A numerical method for the calculation of the composition of two phases in equilibrium is proposed for the case when the composition of one of the phases is known as function of the temperature. The thermodynamic properties of the phases are not needed to be known in the proposed procedure. The feature of this approach is the possibility to use fictitious thermodynamic functions in the intermediate stages of computation. The method has been applied for calculation of solidus in phase diagrams of potassium-rubidium, potassium-cesium and cesium-rubidium systems from experimental liquidus data.
The molar heat capacities of the room temperature
ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate (BMIBF4)
were measured by an adiabatic calorimeter in temperature range from 80 to
390 K. The dependence of the molar heat capacity on temperature is given as
a function of the reduced temperature X
by polynomial equations, CP,m
(J K–1 mol–1)=
195.55+47.230 X–3.1533 X2+4.0733 X3+3.9126 X4 [X=(T–125.5)/45.5] for the solid phase (80~171
K), and CP,m (J
378.62+43.929 X+16.456 X2–4.6684 X3–5.5876 X4 [X=(T–285.5)/104.5] for the liquid phase (181~390
K), respectively. According to the polynomial equations and thermodynamic
relationship, the values of thermodynamic function of the BMIBF4
relative to 298.15 K were calculated in temperature range from 80 to 390 K
with an interval of 5 K. The glass translation of BMIBF4
was observed at 176.24 K. Using oxygen-bomb combustion calorimeter, the molar
enthalpy of combustion of BMIBF4 was determined to
– 5335±17 kJ mol–1. The standard
molar enthalpy of formation of BMIBF4 was evaluated
to be ΔfHmo=
–1221.8±4.0 kJ mol–1 at T=298.150±0.001 K.
The low-temperature heat capacity Cp,m of sorbitol was precisely measured in the temperature range from 80 to 390 K by means of a small sample automated adiabatic
calorimeter. A solid-liquid phase transition was found at T=369.157 K from the experimental Cp-T curve. The dependence of heat capacity on the temperature was fitted to the following polynomial equations with least square
method. In the temperature range of 80 to 355 K, Cp,m/J K−1 mol−1=170.17+157.75x+128.03x2-146.44x3-335.66x4+177.71x5+306.15x6, x= [(T/K)−217.5]/137.5. In the temperature range of 375 to 390 K, Cp,m/J K−1 mol−1=518.13+3.2819x, x=[(T/K)-382.5]/7.5. The molar enthalpy and entropy of this transition were determined to be 30.35±0.15 kJ mol−1 and 82.22±0.41 J K−1 mol−1 respectively. The thermodynamic functions [HT-H298.15] and [ST-S298.15], were derived from the heat capacity data in the temperature range of 80 to 390 K with an interval of 5 K. DSC and TG measurements
were performed to study the thermostability of the compound. The results were in agreement with those obtained from heat capacity
The thermodynamic relationship between crystal modifications of paracetamol was studied by alternative methods. Temperature
dependence of saturated vapor pressure for polymorphic modifications of the drug paracetamol (acetaminophen) was mea sured
and thermodynamic functions of the sublimation process calculated. Solution calorimetry was carried out for the two modifications
in the same solvent. Thermodynamic parameters for sublimation for form I (monoclinic) were found: ΔGsub298=60.0 kJ mol−1; ΔHsub298=117.9�0.7 kJ mol−1; ΔSsub298=190�2 J mol−1 K−1. For the orthorhombic modification (form II), the saturated vapor pressure could only be studied at 391 K. Phase transition
enthalpy at 298 K, ΔHtr298(I→II)=2.0�0.4 kJ mol−1, was derived as the difference between the solution enthalpies of the noted polymorphs in the same solution (methanol). Based
on ΔHtr298 (I→II), differences between temperature dependencies of heat capacities of both modifications and the vapor pressure value
of form II at 391 K, the temperature dependence of saturated vapor pressure and thermodynamic sublimation parameters for modification
II were also estimated (ΔGsub298=56.1 kJ mol−1; ΔHsub298=115.9�0.9 kJ mol−1; ΔSsub298=200�3 J mol−1 K−1). The results indicate that the modifications are monotropically related, which is in contrast to findings recently reported
found by classical thermochemical methods.
The enthalpies of solution of L-phenylalanine in the mixtures of water with the protein denaturant urea have been measured
in the temperature range of 288.15–318.15 K. Using the results of the present research and literature data of free energies,
the standard thermodynamic functions of the solute transfer from water to aqueous urea solutions have been estimated in a
wide temperature range. The enthalpic, heat capacity, entropic and free energy parameters of the solute-urea pair and triplet
interactions have been computed. The amino acid — amide pair interaction was found to be attractive in the temperature range
studied due to the favourable enthalpic term. The triplet interaction being slightly repulsive reveals the enthalpic origin
also. The examination of the Savage and Wood additivity-of-groups approach does indicate the inapplicability of this scheme
to enthalpies and entropies of interaction. It has been found for the first time that the heat capacity of interaction changes
its sign at 303 K, i.e. the temperature dependence of enthalpic and entropic parameters passes through the pronounced extrema
near the temperature of the minimum of the heat capacity of pure water.
In an adiabatic vacuum calorimeter the temperature dependence of the heat capacity Cp0 of 1,3,5,7-tetramethyl-1,3,5,7-tetrahydrocyclotetrasiloxane and polymethylhydrosiloxane on its basis was measured between
6 and 350 K mainly with accuracy of about 0.2%. Two-phase transitions corresponding, probably, to the fusion of cis-and trans-conformations of the monomer as well as the glass transition of the polymer were detected. The results obtained were used
to calculate the thermodynamic functions Cp0, H0(T)-H0(0), S0(T), G0(T)-H0(0) of the monomer and polymer in the range from T→0 to T=340 K, and to estimate the zero entropy S0(0) of amorphous polymer. Standard entropies of formation ΔSf0 of the tested monomer and polymer at T=298.15 K as well as the entropy of synthesis of polymethylhydrosiloxane from 1,3,5,7-tetramethyl-1,3,5,7-tetrahydrocyclotetrasiloxane
over the range from T→0 to 340 K were estimated. The value of fractal dimension D in the heat capacity function of the multifractal variant of
the Debye’s theory of heat capacity was found to be 1.5 for polymer in the 18–35 K range, that testifies to its layer-chain
The 'hydrophobic effect' of the dissolution process of non-polar substances in water has been analysed under the light of
a statistical thermodynamic molecular model. The model, based on the distinction between non-reacting and reacting systems explains the changes of the thermodynamic functions with temperature in aqueous systems. In the dissolution of non-polar
substances in water, it follows from the model that the enthalpy change can be expressed as a linear function of the temperature
(ΔHapp =ΔHø +nwCp,wT ). Experimental solubility and calorimetric data of a large number of non-polar substances nicely agree with the expected
function. The specific contribution of nw solvent molecules depends on the size of solute and is related to destructuring (nw >0) of water molecules around the solute. Then the study of 'hydrophobic effect' has been extended to the protein denaturation
and micelle formation. Denaturation enthalpy either obtained by van't Hoff equation or by calorimetric determinations again
depends linearly upon denaturation temperature, with denaturation enthalpy, ΔHden , increasing with T . A portion of reaction enthalpy is absorbed by a number nw of water molecules (nw >0) relaxed in space around the denatured moieties. In micellization, an opposite process takes place with negative number
of restructured water molecules (nw <0) because the hydrophobic moieties of the molecules joined by hydrophobic affinity occupy a smaller cavity.
The heat capacities of fenpropathrin in the temperature range from 80 to 400 K were measured with a precise automatic adiabatic calorimeter. The fenpropathrin sample was prepared with the purity of 0.9916 mole fraction. A solid—liquid fusion phase transition was observed in the experimental temperature range. The melting point, Tm, enthalpy and entropy of fusion,
fusSm, were determined to be 322.48±0.01 K, 18.57±0.29 kJ mol–1 and 57.59±1.01 J mol–1 K–1, respectively. The thermodynamic functions of fenpropathrin, H(T)—H(298.15), S(T)—S(298.15) and G(T)—G(298.15), were reported with a temperature interval of 5 K. The TG analysis under the heating rate of 10 K min–1 confirmed that the thermal decomposition of the sample starts at ca. 450 K and terminates at ca. 575 K. The maximum decomposition rate was obtained at 558 K. The purity of the sample was determined by a fractional melting method.
The heat capacities of trans-(R)-3-(2,2-dichloroethenyl)-2,2-dimethylcyclopropanecarboxylic acid in the temperature range from 78 to 389 K were measured
with a precise automatic adiabatic calorimeter. The sample was prepared with the purity of 0.9874 mole fraction. A solid-liquid
fusion phase transition was observed in the experimental temperature range. The melting point, Tm, enthalpy and entropy of fusion, ΔfusHm, ΔfusSm, were determined to be 344.75±0.02 K, 13.75±0.07 kJ mol−1, 39.88±0.21 J K−1 mol−1, respectively. The thermodynamic functions of the sample, H(T)-H(298.15), S(T)-S(298.15) and G(T)-G(298.15), were reported with a temperature interval of 5 K. The thermal decomposition of the sample was studied by TG analysis, the
thermal decomposition starts at ca. 421 K and terminates at ca. 535 K, the maximum decomposition rate was obtained at 525
K. The order of reaction, pre-exponential factor and activation energy, are n=0.14, A=1.15·108 min−1, E=66.27 kJ mol−1, respectively.
By kinetics of decomposition of solids in both isothermal and non-isothermal conditions, the compensation effect (CE) is rather
The topic of this work is to suggest an activation mechanism which leads to the dependences similar with CE.
The solid is assimilated to a system of the harmonic oscillator with a Bose-Einstein energy distribution.
Considering an activation process due to a vibrational energy transfer from a homogeneous and isotropic field of thermic oscillators
to the solid-state oscillator, the thermodynamic functions are in the relationship
where ΔH* and ΔS* are the activation functions and Tis is the isokinetic temperature.
Taking into account the definitions of H and S by means of the partition function, the isokinetic temperature is assimilated with the characteristic temperature
An important consequence, a correlation between the isokinetic temperature and the spectroscopic wavenumber of the activated
bond, is illustrated by a number of decomposition reactions under non-isothermal conditions.