 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2022/paper-2/a8/b/ii/solution

^{35} Cl

atoms are interchanged by three proper rotations, so $σ = 3$ . The three mirror operations do not increase the rotational symmetry number to six. Isotopic identity matters for this count.

Using the supplied wavenumber form of

k_{B}

θ_{a} = θ_{b} = \frac{0.110}{0.695} = 0.15827 K, θ_{c} = \frac{0.0593}{0.695} = 0.085324 K .

All are far below

298 K

, justifying the high-temperature nonlinear rigid rotor expression. Then

q_{rot} = \frac{π}{3} [\frac{29 8 ^{3}}{( 0.15827 ) ^{2} ( 0.085324 )}]^{1/2} ≃ 6.5741 \times 1 0^{4},

and

S_{rot, m} = R [ln q_{rot} + 3/2] ≃ 104.71 J K^{- 1} mo l^{- 1} .

The calculation treats the molecule as rigid and separates electronic, vibrational and nuclear-spin contributions from the requested rotational term.

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