In this activity, you will apply statistical thermodynamics to calculate the enthalpy, free energy, and entropy of reaction for the combustion of ethene to form ethylene oxide at 298 K:
|
|
Rxn (1)
|
|
|
To simplify the calculations, you will treat each species as an ideal gas. The thermal entropy (S) (J/mol K) and the internal energy (E) (J/mol) are given by:
|
|
(1)
|
|
|
and
|
|
(2)
|
|
|
where q is the molecular partition function , where the subscript t, e, r, and v refer to the translational, electronic, rotational, and vibrational contributions, respectively. To calculate q, we further assume each species is in the ground electronic state (with degeneracy 2 spin + 1) with rovibrational energies given by harmonic oscillator and rigid rotor approximations. These assumptions lead to the following expressions for q, S, and E:
Translational:
where P = 1 atm = 100.325 kPa.
Electronic:
|
|
(6)
|
|
|
(7)
|
|
|
The thermal contribution to internal energy is 0 since the does not depend on temperature.
Rotational:
Linear Molecule:
where is the rotational symmetry number and is the rotational temperature. Each molecule we will consider in this activity is characterized by
Nonlinear Polyatomic Molecule:
where are the rotational temperatures corresponding to the principal moments of inertia.
Vibrational:
where s = 3N - 5 normal modes for a linear molecule and s = 3N - 6 for a nonlinear polyatomic.
Once the translational, electronic, rotational, and vibrational thermal contributions to the total entropy and internal energy have been calculated, total entropy (S), internal energy (E), enthalpy (H), and free-energy (G) can be calculated as follows:
Note we have corrected for the vibrational zero-point-energy for the internal energy. We will calculate S, H, and G for each of the reactants and product in Rxn (1) and calculate ΔH, ΔG, and ΔS as
etc.
