 Solution

For B, $\Delta V^{‡}=+12\mathrm{c}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$ is consistent with bond fission and release/reorganization of electrostricted solvent on reaching a fragmentation transition state. The ordinary methoxy ester has $\Delta V^{‡}=-13\mathrm{c}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$, consistent with associative hydroxide addition and the compact, strongly solvated developing tetrahedral species.

The opposite signs corroborate distinct mechanisms. Since both values include solvation and any pre-equilibria, they should not be interpreted merely as geometric volumes of isolated molecules.