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- Determine the number of total degrees of freedom and the number of vibrational degrees of freedom for the following species. a Hydrogen sulfide, H2S b Carbonyl sulfide, OCS c The sulfate ion, SO42 d Phosgene, COCl2 e Elemental chlorine, Cl2 f A linear molecule having 20 atoms g A nonlinear molecule having 20 atomsA system consists of three energy levels: a ground level (0 = 0, go = 1); a first excited level (₁ = 2kBT, 91 = 3); and a second excited level (&2 = 8kBT, 92 = 3). Calculate the partition function of the system. .406005 What is the probability for the third energy level? .00247871. Show that the partition function for a harmonic oscillator in the x direction only is given by: qx exp(-ẞhv) 1-exp(-ẞhv)
- 4. What is the form of the total vibrational partition function for a polyatomic molecule?It is possible to approximate the rotational partition function for diatomic molecules by replacing the infinite sum over states with an integral. Why might this be less accurate for H₂? OH₂ has a smaller mass so its rotational constant will be very small. OH₂ has a very high vibrational frequency so the spacings between its energy levels will be large. O the moment of inertia for H₂ is OH₂ has a shorter bond length so its rotational constant will be very small. the integral diverges for smaller-sized diatomic molecules.1. Determine the number of translational, vibrational, and rotational degrees of freedom available to the molecule NH3. 2. Calculate the rotational constant (B) for the molecule H12C14N, given that the H-C and C-N bond distances are 106.6 pm and 115.3 pm respectively.
- Why does the vibrational state of a diatomic molecule affect its rotational constant? Is there an effect even if the potential is strictly parabolic?Consider a diatomic molecule that is highly susceptible to centrifugal distortion in its ground vibrational state. Do you expect excitation to high rotational energy leve ls to change the equilibrium bond length of this molecule? Justify your answer.Ə In q rot to derive the rotational contribution to the energy for a Use the equation Eo1 = NKT² ƏT diatomic molecule
- Q11. The spacing between two adjacent lines in the pure rotational spectrum of a diatomic molecule is 20.0 cm. Given K&T=200 cm¹ (at a specific temperature), calculate the relative population of the J-5 level. E) 0.90 D) 2.4 C) 1.6 A) 2.7 B) 3.8 F) 3.3 Q12. What are the degeneracies of the first and the second excited energy levels of a particle confined to 3-dimensional box? A) 1 and 3 B) 3 and 6 C) 3 and 3 D) 1 and 6 alDemonstrate that the probability of occupying a given vibrational energy level does not depend on whether one includes zero point energy (1/2hcv) or not..Vibrational frequency of iodine molecule Br2 is 414 cm^-1. Calculate ratio populations of 1st excited to ground vibrational states in Br2