P3_Reaction Energies

Repeat your calculations and analysis for propene and

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Unformatted text preview: ange in the energy of isomerism by more than 10%? Repeat your calculations and analysis for propene and its isomer cyclopropane. Temperature Affects Reaction Energy: Using the results from the calculations you performed in the previous problem, evaluate the change in the energy of acetonitrile and methyl isocyanide with change in temperature from 0 K to 298 K. Combine this with the difference in zero-point energies for the two isomers (see previous problem). Does the full correction (zero-point energy + temperature) change in the energy of isomerism by more than 10%? Repeat your calculations and analysis for propene and its isomer cyclopropane. Mass Affects Reaction Energy: As detailed in Chapter xx, the Born-Oppenheimer approximation eliminates nuclear mass from the Schrödinger equation. However, because of differences in zero-point energies, reaction energies actually change with change in nuclear mass (isotope). The most common mass substitution is deuterium for hydrogen. Use the B3LYP/6-31G* 3 model to determine the difference in zero-point energy (and the difference in bond energies) between H2 and D2. Is the change in bond energy likely to be noticed? Assume that a change in bond energy of 5% is detectable. Repeat the calculations and the analysis for the change from molecule. 14 N to 15 N in nitrogen A trivial difference is one of units. Heats of formation are most commonly reported in kJ/mol, whereas total energies are most commonly reported in atomic units (hartrees). 1 hartree = 2625 kJ/mol kJ/mol will be used throughout this text, replacing the more familiar but now defunct kcal/mol (1 kcal/mol = 4.184 kJ/mol). The reason for the difference in units is simply a matter of convention and to some extent convenience. Heats of formation are typically only a few tenths of a hartree while total energies are typically tens of thousands to several million kJ/mol. In their respective units, both lie in a more convenient range from a few tens to a few thousands. Finally, and perhaps most important, while both total energy and heat of formation refer to the energies (heats) of specific chemical reactions, the reactions are different. Heat of formation refers to a balanced chemical reaction in which a molecule is converted to a set of standard products, each corresponding to the most stable form of the element at room temperature. The heat of formation of each standard is defined as zero. For example, the heat of formation of ethylene is defined by the reaction. C2H4 → 2C (graphite) + 2H2 (gas) Graphite and hydrogen molecule are the carbon and hydrogen standards, respectively. Of course, the experimental measurement is not actually carried out for this reaction, but more typically (but not necessarily) for a combustion reaction (reaction with O2), for example, for ethylene: C2H4 + 3O2 → 2CO2 + 2H2O In some cases, combustion leads to products that cannot be fully characterized. The most conspicuous case involves combustion of molecules incorporating silicon where polymeric silicon oxide polymers (sand) are formed. The clever solution is to “burn” the molecule in fluorine rather than oxygen, leading to gaseous SiF4 as a product. 4 Heats of formation may be either positive or negative quantities and their (absolute) values will generally span a range of only a few hundred kJ/mol. Molecules with positive heats of formation much greater than this are likely to the thermodynamically unstable and not likely to “stick around” long enough to be detected let alone characterized. Heats of formation may not be obtained directly from quantum chemical calculations simply because some of the standards are not isolated species on which calculations may be performed. A suitable alternative is to use a hypothetical reaction that splits a molecule into isolated nuclei (not atoms) and electrons, for example, for ethylene: C2H4 → 2C+6 + 4H+ + 16e – Each of the products (H+, C+6 and e-) contains but a single particle, meaning that its energy is zero. Total energies, as the energies of such reactions are termed, are very large negative numbers, (several tens of thousands to several million kJ/mol), but only a few tens to a few thousands of hartrees. There are two important points to be made. First, is it is straightforward to obtain heats of formation indirectly from total energies (or vice versa), either by using experimental atomic data or a mixture of experimental and theoretical atomic data. In fact, combinations of theoretical models (“recipes”) have been developed in order to provide accurate heats of formation. These will be discussed later in this chapter. The second point is more important. Either heats of formation or total energies are suitable for calculations of the energies (heats) of mass-balanced chemical reactions. Here, the “standards” cancel. 5 Sources and Quality of Experimental Thermochemical Data Experimental heats of formation have been reported for approximately three thousand compounds, a large fraction of which are hydrocarbons and oxycarbons. Among the most extensive co...
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This note was uploaded on 02/22/2010 for the course CHEM N/A taught by Professor Head-gordon during the Spring '09 term at Berkeley.

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