(Solved): Methane CH_(4) has tetrahedral symmetry. Methane is a spherical top molecule with three equal moment ...
Methane
CH_(4)has tetrahedral symmetry. Methane is a spherical top molecule with three equal moments of inertial and therefore three equal rotational temperatures i.e.
\theta _(rot ,1)=\theta _(rot ,2)=\theta _(rot ,3)=7.54K. With 5 atoms, a nonlinear molecule has
3\times 5-6=9vibrational modes. In methane there are three asymmetric stretches with vibrational temperatures of
\theta _(vib, 1)=4320K, there is one symmetric stretch with a vibrational temperature of
\theta _(vib ,2)=4170K. There are two twisting modes with vibrational temperatures of
\theta _(cib ,3)=2180Kand three bending modes with vibrational temperatures of
\theta _(eib, 4)=1870K. Assume in the following problem
T=300.KPart A - Rotational Partition Function of Methane Calculate the rotational partition function of methane. ANSWER:
◻
q_(ro )Part B - Translational and Rotational Internal Energies of Methane Calculate the contribution to the molar internal energy of methane from rotational and translational motions motions ANSWER:
◻
U_(V, trans ) U_(V, rot )=Part C - Translational and Rotational Heat Capacities of Methane Calculate the contribution of translations and rotations of methane to the molar heat capacity ANSWER:
◻
C_(V, trans ) C_(V, rot )=Part D - Vibrational Partional Function of Methane Each of the 9 vibrational modes mades a contribution to the molar heat capacity of
C_(V, sil, i)=R((\theta _(j))/(T))^(2)(e^(-(\theta _(i))/(T))(1-e^(-(\theta _(i))/(T)))^(-2))where
\theta _(i)is the vibrational temperature of the ith vibrational mode. Calculate the contribution of the nine vibrational modes to the heat capacity ANSWER:
◻
C_(V, and )Part E Calculate the total heat capacity of methane from translational, vibrational and rotational motions. ANSWER:
◻C) Part F What value for the heat capacity of methane is predicted by the equipartition principle (i.e. the high temperature limit) ANSWER:
◻
C_(V)=