Study the vibrational internal energy section very carefully. What is the refere
ID: 768470 • Letter: S
Question
Study the vibrational internal energy section very carefully. What is the reference point for the calculation of internal energy? It is either the v = 0 vibrational level or the bottom of the harmonic oscillator potential energy function. Justify your answer by converting the zero point energy from Hartree/particle to kcal/mol. The format for the data table is a little off but basically the first number is for N2, the second number is for CO, and the third number is C2H4. Partition functions q N2 CO C2H4 Translational 0.582553D+07 0.582202D+07 0.583338D+07 Rotational 0.525929D+02 0.109134D+03 0.130770D+04 Vibrational (v=0) 0.100001D+01 0.100002D+01 0.104836D+01 Electronic 0.100000D+01 0.100000D+01 0.100000D+01 Total 0.306384D+09 0.635397D+09 0.799717D+10 Rotational Temperatures ?A 2.83451 2.73196 7.05195 ?B 1.44189 ?C 1.19712 Vibrational Temperatures Highest 3536.01 3177.87 4672.35 Lowest 3536.01 3177.87 1202.16 Thermochemical Values Average U (kcal / mol) 4.995 4.639 34.054 Translational U 0.889 0.889 0.889 Rotational U 0.592 0.592 0.889 Total Cv (Cal / mol / K) 4.970 4.973 8.087 Translational Cv 2.981 2.981 2.981 Rotational Cv 1.987 1.987 2.981 Enthalpy (kcal/mol) -109.515225 -113.301118 -78.532246 Gibbs Energy (kcal/mol) -109.536980 -113.323561 -78.557762Explanation / Answer
Molecular vibrations are one of the ways in which a molecule stores chemical energy. For a diatomic molecule, the vibrational can be approximated by the quantum harmonic oscillator. The vibrational energy Ev is Ev = (v + 1/2)hv0 where v is an integer representing vibrational quantum numbers such that v = 0,1,2,3,..., where v=0 for a diatomic molecule at the ground vibrational state; h is Planck's constant; and v0 is the natural frequency of the harmonic oscillator.............................................................................................................................................................................................................................................................................................................................. Internal Energy the energy of an object that depends only on its internal state. The concept of internal energy includes all forms of energy except the energy of its motion as a whole and potential energy, which an object may have if it is in the field of any force (for example, a gravitational field). The concept of internal energy was introduced by W. Thomson (1851), who defined the change in internal energy (?U) of a physical system in any process as the algebraic sum of the amount of heat Q that the system exchanges with the environment during the process and the work A performed by the system or performed on it: ?U = Q ? A The work A is considered positive if it is performed by the system on external objects, and the amount of heat Q is positive if it is transferred to the system. The above equation expresses the first law of thermodynamics