Towards an understanding of the heat capacity of liquids. A
simple two state model for molecular association
Claudio A. Cerdeiriña,a Diego González-Salgado,a Luis Romaní,a María
del Carmen Delgado,b,§ Luis A. Torres,b and Miguel Costasc,*
a
Departamento de Física Aplicada, Universidad de Vigo, Facultad de Ciencias del Campus
de Ourense, E-32004, Spain.
b
Departamento de Química, Centro de Investigación y Estudios Avanzados del I.P.N.,
Apdo. Postal 14-740, México D.F. 07000, México.
c
Laboratorio de Termofísica, Departamento de Fisicoquímica, Facultad de Química,
Universidad Nacional Autónoma de México, Cd. Universitaria, México DF 04510, México.
§
Present address: Unidad Queretaro del CINVESTAV, Apdo. Postal 1-708, Queretaro
76001, México
*Corresponding
authors. E-mails: calvarez@uvigo.es
costasmi@servidor.unam.mx (M. Costas)
(C.A.
Cerdeiriña)
and
SUPPORTING INFORMATION
I. Determination of C op,m
Isobaric molar heat capacities C op, m in the 278.15 – 368.15 K temperature range were
determined for pure 3-methyl-3-pentanol (3M3P), 3-ethyl-3-pentanol (3E3P) and 5-methyl5-nonanol (5M5N).
Materials. 3-methyl-3-pentanol with 99 % purity, 3-ethyl-3-pentanol with 98 % purity and
5-methyl-5-nonanol with 97 % purity were from Sigma-Aldrich Chemical Co. 1-Butanol
and toluene (calibrating liquids) were from Fluka with 99.8+ % purity. All chemicals were
dried using 4 nm molecular sieves (from Fluka) and were degassed prior to use.
Procedures. Heat capacities per unit volume were measured with a differential scanning
calorimeter Micro DSC II from Setaram, that has been described in detail in ref S1. The
measurements were performed using the scanning method (scanning rate of 0.25 K min–1).
The calorimeter was calibrated employing toluene and 1-butanol, whose heat capacities
were taken from ref S2. Using this calorimeter, high sensitivity and optimum accuracy are
reached when the working and reference cells are filled with liquids of similar heat
capacities per unit volume. For this reason, the reference cell was filled with 1-butanol
during the measurements. The heat capacities per unit volume were transformed into molar
heat capacities using pure component densities. These densities were measured every 5
degrees using an Anton-Paar vibrating tube densimeter (model DSA–48) calibrated with
water and n-octane as standard fluids. With this procedure, the uncertainty is less than  1 x
10-4 g cm-3. Cubic splines were used to fit the measured densities, so that the isobaric molar
heat capacities can be calculated at any temperature within the working temperature
interval. The errors associated with the determination of the densities and with the
representation of these densities by cubic splines, do not affect significantly the
repeatability and uncertainty of C op, m that are estimated to be  0.02 and  0.2 J K-1 mol-1,
respectively.
Results. Table S1 shows the pure alcohol heat capacities, C op, m , measured in this work
with a step of 5 K. The data have been correlated using polynomials of the form
n
C po ,m /(J·K 1 ·mol 1 )  Bi T i
(S1)
i 0
The Bi coefficients were obtained by the least squares method and are given in Table S2,
together with the standard deviations of the fits. Figure S1 shows that for the two sterically
2
hindered alcohols 3M3P and 3E3P C op, m (T) go through a maximum. To our knowledge,
this is the first report of this behavior for pure liquids at atmospheric pressure. In order to
verify that the maxima in Figure S1 are not an artifact, we performed two tests, namely:
(1) We measured C op, m (T) for 3M3P using another DSC calorimeter (Perkin-Elmer DSC7), the results being given in Table S1 and displayed in Figure S1. In this measurement,
special reusable gold plated stainless steel high pressure cells and gold plated copper seals
were used. The cells and their content were weighted before and after the scanning and no
mass loss was detected. The calorimeter was calibrated with Indium for the temperatureS3
and power compensation scales. Diphenyl ether was used as the standard reference
material, as recommended by the NIST.S4 The heat capacities of 3M3P displayed in Figure
S1 are the average values from five scans, performed over two independent samples. Both
sets of measurements i.e. those from the Micro DSC II-Setaram and those from the PerkinElmer DSC-7 coincide (less than 1 % deviation) up to 325 K; at higher temperatures, the
deviations are larger but always less than 1.5 %. Despite these small deviations, it is clear
that the measurements with the second calorimeter confirmed the maximum in C op, m (T).
(2) We evaluated the reproducibility of the measurements with de Micro DSC II
calorimeter. The results for two independent runs for 3E3P are given in Table S1. The
differences between the heat capacity values measured in each run are larger at higher
temperatures but they do not exceed 0.1 %. Hence, the reproducibility can be considered
very good.
3
In view of the results of these two tests and the fact that previous C op, m (T) measurementsS1
for other liquids have shown excellent agreement with those reported in the literature, we
are confident that the C op, m (T) values in Table S1 and Figure S1 are reliable.
II. Computation of H–Bond Energies
Hydrogen bond energies for some alcohols and thiols have been estimated using quantum
mechanics MP2 ab initio calculationsS5 These calculations were performed using the
Gaussian 94 program with a 6-31G* basis set. The H–bond energies  were obtained as
the difference between the monomer A and the dimer Ai energies. The starting geometries
for the monomers and dimers were those where all the carbon atoms in the hydrocarbon
chains were in trans conformation. The local minimum character of the energies in the
optimized dispositions was ensured using the harmonic vibration frequencies calculation.
Corrections for the basis set superposition errorS6 (BSSE) constituted the final step in the
calculation of  = A – Ai, whose values are reported in Table S3.
References
[S1] C.A. Cerdeiriña, J.A. Miguez, E. Carballo, C.A. Tovar, E. de la Puente, and L.
Romaní, Thermochimica Acta, 347, 37 (2000).
[S2] M. Zabransky, V. Ruzicka, and E.S. Domalski, E.S., J. Phys. Chem. Ref. Data, 30(5),
1199 (2001).
[S3] H.K. Cammenga, W. Eysel, E. Gmelin, W. Hemminger, and G.W.H. Höhne,
Thermochimica Acta, 219, 333 (1993).
[S4] D.C. Ginnings, and G.T. Furukawa, J. Res. Natl, Bur. Stand., 75, 522 (1953).
[S5] A. Szabo, and N.S. Ostlund, Modern Quantum Chemistry (McGraw Hill, New York,
1990).
[S6] P. Hobza, and R. Zahradnik, Chem. Rev., 88, 871 (1988).
4
Table S1. Isobaric Molar Heat Capacities C op, m (T) for Pure Sterically Hindered Alcohols
T/K
C op, m (T) / J·K–1·mol–1
3-methyl-3-pentanol
278.15
283.15
288.15
293.15
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
343.15
348.15
353.15
358.15
363.15
368.15
373.15
a
3-ethyl-3-pentanol
5-methyl-5-nonanol
DSC IIa
DSC-7b DSC IIa DSC IIa
run 1a
run 2a
DSC IIa
266.34
274.33
282.21
289.77
296.93
303.56
309.57
314.77
319.25
322.85
325.75
327.97
329.50
330.40
331.13
331.01
330.66
329.99
329.15
327.54
337.27
346.26
353.99
360.59
365.80
369.56
371.94
373.16
373.21
372.43
371.07
369.31
367.16
364.98
362.62
360.17
357.69
355.21
351.19
358.33
365.72
373.23
380.98
388.86
396.73
404.60
412.41
420.04
427.50
434.79
441.96
448.84
455.74
462.01
468.01
473.65
478.90
281.30
290.09
296.88
304.23
310.30
316.04
321.42
325.55
329.05
331.33
333.54
334.63
335.23
335.69
335.48
335.06
333.21
332.18
327.50
337.21
346.15
353.95
360.48
365.75
369.45
371.82
373.01
373.06
372.34
370.98
369.22
367.05
365.00
362.69
360.28
357.90
355.47
Measured with the Setaram Micro DSC II. bMeasured with the Perkin–Elmer DSC-7.
5
Table S2. Coefficients Bi of Eq. (S1) and Standard Deviations 
a
3M3P
3M3Pb
3E3Prun1a
3E3Prun2a
5M5Na
a
B0
B1
B2
B3
B4

11976.7
7320.8
1034.66
863.313
1396.87
–157.486
–98.9817
–36.6228
–34.5708
–12.9095
0.771238
0.495048
0.284904
0.275828
0.0471173
–1.63673E-3
–1.05682E-3
–7.89405E–4
–7.71894E–4
–5.11339E–5
1.27764E–6
8.21411E–7
7.39175E–7
7.26794E–7
0.2
0.3
0.4
0.4
0.1
Measured with the Setaram Micro DSC II. bMeasured with the Perkin–Elmer DSC-7.
340
(b)
(a)
380
300
350
-1
/ J K mol
360
310
o
p,m
320
C
C
o
p,m
-1
/ J K mol
-1
370
-1
330
290
340
280
330
270
260
320
280 300 320 340 360 380 280 300 320 340 360 380
T/K
T/K
Figure S1. Isobaric molar heat capacities C op, m measured in this work for (a) 3-methyl-3pentanol using the Setaram Micro DSC II () and the Perkin-Elmer DSC-7 () and for (b)
3-ethyl-3-pentanol ().
6
Table S3. Hydrogen bond energies for some alcohols and thiols, from quantum mechanics
MP2 ab initio calculations
Substance
/ J·mol–1
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
19409
21227
21546
21825
21904
2-Propanol
2-Butanol
2-Methyl-1-Propanol
2-Methyl-2-Propanol
22151
21682
22090
22308
Metanethiol
Etanethiol
1-Propanethiol
5140
5217
5460
7