Energy equivalent of the calorimeter

The determination of T 7 r, and A rco,r has been described in the previous section. As mentioned, the energy equivalent of the calorimeter e0 can be obtained by calibration. Each calibration experiment also requires the recording of a temperature-time curve such as that in figure 7.2. 

The energy equivalent of the calorimeter, s , can therefore be calculated lfom equation 7.23 after determination of the corresponding adiabatic temperature rise. 

The experimental data and the calculations involved in the determination of a reaction enthalpy by isoperibol flame combustion calorimetry are in many aspects similar to those described for bomb combustion calorimetry (see section 7.1) It is necessary to obtain the adiabatic temperature rise, A Tad, from a temperaturetime curve such as that in figure 7.2, to determine the energy equivalent of the calorimeter in an separate experiment and to compute the enthalpy of the isothermal calorimetric process, AI/icp, by an analogous scheme to that used in the case of equations 7.17-7.19 and A /ibp. The corrections to the standard state are, however, much less important because the pressure inside the burner vessel is very close to 0.1 MPa. 

The obtained A 7 a() value and the energy equivalent of the calorimeter, e, are then used to calculate the energy change associated with the isothermal bomb process, AE/mp. Conversion of AE/ibp to the standard state, and subtraction from A f/jgp of the thermal corrections due to secondary reactions, finally yield Ac f/°(298.15 K). The energy equivalent of the calorimeter, e, is obtained by electrical calibration or, most commonly, by combustion of benzoic acid in oxygen [110,111,113]. The reduction of fluorine bomb calorimetric data to the standard state was discussed by Hubbard and co-workers [110,111]. 

The experiments are usually carried out at atmospheric pressure and the initial goal is the determination of the enthalpy change associated with the calorimetric process under isothermal conditions, AT/icp, usually at the reference temperature of 298.15 K. This involves (1) the determination of the corresponding adiabatic temperature change, ATad, from the temperature-time curve just mentioned, by using one of the methods discussed in section 7.1 (2) the determination of the energy equivalent of the calorimeter in a separate experiment. The obtained AT/icp value in conjunction with tabulated data or auxiliary calorimetric results is then used to calculate the enthalpy of an hypothetical reaction with all reactants and products in their standard states, Ar77°, at the chosen reference temperature. This is the equivalent of the Washburn corrections in combustion calorimetry... 

The value of s (e, or sr) is usually determined by electrical calibration (note that contrary to combustion calorimetry, it is not common practice to separate the initial and final energy equivalents of the calorimeter into the contribution of the reference calorimeter, e0, and those of the contents present in the initial, C1, and, final, ecf, states see section 7.1). In the case of the calorimeter in figure 8.1, a current I is passed trough the resistance F for a known period of time t and the potential change V across F is measured. Then ... 

Although this method ignores the variation of the energy equivalent of the calorimeter with temperature, it is a good approximation for many systems. 

The energy equivalent of the calorimeter, e, and the enthalpy of the isothermal calorimetric process, A//icp, were derived from equations 8.2 and 8.4, respectively. The standard enthalpy of reaction 8.5 was computed as Ar//°(8.5) = AZ/icp/n, where n is the amount of substance of Mo(ri5-C5H5)2(C2H4) used in the experiment. The data in table 8.1 lead to a mean value Ar//°(8.5) = — 186.0 2.1 kJ mol-1, where the uncertainty is twice the standard deviation of the mean (section 2.6). This value was used to calculate the enthalpy of reaction (8.6), where all reactants and products are in their standard reference states, at 298.15 K, from... 

The value of e0 is only constant for a fixed volume V of solution inside the calorimetric vessel. The change of e0 with V is primarily due to an increase of the reaction vessel wall in contact with the liquid as the liquid volume increases [ 197,200]. This change, de0/dV, which is constant for well-designed calorimeters [197,200], can be determined by measuring e0 as a function of V. Because it has been found that as expected, e0 and d 0/dV are independent of the nature of the liquid used in the calorimeter, they are normally determined by performing electrical calibrations with the calorimeter filled with different volumes of water [200]. The energy equivalent of the calorimeter at any point during a titration can therefore be calculated from... 

Method 1 is the more accurate from the two methods because the energy equivalent of the calorimeter is directly measured as a function of V for each system under study. Method 2 is less time-consuming because once s0 and ds0/dV have been determined, no further calibrations are necessary as long as the data needed to evaluate sc are available. 

Analogously to the dynamic method, the energy equivalent of the calorimeter, k.Q, can be obtained by performing calibration experiments in the isothermal mode of operation, using electrically generated heat or the fusion of substances with well-known A us//. Recommendations for the calibration of the temperature scale of DSC instruments for isothermal operation have also been published [254,270]. 

Calibration. The energy equivalent of the calorimeter was determined by burning NBS sample 39h benzoic acid. The combustions were... 

The energy equivalent of the calorimeter, (calor) is defined as the amount of energy required to increase the temperature of the calorimeter by 1 K. The most precise determination of (calor) is based on the transfer of a determined quantity of electrical energy through a heater placed at the same location as the combustion crucible. Because most of the calorimeters used are of the isoperibol type and are not equipped for electrical calibration, a standard reference material, benzoic acid, is used. Its certified energy of combustion in O2 must have been measured in an electrically calibrated calorimeter. Because the conditions under which the specific energy of combustion reported on the certificate was determined usually differ from those ones used in combustion calorimeters, certain corrections must be applied [31]. Details of these corrections are given in the certificate. 

King and Grover [22] described the calorimetric bomb in terms of a two-domain model with a concentric configuration. As a result, in the method of corrected rise the heat capacity C was replaced by a corrected term, called the energy equivalent of the calorimeter ... 

The value of A//(expt) at constant pressure would be zero if the process were perfectly adiabatic and the only work were expansion work, but this is rarely the case. There may be unavoidable work from stirring and from electrical temperature measurement. We can evaluate A//(expt) by one of the methods described in Sec. 7.3.2. For an adiabatic calorimeter, the appropriate expression is A//(expt) = er(t2 — h) (Eq. 7.3.19 on page 170 with Kiel set equal to zero), where e is the energy equivalent of the calorimeter, r is the slope of the heating curve when no reaction is occurring, and ti and t2 are the times at temperatures Ti... 

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