23 153.32 156.40 159.46 162.49 165.51 168.52 171.55 174.58 177.61 180.78 184.07 187.36 190.65 193.92 197.18 200.44 203.69 206.93 210.16 213.52 217.00 220.48 223.95 227.41 230.87 237.76 241.21 244.64 248.18 251.85 255.51 259.17 262.82 266.46 270.10 273.73 277.37 281.00 284.75 288.59 292.42 296.24 300.07
C~,m/R AT/K 19.767 20.02 20.22 20.47 20.75 21.03 21.37 21.79 22.39 21.75 21.24 21.15 21.18 21.30 21.47 21.60 21.76 21.91 22.09 22.26 22.44 22.61 22.77 22.95 23.12 23.33 23.51 23.72 23.97 24.29 24.48 24.66 24.81 25.03 25.24 25.41 25.66 25.79 26.05 26.23 26.48 26.68 26.82 27.12 27.31 27.55 27.72
2.848 2.834 2.819 3.101 3.082 3.065 3.046 3.028 3.001 3.020 3.032 3.036 3.028 3.300 3.293 3.285 3.278 3.267 3.263 3.255 3.240 3.236 3.231 3.489 3.481 3.472 3.470 3.461 3.455 3.447 3.440 3.429 3.674 3.668 3.660 3.658 3.654 3.641 3.641 3.639 3.63t 3.650 3.857 3.838 3.828 3.832 3.831 4
21.07 21.06 21.03 21.06 21.17 21.18
0.1992 0.1989 0.1987 0.1988 0.1986 0.1981
Experimental values around the higher-order phase transition
154.44 154.64 154.84 155.05 155.25
series 4 20.84 20.81 20.92 20.90 20.89
0.2003 0.2000 0.2004 0.2005 0.1998
155.45 155.65 155.85 156.05 156.25 156.45
20.93 20.97 20.90 20.95 20.99 21.04
0.1995 0.1996 0.1998 0.1993 0.1994 0.1992
156.65 156.85 157.05 157.25 157.45 157.65
TABLE
1--continued
T/K
Cp,m/R
AT/K
T/K
C.p,~/R AT/K
T/K
157.85 158.05 158.24 158.44 158.64 158.84 159.04 159.24 159.44 159.64 159.83 160.03 160,23 160.43 160.63 160.82 161.02
21.14 21.25 21.22 21.29 21.26 21.32 21.33 21.30 21.36 21.37 21.39 21.40 21.44 21.48 21.49 21.51 21.48 series 5 21.39 21.43 21.46 21.48 21.52 21.54 21.54 21.54 21.55 21.62 21.68 21.67 21.69 21.74 21.77 21.79 21.85 21.89 21.92 21.96 21.95 22.02 22.03 22.09 22.11 22.15 22.23 22.31 22.31 22.32 22.40 22.44 22.47 22.56 22.60 22.74 22,89 22.63 22.23 22.03 21.93
0.1984 0.1983 0.1979 0.1980 0.198l 0.1980 0.1979 0.1975 0.1972 0.1971 0.1970 0.1971 0.1969 0.1968 0.1968 0.1966 0.1962
167.94 168.14 168.33 168.53 168.72 168.92 169.11 169.31 169.51 169.70 169.90 170.09 170.29 170.48 170.68 170.88 171.07 171.27 171.47 171.67 171.86 172.06 172.26 172.45 172.65 172.85 173.04 173.24 173.44 173.64 173.83 174.03 174.23 174.42 174.62 174,81 175.01 175.20 175.40 175.59 175.79 175.98 176.18 176.37 176.57 176.76 176.96 177.15 177.35 177.54 177.73 177.93 178.12 178.31 178.70 178.90 179.09 179.28 179.48
21.81 21.73 21.68 21.61 21.56 21.51 21.48 21.44 21.41 21.40 21.35 21.35 21.32 21.29 21.26 21.30 21.25 21.29 21.28 21.24 21.16 21.14 21.20 21.20 21.20 21.19 21.22 21.21 21.19 21.~7 21.20 21.17 21.17 21.20 21.16 21.20 21.18 21.17 21.16 21.19 21.16 21.16 21.17 21.16 21.19 21,20 21.18 21.21 21.21 21.20 21.19 21.16 21.15 21.21 21.23 21.23 21.20 21.31 21.24
179.67 179.86 180.06 180.46 180.65 180.84 181.03 181.23
159.90 160.10 160.30 160.50 160.70 160.89 161.09 161.29 161.49 161.68 161.88 162.08 162.27 162.47 162.67 162.86 163.06 163.25 163.45 163.65 163.84 164.04 164.23 164.43 164.62 164.82 165.01 165.21 165.40 165.60 165.79 165.99 166.18 166.38 166.57 166.77 166.96 167.16 167.35 167.55 167.74
0.1973 0.1972 0.1971 0.1969 0,1968 0.1965 0.1964 0.1963 0.1963 0.1962 0.1960 0.1958 0.1956 0.1953 0.1954 0.1953 0.1951 0.1950 0.1949 0.1947 0.1946 0.1944 0.1944 0.1942 0.1941 0.1940 0.1937 0.1935 0.1933 0.1930 0.1927 0.1934 0.1942 0.1947 0.1940 0.1937 0.1936 0.1943 0.1952 0.1945 0.1945
0.1945 0.1947 0.1941 0.1939 0.1942 0.1946 0.1948 0.1957 0.1950 0.1949 0.1940 0,1939 0.1942 0.1942 0.1949 0.1962 0.1961 0.1960 0.1961 0.1960 0.1963 0.1959 0.1958 0.1958 0.1956 0.1957 0.1955 0.1956 0.1957 0.1960 0.1958 0.1958 0.1955 0.1951 0.1945 0.1943 0.1944 0.1943 0.1942 0.1942 0.1944 0.1942 0.1941 0.1938 ~ 0.1936 0.1935 0.1935 0.1933 0.1933 0.1932 0.1930 0.1930 0.1931 0.1930 0.1929 0.1927 0.1932 0.1927 0.1925
165.06 165.15 165.23 165.31 165.40 165.48 165.56 165.65 165.73 165.81 165.89 165.98 166.06 166.14 166.23 166.31 166.39 166.47 166.56 166.64 166.72 166.80 166.89 166.97 167.05 167.13 167.21 167.30 167.38 167.46 167.55 167.63 167.71 167.79 167.88 167.96 168.04 168.12 168.21 168.29 168.38 168.46 168.54 168.63 168.71 168.80 168.88 168.96 169.05
G,m/R AT/K 21.30 21.31 21.27 21.29 21.35 21.34 21.31 21.27 series 6 22.19 22.21 22.22 22.29 22.27 22.29 22.30 22.25 22.22 22.36 22.40 22.45 22.38 22.46 22.50 22.48 22.40 22.60 22.55 22.61 22.60 22.77 22.87 22.82 22.71 22.52 22.32 22.20 22.12 22.08 21.92 21.86 21.80 21.77 21.79 21.77 21.72 21.71 21.70 21.59 21.64 21.62 21.63 21.63 21.60 21.46 21.42 21.47 21.41
0.1924 0.1923 0.1926 0.1915 0.1914 0.1913 0.1913 0.1914 0.0824 0.0825 0.0828 0.0825 0.0825 0.0824 0.0822 0.0824 0.0824 0.0820 0.0821 0.0822 0.0824 0.0820 0.0817 0.0820 0.0816 0.0814 0.0815 0.0814 0.0817 0.0816 0.0819 0.0816 0.0817 0.0817 0.0817 0.0819 0.0823 0.0818 0.0824 0.0822 0.0822 0.0819 0.0818 0.0822 0.0817 0.0822 0.0830 0.0830 0.0826 0.0846 0.0830 0.0831 0.0825 0.0834 0.0827 0.0824 0.0821
Y. OHTA, T. MATSUO, AND H. SUGA
1194 I
I
50
100
I
I
I 0
'7 E
.el
150
200
T/K
FIGURE 4. Excess molar entropy associated with the transitions in Sc(CH3CO2) 3.
transition was calculated by summing the Joule energies supplied to the sample and cell in a series of measurement covering the transition, and subtracting the enthalpy increment of the empty cell and base-line contribution. The entropy change was similarly calculated by summing the Joule energies divided by T. For the higherorder transition, integration of ACp, m and ACp, m/T gave the transition enthalpy and entropy, respectively, where ACp, m is the excess molar heat capacity. Transition enthalpies and entropies thus determined are tabulated in table 2. Two determinations made on the phase transition at T = 59 K gave 3.696 and 3.701 for AtrsSm/(J-K-l'mol-1), and 213.0 and 213.3 for AtrsHm/(J.mo1 1). The difference between the two measurements was insignificant and only the mean values are given in table 2. Figure 4 shows the temperature dependence of the excess molar entropies associated with the transitions. In this figure one confirms that a discontinuous increase of the entropy occurs at the first-order transition, with a small gradual part below the transition temperature which amounts to about 1/4 of the total entropy change of this phase transition. For the phase transition at T -- 167 K, the entropy increases without discontinuity. The excess heat capacity above the transition temperature (figure 3) is due to local ordering and a characteristic of a critical phase TABLE 2. Thermodynamicquantities for the phase transitions in Sc(CH3CO2) 3
First-order transition Higher-order transition
Ttrs/K
AtrsHm/(J'mo1-1)
AtrsSm/(J'K1.mo1-1)
59.0 167.0
2.13.102 5.36.102
3.70 3.81
H E A T C A P A C I T Y A N D P H A S E T R A N S I T I O N S O F Sc(CH3CO2) 3
1195
)
I
k O
F I G U R E 5. Two types of equivalent orientations of the methyl groups in vertical and horizontal mirror planes.
S c ( C H 3 C O 2 )
3.
-
-
-
, The
T A B L E 3. Molar thermodynamic functions of Sc(CH3CO2) 3. R = 8 . 3 1 4 4 1 J . K - l . m o l 1, ~mo = AoSm T o AoHm/T r o
T/K 5 10 15 20 25
C~,m/RATH~,/RT ATS~,/R ~m/R 0.0607 0.437 1.236 2.310 3.485
0.015 0.115 0.344 0.699 1.137
0.0205 0.154 0.469 0.969 1.609
0.0052 0.0397 0.125 0.270 0.472
T/K 30 35 40 45 50
C~,m/RA~H~,/RT A~S~/R 4.713 5.959 7.209 8.471 9.775
1.630 2.160 2.713 3.282 3.866
2.352 3.173 4.050 4.972 5.931
~P~/R 0.722 1.013 1.337 1.689 2.065
first-order phase transition at 59.0 K 70 80 90 100 110 120 130 140 150 160 170 180 190
12.768 14.042 15.207 16.260 17.205 18.063 18.864 19.647 20.47 21.40 21.34 21.29 21.74
6.336 7.221 8.045 8.814 9.535 10.210 10.846 11.446 12.020 12.575 13.124 13.573 13.991
10.121 11.910 13.633 15.290 16.885 18.419 19.897 21.32 22.71 24.06 25.38 26.60 27.76
3.785 4.689 5.588 6.476 7.350 8.209 9.052 9.877 10.687 11.481 12.260 13.023 13.768
200 210 220 230 240 250 260 270 273.15 280 290 298.15 300
22.24 22.76 23.30 23.85 2&40 24.94 25.49 26.04 26.21 26.59 27.17 27.65 27.77
14.391 14.777 15.152 15.518 15.877 16.228 16.574 16.914 17.021 17.250 17.582 17.851 17.912
28.89 29.98 31.06 32.10 33.13 34.14 35.13 36.10 36.40 37.05 38.00 38.76 38.93
14.496 15.207 15.903 16.585 17.253 17.908 18.551 19.183 19.380 19,805 20.42 20.91 21.02
1196
Y. OHTA, T. MATSUO, AND H. SUGA
transition. The entropy associated with this fluctuation effect is 0.42 J. K - 1 . tool-1 which is 0.11 of the entropy change of this phase transition. The molar transition entropy AtrsSm is related to the ratio Wn/W0 of the number of the allowed equiprobable orientations of a molecule in the high- and lowtemperature phases by the equation: AtrsSm = R" ln(Wh/W3. This supposes that the phase transition is an order-disorder type which is reasonable for the present case in view of large value (7.51 J. K -1. mo1-1) of the total transition entropy. As can be seen in figure 1, all methyl groups are located at the intersection of the two mirror planes. Because of this site symmetry and the threefold rotational symmetry of methyl groups, each methyl group should be allowed to have at least two equivalent orientations. There are two possibilities for this disorder depending on which of the mirror planes (vertical and horizontal) relates the alternative orientations of a methyl group as shown in figure 5. Both pairs satisfy the symmetry, but their energies are in general different and if one of them is realized, the other will not correspond to the actual structure. There are three ethanoate groups, i.e. three methyl groups in Sc(CH3CO2) 3. Assuming that the methyl groups are ordered in the low-temperature phase and disordered in the high-temperature phase, we may put W1 = 1 and Wh = 23. Consequently Atrs Sm(calc) = R ' ln(23) ~ 17.3 J" K - 1. mol 1. This value, however, is 2.3 times as large as the sum of the molar transition entropies. The difference, 9.8 J. K 1. mol 1, cannot be explained by a change of the base-line heat capacity within a reasonable range. A possible explanation for this discrepancy is that the methyl groups are either disordered to some extent in the low-temperature phase or ordered to some extent in the high-temperature phase. These should be amenable to experimental tests by neutron-diffraction and scattering experiments. Standard molar thermodynamic functions of Sc(CH3CO2)3(cr) were calculated from the heat capacities and are presented in table 3. For the calculation the heat capacities were extrapolated below 15 K by the use of a polynomial in temperature of the form: Cp, m = a T 3 + b T S + c T 7.
Parameters a, b, and c were determined so as to reproduce the experimental points up to T = 20 K. For T > 15 K, polynomial interpolation functions were employed to represent the heat capacities, except in the first-order phase-transition regions where direct numerical integration was performed. We wish to thank Mr M. Okumiya and Mrs K. Hayashi for the chemical ana,lysis of the sample. This work was financed partly by the Japanese Ministry of Education. REFERENCES 1. Fuchs, R.; Strfihle,J. Z. Naturforsch. B 1984, 39, 1662. 2. O'Keeffe, M.; Andersson, S. Acta Crystallogr. 1977, A33, 914. 3. Matsuo, T.; Suga, H. Thermochim. Acta 1985, 88, 149.