Question #43987

Consider the acid dissociation of the glycine cation ($\ce{^+NH3-CH2-COOH}$, Acid I) and cyanoacetic acid ($\ce{NC-CH2-COOH}$, Acid II) at $298\ K$. Let $K_{a}(\text{I})$ and $K_{a}(\text{II})$ be their respective acid dissociation constants for the $\ce{-COOH}$ proton. Define the ratio of their dissociation constants as $R = \frac{K_{a}(\text{I})}{K_{a}(\text{II})}$. Let $R_W$ be the ratio in pure water (dielectric constant $\epsilon \approx 78$), where the $pK_a$ values are $2.34$ and $2.45$, respectively. Let $R_E$ be the ratio in an $80\%$ aqueous ethanol mixture ($\epsilon \approx 30$). Assuming no change in the primary structural conformations, which of the following mathematically represents the correct relationship between $R_W$ and $R_E$?