Determination of standard enthalpy of vaporization and thermal decomposition reactions from derivative thermogravimetric (DTG) curves
Introduction
Vapor pressure measurements have been frequently used in the determination of thermodynamic data for the condensed phases [1], [2], [3], [4], [5], [6], [7]. Among the several techniques available for vapor pressure measurements [8], [9], [10] the transpiration, which is also known as the gas entrainment technique is more versatile and enables determination of the vapor pressure of the materials over a wide range of pressures in the presence of large amount of the desired reactive as well as inert ambient gaseous atmosphere [2], [9], [13]. This technique, proposed originally by Regnault for the determination of the vapor pressure of liquids [11] has undergone several innovations and improvements and has been utilized in recent years for the acquisition of the vapor pressure and other thermodynamic stability data over a wide temperature range, for the most complex systems including high temperature ceramics, metals and alloys [2], [3], [6], [7].
The transpiration technique essentially involves measurement of the number of moles of the vapor of the condensed phase transported by the known volume of the carrier gas swept over the sample located in uniform temperature zone of the furnace, without disturbing the thermodynamic equilibrium between the vapor and the condensed phase undergoing vaporization at the desired temperature. The experiments involve two steps:
- 1.
determination of apparent vapor pressure at different flow rates at the selected temperature to identify the range of flow rates over which the vapor pressure is independent of the flow rates employed, a criterion which ensures that the condensed phase is virtually in equilibrium with its vapor and
- 2.
measurement of the vapor pressure of the materials at different temperatures at “the selected flow rate” chosen from the flow rate independent region.
The enthalpy of vaporization and other thermodynamic quantities are then derived from the vapor pressure data employing the Gibbs Helmholtz equation [12].
In a typical transpiration experiment, the material for which the vapor pressure has to be measured is contained in a boat located in the uniform temperature zone of the tubular horizontal or vertical furnace. The vapor generated above the sample is swept away by the carrier gas, condensed in the colder region downstream and analyzed. Alternately, in few cases, where the sample under investigation is non-hygroscopic and the sample container does not undergo any significant mass change during heating, the mass loss of the sample due to vaporization is determined by weighing the sample before and after the experiment. The vapor pressure is then calculated, knowing the amount of the vapor swept by the unit volume of the carrier gas and the molecular weight of the vapor species. The molecular weight of the vapor species has to be known or determined prior to the detailed vapor pressure measurements. Merten and Bell [13] and more recently Kvande and Wahlbeck [14] have presented excellent reviews of this technique.
In conventional transpiration method, the experiment performed at each flow rate and temperature has to be terminated in order to determine the number of moles of the vapor of the sample under investigation transported by the known volume of the carrier gas. The condenser has to be taken out of the assembly, for the chemical analysis of the vapor deposited in it or the boat containing the sample should be taken out and weighed to assess the mass loss during the vaporization process. This process, besides being tedious and time consuming is prone to large experimental errors.
Dharwadkar and his co-investigators [15] designed and fabricated an automatic recording assembly to measure the vapor pressure by transpiration technique. The assembly was built incorporating the electronic microbalance used for continuous monitoring of the mass loss of the sample during vaporization. All the measurements at different flow rates and temperatures could be done on a single sample by automatic recording of the mass loss of the sample during vaporization, without interrupting the experiment or dismantling the experimental assembly, thereby reducing the experimental time to a very large extent.
Section snippets
The objective of the present investigation
In the present paper we attempted the use of a single derivative thermogravimetric (DTG) curve recorded for the congruent vaporization of CdI2 for acquisition of its vapor pressure and determination of the standard enthalpy of vaporization. Similar procedure was employed to obtain the dissociation pressure and standard enthalpy of decomposition of CaCO3. The standard enthalpy of formation of these compounds could also be derived from these data. This approach reduced the time duration of the
Thermogravimetric system and mass measurements
The thermogravimetric curves for pure CdI2 (BDH, AnalaR Grade, >99%) and CaCO3 (GR, Merk, >99.5%) samples were recorded in flowing argon and Ar–CO2 mixtures at the flow rates ranging between 0.2 and 16 ml/min, employing a simultaneous recording bottom loading TG–DTA system supplied by SETARAM, France (Model SETSYS), having room temperature sensitivity of 1 μg, at the heating rates of 5 and 1 K/min. The mass measurements in the bottom loading thermogravimetric systems of the type used in the
Vaporization of cadmium iodide
Fig. 1 represents the typical simultaneously recorded DTG and DTA curves for the vaporization of CdI2 sample recorded in argon flowing at the rate of 8 ml/min, employing the heating rate of 5 K/min. The DTA curve indicates melting of CdI2 prior to vaporization. A typical DTG curve derived from the thermogravimetric (TG) curve recorded for molten CdI2 at 1 K/min in flowing argon (flow rate 8 ml/min) is presented in Fig. 2. Derivation of vapor pressure from this curve needs prior knowledge of the
The conventional transpiration measurements
The main objective of the present investigation was to ascertain the possibility of using the derivative thermogravimetric (DTG) curve for acquisition of reliable thermodynamic data for the vaporization and thermal decomposition processes involving the evolution of the gaseous products. The conventional transpiration technique (see Section 2) can be suitably adopted to obtain such data. The first step in this procedure is to establish thermodynamic equilibrium between the vaporizing condensed
Conclusion
The vapor pressure and dissociation pressure of materials can be evaluated and the enthalpy of vaporization/dissociation derived from a single DTG curve recorded for the process at the slowest possible heating rate and the optimum sweep rate of the carrier gas. This method enables determination of the relevant thermodynamic quantities such as the standard enthalpy and the Gibbs energy change for the reaction and hence the standard enthalpy of formation of the materials, in the shortest possible
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