Question #44834

A gaseous reactant \ce{A(g)} is continuously bubbled into an ideal solvent at a constant partial pressure of $1\text{ bar}$. The dissolved gas undergoes a second-order dimerization reaction: $\ce{2A(aq) ->[k] A2(aq)}$ The temperature coefficient of the intrinsic rate constant $k$ for a $10\text{ K}$ rise from $300\text{ K}$ to $310\text{ K}$ is exactly $3.0$. The standard enthalpy of dissolution of \ce{A(g)} in the solvent is $\Delta H^\circ_{\text{sol}} = -42.47\text{ kJ mol}^{-1}$. Assuming both the activation energy ($E_a$) and enthalpy of dissolution are temperature-independent, determine the observed temperature coefficient ($\mu_{\text{obs}} = \frac{r_{310}}{r_{300}}$) for the overall rate of formation of \ce{A2(aq)}. (Given: $\ln 3 = 1.0986$, $R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}$)