Calorimetric measurements, calculation

The error attributed to the determination of the NHV (calorimetric measurement, determination of hydrogen content, and final calculation) is satisfactory with a repeatability of 0.3% and a reproducibility of 0.4%. 

The equation just written is basic to calorimetric measurements. It allows you to calculate the amount of heat absorbed or evolved in a reaction if you know the heat capacity, Ccd, and the temperature change, At, of the calorimeter. 

Other methods can be used to obtain L and L2 from calorimetric measurements. For example, the derivation that lead to equations (5.33) and (5.34) in Chapter 5 for calculating V and V2 can be applied to give... 

A is the manufacturer s rated activity based on calorimetric measurement of the heat evolved by the source. Since one 3-m.e.v. alpha particle produces 3 X 104 ion pairs in air of 1 mg. sq. cm. 1 density we calculate 7, the number of ion pairs produced per second above the leak in 1 cc. air at p torr pressure as ... 

It should be pointed out that a finite residual entropy calculated for a substance from experimental data obtained at temperatures extending down to a certain temperature, with extrapolation below that point, may arise either from failure of the experimenter to obtain thermodynamic equilibrium in his calorimetric measurements or from error in the extrapolation. Measurements made under ideal conditions and extended to sufficiently... 

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. 

On the other hand, Arnett and his coworkers have reported both the enthalpies of the protonation (AHJ and the hydrogen bond (AHf) for acid-base reactions. They calculated Hj by measuring the association constants for the proton transfer (ionization) in a number of bases by using FSO3H as the acid and determined Ai/j by calorimetric measurements of the heat of dissolution of P-FC6H4OH in various hydrogen bond acceptors, including sulphoxides, in They have also tried to correlate and... 

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. 

In this section, you learned how to calculate the enthalpy change of a chemical reaction using Hess s law of heat summation. Enthalpies of reaction can be calculated by combining chemical equations algebraically or by using enthalpies of formation. Hess s law allows chemists to determine enthalpies of reaction without having to take calorimetric measurements. In the next section, you will see how the use of energy affects your lifestyle and your environment. 

From classic thermodynamics alone, it is impossible to predict numeric values for heat capacities these quantities are determined experimentally from calorimetric measurements. With the aid of statistical thermodynamics, however, it is possible to calculate heat capacities from spectroscopic data instead of from direct calorimetric measurements. Even with spectroscopic information, however, it is convenient to replace the complex statistical thermodynamic equations that describe the dependence of heat capacity on temperature with empirical equations of simple form [15]. Many expressions have been used for the molar heat capacity, and they have been discussed in detail by Frenkel et al. [4]. We will use the expression... 

We can calculate AH from thermal data alone, that is, from calorimetric measurements of enthalpies of reaction and heat capacities. It would be advantageous if we could also compute AS from thermal data alone, for then we could calculate AG or Ay without using equilibrium data. The requirement of measurements for an equilibrium state or the need for a reversible reaction thus could be avoided. The thermal-data method would be of particular advantage for reactions for which AG or AT is very large (either positive or negative) because equilibrium measurements are most difficult in these cases. 

Ulbrich and Waldbaum [14] pointed out that calorimetrically determined third law entropies for many geologically important minerals may be in error because site mixing among cations, magnetic spin disorder, and disorder among water molecules in the crystals is frozen in the samples used for calorimetric measurements. They have calculated corrections based on known crystallographic data for several minerals. 

Figure 5.16A shows, for example, how calculated Cp values for pyrope compare with low-T calorimetric measurements of Haselton and Westrum (1980). Adopting the initial guess value of (115.7 cm see table 5.25) leads to an entropy estimate at =... 

To what is this discrepancy due As noted in the chapter in the current volume by Schulz, Brand and ViUinger on derivatives of formaldoxime, the parent species and its ionic salts are prone to polymerization and to decomposition. This most assuredly com-phcates calorimetric measurements. That the calculated enthalpy of formation is more negative than the experimental is surprising in that the polymer is expected to be more stable (with lower AHf as well as necessarily AGf) than the monomer. 

Calculation of the heats of fusion of 100% crystalline polymers from calorimetric data is not clear cut. Because of the partial crystallinity of all polymers (a possible exception are single crystals of polyethylene and other polymers, but these single crystals have not yet been investigated calorimetrically), calorimetric measurements do not yield the true heat of fusion AHf, in calg-1, but only AH where these two quantities are related by the expression... 

SbCl3 (liq.)- Tolloczko,1 2 from cryoscopic and calorimetric measurements, deduced the heat of fusion of the solid to be — 3.0173. Rideal1 calculated —3.40. 

In the calorimetric approach, it is necessary to know the heat of fusion of the totally crystalline polymer. This can be obtained from melting-point depression measurements, as described in the following section. The basic idea depends on the fact that the melting temperature is independent of the size of the system, since it is an intensive property. The extent to which it is depressed by the presence of solvent can be used to calculate a heat of fusion characteristic of the crystallites, irrespective of how many are present. This is therefore the heat of fusion of the 100% crystalline polymer. The fractional crystallinity in an actual sample is then the ratio of its calorimetrically measured heat of fusion per gram to that of the 100% crystalline polymer. For example, if the actual polymer has a heat of fusion of 7 cal per gram, and the 100% crystalline polymer a heat of fusion of 10 cal per gram, then the fractional crystallinity is 0.7, and the percentage crystallinity is 70%. 

Though entropies in principle can be determined from the temperature dependence of the heat capacity starting from zero Kelvin, in all practical instances it is obtained by calculation from AG and AH. Since both state functions are available from the same calorimetric measurement e.g. by ITC, this provides also the immediate access to the relevant entropy change possessing no equally precise alternative way of determination [12]. 

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... 

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