P.W. Seakins, M.J. Pilling, L.T. Niiranen, D. Gutman, and L.N. Krasnoperov (J. Phys

Chapter 22, Problem 22.18

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P.W. Seakins, M.J. Pilling, L.T. Niiranen, D. Gutman, and L.N. Krasnoperov (J. Phys. Chem. 96, 9847 (1992)) measured the forward and reverse rate constants for the gas-phase reaction \(\mathrm{C}_2 \mathrm{H}_5(\mathrm{~g})+\mathrm{HBr}(\mathrm{g}) \rightarrow \mathrm{C}_2 \mathrm{H}_6(\mathrm{~g}) +\operatorname{Br}(\mathrm{g})\) and used their findings to compute thermodynamic parameters for \(\mathrm{C}_2 \mathrm{H}_5\). The reaction is bimolecular in both directions with Arrhenius parameters \(A=1.0 \times 10^9 \mathrm{dm}^3 \mathrm{~mol}^{-1} \mathrm{~s}^{-1}, E_{\mathrm{a}}=-4.2 \mathrm{~kJ} \mathrm{~mol}^{-1}\) for the forward reaction and \(k^{\prime}=1.4 \times 10^{11} \mathrm{dm}^3 \mathrm{~mol}^{-1} \mathrm{~s}^{-1}, E_{\mathrm{a}}=53.3 \mathrm{~kJ} \mathrm{~mol}^{-1}\) for the reverse reaction. Compute \(\Delta_{\mathrm{f}} H^{\ominus}, S_{\mathrm{m}}^{\ominus}\), and \(\Delta_{\mathrm{f}} G^{\ominus}\) of \(\mathrm{C}_2 \mathrm{H}_5\) at \(298 \mathrm{~K}\).