High-temperature molecular heat capacity

The above value is valid at ordinary temperature when the vibrational energy is very less. When vibration is more at a high temperature, then the molecular heat capacity becomes nearly equal to 7.0 calories/mole. 

The expressions in (3.72) and (3.73) are valid only for monatomic ideal gases such as He or Ar, and must be replaced by somewhat different expressions for diatomic or polyatomic molecules (Sidebar 3.8). However, the classical expressions for polyatomic heat capacity exhibit serious errors (except at high temperatures) due to the important effects of quantum mechanics. (The failure of classical mechanics to describe the heat capacities of polyatomic species motivated Einstein s pioneering application of Planck s quantum theory to molecular vibrational phenomena.) For present purposes, we may envision taking more accurate heat capacity data from experiment [e.g., in equations such as (3.84a)] if polyatomic species are to be considered. The term perfect gas is sometimes employed to distinguish the monatomic case [for which (3.72), (3.73) are satisfactory] from more general polyatomic ideal gases with Cv> nR. 

In spite of the wealth of information available on the preparative and structural aspects of the lanthanide chlorides (1-3), experimental thermodynamic, and, in particular, high-temperature vaporization data are singularly lacking. The comprehensive estimates of the enthalpies of fusion, vaporization, heat capacities and other thermal functions for the lanthanide chlorides by Brewer et ah (4, 5) appear internally consistent, but the relatively few experimental measurements (6-/2) do not permit confirmation of the estimates due to the narrow temperature ranges of study. Additionally, the absence of accurate molecular data for the gaseous species has hampered third-law treatment of the limited experimental vapor pressure data available. The one reported study (12) of the vaporization of EuC12 effected by a boiling-point method lacks accuracy for these reasons. 

There are relatively few chemical reactions capable of heating matter to temperatures greater than 3000°K. Table II contains a list of some of these reactions and the theoretical flame temperatures attainable. These reactions have two characteristics in common (1) high exothermic heats of reaction and (2) stable molecular products with low heat capacities, since dissociation consumes energy and results in additional products which must be heated to the flame temperature. 

However, these states are not included for two reasons. First, the electronic and molecular constants are not all well-defined. Second, many of these levels have a sufficiently shallow potential energy well, which would lead to unreasonably large heat capacity values at high temperatures. 

In order to bring the sample rapidly into a hot environment, use is often made of the platform technique, as was first introduced in atomic absorption spectrometry by L vov [179]. Here the very rapid heating may enable the formation of double peaks to be avoided, which are a result of various subsequent thermochemical reactions, all of which have their own kinetics. Also the high temperature avoids the presence of any remaining molecular species, which are especially troublesome in the case of atomic absorption spectrometry. Thin platforms can be made of graphite, which have a very low heat capacity, or from refractory metals. In the latter case wire loops, on which a drop can easily be previously dried, are often used. 

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