Standard calorimetric measurements

As seen in previous sections, the standard entropy AS of a chemical reaction can be detemiined from the equilibrium constant K and its temperature derivative, or equivalently from the temperature derivative of the standard emf of a reversible electrochemical cell. As in the previous case, calorimetric measurements on the separate reactants and products, plus the usual extrapolation, will... 

P. A. G. O Hare, "Thermochemistry of Uranium Compounds XV. Calorimetric Measurements on UCI4, UOiCl . and UCFF . and the Standard Molar Enthalpy of Formation at 298.15 K of UC14", J. Chem. Thermodyn.. 17. 611-622 (1985). 

Equation can also be used to calculate the standard enthalpy of formation of a substance whose formation reaction does not proceed cleanly and rapidly. The enthalpy change for some other chemical reaction involving the substance can be determined by calorimetric measurements. Then Equation can be used to calculate the unknown standard enthalpy of formation. Example shows how to do this using experimental data from a constant-volume calorimetry experiment combined with standard heats of formation. 

Simple amides of this type are the bis(trimethylsilyl)amides M[N(SiMe3)2]2 (M = Cd and Hg) the essential thermodynamic data of which have been determined in calorimetric measurements of the heats of hydrolysis in dilute H2S04.146 Evaluation of the measured data yielded the standard enthalpies of formation AH° = —854(21)kJmoU1 and —834(9)kJmol-1 for M =Cd and Hg, respectively. Using subsidiary data, the average thermochemical bond energies E—(Cd—N) 144 and E(Hg—N) 108 kJ mol-1 were also obtained, i.e., the Cd—N bonds are considerably stronger than the Hg—N bonds. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

Although in crystalline phases determination of the enthalpy of formation from the constituent elements (or from constituent oxides) may be carried out directly through calorimetric measurements, this is not possible for molten components. If we adopt as standard state the condition of pure component at T = 298.15 K and P = bar , it is obvious that this condition is purely hypothetical and not directly measurable. If we adopt the standard state of pure component at P and T of interest , the measurement is equally difficult, because of the high melting temperature of silicates. 

Polymerizations were carried out at 30°C in all glass, sealed reactors using breakseals and standard high vacuum techniques (3). For the calorimetric measurements, a 1 liter sample of a 0.03M solution of each polymeric lithium compound with M of ca. 4,000 was prepared in benzene solution using sec-butyl-lithium as initiator and transferred to the glove box. 

A combined application of direct calorimetric measurements and thermochemical investigations has made possible to obtain a number of important thermochemical quantities characterizing the interaction of the N—H bond of the amine with the epoxy ring 53). Combustion and evaporation enthalpies of phenylglycidyl ether and its condensation products with aniline and butylamine have been determined. Standard enthalpies of the formation of these compounds, strain energies of the epoxy ring in the phenylglycidyl ether molecule and — AH values for the three-phase states, which are most important for the determination of the true thermodynamic reaction characteristics, have been estimated. 

The standard enthalpies of formation of crystalline (25 L=H20), (26), (67), (39), (55), [Mo2(02CMe)4] and [Mo2(02CMe)2(acac)2] have been derived from calorimetric measurements of oxidative hydrolysis in solution. It has not been possible to distinguish between various theoretical treatments from the thermochemical data. 494... 

Calorimetric measurements were carried out on scanning microcalorimeters developed at the Biocalorimetry Center at the John Hopkins University following standard procedures for sample preparation and data retrieval.[1361... 

O Hare, P.A.G. (1993) Calorimetric measurements of the specific energies of reaction of arsenic and of selenium with fluorine. Standard molar enthalpies of formation Af7/°m at the temperature 2.98.15 K of AsFs, SeF6, As2Se3, AS4S4, and As2S3. Thermodynamic properties of AsFs and SeF6 in the ideal-gas state. Critical assessment of AfH°m (AsF3, 1)), and the dissociation enthalpies of As-F bonds. Journal of Chemical Thermodynamics, 25, 391-402. 

The heat capacity of coal can be measured by standard calorimetric methods that have been developed for other materials (e.g., ASTM C-351). The units for heat capacity are Btu per pound per degree Fahrenheit (Btu/lb-0F) or calories per gram per degree Celsius (cal/g °C), but the specific heat is the ratio of two heat capacities and is therefore dimensionless. 

The determination of standard transformed enthalpies of biochemical reactions at specified pH, either from temperature coefficients of apparent equilibrium constants or by calorimetric measurements, makes it possible to calculate the corresponding standard transformed entropy of reaction using... 

Calorimetric measurements yield enthalpy changes directly, and they also yield information on heat capacities, as indicated by equation 10.4-1. Heat capacity calorimeters can be used to determine Cj , directly. It is almost impossible to determine ArCp° from measurements of apparent equilibrium constants of biochemical reactions because the second derivative of In K is required. Data on heat capacities of species in dilute aqueous solutions is quite limited, although the NBS Tables give this information for most of their entries. Goldberg and Tewari (1989) have summarized some of the literature on molar heat capacities of species of biochemical interest in their survey on carbohydrates and their monophosphates. Table 10.1 give some standard molar heat capacities at 298.15 K and their uncertainties. The changes in heat capacities in some chemical reactions are given in Table 10.2. 

Calculation of A//e -quantities from the dependence of AG on temperature is less reliable than direct calorimetric measurements (Franks and Reid, 1973 Frank, 1973 Reid et al., 1969). However, disagreement between published A//-functions for apolar solutes in aqueous solutions may also stem from practical problems associated with low solubilities (Gill et al., 1975). Calorimetric data have the advantage that, as theory shows, the standard partial molar enthalpy H3 for a solute in solution is equal to the partial molar enthalpy in the infinitely dilute solution, i.e. x3 - 0. A similar identity between X3 and X3 (x3 - 0) occurs for the volumes and heat capacities but not for the chemical potentials and entropies. The design of a flow system for the measurement of the heat capacity of solutions (Picker et al., 1971) has provided valuable information on aqueous solutions. 

Another remarkable Lewis basicity scale for 75 non-HBD solvents has been established by Gal and Maria [211, 212]. This involved very precise calorimetric measurements of the standard molar enthalpies of 1 1 adduct formation of EPD solvents with gaseous boron trifluoride, A//p gp, in dilute dichloromethane solution at 25 °C, according to Eq. (2-10a). 

Transfer functions can also be defined for the thermodynamic state functions AH° and AS° [102], The ease of calorimetric measurements has made the standard molar transfer enthalpy, AH X,1 II), readily available. If both transfer Gibbs energies and... 

By way of illustrations we display in Fig. 1.17.2a plot of the molar heat capacity of oxygen under standard conditions. The plot of Cp vs. In T is then used to determine the entropy of oxygen from the area under the curves. Note that the element in the solid state exists in three distinct allotropic modifications, with transition temperatures close to 23.6 and 43.8 K the melting point occurs at 54.4 K, and the boiling point is at 90.1 K. All the enthalpies of transition at the various phase transformations are accurately known. An extrapolation procedure was employed below 14 K, which in 1929 was about the lower limit that could conveniently be reached in calorimetric measurements. 

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