Question #44241

The chelate effect is classically responsible for the enhanced stability of complexes containing polydentate ligands. Consider the ligand substitution reaction of a $d^{10}$ Cadmium(II) complex at $300 \text{ K}$:

$\ce{[Cd(NH3)4]^{2+}(aq) + 2en(aq) <=> [Cd(en)2]^{2+}(aq) + 4NH3(aq)}$

The thermodynamic parameters for the formation of these complexes from $\ce{[Cd(H2O)6]^{2+}}$ at $300 \text{ K}$ are provided below: Overall formation constant ($\log \beta_4$) for $\ce{[Cd(NH3)4]^{2+}} = 7.0$ Overall formation constant ($\log \beta_2$) for $\ce{[Cd(en)2]^{2+}} = 10.5$ Standard enthalpy of complexation ($\Delta H^\circ_c$) for $\ce{[Cd(NH3)4]^{2+}} = -53.0 \text{ kJ mol}^{-1}$ Standard enthalpy of complexation ($\Delta H^\circ_c$) for $\ce{[Cd(en)2]^{2+}} = -56.0 \text{ kJ mol}^{-1}$

Evaluate the standard entropy change ($\Delta S^\circ_{sub}$) for this substitution reaction and identify the dominant thermodynamic driving force. (Given: $2.303 RT = 5.75 \text{ kJ mol}^{-1}$ at $300 \text{ K}$)