What are minimum values for q_nuc and q_rot for a gas-phase molecule? What about

Question

What are minimum values for q_nuc and q_rot for a gas-phase molecule? What about q_vib? The moment of inertia for F_2 is 3.167 Times 10^-46 g middot m^2. What is the value of the rotational partition function for F_2 at 335 K? lf theta_r for Br_2 is 0.116 at 298 K, what is the moment of inertia for Br_2? Determine the temperature at which q_rot for HCI equals the q_rot value for HBr at 298 K. See Table 18.3 for necessary data. What is the expected ratio of rotational partition functions for H_2 and D_2? Compare this ratio with the answer from exercise 18.18. What are the expected ratios of molecules in odd rotational states to even rotational states for I_2 (I = 5/2) and Cl_2 (I = 2)? What are the expected ratios of molecules in odd rotational states to even rotational states for^14N_2 (I = 1.0) and

Explanation / Answer

18.27 The rotational partition function is given by

zrot = 82 IkT/h2 = 8 x 3.14152 x 3.167 x 10-46 x 1.3807 X 10-23 J/K X 335 K/ 2 x (6.6262 X 10-34J s)2

zrot = 0.393 is the rotational partition function

18.28) rotational temperature

rot = h2/82Ik

0.116 K = (6.6262 X 10-34J s)2/8 x 3.1412 x I x 1.3807 X 10-23 J/K

I = (6.6262 X 10-34J s)2/8 x 3.1412 x 0.116 K x 1.3807 X 10-23 J/K

I = 3.47 x 10-45 Kg/m2

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