Question #44055

The specific acid-catalyzed hydrolysis of ethyl acetate in a dilute aqueous $\ce{HCl}$ solution follows the rate law: $\text{Rate} = k[\text{Ester}][\ce{H+}][\ce{H2O}]$, where $k$ is the true third-order rate constant. The rate constant $k$ follows the Arrhenius equation with an activation energy parameter $\frac{E_a}{2.303 R} = 3000 \text{ K}$.

The reaction is studied at two different temperatures, $300 \text{ K}$ and $375 \text{ K}$, in a variable-volume reactor maintained at a pressure sufficient to keep the mixture entirely in the liquid state. The density of the reaction mixture is $1.00 \text{ g mL}^{-1}$ at $300 \text{ K}$ and drops to a hypothetical value of $0.80 \text{ g mL}^{-1}$ at $375 \text{ K}$.

If $k_{obs}$ is the observed pseudo-first order rate constant (defined by $\text{Rate} = k_{obs}[\text{Ester}]$), determine the ratio $\frac{k_{obs}(375 \text{ K})}{k_{obs}(300 \text{ K})}$.

(Assume the total mass of the mixture and the moles of the acid catalyst remain constant, and the ester is present in trace amounts.)